Possibilistic Kalman filtering for radar 2D tracking ?
Standard Kalman filter (SKF) introduced by Kalman in the 60s has gained a non-estimated importance in control as well as in robotics community. Its importance arises from the obtained optimal result in the sense of variance minimization under stochastic, Gaussian and unbiased perturbations, and when the state model as well as the measurement model are precisely known. However, when the last requirement is relaxed such that one or more parameters governing the models are ill-defined and rather given in terms of interval evaluations, Chen et al. (IEEE Trans. Aerospace Electr. Syst. 33 (1) (1997) 251259) have proposed Interval Kalman Filter (IKF) by extending the arithmetic operations to interval calculus. In this paper, we rather assume that the uncertainty pervading some parameters of the models are given in terms of possibility distributions [21]. This leads to a formulation of possibilistic Kalman Filtering (PKF), which agrees with IKF. The same example of 2D-radar tracking is tackled. Comparisons with IKF are investigated as well the influence of the modelling process on the performance of the filter. Besides, the proposal permits to capture certainty qualified information, which cannot be obtained from IKF.
kalman filter possibility theory interval analysis