Fancy mean with Kalman filter

kalmanmean.jl

using Kalman
using Kalman.GaussianDistributions
using Statistics, LinearAlgebra

# prior for time 0
x0 = 0.0
P0 = floatmax(x0)

# observation operator
H = 1.0

# (mock) data
ys = [2, 3, 2, 2, 1, 5, 4, 4, 4, 4]

# Kalman filter
R = var(ys)
p = Gaussian(x0, P0)
for i in 1:length(ys)
    global p
    p, yres, _ = Kalman.correct(Kalman.JosephForm(), p, (Gaussian(ys[i], R), H))
end
@show p

julia> include("test/mean.jl")
p = Gaussian{Float64, Float64}(3.1, 0.16555555555555562)
Gaussian{Float64, Float64}(3.1, 0.16555555555555562)

julia> mean_and_var(ys) ./ (1, (length(ys)))
(3.1, 0.1655555555555556)