moorepants · July 3, 2024 09:39
diff --git a/kalman_filter.m b/kalman_filter.m
 function [x, P] = kalman_filter(A, B, C, Q, R, x, u, y, P)
 % kalman_filter - Returns the next state estimate and its covariance matrix
 % using the Kalman Filter predict & update. Note that this implementation is
 % not numerically stable, use production code for non-textbook problems.
 %
 % Syntax: [x, P] = kalman_filter(A, B, C, Q, R, x, u, y, P)
 %
 % Inputs:
 %   A - State matrix, size 5 x 5
 %   B - Input matrix, size 5 x 1
 %   C - Output matrix, 2 x 5
 %   Q - Model covariance matrix, size 5 x 5
 %   R - Measurement convariance matrix, size 2 x 2
 %   x - Current state, size 5 x 1
 %   u - Current input, size 1 x 1
 %   y - Current measurement, size 2 x 1
 %   P - Current state covariance matrix, size 5 x 5
 % Outputs:
 %   x - New state, size 5 x 1
 %   P - New state covariance matrix, 5 x 5

 x = A*x + B*u;
 P = A*P*A' + Q;
 L = P*C'*inv(C*P*C' + R);
 P = (eye(length(x)) - L*C)*P;
 x = x + L*(y - C*x);

 end
diff --git a/run_kalman_filter.m b/run_kalman_filter.m
 data = csvread('smartphone-data.csv', 1, 0);

 t = data(:, 1);
 v = data(:, 5);
 omega = data(:, 6);
 a = data(:, 7);
 theta_true = data(:, 8);
 v_true = data(:, 9);

 dt = % 1 x 1
 g = 9.81;

 A = % 5 x 5
 B = % 5 x 1
 C = % 2 x 5

 Q_scale = 1.0;  % adjust this number, model covariance
 R_scale = 1.0;  % adjust this number, measurement covariance

 Q = Q_scale*diag([0.0, 0.0, 0.0, 0.0, 1.0]);
 R = R_scale*diag([2.5e-01, 9.0e-04]);

 % initial P and x
 P = diag([1.0e+02, 2.5e-01, 1.0e-04, 4.0e-04, 9.0e-04]);
 x = % 5 x 1, initial state

 xs = zeros(length(?), 5);  % add correct length of time vector
 xs(1, :) = x;
 for i=2:length(?) % add correct length of time vector
    u = % 1 x 1, model input
    y = % 2 x 1, actual measurements
    % run the filter for this time step, updating x and P
    [x, P] = kalman_filter(A, B, C, Q, R, x, u, y, P);
    % store the estimated state vector
    xs(i, :) = x;
 end

 % make some plots
 figure();
 plot(t, v_true, t, v, '.', t, xs(:, 2));
 figure();
 plot(t, theta_true, t, xs(:, 4));
 figure();
 plot(t, omega, '.', t, xs(:, 5));
diff --git a/run_kalman_filter.py b/run_kalman_filter.py
 import numpy as np
 import matplotlib.pyplot as plt

 def kalman_filter(A, B, C, Q, R, x, u, y, P):
    """Returns the next state estimate and its covariance matrix.

    Parameters
    ==========
    A : shape(5, 5)
        State matrix
    B : shape(5, 1)
        Input matrix
    C : shape(2, 5)
        Output matrix
    Q : shape(5, 5)
        Model covariance matrix
    R : shape(2, 2)
        Measurement convariance matrix
    x : shape(5, 1)
        Current state
    u : shape(1, 1)
        Current input
    y : shape(2, 1)
        Current measurement
    P : shape(5, 5)
        Current state covariance matrix

    Returns
    =======
    x : shape(5, 1)
        New state
    P : shape(5, 5)
        New state covariance matrix

    """
    x = A@x + B@u
    P = A@[email protected] + Q
    L = [email protected]@np.linalg.inv(C@[email protected] + R)
    P = (np.eye(len(x)) - L@C)@P
    x = x + L@(y - C@x)
    return x, P


 data = np.loadtxt('smartphone-data.csv', skiprows=1, delimiter=',')

 t = data[:, 0];
 v = data[:, 4];
 omega = data[:, 5];
 a = data[:, 6];
 theta_true = data[:, 7];
 v_true = data[:, 8];

 dt = # 1 x 1

 A = # 5 x 5
 B = # 5 x 1
 C = # 2 x 5

 Q_scale = 1.0  # adjust this number, model covariance
 R_scale = 1.0  # adjust this number, measurement covariance

 Q = Q_scale*np.diag([0.0, 0.0, 0.0, 0.0, 1.0])
 R = R_scale*np.diag([2.5e-01, 9.0e-04])

 P = np.diag([1.0e+02, 2.5e-01, 1.0e-04, 4.0e-04, 9.0e-04])

 x = # 5 x 1, initial state

 us =  # n x 1 x 1, inputs
 ys =  # n x 2 x 1, measurements

 xs = np.zeros((len(us), 5, 1)) # n x 5 x 1
 for i, (u, y) in enumerate(zip(us, ys)):
    x, P = kalman_filter(A, B, C, Q, R, x, u, y, P)
    xs[i] = x

 # make some plots
 plt.figure()
 plt.plot(t, v_true, t, v, '.', t, xs[:, 1, 0]);

 plt.figure()
 plot(t, theta_true, t, xs[:, 3, 0]);

