On stability of a class of filters for non-linear stochastic systems

Understand

This article develops a comprehensive framework for stability analysis of a broad class of commonly used continuous and discrete time-filters for stochastic dynamic systems with non-linear state dynamics and linear measurements under certain strong assumptions.

• The class of filters encompasses the extended and unscented Kalman filters and most other Gaussian assumed density filters and their numerical integration approximations.
• The stability results are in the form of time-uniform mean square bounds and exponential concentration inequalities for the filtering error.
• In contrast to existing results, it is not always necessary for the model to be exponentially stable or fully observed.