Particle methods for multimodal filtering. Application to terrain navigation

We consider a target following a noisy dynamical equation which is partially observed. The Extended Kalman Filter (EKF) is widely used to estimate recursively the mean and the variance of the state given the past measurement. The EKF assumes that the conditional density is Gaussian. But, in the case of multimodality, the EKF is inefficient. The goal of the nonlinear filtering is to estimate the whole law of the state. For example, in the tracking context, we will be able to estimate precisely the probability of the presence of a target in any portion of the state space and consequently to estimate the position of the target. For this filter there is no hypothesis concerning the linearity and no conditions about the nature of the noise. We present an application of particle filtering (bootstrap filter and local rejection regularised particle filter) in terrain navigation