 plt.figure()
 plot(t, omega, '.', t, xs[:, 4, 0]);
diff --git a/smartphone-data.csv b/smartphone-data.csv
 time [s],altitude [m],latitude [deg],longitude [deg],speed [m/s],rate_gyro_z [rad/s],accelerometer_x [m/s/s],true_slope_angle [rad],true_speed [m/s]
 0.0,29.349255038655915,34.14528015694175,133.02109942426688,5.0,0.02743613603825991,0.19624320475316748,0.03977464905028287,5.0
 0.1,28.98532874791777,34.14530224788589,133.0210677537201,5.0,-0.050001858885091,0.20115685586216087,0.03562063913485901,4.981922246361347
 0.2,30.12374256600749,34.145165581670916,133.02100808295805,5.0,-0.014990206694255746,0.19773983621018504,0.031479264841759405,4.968104748684157
 0.30000000000000004,29.651512134560015,34.14530215592312,133.02117868846744,5.0,0.024343713701225754,0.22872029208253056,0.027347088343894963,4.958485910241052
 0.4,29.7162295894864,34.145327818039526,133.02098691765065,5.0,-0.07914181593345203,0.18268057290285417,0.023220734000403667,4.953008284578877
 0.5,29.627047871908914,34.14516285913839,133.0211686071004,5.0,-0.04135677467297087,0.20482025973275425,0.0190968588638307,4.951618031703902
 0.6000000000000001,29.66727825395798,34.14528407201074,133.02122356373013,5.0,-0.028509036006478215,0.2132818850708582,0.014972152680128418,4.95426491808181
 0.7000000000000001,29.135455821873695,34.14531894979247,133.0210908026624,5.0,0.002360827094701465,0.18189588561354084,0.010843337888656431,4.9609023166377115
 0.8,29.476509691217345,34.14513657524417,133.02114513301734,5.0,-0.016837110179394293,0.20977211752802896,0.006707169622181531,4.971487206756135
 0.9,29.791863279051945,34.14531889327758,133.02118166503502,5.0,-0.09042887648926684,0.20409333024985823,0.002560435706877716,4.98598017428103
 1.0,29.309797156236918,34.145315713274854,133.02110373066606,5.0,-0.03383078390325187,0.18571071790566973,-0.0016000433376738253,5.004345411515768
 1.1,28.66937817638784,34.145163520336155,133.02102575528517,5.0,-0.05312921715650932,0.19034361039800496,-0.005776904709968868,5.026607014057085
 1.2000000000000002,30.216955430972863,34.14520413668664,133.0210104997868,5.0,-0.07730042473012397,0.19057036597890908,-0.009972792785046307,5.052840232500631
 1.3,28.531122766284163,34.14525343463812,133.02110519660508,5.0,-0.03133444968026107,0.18111322083592993,-0.014191613530303357,5.082993727950669
 1.4000000000000001,28.575910706433287,34.145252555329975,133.0211630035638,5.0,-0.022343312347815676,0.1769402865573584,-0.018437082723504312,5.1169929224698185
 1.5,29.318899535867097,34.145244238958895,133.0211023784559,5.0,-0.05871091464947488,0.17518916497791082,-0.022712692376996406,5.154743018578305
 1.6,29.661416127136366,34.14519361258572,133.02095553790605,5.0,-0.019393545734648687,0.16847804289742188,-0.0270217107377098,5.196128999253955
 1.7000000000000002,28.940921777650836,34.14521280223687,133.0211357983949,5.0,-0.11935520462982002,0.17512915033994347,-0.03136718228715761,5.241015627932199
 1.8,29.336982233838917,34.145212202015635,133.0210622633263,5.0,0.012599858249781722,0.16905921724055178,-0.03575192774143587,5.28924744850607
 1.9000000000000001,28.62173476167685,34.14523917906292,133.02126232538825,5.0,-0.07135185732785028,0.14264329585236182,-0.040178544051223564,5.3406487853262075
 2.0,28.77602678940273,34.14519665156262,133.02105350864665,5.0,-0.07375672853114955,0.1411261146470797,-0.04464940440178261,5.395023743200849
 2.1,29.151205959852806,34.14515266735049,133.02113517363136,5.0,-0.05418209267198555,0.15239724506541352,-0.04916665821295786,5.452156207395841
 2.2,28.29404048977968,34.14521397342533,133.02103465334616,5.0,-0.045087883820343316,0.1431369040648526,-0.05373223113917712,5.51180984363463
 2.3000000000000003,29.416321590469543,34.14518229569743,133.02113883128797,5.0,-0.048092291405778836,0.09108039249247948,-0.05834782506945112,5.5737280980982655
 2.4000000000000004,29.833478076463425,34.14519411741133,133.02109838502207,5.0,-0.05988963360821839,0.12255864907354859,-0.06301491812737352,5.6376341974254025
 2.5,28.72434107236792,34.14519644777341,133.02109493684935,5.0,-0.06957854538301318,0.12472667154080931,-0.0677347646711209,5.703231148712296
 2.6,28.89410575848845,34.145113570563964,133.0211788555839,5.0,-0.09494939752505362,0.11983015981135742,-0.07157716540621724,5.77020173951281
 2.7,28.64032337654543,34.14517452717872,133.02119237965854,5.0,0.018552641221322906,0.09108689367555235,-0.06985516978670644,5.8382085378384065
 2.8000000000000003,29.119408407699073,34.14500313278784,133.0210160776851,5.0,-0.04433186486281754,0.10174577901069665,-0.06811349625258531,5.906893892158153
 2.9000000000000004,29.20795686418919,34.14525199440929,133.02100649402564,5.0,0.007468065132514596,0.07935041346164882,-0.06635201665997933,5.975879931398719
 3.0,28.597230150350235,34.145163524224394,133.0210028079891,6.04476856494438,-0.009498135398803086,0.07950660983186157,-0.06457068267143257,6.04476856494438
 3.1,28.625224327056383,34.14502946302539,133.02100045563046,6.04476856494438,-0.0016206521996081531,0.07810021872301891,-0.06276952575590754,6.113141482637011
 3.2,28.642600552546,34.1451894622221,133.02106903273113,6.04476856494438,-0.05003394452499754,0.08294143870904283,-0.060948657188785296,6.180560154776095
 3.3000000000000003,28.905571856144455,34.14507828153979,133.02115226454453,6.04476856494438,0.049809155780152395,0.04340104923736859,-0.05910826805186549,6.246565832118714
 3.4000000000000004,29.423119808693226,34.14521440736125,133.0210358458253,6.04476856494438,-0.018342955129499714,0.044145254456619536,-0.057248629233366176,6.310679545879555
 3.5,28.69651014973521,34.145066824566705,133.02106065739406,6.04476856494438,0.05092948798656975,0.04110642395098102,-0.055370091427924,6.3724021077309105
 3.6,28.878209687251264,34.145114391070805,133.02108749482434,6.04476856494438,-0.000723564905541537,0.03864807769503839,-0.053473085136594066,6.431214109802673
 3.7,28.98402466840695,34.14509722180211,133.02105073075657,6.04476856494438,0.03314539030708066,0.03891685735024559,-0.05155812066685006,6.48657592468234
 3.8000000000000003,29.390788703347614,34.14501649715185,133.0211802599904,6.04476856494438,0.01467549685076643,0.032680480945144336,-0.04962591063733221,6.538246193392969
 3.9000000000000004,28.26377845250957,34.14509608196809,133.02107224587905,6.04476856494438,0.004127876084913294,0.016410611320983218,-0.04767787729652914,6.587569031349582
 4.0,29.018808534423837,34.145062692042245,133.02095297948577,6.04476856494438,0.0601433709049655,0.010989949550461401,-0.04571502787435793,6.634695431875715
 4.1000000000000005,28.770572821677128,34.14499395790999,133.02112509045583,6.04476856494438,-0.03089864886192952,0.010151806036963178,-0.04373825530329076,6.679545135111055
 4.2,29.104161219559916,34.14499468816002,133.02106176769934,6.04476856494438,0.029700053303059457,-0.010783103425614891,-0.04174842849058,6.722050093085105
 4.3,28.934604878840634,34.14511353563532,133.02114385172342,6.04476856494438,0.04184051062713352,0.0007791201581662435,-0.03974639231825808,6.762154469717191
 4.4,28.4584938603066,34.14516357145351,133.0211124715348,6.04476856494438,0.024275139740674086,-0.0016133372745628996,-0.037732967643137515,6.7998146408164555
 4.5,29.64315841641136,34.14505765346557,133.02108222550547,6.04476856494438,0.024467212745136364,-0.00833072827034034,-0.03570895129681103,6.834999194081859
 4.6000000000000005,28.67836406850687,34.14504898371229,133.02108729892325,6.04476856494438,0.035435268706487305,-0.022301543129598495,-0.033675116085651366,6.867688929102181
 4.7,29.086193691439792,34.145080206178896,133.02102152996537,6.04476856494438,0.014876725073242003,-0.025111143355962103,-0.031632210790811445,6.897876857356023
 4.800000000000001,28.202214777331147,34.14507604085541,133.02105984631172,6.04476856494438,0.006114665514421313,-0.026059463594297207,-0.029580960168224257,6.925568202211801
 4.9,28.450180943595107,34.144979836169576,133.02091487364098,6.04476856494438,0.06420332117501647,-0.017903343435868305,-0.027522064948602966,6.950780398927753
 5.0,28.883454903552522,34.14505782107446,133.0210175287104,6.04476856494438,-0.012717737878376743,-0.004662854556825795,-0.025456201837440774,6.973543094651934
 5.1000000000000005,29.540851498782256,34.145154231877676,133.02104643050197,6.04476856494438,0.012692414623038353,-0.016746369875407438,-0.023384023515011024,6.993898148422217
 5.2,29.470480818036712,34.14484920948979,133.02100152549923,6.04476856494438,0.07192731345004372,-0.03273150353820682,-0.021306158636367194,7.011899631166298
 5.300000000000001,29.410567425759304,34.14507994616729,133.0210570677702,6.04476856494438,0.010428382793720388,-0.026030741074544225,-0.019223211831342867,7.027613825701689
 5.4,28.76248612458453,34.14502122993172,133.02108594696887,6.04476856494438,0.05595877880595168,-0.034069563102708166,-0.017135763704551783,7.041119226735718
 5.5,28.836882080874002,34.14494545882127,133.02113834767826,6.04476856494438,-0.007893726430722652,-0.030810874314993884,-0.01504437083538767,7.052506540865537
 5.6000000000000005,27.85378295822077,34.14504027487776,133.02100644951088,6.04476856494438,0.017602551602162765,-0.03453414233202355,-0.012949565778024454,7.0618786865781145
 5.7,29.188454210939604,34.144997925408695,133.02101281654862,6.04476856494438,0.031604743838807015,-0.02341271768292613,-0.01085185706141624,7.069350794250237
 5.800000000000001,28.92474571984039,34.14501952677166,133.0210716537407,6.04476856494438,-0.04034975470281493,-0.023456170226680742,-0.00875172918929712,7.0750502061485125
 5.9,29.182521871405232,34.14501783693285,133.02093256040519,6.04476856494438,-0.03385743604533995,-0.02423106883452283,-0.0066496426401813635,7.0791164764293635
 6.0,28.581409543081676,34.144917529204584,133.0209813734641,7.081701371139036,-0.03933892600468611,-0.027509281847533863,-0.004546033867363353,7.081701371139036
 6.1000000000000005,29.02385124091551,34.144866687747395,133.02101963891718,7.081701371139036,-0.04242731792314935,-0.041342930538322574,-0.004271452460684626,7.082968868213591
 6.2,28.934472361895256,34.14498669227919,133.02103711382225,7.081701371139036,-0.06134239202248967,-0.03269977974024073,-0.004126635683033597,7.083095157478911
 6.300000000000001,29.151521646608117,34.144990835477124,133.02096961427023,7.081701371139036,-0.02016782513577389,-0.031228534182739572,-0.003981794349098432,7.082268640650697
 6.4,29.339941132492314,34.14491457417555,133.02101124540118,7.081701371139036,0.019281601856275542,-0.04350248531707281,-0.0038369518690645962,7.080689931334467
 6.5,29.703166017001543,34.14486748364515,133.02099572373177,7.081701371139036,0.0014209214413551357,-0.030477504731585163,-0.003692130000610247,7.07857185502556
 6.6000000000000005,29.15876861870949,34.144911990492226,133.0208615950071,7.081701371139036,-0.06544543515892473,-0.04206403861894391,-0.0035473488489062327,7.076139449109132
 6.7,29.24272404838235,34.14489555655268,133.0209065656782,7.081701371139036,0.07148131321482805,-0.03646948636158421,-0.0034026268666160894,7.073629962860159
 6.800000000000001,29.40772147920002,34.14495224261369,133.02095759437285,7.081701371139036,0.04631450303257414,-0.03190945742321859,-0.003257980853896044,7.071292857443435
 6.9,29.3141775123176,34.14489737780459,133.02087655407905,7.081701371139036,0.06937912128718897,-0.02595315741666299,-0.0031134259583950187,7.069389805913574
 7.0,28.78660674922436,34.14491531977582,133.02100338980526,7.081701371139036,-0.008740152399793977,-0.03697837066396006,-0.002968969968207149,7.068128711727557
