Robust Estimation in Non-Linear State-Space Models With State-Dependent Noise

In this paper, we present a robust estimation algorithm for non-linear state-space models driven by state-dependent noise. The algorithm is robust to outliers in the data. We derive the algorithm step by step from first principles, from theory to implementation. The implementation is straightforward and consists mainly of two components: 1) a slightly modified version of the Rauch-Tung-Striebel recursions, and 2) a backtracking line search strategy. Since it preserves the underlying chain structure of the problem, its computational complexity grows linearly with the number of data. The algorithm is iterative and is guaranteed to converge, under mild assumptions, to a local optimum from any starting point. We validate our approach via experiments on synthetic data from a multi-variate stochastic volatility model.