set process noise 1D Constant Velocity

Hi,

I can define a Kalman filter with the code:

KF = trackingKF ('MotionModel','1D Constant Velocity');

How do I set the process noise? I mean I can set it with e.g:

KF.ProcessNoise=eye(2);

but since the process noise should be a function of one parameter only there should be som other way.

BR/

Per

Answer 1

[Elad Kivelevitch]

Per,

Thanks for the question.

I think I understand your confusion, but let's see if I do. You expect the process noise to be a*Bmat(dt) where a represents the magnitude of the process noise and Bmat(dt) is a time dependent factor that multiplies the acceleration according to the time difference, dt.

We currently don't have that option when you use trackingKF with a defined MotionModel. When you call predict(KF, dt), we assume that a=1 and then the process noise is simply [0.25 0.5;0.5 1];

There are two ways around that:

1. You can use a trackingEKF (or a trackingABF) and set it to a constant velocity model.
2. You can use trackingKF with a Custom motion model and set ProcessNoise yourself at every step.

Option 1: trackingEKF

sigmasq = 3;
EKF = trackingEKF(@constvel,@cvmeas,zeros(2,1),'HasAdditiveProcessNoise', false,'ProcessNoise',sigmasq)
[x_pred,P_pred] = predict(EKF,2) % Predict 2 seconds to the future

Note that P_pred is calculated correctly by taking into account the process noise, sigma, as an acceleration term.

Option 2: trackingKF with custom model:

% Defind the KF custom model:
A = [1 1;1 0];
H = [1 0];
KF = trackingKF(A,H)

% Now predict with sigma = 3 and dt = 2
sigmasq = 3;
dt = 2;
Q = sigmasq * [dt^4/4 dt^3/2; dt^3/2 dt^2];
A = [1 dt; 0 1];
[x_pred, P_pred] = predict(KF, A, Q)

Hope this helps,

Elad