 7.1000000000000005,27.735920210280405,34.144909558688745,133.02097103590668,7.081701371139036,0.04887020614501261,-0.02988351293668244,-0.0028245557266821566,7.0669382034062345
 7.2,28.791556011155976,34.14482036296013,133.02103315015847,7.081701371139036,0.06981443049586732,-0.04166391041337182,-0.002680167391093455,7.06561929399491
 7.300000000000001,29.35081411344261,34.14501632810638,133.02095145238667,7.081701371139036,0.023086516396053008,-0.02351870058533126,-0.0025358075086423758,7.064173318778519
 7.4,28.214634663189287,34.14479525854635,133.02099158329278,7.081701371139036,-0.041008875905307225,-0.01977584009265334,-0.0023914786048564096,7.062601604011104
 7.5,29.18761390726787,34.14493893158244,133.02092485746368,7.081701371139036,-0.016466911767226547,-0.01912933649679279,-0.0022471831835892135,7.060905466915815
 7.6000000000000005,29.01851790215398,34.14501194526334,133.02085561648562,7.081701371139036,0.006262631959040779,-0.024088667491270307,-0.002102923727020606,7.059086215684914
 7.7,29.74486204998996,34.144850298373576,133.02092346145022,7.081701371139036,0.022031798601549104,-0.0284817762249146,-0.00195870269565657,7.057145149479769
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 15.0,30.33083826517082,34.14446607908679,133.02069718862398,6.656687666282686,-0.0038828795680290037,0.019056836733253237,0.008707968476564023,6.656687666282686
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 104.2,40.96080316154521,34.1426055130426,133.02046331545108,4.82891595985551,0.023897537651946278,0.1868256196651457,0.0011182294769418507,5.12275833389661
 104.30000000000001,39.835413005341245,34.14263999335029,133.02047214871186,4.82891595985551,-0.021183969610389174,0.1734970156517168,0.0007225639929070264,5.137086254987605
 104.4,41.33197965493487,34.142678786853395,133.02062520902797,4.82891595985551,-0.016126782473252298,0.1792814983076488,0.0003258075108453877,5.151404328186574
 104.5,41.61415830810681,34.14265888903159,133.02049457763013,4.82891595985551,0.01980053647794236,0.17611850609554178,3.737704792559115e-05,5.165698517794997
 104.60000000000001,40.959277894502684,34.142497169426065,133.02044330834372,4.82891595985551,-0.022735838690679598,0.18099383504417407,0.00024436530558795373,5.1799544288379
 104.7,40.094867424323446,34.14257885154541,133.02056928230738,4.82891595985551,0.004259343880694838,0.18455480650580627,0.0004519129379577223,5.194157307063846
 104.80000000000001,40.602092598477384,34.14249244395258,133.02052718764762,4.82891595985551,-0.001497553739142112,0.1600291776296589,0.0006600167427841547,5.208292038944952
 104.9,40.75219959348476,34.14246446848677,133.0205571746949,4.82891595985551,0.011380100532204404,0.161797840598837,0.0008686730337983503,5.222343151676871
 105.0,40.89468014648083,34.14250872439334,133.0205022018654,5.236294813178805,0.03971449877963248,0.16521389371023015,0.0010778776407134772,5.236294813178805
 105.10000000000001,40.545492850906435,34.1424588451794,133.02066590376148,5.236294813178805,-0.02593108165606406,0.16635871530446236,0.001287625909224681,5.250130832093502
 105.2,41.18609061634264,34.14253195724527,133.0206197843083,5.236294813178805,0.035057212709888326,0.1810861933162507,0.0014979127010089717,5.26383465778725
 105.30000000000001,40.318388131833316,34.14253547192943,133.0206268713872,5.236294813178805,-0.038443769821795065,0.1480449658275295,0.0017087323937254504,5.2773893803498835
 105.4,41.262957000073584,34.14253530321567,133.02054445655352,5.236294813178805,-0.004616659847517636,0.16650506791044017,0.0019200788810150601,5.29077773059478
 105.5,40.655022610254704,34.14250832634674,133.02054879680693,5.236294813178805,0.021965716925782877,0.15829237535576873,0.002131945572500835,5.303982080058864
 105.60000000000001,41.6938389321195,34.14249191295779,133.02053966590623,5.236294813178805,0.032910790503385676,0.17181984582975296,0.0023443253937877185,5.316984441002605
 105.7,40.36826420922494,34.142572406016015,133.02060028466036,5.236294813178805,0.04688030514287407,0.1494576947360501,0.002557210786462564,5.32976646641001
 105.80000000000001,42.1790014120021,34.14255230539677,133.0204621478583,5.236294813178805,0.04787799048517988,0.15075151054530325,0.0027705937080943167,5.342309449988641
 105.9,40.629493343246246,34.142461130003916,133.02042272677528,5.236294813178805,-0.014600332247726706,0.14775311942092453,0.002984465632233785,5.354594326169595
 106.0,41.68704016125709,34.14242930642539,133.02052275530176,5.236294813178805,0.06958110300355472,0.1615973441775111,0.003198817548413778,5.366601670107517
 106.10000000000001,40.54768503818678,34.14245048680737,133.0205531743625,5.236294813178805,0.028969043836216884,0.14855433445846233,0.003413639962149129,5.3783116976806005
 106.2,41.76042554276963,34.142473843543016,133.02055751532018,5.236294813178805,0.07049431713904476,0.13957506345154883,0.0036289228949365113,5.389704265490575
 106.30000000000001,39.81203973901654,34.14252130732725,133.02049050027483,5.236294813178805,-0.009753278468587642,0.14277853025780038,0.003844655884254736,5.400758870862722
 106.4,40.78003236786064,34.14251519010272,133.02048213340066,5.236294813178805,0.027408341199576063,0.1389788736677842,0.004060827983564365,5.411454651845863
 106.5,40.91413186784738,34.1424687057854,133.0205444806173,5.236294813178805,-0.04950345876572934,0.14426488666386791,0.0042774277623081405,5.421770387212364
 106.60000000000001,42.182860028073954,34.14243650071474,133.02046574989953,5.236294813178805,-0.005153762015982,0.15477749337103583,0.0044944433059106725,5.43168449645814
 106.7,40.7604917626056,34.1424815406547,133.02057344135355,5.236294813178805,0.03749952104117097,0.1354453956294239,0.004711862215778499,5.441175039802643
 106.80000000000001,40.07969333823821,34.14245420924598,133.0205079303212,5.236294813178805,0.09883385064801214,0.14758048402127424,0.00492967160930023,5.450219718188878
 106.9,40.57942550246721,34.142407511089694,133.02052331908638,5.236294813178805,-0.05265353564353165,0.1307096049911096,0.0051478581198463385,5.4587958732833854
 107.0,41.11933642349896,34.14245180921662,133.02044323900625,5.236294813178805,0.027581996787229415,0.1458618715798097,0.00536639217653005,5.466834280138005
 107.10000000000001,41.408665307651056,34.142477049833424,133.02054642354724,5.236294813178805,0.029675767366701553,0.14448114191473857,0.0055852230442076985,5.474245011464573
 107.2,41.79914652810354,34.14244372818241,133.02053971996003,5.236294813178805,-0.0682601517233027,0.14056744166326754,0.005804330070496802,5.481059647454017
 107.30000000000001,41.01087288684582,34.142430060592744,133.02055188664676,5.236294813178805,-0.0767469819155849,0.1267245712386267,0.006023694375870081,5.487312552337167
 107.4,41.464490107789054,34.14242641850118,133.0204113400326,5.236294813178805,0.03942861945710226,0.1174537473204895,0.006243297801470241,5.493037216341478
 107.5,41.12984342111701,34.14248582204967,133.02048049326172,5.236294813178805,-0.0026161202333674885,0.15386054634763902,0.006633095689419535,5.498266255691023
 107.60000000000001,41.126454039117434,34.14249645347177,133.02050483773024,5.236294813178805,-0.0005254019476419718,0.14350303314341237,0.007123732581148834,5.503031412606499
 107.7,40.65027436326368,34.14240766904373,133.020490527679,5.236294813178805,0.04211284547849534,0.14282076155659829,0.007614790844882938,5.507363555305223
 107.80000000000001,41.04233178396928,34.14243518256906,133.02057774304723,5.236294813178805,-0.030833088162673054,0.12851123265031347,0.008106236416840877,5.511292678001135
 107.9,41.85411990564433,34.14244380715676,133.02057665452088,5.236294813178805,0.05857417025817987,0.15381276828756815,0.008598036840236871,5.514847900904796
 108.0,41.19534390410533,34.14243356362954,133.0204536467825,5.518057470223389,0.06788661310186687,0.1503485841675972,0.009090161265280486,5.518057470223389
 108.10000000000001,40.762237153629655,34.142507641939964,133.0205402184637,5.518057470223389,0.07187873744620944,0.14036096998460643,0.00958258044917658,5.520948758160719
 108.2,40.81202995740494,34.14246540546857,133.02040672447222,5.518057470223389,-0.026730878535546128,0.1391870069364014,0.010075266756124898,5.523548262917211
 108.30000000000001,40.977555680157664,34.14237242135011,133.02051303529183,5.518057470223389,0.04615683323452376,0.14436964478498293,0.010568194157320934,5.5258816086899145
 108.4,41.191931353640044,34.1424259560859,133.02045802108995,5.518057470223389,-0.005328093361925462,0.13037537493731968,0.011061338230955023,5.5279735456724985
 108.5,40.953060256554956,34.14239763386238,133.0205359016851,5.518057470223389,-0.03678452506917149,0.1426062133514899,0.011554676162212936,5.529847950055254
 108.60000000000001,41.681171393723325,34.142388516806186,133.02068054467827,5.518057470223389,0.01353989950325159,0.12312629415046168,0.012048186743275697,5.531527824025096
 108.7,40.723457533663534,34.142328826294424,133.0205868234295,5.518057470223389,0.02977449428501345,0.15105697126952145,0.012541850373319462,5.533035295765557
 108.80000000000001,42.13778503755799,34.14234287352023,133.02071376619568,5.518057470223389,-0.01035550281089314,0.12325122603238663,0.01303564905851574,5.534391619456794
 108.9,41.58950566095087,34.14243363428924,133.02058086543857,5.518057470223389,-0.029449556147025963,0.13069901352395263,0.013030967321400166,5.535617175275585
 109.0,41.890336310113675,34.14242513204398,133.02060699197642,5.518057470223389,0.015367107984335972,0.12718229756350682,0.01291991524061774,5.536731469395331
 109.10000000000001,41.26729680796864,34.14236317134429,133.02057452927076,5.518057470223389,-0.013137456098856108,0.1328315447514706,0.012808842767674905,5.537753133986053
 109.2,41.21934367893041,34.14232232042862,133.02059874481503,5.518057470223389,-0.057327464756107116,0.1473783278540276,0.012697752502483069,5.5386999272143935
 109.30000000000001,41.04274826864597,34.14236215939089,133.02058992075683,5.518057470223389,-0.0032118508890025994,0.1302938667884844,0.012586646683713692,5.539588733243619
 109.4,41.255109750656146,34.14228866654475,133.02056519216345,5.518057470223389,0.005523058848403789,0.14949238445385982,0.012475527188798434,5.540435562233614
 109.5,40.4662155820709,34.14231773755704,133.02048061705776,5.518057470223389,0.022417105960550177,0.14406793152907157,0.012364395533929047,5.541255550340888
 109.60000000000001,41.47460121085475,34.14238456725108,133.02055698211802,5.518057470223389,-0.024949932501088852,0.12583811022064484,0.012253252874057418,5.542062959718571
 109.7,40.880009752940936,34.14234355431185,133.0204947150744,5.518057470223389,-0.028123274885691253,0.13681258129326362,0.012142100002895631,5.542871178516415
 109.80000000000001,40.964126936437665,34.14229951827085,133.02062138822674,5.518057470223389,-0.03816003585824966,0.1249277523871631,0.012030937352915837,5.5436927208807925
 109.9,41.205840869005236,34.14227808001378,133.02058912581043,5.518057470223389,0.00719798688130457,0.12048995726112478,0.011919764995350371,5.544539226954699
 110.0,41.245465903711775,34.14231719225696,133.02061756954382,5.518057470223389,-0.003783920303972954,0.12208585280897673,0.011808582640191684,5.545421462877751
 110.10000000000001,41.449761151320416,34.14240765045489,133.02060385780234,5.518057470223389,0.00886487401041249,0.1131669830043539,0.011697389636192341,5.546349320786188
 110.2,40.81912058256504,34.142449949962185,133.02056989563374,5.518057470223389,0.024256701948933795,0.1621758841124999,0.011586184970865112,5.54733181881287
