Using Bayesian Kalman Filter to predict positions of moving particles / objects in 2D

In this article, the Bayesian Kalman Filter is used to predict positions of moving particles / objects in 2D.

1. The following equations / algorithms are used to compute the Bayesian state updates for the Kalman Filter.

2. For the first set of experiemnts, a few 2D Brownian Motion like movements are simulated for a particle. Now the noisy position measurments of the particle are captured at different time instants (by adding random Gaussian noise). Now, Kalman Filter is used to predict the particle’s position at different time instants, assuming different position, velocity and measurment uncertainties. Both the actual trajectory and KF-predicted trajectory of the particle are shown in the following figures / animations. The positional uncertainty (as 2D-Gaussian distribution) assumed by the Kalman Filter is also shown as gray / black contour.

3. The next set of figures / animations show how the position of a moving bug is tracked using Kalman Filters.Having obtained the noisy measurements of the positions of the bug at different times, first the correction steps and then the prediction steps were used, after assuming some uncertainties in position, velocity and the measurements with some Gaussian distributions.

4. Next the GPS dataset from the UCI Machine Learning Repository is used to get the geo-spatial positions of a vehicle at different times. Again some noisy measurement is simulated by adding random noise to the original data. Now, Kalman Filter is again used to predict the vehicle’s position at different time instants, assuming different position, velocity and measurment uncertainties. Both the actual trajectory and KF-predicted trajectory of the vehicle are shown in the following figures.