Comparing Kalman Filter: Maximize Gaussian math

1_maximize_gaussian.py

from math import *

def f(mu, sigma2, x):
    return 1 / sqrt(2. * pi * sigma2) * exp(-.5 * (x - mu) **2 / sigma2)

print f(10., 4., 10.)

1_maximize_gaussian.rb

class KalmanFilter
  def maximize_gaussian(mu:, sigma2:, x:)
    return 1 / Math.sqrt(2.0 * Math::PI * sigma2) * Math.exp(-0.5 * (x - mu) **2 / sigma2)
  end
end

kalman_filter = KalmanFilter.new

puts kalman_filter.maximize_gaussian(mu: 10.0, sigma2: 4.0, x: 10.0)

2_new_mean_and_variance.py

def update(mean1, var1, mean2, var2):
    new_mean = (var2 * mean1 + var1 * mean2) / (var1 + var2)
    new_var = 1 / (1 / var1 + 1 / var2)
    return [new_mean, new_var]

print update(10., 8., 13., 2.)

2_new_mean_and_variance.rb

class KalmanFilter
  def update(mean1:, var1:, mean2:, var2:)
    new_mean = (var2 * mean1 + var1 * mean2) / (var1 + var2)
    new_var = 1.0 / (1.0 / var1 + 1.0 / var2)
    return ['%.10f' % new_mean, '%.10f' % new_var]
  end
end

kalman_filter = KalmanFilter.new

puts kalman_filter.update(mean1: 10.0, var1: 8.0, mean2: 13.0, var2: 2.0)

3_predict_function.py

def predict(mean1, var1, mean2, var2):
    new_mean = mean1 + mean2
    new_var = var1 + var2
    return [new_mean, new_var]

print predict(10., 4., 12., 4.)

3_predict_function.rb

class KalmanFilter
  def predict(mean1:, var1:, mean2:, var2:)
    new_mean = mean1 + mean2
    new_var = var1 + var2
    return ['%.10f' % new_mean, '%.10f' % new_var]
  end
end

kalman_filter = KalmanFilter.new

puts kalman_filter.predict(mean1: 10.0, var1: 4.0, mean2: 12.0, var2: 4.0) 

4_kalman_filter.py

# Write a program that will iteratively update and
# predict based on the location measurements
# and inferred motions shown below.

def update(mean1, var1, mean2, var2):
    new_mean = float(var2 * mean1 + var1 * mean2) / (var1 + var2)
    new_var = 1./(1./var1 + 1./var2)
    return [new_mean, new_var]

def predict(mean1, var1, mean2, var2):
    new_mean = mean1 + mean2
    new_var = var1 + var2
    return [new_mean, new_var]

measurements = [5., 6., 7., 9., 10.]
motion = [1., 1., 2., 1., 1.]
measurement_sig = 4.
motion_sig = 2.
mu = 0.
sig = 10000.

#Please print out ONLY the final values of the mean
#and the variance in a list [mu, sig].

# Insert code here
for n in range(len(measurements)):
    [mu, sig] = update(mu, sig, measurements[n], measurement_sig)
    print 'update: ', [mu, sig]
    [mu, sig] = predict(mu, sig, motion[n], motion_sig)
    print 'predict: ', [mu, sig]

4_kalman_filter.rb

class KalmanFilter

  def update(mean1:, var1:, mean2:, var2:)
    new_mean = (var2 * mean1 + var1 * mean2) / (var1 + var2)
    new_var = 1.0/(1.0/var1 + 1.0/var2)
    return [new_mean, new_var]
  end

  def predict(mean1:, var1:, mean2:, var2:)
    new_mean = mean1 + mean2
    new_var = var1 + var2
    return [new_mean, new_var]
  end

  def measurement_output
    @measurements = [5.0, 6.0, 7.0, 9.0, 10.0]
    @motion = [1.0, 1.0, 2.0, 1.0, 1.0]
    @measurement_sig = 4.0
    @motion_sig = 2.0
    @mu = 0.0
    @sig = 10000.0

    puts "\n"
    @measurements.zip(@motion).each do |measurement, motion|
      update_array = update(mean1: @mu, var1: @sig, mean2: measurement, var2: @measurement_sig)
      @mu = update_array[0]
      @sig = update_array[1]
      update_mu_and_sig = [@mu, @sig]
      puts "Update: " + update_mu_and_sig.inspect

      predict_array = predict(mean1: @mu, var1: @sig, mean2: motion, var2: @motion_sig)
      @mu = predict_array[0]
      @sig = predict_array[1]
      predict_mu_and_sig = [@mu, @sig]
      puts "Predict: " + predict_mu_and_sig.inspect

      puts "\n ==============================================="
      puts "\n"
    end
  end

end

@kalman_filter = KalmanFilter.new
@kalman_filter.measurement_output