 110.30000000000001,41.49680675583609,34.14231583179813,133.02062255331538,5.518057470223389,0.0367669305128191,0.14569771432869655,0.011474967270482838,5.548377101087277
 110.4,41.237727744844584,34.14234084639959,133.02060125656388,5.518057470223389,-0.008961415917352278,0.12920926408657973,0.011363734800078542,5.549492437735514
 110.5,41.765694775934556,34.142367362760716,133.02055091498266,5.518057470223389,0.020231453891514307,0.14725915500825004,0.011252485463445362,5.550684224880307
 110.60000000000001,41.17296386491885,34.14238781971158,133.0206350603681,5.518057470223389,-0.011352994006706302,0.1445274098212952,0.01114121680313655,5.551957984641001
 110.7,41.52128374181573,34.142437274106676,133.02057902756823,5.518057470223389,-0.05641164986833858,0.12052941182608005,0.011029926000465554,5.553318365133567
 110.80000000000001,40.99705853202562,34.14239337828468,133.0206744378343,5.518057470223389,-0.014257964965086222,0.12373414744871568,0.010918609875505893,5.554769140470594
 110.9,41.05616458047978,34.142439143826486,133.02068028431538,5.518057470223389,-0.0014673026077306954,0.13729434806672938,0.010807264887091309,5.556313210761292
 111.0,40.884859529282636,34.142387151579285,133.02069902634446,5.557952602111499,-0.02011239879852112,0.13076050523576876,0.010695887132815586,5.557952602111499
 111.10000000000001,40.910541190496964,34.142356383760635,133.0206734748286,5.557952602111499,-0.05558784488641335,0.13719679280967842,0.010584472349032696,5.559688466623667
 111.2,41.21331174757984,34.14234780785892,133.0207557542482,5.557952602111499,-0.01734697202496048,0.12786038207571696,0.010473015910856755,5.561521082396874
 111.30000000000001,41.19536971544136,34.14238028528052,133.0207403017135,5.557952602111499,0.01194964272001575,0.12171350091490497,0.010361512832161976,5.56344985352682
 111.4,41.952984109417784,34.1422125932597,133.02076277451778,5.557952602111499,0.04245412855423625,0.15696492487263597,0.010249957765582785,5.565473310105824
 111.5,40.81978627366061,34.14224828000389,133.02071379029238,5.557952602111499,0.057132157869224036,0.11510018089526404,0.010138339983661258,5.567640515532653
 111.60000000000001,41.37419456591117,34.1423210769077,133.0207160861764,5.557952602111499,0.004970983732497337,0.1266157229094805,0.010026467021927093,5.571816028227617
 111.7,41.346131655483745,34.14244739320893,133.02066178711075,5.557952602111499,-0.04256948087836774,0.1301464982668595,0.009914265499180244,5.5785371403644355
 111.80000000000001,41.20476985040675,34.14226496001416,133.02070366201247,5.557952602111499,-0.027837135541165993,0.12439585803178642,0.009801766873363784,5.587275157957348
 111.9,42.20841284254867,34.14235399604361,133.02074663306766,5.557952602111499,-0.017387715866889544,0.11433880031607013,0.00968900305463189,5.597526296400282
 112.0,41.24440276041742,34.14235564783832,133.0207960933575,5.557952602111499,-0.007709444462378118,0.1326639203099191,0.009576006405349788,5.6088116804668635
 112.10000000000001,41.59776335962967,34.142317374441404,133.02085356464335,5.557952602111499,0.024884359600592203,0.13609889302860734,0.009462809740093753,5.620677344310408
 112.2,42.32813169643341,34.14236445285341,133.0208180710453,5.557952602111499,0.02484493614306451,0.10419132417631422,0.009349446325651137,5.632694231463922
 112.30000000000001,41.74631156122077,34.14234320905847,133.02074861480702,5.557952602111499,0.03543341205652882,0.10321882739859824,0.009235949881020384,5.644458194840107
 112.4,41.088329772045775,34.14231200563804,133.0207642121208,5.557952602111499,0.0110785301815808,0.1086918809997299,0.009122354577410976,5.655589996731355
 112.5,40.62685709902772,34.14233476017979,133.02087052339508,5.557952602111499,-0.022423958692625326,0.13093260506510251,0.009008695038243484,5.665735308809753
 112.60000000000001,40.50730782929477,34.142357333076674,133.02081286466264,5.557952602111499,-0.06299905659634435,0.1259037095360215,0.008895006339149494,5.674564712127079
 112.7,41.26541614040801,34.142333358872534,133.02078942210787,5.557952602111499,-0.05966422541178979,0.1165632768822813,0.008781324007971743,5.681773697114803
 112.80000000000001,41.118738304637525,34.142296688086994,133.0208310056991,5.557952602111499,0.0076870304499166014,0.11838539828359251,0.00866768402476395,5.687082663584089
 112.9,42.10215807998851,34.14232474582744,133.0208087808011,5.557952602111499,0.013790948571305134,0.11358432715406919,0.008554122821790956,5.690236920725792
 113.0,41.31126604025375,34.14237700037292,133.02078080726045,5.557952602111499,0.003821471556649093,0.11034779164952555,0.00844067728352867,5.691006687110462
 113.10000000000001,40.87719955166426,34.14238601734446,133.02092310539993,5.557952602111499,-0.011397633163002643,0.11451299070568605,0.00832738474666402,5.689187090688338
 113.2,41.68367602623682,34.14239491726306,133.0206919416061,5.557952602111499,0.045666246959511624,0.1064975134863467,0.01017516407070306,5.684598168789355
 113.30000000000001,41.26677521937008,34.14240828912534,133.02088540031963,5.557952602111499,0.05223802650828645,0.10445097152199995,0.013569330189476342,5.677084868123138
 113.4,41.45910487315827,34.14226122053083,133.02080813244004,5.557952602111499,-0.005722185691086221,0.12926918524075248,0.01695544562754023,5.666517044779005
 113.5,41.75734231211499,34.142394553671906,133.02082631455914,5.557952602111499,0.00030800346046874066,0.11807051061425433,0.020332333249787834,5.652789464225969
 113.60000000000001,42.141028818173886,34.1423617994068,133.020850586117,5.557952602111499,0.06326092097901159,0.1308381856469468,0.023698802322788703,5.635821801312731
 113.7,41.57294292319117,34.14241321910907,133.02081603219702,5.557952602111499,0.042881605750947946,0.13546635712276595,0.027053648514791577,5.6155586402676905
 113.80000000000001,41.02566736388846,34.14233407743313,133.02083059588813,5.557952602111499,0.005201835735602577,0.11950711960767574,0.030395653895722997,5.591969474698931
 113.9,42.083589642537405,34.14240098586475,133.02083060434188,5.557952602111499,0.0760023203141249,0.1270118527494824,0.03372358693718869,5.565048707594239
 114.0,41.04468334597698,34.14219828890985,133.02079063091526,5.534815651321088,0.04694267092923897,0.13651959635463434,0.03703620251247152,5.534815651321088
 114.10000000000001,42.02705081798172,34.14230721171794,133.02082785389877,5.534815651321088,0.043123597691115914,0.14951009353372213,0.0403322418965349,5.501314527626636
 114.2,41.96276380354596,34.14232767634494,133.0208273687047,5.534815651321088,0.0671805583332572,0.14196304998535123,0.04361043276601799,5.464614467637755
 114.30000000000001,42.121085941326115,34.142341683155486,133.02089293105897,5.534815651321088,0.061270385979903697,0.1532148862079179,0.0468694891992412,5.424809511860983
 114.4,42.947310509960154,34.142319422324924,133.02090141267618,5.534815651321088,0.05391834124257411,0.1384761158290859,0.05010811167620001,5.382018610182575
 114.5,41.83756850991604,34.14227544676078,133.02075257886736,5.534815651321088,0.07684972417491613,0.15503395851983032,0.05332498707857181,5.336385621868465
 114.60000000000001,41.727240897669326,34.142291527810855,133.02085182979278,5.534815651321088,0.050367788033771635,0.16763188761404807,0.05651878868970978,5.288079315564271
 114.7,42.28319395515724,34.14227474478421,133.02087301397722,5.534815651321088,0.049655497949817835,0.15571268828897086,0.059688176194646246,5.237293369295331
 114.80000000000001,42.494412650209156,34.14236418483709,133.02085555401362,5.534815651321088,0.033546062063117416,0.17571258917397053,0.06283179568009274,5.184246370466644
 114.9,42.567359619655754,34.1422112939595,133.02089097879312,5.534815651321088,0.06229176924343853,0.1908112372426934,0.06594827963443722,5.129181815862931
 115.0,41.478654991417024,34.14241370958306,133.02083976141637,5.534815651321088,0.0253326318228992,0.20180895683631056,0.0690362469477489,5.072368111648584
 115.10000000000001,42.065537193430096,34.14227978535586,133.02099671562203,5.534815651321088,0.04393931200237225,0.19662424156399166,0.07209430291177342,5.0140985733676855
 115.2,42.442409511725266,34.14229868661209,133.02090419305432,5.534815651321088,0.058830642426548334,0.20389316958437081,0.07512103921993495,4.954691425944039
 115.30000000000001,41.67492309271718,34.14226016221915,133.02096376327168,5.534815651321088,-0.0045886082629609075,0.2086941334082689,0.07786029618028743,4.8944898036811
 115.4,41.78590163252681,34.14214571452431,133.02093986782933,5.534815651321088,-0.012806858654263516,0.22685613968521887,0.07798792035766332,4.833861750262057
 115.5,42.81094054382173,34.142293793812094,133.02101026870943,5.534815651321088,0.001490302567186086,0.20460705094583576,0.07811400837283135,4.773200218749764
 115.60000000000001,41.85991314579071,34.14226454722086,133.02092891080267,5.534815651321088,-0.0314298132348231,0.2191300203138322,0.07823849715573566,4.712923071586767
 115.7,43.154215895148816,34.14238144153978,133.0210468739381,5.534815651321088,-0.03402651386465425,0.24419603362409426,0.0783613230499753,4.653473080595328
 115.80000000000001,43.038174709122785,34.142253645778105,133.02094027728856,5.534815651321088,0.04448587011663128,0.24221355366845887,0.07848242181280414,4.595317926977369
 115.9,42.30453990708932,34.14230417301269,133.0209499496762,5.534815651321088,-0.04252522590392062,0.27268829144017664,0.07860172861513105,4.5389502013145435
 116.0,42.60648837516492,34.142188688031695,133.0209072809455,5.534815651321088,0.01341962586507944,0.24726003463439322,0.07871917804151973,4.484887403568161
 116.10000000000001,42.345258265103034,34.14223753604128,133.0209828677889,5.534815651321088,0.021228628419426958,0.27583667532858325,0.0788348122063595,4.433236817433867
 116.2,41.77340695120498,34.14238212187337,133.02095677216965,5.534815651321088,-0.041286722878474943,0.27341856099744594,0.07894908486166294,4.382367176964283
 116.30000000000001,42.21232983531829,34.14225406934247,133.0209408929496,5.534815651321088,0.013139959744019544,0.2854085811551373,0.0790620653763856,4.332063835307996
 116.4,42.75579370824285,34.142244306311106,133.0210084636308,5.534815651321088,0.022856725753987922,0.2886497381115589,0.07917376639068562,4.282333510979575
 116.5,42.513348940241784,34.14228633775087,133.0209841778572,5.534815651321088,-0.02762863708764029,0.2963037981383957,0.07928420070855906,4.23318260459967
 116.60000000000001,43.2441180663694,34.142283102110255,133.02104304882525,5.534815651321088,-0.011861364747666199,0.31544380780487985,0.07939338129783978,4.184617198895044
 116.7,42.72191926305076,34.142295160500865,133.02097299160533,5.534815651321088,-0.021643069269410852,0.3144489567118869,0.07950132129019935,4.136643058698585
 116.80000000000001,43.49810799674205,34.14225558879178,133.02109012281835,5.534815651321088,-0.00345707758992208,0.3039021477122049,0.0796080339811473,4.089265630949263
 116.9,42.94422432714649,34.14221518729615,133.0210555885988,5.534815651321088,0.021851438125647483,0.3392216118325614,0.07971353283003084,4.042490044692184
 117.0,43.38821129741021,34.14238866575809,133.02091946146413,3.99632111107854,0.02367404619040395,0.33645391757597015,0.07981783146003507,3.99632111107854
 117.10000000000001,43.22375214927677,34.14235277218809,133.02103355820554,3.99632111107854,0.007925276026124228,0.34291985994814145,0.07992094365818289,3.9507633233656323
 117.2,43.609138511788736,34.14221146730424,133.0210224574029,3.99632111107854,0.03307176761846846,0.35797973236560704,0.080022883375335,3.9058208569168884
 117.30000000000001,43.425575071098606,34.14227128605744,133.02104496259813,3.99632111107854,0.002523128720520058,0.351708083248794,0.08012366472618988,3.8614975692018194
