Here we will describe the Unscented Kalman filter. The state evolves discretely and the measurements are discrete in time. The code is in matlab_implementation/unscented of https://github.com/mannyray/KalmanFilter. The function header in ukf.m is:

function [estimates, covariances] = ukf(f_func, state_count, sensor_count, measurement_count,C,Q,R,P_0,x_0, measurements)

For those familiar with the Kalman filter and notation are familiar with the naming of the variables. However, to be extra sure it is always best to run help ukf. We will break down an example below.

Example 1

We will use the same model as in the DD-EKF tab - discrete logistic growth model with discrete measurements. The example is located in matlab_implementation/unscented/examples/logistic2.m and first runs the code from matlab_implementation/discrete_discrete/examples/logistic.m to define system parameters and then runs the ukf. The ukf only takes models that are state dependent and not 'time' dependent - this is reflect in the example code. The modification to make the code 'time' dependent is simple and easy way for contributing to the project.

clear all;
addpath('..');
addpath('../../discrete_discrete');
addpath('../../discrete_discrete/examples');
logistic;
%close plots generated as they are not needed here.
close all;
C_ukf = @(x,i) C*x + 0.*i;
Q_d_ukf = @(i) Q_d + 0.*i;
R_d_ukf = @(i) R_d + 0.*i;
%ukf implementation here does not allow for a time argument 
%this can be implemented
next_func = @(x) next_func(x,0);
[estimates_ukf, covariances_ukf] = ukf(next_func, state_count, sensor_count,...
     outputs,C_ukf,Q_d_ukf,R_d_ukf,P_0,x_0, measurements);
max_rel_err = max(abs(estimates - estimates_ukf)./estimates)

The max relative error is between estimates of ddekf and ukf is 0.011142 or around one percent. ukf2 is an equivalent implementation to ukf but gets rid of the clunky matrix wrappers (for example Q_d_ukf). The wrappers are useful if you have 'time' dependent but if your matrices are fixed and you are looking for a faster solution then go for ukf2. For a lot of the Matlab code, the code and examples are such that the noise covariance matrices and measurement matrices are usually fixed - by observing the different between ukf2 and ukf you can appropriately modify the code to fit your exact purposes.

[estimates_ukf2, covariances_ukf2] = ukf2(next_func, state_count, sensor_count, outputs,C,Q_d,R_d,P_0,x_0, measurements);
max_err = max(abs(estimates_ukf - estimates_ukf2))

The error computed is 1.4211e-14.

Example 2

We will run Example 2 from DD-EKF tab in matlab_implementation/discrete_discrete/examples/linear.m for the UKF in matlab_implementation/unscented/examples/linear2.m:

clear all;
addpath('..');
addpath('../../discrete_discrete');
addpath('../../discrete_discrete/examples');
linear;
C_ukf = @(x,i) C*x + 0.*i;
Q_d_ukf = @(i) Q_d + 0.*i;
R_d_ukf = @(i) R_d + 0.*i;
func = @(x) func(x,0);
[estimates_ukf, covariances_ukf] = ukf(func, state_count, sensor_count,...
    outputs,C_ukf,Q_d_ukf,R_d_ukf,P_0,x_0, measurements);%no need for jacobian 
covariances_ukf{end}

to produce

ans =
   5.0540e-07   2.4509e-08
   2.4509e-08   4.9806e-07
ans =
   5.0540e-07   2.4509e-08
   2.4509e-08   4.9806e-07

The first is output by linear script and the second is the one computed by ukf.