Robust state estimation based on multi-kernel correntropy

In this paper, the problem of robust state estimation under multi-mode non-Gaussian noise environment is investigated. The standard Kalman filter is optimal under Gaussian noise assumption. However, when noise is generated by multiple sources and corrupted by outliers, it means that the noise distribution is multimodal and non-Gaussian, then the performance of the standard Kalman filter will be severely degraded. In this work, a multi-kernel correntropy based state filter is developed. Correntropy is a generalized similarity measure between two random variables, and is insensitive to outliers. Since the noise distribution is multimodal instead of unimodal, a new multi-kernel correntropy based optimization objective function is constructed. The proposed state filter mainly consists of two steps, prediction step and correction step, where priori estimate and posterior estimate are computed respectively. The capabilities of the proposed filter are demonstrated on a benchmark navigation problem.