 117.4,43.11722122704896,34.14224518620713,133.0210120371491,3.99632111107854,-0.015674516550447718,0.3787589495919832,0.08022330198928387,3.8177969997960695
 117.5,43.788302342860234,34.14224097139864,133.02097780384793,3.99632111107854,-0.0031748208919895565,0.35480873955913467,0.08032180960699115,3.7747223703813697
 117.60000000000001,43.03342470382536,34.14218395576388,133.02106841342697,3.99632111107854,-0.04413454351223266,0.3900885888786572,0.0804192021855236,3.732276584745563
 117.7,43.24008225237618,34.142380172845414,133.02097295686818,3.99632111107854,0.004220114505159667,0.3825646507986381,0.08051549449493102,3.690462228782615
 117.80000000000001,43.34165562305511,34.14235822514893,133.02115585713983,3.99632111107854,-0.07020109104844452,0.3777852676959893,0.08061070146910096,3.6492815704925774
 117.9,43.230774137767334,34.14233322331756,133.0210748666379,3.99632111107854,-0.03937547059876191,0.41760608153042483,0.08070483820575881,3.608736559981632
 118.0,43.385698303277735,34.14227745928795,133.0210374493822,3.99632111107854,0.008024988397291502,0.41839708239053625,0.08079791996646778,3.5688288294620527
 118.10000000000001,44.03559835849851,34.142227711595055,133.02095808484907,3.99632111107854,-0.0018935051102455555,0.4202486334830982,0.08088996217662886,3.5295596932522195
 118.2,43.591834741940524,34.1422574297484,133.02115358733275,3.99632111107854,0.0032647465166361364,0.40782377341104653,0.08098098042548088,3.490930147776639
 118.30000000000001,43.82944445014351,34.14222415456558,133.02107982085693,3.99632111107854,0.03794276384834687,0.41508440297294574,0.08107099046610046,3.452940871565902
 118.4,43.193907302353004,34.14234116414487,133.0211114304287,3.99632111107854,-0.014347129255788673,0.418643122946382,0.08116000821540202,3.41559222525673
 118.5,43.07165948574504,34.142342317387154,133.02109905752397,3.99632111107854,0.004441530199469423,0.45330057088229075,0.08124804975413785,3.378884251591936
 118.60000000000001,43.407455241843216,34.14221582990285,133.02102017243487,3.99632111107854,0.04175636765030669,0.4380722489556276,0.081335131326898,3.3428166754204405
 118.7,43.33024578046273,34.14227171761172,133.020989633081,3.99632111107854,-0.011182078631778416,0.4403311375031157,0.08142126934211033,3.307388903697289
 118.80000000000001,43.80707247268947,34.14222155371168,133.0210947295301,3.99632111107854,-0.015238580531414345,0.4424948655520255,0.08150648037204057,3.272600025483613
 118.9,43.31087700628191,34.142198790319874,133.0210161784635,3.99632111107854,-0.013173904891858414,0.4641283053326942,0.08159078115279217,3.2384488119466726
 119.0,45.008240543933255,34.142316591643926,133.0209990830545,3.99632111107854,-0.004943333092130598,0.4831892573160127,0.08167418858430649,3.20493371635982
 119.10000000000001,43.252914770769685,34.14230736430384,133.02113115710804,3.99632111107854,0.01768746533469196,0.4928716974250764,0.08175671973036261,3.172052874102518
 119.2,42.75867171762898,34.14215853523915,133.02096879771125,3.99632111107854,-0.01635276449092271,0.4918271110445479,0.0818383918185775,3.1398041026603476
 119.30000000000001,44.07048067123771,34.142168278562345,133.0210968975586,3.99632111107854,-0.015371884983935168,0.4906497329211207,0.08191922224040585,3.108184901624984
 119.4,43.30786122162224,34.1421517449282,133.02110103625134,3.99632111107854,0.02812161848880953,0.5073173691324878,0.08199922855114028,3.077192452694224
 119.5,44.37434261032888,34.142329416502704,133.02111770572603,3.99632111107854,-0.007296049595061381,0.520774138793352,0.08207842846991113,3.046823619671961
 119.60000000000001,44.372262473220985,34.1422928820775,133.0211124969715,3.99632111107854,-0.0233295542967618,0.5342520765817566,0.08215683987968661,3.0170749484681965
 119.7,44.819038978386146,34.142203659325745,133.02114668862765,3.99632111107854,0.011108156742424028,0.5276269593659355,0.0822344808272727,2.9879426670990528
 119.80000000000001,44.19712932187034,34.14223376843306,133.02101241948804,3.99632111107854,0.011368487439964152,0.5185836239048229,0.08231136952331317,2.959422685686742
 119.9,44.22098605865789,34.14220575284049,133.02105096217693,3.99632111107854,-0.03350875326558459,0.5389965514473918,0.08238752434228966,2.931510596459603
 120.0,43.87468415576375,34.142269207578266,133.02103906302477,2.904201673752067,-0.03195165070641215,0.5414714771958892,0.0824629638225216,2.904201673752067
 120.10000000000001,42.99029073880603,34.14226577544097,133.0211096676265,2.904201673752067,0.018180891872528852,0.5653436024998756,0.08253770666616628,2.8774908740046774
 120.2,44.0932219387844,34.14231005948493,133.0211044122226,2.904201673752067,0.009057751598177049,0.5719047795040044,0.08261177173921865,2.851372835764093
 120.30000000000001,43.779094997616056,34.142295839664754,133.0211196453211,2.904201673752067,0.016593760573457086,0.5617082026314114,0.08268517807151164,2.825841879683069
 120.4,43.95783992302482,34.14215345593522,133.02119073229886,2.904201673752067,0.008992218838631548,0.5697382028573298,0.08275794485671592,2.800892008520481
 120.5,43.77428148847964,34.14213675323821,133.0211526883798,2.904201673752067,0.008508090061979936,0.5807947180243453,0.08283009145233998,2.7765169071413016
 120.60000000000001,44.279566805973516,34.14229646404323,133.02117264445403,2.904201673752067,0.0009471603423451012,0.5920242338224904,0.08290163737973008,2.752709942516613
 120.7,44.21331056236058,34.14223885011647,133.02111014064118,2.904201673752067,0.034426372628369555,0.604855588013055,0.08297260232407039,2.729464163723615
 120.80000000000001,44.776458820492095,34.14226110939321,133.0211103823544,2.904201673752067,-0.00018656536872934857,0.5849413498822096,0.08304300613438276,2.7067723019456
 120.9,44.15064070725275,34.14216996130009,133.02107435751537,2.904201673752067,0.021752167512818256,0.6002625681787266,0.08311285423540331,2.6846323074626666
 121.0,44.78261410960573,34.142130258751465,133.02120494784154,2.904201673752067,-0.00741496473699682,0.6321745719682111,0.08318213819485597,2.66304675586097
 121.10000000000001,44.076505212067296,34.14221141102104,133.02119342958622,2.904201673752067,0.04822041018159416,0.6345976206769689,0.08325087122140647,2.64200945792425
 121.2,43.87156031624107,34.14228932998573,133.02117672720425,2.904201673752067,-0.038745816868220075,0.6357845983682336,0.08331906679640068,2.6215138388116763
 121.30000000000001,43.518402230573585,34.142094627950556,133.0211318643661,2.904201673752067,-0.019654430321132687,0.6178103834881707,0.08338673828054194,2.6015530895956815
 121.4,44.0253231282878,34.14222257531209,133.0212234544754,2.904201673752067,-0.048017647396930985,0.6376466236882976,0.08345389891389073,2.582120167261984
 121.5,44.40645608384993,34.142181692598626,133.02113779661704,2.904201673752067,0.02481074161285242,0.6358917372936277,0.08352056181586487,2.5632077947095677
 121.60000000000001,44.35900637542424,34.14213171882796,133.0211735861892,2.904201673752067,-0.04515982549631932,0.6579636302072768,0.08358673998523954,2.544808460750691
 121.7,44.571685530827146,34.14225180103733,133.02115964157255,2.904201673752067,-0.03859395069306862,0.6603555994592892,0.08365244630014704,2.526914420110894
 121.80000000000001,44.81922077595438,34.14215922105757,133.02116744840532,2.904201673752067,-0.031823007486094235,0.6712817278590001,0.08371769351807716,2.509517693428982
 121.9,44.41838031472138,34.14209229149932,133.02114639794905,2.904201673752067,-0.005772355076631465,0.6650201868180746,0.08378249427587676,2.492610067257043
 122.0,44.873468432915246,34.14219093669261,133.02118941108088,2.904201673752067,0.059802252809153675,0.6691518072168078,0.08384686108975019,2.4761830940604335
 122.10000000000001,44.10174116613775,34.1421278835313,133.02114151590237,2.904201673752067,0.002052766366209797,0.6910978247768311,0.08391080635525897,2.4602280922177826
 122.2,44.35318893331934,34.14213070721041,133.02123454062365,2.904201673752067,0.01601731811446233,0.6930104456228885,0.08397434234732193,2.444736146021002
 122.30000000000001,44.79465946864247,34.142220678169004,133.0211085626652,2.904201673752067,0.019302241895646617,0.6529903646370112,0.08403748122021519,2.4296981056752682
 122.4,44.06664130079002,34.142186373511436,133.0212091254155,2.904201673752067,-0.009391714140887379,0.6936105377157612,0.08410023500757212,2.415104587299041
 122.5,44.262846341924615,34.14222366614139,133.02122720764618,2.904201673752067,-0.0047116485303665976,0.7013957168152815,0.08416261562238346,2.4009459729240463
 122.60000000000001,44.56639945128394,34.14231407337525,133.02102058969743,2.904201673752067,-0.010457176320952534,0.6896131910806171,0.08422463485699717,2.3872124104952874
 122.7,44.36027343947992,34.14221593310705,133.021113824275,2.904201673752067,-0.0499284542657958,0.6856478475677619,0.08428630438311852,2.3738938138710455
 122.80000000000001,44.42944939617933,34.1422328246038,133.02116511203232,2.904201673752067,-0.028991280919627847,0.716117002294867,0.08434763575181009,2.360979862822869
 122.9,45.39072151684996,34.1421574838734,133.02121850964073,2.904201673752067,0.019235169973246504,0.722021322511829,0.08440864039090211,2.3484600033898557
 123.0,44.3811638471564,34.142284910036416,133.0211573538192,2.336323963025635,0.09296057781049144,0.7253485918004688,0.08446932891411633,2.336323963025635
 123.10000000000001,45.01776431143854,34.14225351261399,133.0211490837224,2.336323963025635,0.02501595810716431,0.7263014467114701,0.08452971026621545,2.324562820284799
 123.2,44.227553174848524,34.14217351777322,133.02114524395654,2.336323963025635,0.0006409492771669601,0.7244233501958177,0.08458979307619946,2.313167906011979
 123.30000000000001,45.03750822004608,34.142157542455735,133.0211090153822,2.336323963025635,-0.06396282538222221,0.7319738555312844,0.08464958586146165,2.3021305495733073
 123.4,44.18978339736531,34.14212983612502,133.021211340522,2.336323963025635,0.022285797413439015,0.7320324674071015,0.08470909702778856,2.2914420788564307
 123.5,44.57817550254852,34.142276252309344,133.02118519733295,2.336323963025635,-0.015274657496306515,0.7420218091133338,0.08476833486935983,2.2810938202705
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 126.2,45.27921655445203,34.1422422631981,133.02126243765153,2.108102933501183,0.03335299172084693,0.8168930077741472,0.08629126530622269,2.0992026616437376
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 126.4,44.555190598440284,34.14210812967957,133.02126356001494,2.108102933501183,-0.003574428225304877,0.8238062131407228,0.08639985896347221,2.090595676158524
 126.5,45.25900486538182,34.142140731802414,133.02119621565708,2.108102933501183,0.04307072152189714,0.8363138225557576,0.086453984272547,2.0863625937295276
 126.60000000000001,44.93229034589459,34.14213122448918,133.02132977194827,2.108102933501183,-0.028292645462794086,0.8366895865734181,0.08650799535170267,2.082154124094211
 126.7,45.36791646653361,34.14224115399052,133.02122562719342,2.108102933501183,0.05860695794999942,0.8020160112664978,0.08656189179759526,2.077952757748402
 126.80000000000001,44.96578705175919,34.14216779246912,133.0211647647814,2.108102933501183,-0.005569341294616373,0.8270704786344569,0.08661567281433734,2.073740374033823
 126.9,46.003569231433055,34.14221397145279,133.0213321228461,2.108102933501183,0.0010308993042631913,0.8237927963438452,0.08666933721349782,2.0694982411380964
 127.0,45.39579848374981,34.142159625753536,133.02135745672703,2.108102933501183,0.006480065104213443,0.8336373572114694,0.08672288341410209,2.0652070160947402
