Jeffreys divergence between state models: Application to target tracking using multiple models

In the field of recursive estimation, the choice of the state model has a significant impact on the algorithm performance. Multiple Model (MM) approaches partly address this issue. However, the improvement over a single-model based estimator directly depends on the considered model set. It was theoretically shown that using either too many or too few models can degrade the estimation accuracy. In addition, the diversity of the selected models plays a crucial role. The contribution of this paper is twofold. 1/ We propose to use the Jeffreys divergence (JD) to measure the degree of mismatch between two models. We derive its recursive expression when the state vector is a priori modeled as a Markov chain. Then, we focus our attention on tracking applications and provide a detailed analysis of the JD between classical motion models. 2/ We investigate the impact of the similarity between the set of possible models on the estimation error of a MM algorithm. This survey can hence serve as a guideline for model set design.