A Sequential $L_{p}$-norm Filter for Robust Estimation

Abstract

A novel robust sequential $L_{p}$ filter is developed in this paper by leveraging the maximum a posteriori estimation theory and using generalised normal distributions to represent both state prediction errors and measurement residuals. The formulation leads to the flexibility of choosing the parameter $p$ for two different types of aforementioned error sources. Numerical simulations are given for a nonlinear ground tracking scenario, with measurements corrupted with outliers. Results indicate the new $L_{p}$ -norm filter presents robustness to filter initialisation errors and measurement outliers and outperforms a standard unscented Kalman filters and the Huber unscented Kalman filter in terms of error statistics.