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 127.4,45.26279113960677,34.142147601630676,133.02132225013565,2.108102933501183,0.034442646859136,0.8372322353237953,0.08849202348058224,2.0471429447217844
 127.5,45.995699516015215,34.14218831449799,133.02126233395285,2.108102933501183,-0.024709045480671998,0.8151832959921781,0.08920723510729073,2.042294724049457
 127.60000000000001,45.07644791539215,34.14212115776221,133.0214014229984,2.108102933501183,-0.017454546521605805,0.8444633042524539,0.08992060959713526,2.03726851919445
 127.7,45.00586143888084,34.14217706231073,133.02135462407173,2.108102933501183,0.0017070099013880612,0.8542774386150712,0.09063208844435139,2.0320407091115653
 127.80000000000001,45.415653176923136,34.14213894977903,133.0212758262824,2.108102933501183,0.04096730107512948,0.8524709008629412,0.09134160783773956,2.0265870616014965
 127.9,46.0475602390518,34.142205900209596,133.02129180871896,2.108102933501183,0.008659288690157214,0.8631663747323314,0.09204909866066505,2.020882733310839
 128.0,45.22811944243384,34.14217651275261,133.02131976609562,2.108102933501183,0.008637928509847462,0.8488817555821553,0.09275448649105597,2.014902269732082
 128.1,45.26242384213244,34.14216243174461,133.02128951924297,2.108102933501183,0.013593416758137697,0.8713649581329346,0.09345769160140575,2.0086196052036143
 128.20000000000002,45.61677535131868,34.142124313180965,133.02127947097873,2.108102933501183,0.014354740590987004,0.8694163641408528,0.09415862895877304,2.0020080629097183
 128.3,45.17970424696228,34.14221649333615,133.02139685932286,2.108102933501183,0.0666864679796277,0.868661354397269,0.09485720822477815,1.9950403548805804
 128.4,45.767505057871446,34.142201684408235,133.02127186140197,2.108102933501183,-0.010761122677127886,0.8654180687005452,0.09555333375560865,1.9876885819922783
 128.5,44.71920419529037,34.142158525731794,133.02135652806913,2.108102933501183,-0.016108516724032268,0.8676413995427097,0.09624690460201495,1.9799242339667884
 128.6,45.971528301319864,34.14224496394305,133.02121755051388,2.108102933501183,0.01012913237557727,0.8862323630840934,0.09693781450931155,1.971718189371985
 128.70000000000002,44.766368916661236,34.14212248112807,133.02126756159154,2.108102933501183,0.06540701069165392,0.8771096195213707,0.09762586107295884,1.9631155383506624
 128.8,45.92205868981609,34.14221297950202,133.02125919123762,2.108102933501183,-0.01698349700110679,0.8752792198636691,0.09831059203377908,1.954400336733504
 128.9,46.07255538893768,34.14219221845875,133.02128048059234,2.108102933501183,-0.015574446058399392,0.8720938661930044,0.09899195004917036,1.945580719917771
 129.0,45.995887751813086,34.14206819170382,133.02126799890004,1.9366338448811447,0.050722433558631486,0.9076223061829868,0.09966992283518133,1.9366338448811447
 129.1,46.71514748343448,34.14218417484163,133.02117184525537,1.9366338448811447,0.04388676488935266,0.8960306980098832,0.10034449810164744,1.9275406619635895
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 129.3,45.29156308708919,34.14208895745341,133.02126712910635,1.9366338448811447,0.0053567162301759,0.8831815679150326,0.1016834068842075,1.9088581406569607
 129.4,45.48486448944932,34.142099375659285,133.02138037049116,1.9366338448811447,-0.003820145563847588,0.9056904288536914,0.10234771578889743,1.8992496697592316
 129.5,47.30818594629424,34.14213306208896,133.0213970251268,1.9366338448811447,0.00739369073012113,0.9107320691550869,0.10300857795123364,1.889456625963258
 129.6,45.95747885208451,34.14217334389312,133.0213655158846,1.9366338448811447,0.0227379637185256,0.9199491615327826,0.1036659810499779,1.879478926420417
 129.70000000000002,45.80799374073781,34.142105925139376,133.0213184593115,1.9366338448811447,0.02259801396339816,0.922799547436277,0.10431991275767635,1.8693202816443666
 129.8,45.95360556546358,34.14223899182246,133.0214358333707,1.9366338448811447,-0.0039556620011833524,0.9308484593806325,0.10497036074066152,1.8589881955110554
 129.9,46.059769793756814,34.142129187372596,133.02127856586665,1.9366338448811447,-0.01259889379584377,0.9439192034780284,0.10561731265905107,1.8484939652587062
 130.0,45.110941386276245,34.142122096684865,133.02119525703398,1.9366338448811447,0.019933195348393308,0.9445546056196166,0.10626075616674752,1.8378526814878278
 130.1,46.016304018319424,34.14212969198988,133.02138532441555,1.9366338448811447,0.013465683564722495,0.9578091382982443,0.10690067891143973,1.827083228161211
 130.20000000000002,44.702647838941395,34.14213493895431,133.02128134811812,1.9366338448811447,0.039882175253490845,0.9625477237057228,0.10753706853460096,1.8162082826039265
 130.3,45.3816144978903,34.142139348264216,133.02132679648304,1.9366338448811447,-0.034949174857329644,0.9635224568123256,0.10816991267149004,1.8052543155033367
 130.4,45.495660826003075,34.142214871201816,133.02134392264108,1.9366338448811447,0.046694235127076864,0.9673554334361396,0.10879919895115181,1.7942515909090782
 130.5,46.022259486422,34.142077353929395,133.02138117655005,1.9366338448811447,-0.03146506646648374,0.9711356577807444,0.10942491499641628,1.7832341662330722
 130.6,46.896300739767,34.142021905599215,133.02135015666465,1.9366338448811447,-0.036018440481483775,0.9974828957181381,0.11004704842389862,1.7722398922495235
 130.70000000000002,46.63696642998785,34.14206360504858,133.02133490040205,1.9366338448811447,0.020828847374947668,0.9835645192844003,0.11066558684399883,1.761310413094916
 130.8,45.64770115053056,34.142044645422374,133.02131631457095,1.9366338448811447,0.00020580435752026553,1.0112848726699712,0.11128051786090364,1.750491166268026
 130.9,46.61523538604602,34.14213583456141,133.0212829892144,1.9366338448811447,0.0028767411184752022,1.0067065790003324,0.1118918290725838,1.7398313826299026
 131.0,46.340589760079055,34.1420705124002,133.021342099802,1.9366338448811447,0.02279391734324686,1.018451645485091,0.11249950807079606,1.729384086403881
 131.1,46.11597296567418,34.142025969556315,133.02133739102348,1.9366338448811447,0.05538866923138233,1.0055600804735396,0.11310354244108312,1.719206095175579
 131.20000000000002,46.17160529290561,34.142041052341575,133.02137701049546,1.9366338448811447,0.04197442180308227,1.011175038065152,0.11370391976277205,1.7093580198928944
 131.3,46.15505201303864,34.142243235980224,133.02131108661047,1.9366338448811447,0.0025978143217928375,1.027943508847096,0.11430062760897597,1.6999042648660163
 131.4,46.668396570991696,34.14217839922321,133.02133700626345,1.9366338448811447,0.0659655077841068,1.0256110742828832,0.11411554544415797,1.6909130277674074
 131.5,45.98221565393355,34.142166013115634,133.02119915978747,1.9366338448811447,0.05222352936761999,1.0482672066835121,0.11386238166278422,1.6824562996318164
 131.6,45.83358551658755,34.142100266334154,133.02137557327245,1.9366338448811447,-0.04837896069700732,1.053892609215684,0.11361059850558781,1.6746605005780246
 131.70000000000002,46.65923718645955,34.14217568451975,133.02132777035754,1.9366338448811447,0.008909710879375877,1.0411292886876045,0.11335986562956384,1.667598829886037
 131.8,46.54723203174438,34.14209927048348,133.0212494704527,1.9366338448811447,0.011688842384618703,1.0532830933054957,0.1131101043758972,1.6612322497638228
 131.9,46.71190885831885,34.14215831500873,133.02131951229867,1.9366338448811447,0.03857168337499779,1.0564429676948766,0.11286123795936046,1.6555222222292425
 132.0,46.77438851115715,34.14205370830307,133.02129471390168,1.6504311893175418,-0.01958591746887494,1.0783811194392026,0.11261319004739759,1.6504311893175418
 132.1,46.5900739560331,34.14213316521563,133.02131992330902,1.6504311893175418,-0.029783950735034655,1.081688021547655,0.11236588476012367,1.64592257308135
 132.20000000000002,46.92127725210921,34.142149085867395,133.02131847653516,1.6504311893175418,-0.018224051525990503,1.0947136519237641,0.11211924667032575,1.6419607755906789
 132.3,45.63167452131217,34.14221041275963,133.02139140516363,1.6504311893175418,-0.004325161556854912,1.0907635611195412,0.11187320080346157,1.6385111789329265
 132.4,46.59984661179671,34.14213048043601,133.02137868476316,1.6504311893175418,-0.019570458067274598,1.0848082407441684,0.11162767263766037,1.6355401452128717
 132.5,46.905338729424365,34.142023683716275,133.0214024970574,1.6504311893175418,0.024799675784122843,1.083408181036293,0.11138258810372277,1.6330150165526778
 132.6,46.59855605704348,34.14213409305483,133.0213960652128,1.6504311893175418,0.009644443076162967,1.077039190941665,0.11113787358512087,1.630904115091891
 132.70000000000002,46.49338405513307,34.14212943720618,133.02133359687883,1.6504311893175418,0.018122400274527273,1.0901121506878995,0.11089345591799762,1.6291767429874418
 132.8,46.055403524338466,34.1420747445137,133.02131109891806,1.6504311893175418,0.00043784579627934635,1.0768900434210094,0.11064926239116785,1.627803182413644
 132.9,46.29269289796368,34.14221641161733,133.02124390791076,1.6504311893175418,-0.011518559301753162,1.073235129649536,0.11040522074611736,1.6267546955621952
 133.0,45.961119228481934,34.14209028219796,133.02137704459693,1.6504311893175418,0.025158628596489242,1.0799808937640503,0.11016125917700331,1.6260035246421753
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 280.3,13.856901898175156,34.13383317142944,133.0190305246942,3.3953847126059267,-0.011787469694512557,0.4523175172166275,0.04639761578229792,3.364664390279091
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 310.1,18.03620855235082,34.13286289670786,133.018935156552,4.093838196440998,0.03891970663930359,0.3155883308092466,0.027719751041065624,4.1303735069296055
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 310.3,18.26726176825202,34.13282697608181,133.0188456599468,4.093838196440998,0.011981285188573183,0.3158249405994669,0.027640723077914917,4.1368878260216055
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 311.0,18.20584341155656,34.132766053438715,133.01882350072515,4.093838196440998,0.03807529233661052,0.31774245720425115,0.02736315392975999,4.159402532545529
 311.1,18.48081126028792,34.13285590729007,133.01889968339225,4.093838196440998,0.014851006563844117,0.3025381698468256,0.02732337833399701,4.162584352677358
 311.20000000000005,18.671140357074297,34.13284770351009,133.01886891586275,4.093838196440998,0.027619989767321454,0.3048317831674243,0.0272835721336517,4.1657579122503074
 311.3,17.76151214539136,34.132846828874996,133.01886209312627,4.093838196440998,-0.026157668505199586,0.29226157228494615,0.027243735366553255,4.168923339486266
 311.40000000000003,18.529672267466538,34.13289344831558,133.01891711481986,4.093838196440998,0.017949166975383426,0.3084612142262708,0.02720386807092972,4.17208076308659
 311.5,17.75090956436746,34.13287007485272,133.0188858696743,4.093838196440998,-0.03561754611337491,0.2805520370214636,0.027163970285408078,4.175230312232082
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 311.8,17.754345229730916,34.13283126178343,133.0189525912327,4.093838196440998,0.025633630100831,0.31787792169288415,0.027044094381707677,4.184633011939571
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 312.0,17.77842679658302,34.13285578371751,133.01892313946593,4.190864496027582,0.027479498133321487,0.31855072735801215,0.0269640253891952,4.190864496027582
 312.1,18.61798778297978,34.132884324343486,133.01888741811268,4.190864496027582,0.0010099941505903323,0.31616065441441055,0.026923945497789734,4.193969538090808
