Department of Biomedical Engineering and Computational Science

2D CWPA-model demonstration with Kalman filter, 'kf_cwpa_demo'

In this demonstration program the classical Kalman filter is used to estimate the position and velocity of a moving object, whose dynamics follow two dimensional continous Wiener process acceleration (CWPA) model, which basically means that the object's acceleration is perturbed by Gaussian noise.

The continous-time dynamics (which follow the CWPA-model) are discretized and the obtained system is simulated 50 steps. One realization of such simulation is plotted in figure 1 as well as measurements obtained from target's position.

In figure 2 we have plotted the estimates for target's position and velocity produced by classical Kalman filter. Notice how the position estimates are more accurate as only the position of the object was observed directly.

Last we smooth the estimates produced by Kalman filter with Kalman smoother. The results are plotted in figure 3.

Files used in this example:

KF_CWPA_DEMO CWPA model demonstration with Kalman filter
Figure 1

Figure 1. One realization of object's trajectory and measurements from it.

Figure 1

Figure 2. Estimates for position and velocity produced by Kalman filter.

Figure 1

Figure 3. Estimates for position and velocity produced by Kalman smoother.