Non-overlapping deterministic Gaussian particles in maximum likelihood non-linear filtering: phase tracking application

In a former paper (G. Salut and A. Ziadi, 2004), a deterministic particle filtering method was introduced using extended Gaussian particles and nonrandom state space exploration. This yields higher estimation performances and an important reduction of particle number, due to deterministic properties in 1/N instead of 1/N² for random method. Apart from those improvements, a particle overlapping was observed under more critical dynamics and observation (signal to noise ratio) conditions. Similarly to support degeneration in random particle filtering method, this high particle concentration decreases filter performances and limits its efficiency in long duration signal processing application. In this paper, we propose a new deterministic Gaussian particle algorithm to improve filter performance as well as particle number. Overlapping drawbacks and improved filtering algorithm performances are illustrated through a modified version of phase tracking problem from noisy observation.