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 312.3,18.18115234854619,34.13282789099167,133.01895755212996,4.190864496027582,-0.024088885759875223,0.29882763247255617,0.02684369513177676,4.200158884940812
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 312.5,17.40359527277717,34.13278197803503,133.01894879166397,4.190864496027582,0.038996371803721445,0.29351873057032163,0.026763324268943425,4.206321471262724
 312.6,18.680927982644715,34.13286511582294,133.01888633296247,4.190864496027582,0.017411817849625404,0.2963199301018273,0.026723093758008406,4.209393064463808
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 312.8,17.664994280674144,34.13281755216838,133.0189454348894,4.190864496027582,0.015495476958031282,0.30988007834107234,0.026642542794170585,4.215517525617816
 312.90000000000003,18.234674033616677,34.13288288566058,133.01891292728953,4.190864496027582,-3.8246521797951065e-05,0.3055693842587161,0.02660222242929207,4.218570664877755
 313.0,18.08538581777234,34.13277493862314,133.01889761961954,4.190864496027582,-0.021271079871670446,0.2978538936922093,0.026561872201788177,4.221617924930087
 313.1,19.134351218919946,34.13281218228133,133.0189113638309,4.190864496027582,0.01925523790330843,0.29143698943569146,0.02652149215666828,4.2246594426269715
 313.20000000000005,18.14771511740098,34.13290842259182,133.01887066115557,4.190864496027582,-0.02091095697647258,0.29775312154942524,0.026481082339340677,4.227695355300018
 313.3,17.51031729696495,34.13274525584666,133.01906637277153,4.190864496027582,0.0007191021041795312,0.28579135656554383,0.026440642795612604,4.230725800760297
 313.40000000000003,18.822167578972742,34.13280950256895,133.0188735888584,4.190864496027582,0.0441621115220665,0.3135234434941388,0.026400173571690097,4.233750917298343
 313.5,19.152625139285167,34.132723252458675,133.01881765895772,4.190864496027582,0.016263167646880457,0.29184781207808014,0.026359674714178202,4.236770843684141
 313.6,17.864516204572226,34.132783117813176,133.01894873731058,4.190864496027582,-0.006554093873440949,0.3019982324591635,0.0263191462700808,4.239785719167146
 313.70000000000005,17.716643311978583,34.13266001537689,133.01888965630343,4.190864496027582,0.01544846293911919,0.29849566385861726,0.026278588286800665,4.2427956834762615
 313.8,17.598481793615605,34.13280477403551,133.01890484327117,4.190864496027582,0.006310524887066556,0.30481991715518336,0.026238000812139582,4.245800876819854
 313.90000000000003,18.23583815437847,34.13273590780871,133.01899610668696,4.190864496027582,0.007249958631696196,0.3184419431710844,0.02619738389429806,4.248801439885753
 314.0,18.416324189786916,34.132861350471444,133.01887539741946,4.190864496027582,-0.02504514543722326,0.3000805199184829,0.02615673758187565,4.2517975138412405
 314.1,17.77079102573556,34.13275941195753,133.01896790106724,4.190864496027582,-0.03968892225004294,0.3009248719559651,0.026116061923870754,4.2547892403330625
 314.20000000000005,18.84886654742957,34.132714884693904,133.0187885609788,4.190864496027582,0.02777257466466174,0.2901666586459097,0.02607535696968067,4.257776761487421
 314.3,18.028865953756704,34.132807837276054,133.01897235910224,4.190864496027582,-0.00856321913134971,0.3029773449310528,0.02603462276910164,4.260760219909977
 314.40000000000003,18.24060174543561,34.13275369541082,133.01893275376608,4.190864496027582,0.022932476970461343,0.3078611077472988,0.025993859372328718,4.263739758685854
 314.5,18.299287089675524,34.132826574155764,133.01894173405927,4.190864496027582,-0.003780458305543823,0.2899348865302635,0.025953066829955983,4.266715521379628
 314.6,18.068250151407405,34.132723147970296,133.01892843735104,4.190864496027582,0.04170248745677423,0.29217658487591974,0.025912245192976285,4.269687652035343
 314.70000000000005,18.15268015610771,34.132679381722,133.01887951063438,4.190864496027582,-0.032495695757560505,0.29331917643326716,0.025871394512781472,4.272656295176496
 314.8,18.373291601734607,34.13275859584251,133.01896690046158,4.190864496027582,-0.01474064670950551,0.2957440176987122,0.025830514841162267,4.27562159580604
 314.90000000000003,18.673340041477935,34.132729446507454,133.0187984492362,4.190864496027582,-0.021917719722881954,0.2948531495041616,0.025789606230308265,4.278583699406396
 315.0,18.201048086335668,34.132661675745545,133.01897173578865,4.281542751939436,-0.03989902400289373,0.30564188696004724,0.025748668732808,4.281542751939436
 315.1,18.082037826449326,34.13270737185919,133.0189054748485,4.281542751939436,0.06601845730781068,0.291679371938088,0.025707702401648897,4.284498899846497
 315.20000000000005,18.278209009149965,34.13263306093861,133.01890220133083,4.281542751939436,0.013004087613450632,0.2891570976809128,0.02566670729021724,4.28745229004837
 315.3,17.49129031276897,34.132707810693084,133.01887482563725,4.281542751939436,0.023671785052504817,0.28666091400489696,0.025625683452298303,4.290403069945307
 315.40000000000003,18.763279521990132,34.1326737581605,133.01892069203566,4.281542751939436,-0.01164783298664624,0.2777748712043716,0.025584630942076178,4.2933513874170215
 315.5,18.23215505407313,34.13265730173181,133.0189749151204,4.281542751939436,-0.04214357322207454,0.3027426103431317,0.025543549814133915,4.296297390822681
 315.6,19.52088537416866,34.13277252428436,133.01890893763368,4.281542751939436,0.02859981687748006,0.29927477846847517,0.025502440123453415,4.299241229000918
 315.70000000000005,18.630959723871207,34.13278460605692,133.0189233016698,4.281542751939436,-0.025250377162848368,0.2837997278749408,0.02546130192541551,4.302183051269819
 315.8,18.548205286995678,34.13274072878334,133.01894564116122,4.281542751939436,-0.051650291983735976,0.2904693653311155,0.02542013527579996,4.305123007426929
 315.90000000000003,19.02789484804604,34.13270232410855,133.01895492417106,4.281542751939436,0.033351041528146635,0.28005848364099073,0.025378940230785345,4.308061247749259
 316.0,18.25545287579427,34.13265312325619,133.01894117437254,4.281542751939436,-0.0021532774795782845,0.27559058977136414,0.025337716846949247,4.31099792299327
 316.1,18.326701697601614,34.132641211248185,133.01891602824975,4.281542751939436,-0.01319923914835228,0.27612413722365636,0.025296465181268043,4.31393318439489
 316.20000000000005,18.460111062638173,34.132659607060155,133.01890223648883,4.281542751939436,0.042856267829596284,0.2792498069525806,0.02525518529111713,4.316867183669501
 316.3,17.886778237179982,34.13262668738164,133.01902634932463,4.281542751939436,0.06934103928911357,0.30581527925830454,0.025213877234270727,4.319800073011944
 316.40000000000003,18.855399499588223,34.132653923865064,133.01909463611432,4.281542751939436,0.0006713348269814238,0.3052009253588714,0.025172541068901922,4.322732005096523
 316.5,18.624092102806046,34.13262732475218,133.01895029691337,4.281542751939436,0.026626131010429543,0.2765377952825253,0.02513117685358283,4.325663133076995
 316.6,18.535949370107062,34.13268301920522,133.01900861536842,4.281542751939436,-0.041927307031527174,0.29125914836014277,0.025089784647284338,4.3285936105865845
 316.70000000000005,18.020579995946154,34.132626756306934,133.01890465557514,4.281542751939436,0.007467336298971655,0.2841420416900092,0.025048364509376322,4.331523591737966
 316.8,18.022483039568716,34.13247789380626,133.01888854211182,4.281542751939436,-0.026281482365744003,0.28039275615791903,0.025006916499627496,4.334453231123277
 316.90000000000003,18.696137620019467,34.13259032818873,133.0190080601636,4.281542751939436,0.007429473623567586,0.28641738702548936,0.024965440678205515,4.337382683814117
 317.0,17.948256882754308,34.13263067119297,133.01895195759283,4.281542751939436,-0.01731417807922515,0.29121414367232834,0.02492393710567696,4.340312105361538
 317.1,18.15305203738528,34.13263885681798,133.01900852412027,4.281542751939436,0.03721058538098077,0.27297001635920914,0.02488240584300721,4.343241651796058
 317.20000000000005,18.05542346443898,34.132629394359334,133.0189205971018,4.281542751939436,0.02474614329345272,0.2926494867471195,0.024840846951560643,4.34617147962765
 317.3,18.66771371691168,34.13269437262592,133.01901900655787,4.281542751939436,-0.05729152251924014,0.27841462626661495,0.024799260493100547,4.349101745845743
 317.40000000000003,18.437204033292687,34.13251386741469,133.0188940214306,4.281542751939436,0.04607456801733082,0.2800127941746507,0.024757646529789026,4.352032607919233
 317.5,18.268620593560644,34.13258680321291,133.01891133767808,4.281542751939436,-0.01722778653362568,0.2743981181247303,0.024716005124187167,4.3549642237964665
 317.6,17.138791024953544,34.13263723809596,133.01897211393018,4.281542751939436,0.020106244231728212,0.2563922526995267,0.024674336339254872,4.357896751905258
 317.70000000000005,18.663420009648423,34.1325354976416,133.01890292201702,4.281542751939436,-0.0020020713188723623,0.2662137462865759,0.02463264023835104,4.360830351152874
 317.8,17.98629953702877,34.13261210986293,133.0189189040675,4.281542751939436,-0.02459087098284509,0.28577930734942575,0.02459091688523344,4.36376518092604
 317.90000000000003,17.856681298886368,34.13270507030212,133.0189151536802,4.281542751939436,0.005491481397092064,0.2744251513840126,0.024549166344058695,4.366701401090947
 318.0,18.17657011099252,34.13258339983924,133.0189152816199,4.369639171993237,0.06034469571097433,0.2799252613671802,0.024507388679382396,4.369639171993237
 318.1,19.040946971717634,34.13248055806151,133.01892774083635,4.369639171993237,0.028483666519934843,0.27631940928915977,0.02446558395615897,4.372578654458017
 318.20000000000005,18.453689237265422,34.13257746617042,133.01886517404543,4.369639171993237,-0.04972162807317351,0.2801127724238625,0.02442375223974177,4.375520009789851
 318.3,18.287023342110118,34.13260176844639,133.018950220596,4.369639171993237,-0.030899383676655037,0.26676946357579095,0.024381893595883133,4.378463399772759
 318.40000000000003,18.137325260814077,34.132568409410084,133.01898847046584,4.369639171993237,0.004845506094937372,0.2728388302542977,0.024340008090734142,4.381408986670227
 318.5,19.336065784991558,34.132555290458185,133.01903373851218,4.369639171993237,-0.08039552566849326,0.2864872939472435,0.024298095136922795,4.3843497990954505
 318.6,18.267324244332805,34.132592831785715,133.01895547236654,4.369639171993237,0.022844223448896212,0.27143593874512345,0.0242561515237299,4.387247916706135
 318.70000000000005,18.779528804909017,34.132587811572876,133.01903642703695,4.369639171993237,-0.009137948168295622,0.27318804222925813,0.024214177338412437,4.390098016898652
 318.8,18.053811315535864,34.13251011709214,133.0189850944064,4.369639171993237,-0.022137995588015023,0.28205741285129127,0.024172173199575476,4.39290042464344
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diff --git a/xtra_kalman.m b/xtra_kalman.m
	function [x, P] = kalman_filter(A, B, C, Q, R, x, u, y, P)
	% kalman_filter - Returns the next state estimate and its covariance matrix
	% using the Kalman Filter predict & update. Note that this implementation is
	% not numerically stable, use production code for non-textbook problems.
	%
	% Syntax: [x, P] = kalman_filter(A, B, C, Q, R, x, u, y, P)
	%
	% Inputs:
	% A - State matrix, size 5 x 5
	% B - Input matrix, size 5 x 1
	% C - Output matrix, 2 x 5
	% Q - Model covariance matrix, size 5 x 5
	% R - Measurement convariance matrix, size 2 x 2
	% x - Current state, size 5 x 1
	% u - Current input, size 1 x 1
	% y - Current measurement, size 2 x 1
	% P - Current state covariance matrix, size 5 x 5
	% Outputs:
	% x - New state, size 5 x 1
	% P - New state covariance matrix, 5 x 5

