Sketch of Extended Kalman Filter package usage

ekf_usage.jl

using ExtendedKalmanFilters
using Distributions
using DelimitedFiles

# We may also want to look at DynamicalSystems.jl
# The package should accept AbstractArrays wherever possible so people can use StaticArrays

# Model semantics
# x_{t+1} = f(x_t, u_t) + w_t
# y_t = h(x_t) + v_t # should the control be an argument of h?
# w_t ~ N(0,W)
# v_t ~ N(0,V)

# van der pol oscillator with Euler integration
function f(x, u)
    xdot = [x[2], mu*(1-x[1]^2)*x[2] - x[1] + u]
    return x + dt*xdot
end

h(x) = x[2]

W = [1.0 0.0; 0.0 1.0]
V = 1.0

dmodel = DiscreteTimeDynamics(f, W) # maybe something from DynamicSystems.jl
omodel = NonlinearObservationModel(h, V)

ekf = ExtendedKalmanFilter(dmodel, omodel)

b0 = MvNormal([1.0 0.0; 0.0 1.0]) # initial belief
u = [1.0] # example control
y = [1.1] # example observation


### Usage option 1: single step updating ###

# b_{k+1|k}
bkp1k = predict(ekf, b0, u)
# b_{k+1|k+1}
b = measure(ekf, bkp1k, y) # could also just be called update


### Usage option 2: with POMDPs.jl ###

# does both predict and measurement in one shot
b = POMDPs.update(ekf, b0, u, y)


### Usage Option 3: post-processing data ###

# filter a whole time series
ys = vec(readdlm("y.txt")) # vector of measurements
us = vec(readdlm("u.txt")) # vector of controls

bs = runfilter(ekf, b0, us, ys) # return a vector of normal distributions