	x = Ax + Bu;
	P = APA' + Q;
	L = PC'inv(CPC' + R);
	P = (eye(length(x)) - LC)P;
	x = x + L(y - Cx);

	end
	data = csvread('smartphone-data.csv', 1, 0);

	t = data(:, 1);
	v = data(:, 5);
	omega = data(:, 6);
	a = data(:, 7);
	theta_true = data(:, 8);
	v_true = data(:, 9);

	dt = % 1 x 1
	g = 9.81;

	A = % 5 x 5
	B = % 5 x 1
	C = % 2 x 5

	Q_scale = 1.0; % adjust this number, model covariance
	R_scale = 1.0; % adjust this number, measurement covariance

	Q = Q_scale*diag([0.0, 0.0, 0.0, 0.0, 1.0]);
	R = R_scale*diag([2.5e-01, 9.0e-04]);

	% initial P and x
	P = diag([1.0e+02, 2.5e-01, 1.0e-04, 4.0e-04, 9.0e-04]);
	x = % 5 x 1, initial state

	xs = zeros(length(?), 5); % add correct length of time vector
	xs(1, :) = x;
	for i=2:length(?) % add correct length of time vector
	u = % 1 x 1, model input
	y = % 2 x 1, actual measurements
	% run the filter for this time step, updating x and P
	[x, P] = kalman_filter(A, B, C, Q, R, x, u, y, P);
	% store the estimated state vector
	xs(i, :) = x;
	end

	% make some plots
	figure();
	plot(t, v_true, t, v, '.', t, xs(:, 2));
	figure();
	plot(t, theta_true, t, xs(:, 4));
	figure();
	plot(t, omega, '.', t, xs(:, 5));
	import numpy as np
	import matplotlib.pyplot as plt

	def kalman_filter(A, B, C, Q, R, x, u, y, P):
	"""Returns the next state estimate and its covariance matrix.

	Parameters
	==========
	A : shape(5, 5)
	State matrix
	B : shape(5, 1)
	Input matrix
	C : shape(2, 5)
	Output matrix
	Q : shape(5, 5)
	Model covariance matrix
	R : shape(2, 2)
	Measurement convariance matrix
	x : shape(5, 1)
	Current state
	u : shape(1, 1)
	Current input
	y : shape(2, 1)
	Current measurement
	P : shape(5, 5)
	Current state covariance matrix

	Returns
	=======
	x : shape(5, 1)
	New state
	P : shape(5, 5)
	New state covariance matrix

	"""
	x = A@x + B@u
	P = A@[email protected] + Q
	L = [email protected]@np.linalg.inv(C@[email protected] + R)
	P = (np.eye(len(x)) - L@C)@P
	x = x + L@(y - C@x)
	return x, P


	data = np.loadtxt('smartphone-data.csv', skiprows=1, delimiter=',')

	t = data[:, 0];
	v = data[:, 4];
	omega = data[:, 5];
	a = data[:, 6];
	theta_true = data[:, 7];
	v_true = data[:, 8];

	dt = # 1 x 1

	A = # 5 x 5
	B = # 5 x 1
	C = # 2 x 5

	Q_scale = 1.0 # adjust this number, model covariance
	R_scale = 1.0 # adjust this number, measurement covariance

	Q = Q_scale*np.diag([0.0, 0.0, 0.0, 0.0, 1.0])
	R = R_scale*np.diag([2.5e-01, 9.0e-04])

	P = np.diag([1.0e+02, 2.5e-01, 1.0e-04, 4.0e-04, 9.0e-04])

	x = # 5 x 1, initial state

	us = # n x 1 x 1, inputs
	ys = # n x 2 x 1, measurements

	xs = np.zeros((len(us), 5, 1)) # n x 5 x 1
	for i, (u, y) in enumerate(zip(us, ys)):
	x, P = kalman_filter(A, B, C, Q, R, x, u, y, P)
	xs[i] = x

	# make some plots
	plt.figure()
	plt.plot(t, v_true, t, v, '.', t, xs[:, 1, 0]);

	plt.figure()
	plot(t, theta_true, t, xs[:, 3, 0]);

	plt.figure()
	plot(t, omega, '.', t, xs[:, 4, 0]);