Skew-t Filter and Smoother with Improved Covariance Matrix Approximation
For researchers and practitioners in state estimation and robust filtering, this work offers an improved low-complexity algorithm for handling non-Gaussian noise, though it is an incremental improvement over existing variational methods.
The paper proposes filtering and smoothing algorithms for linear state-space models with skew-t-distributed measurement noise, using a variational Bayes approximation that couples location and skewness variables. The proposed method achieves more accurate posterior covariance approximation and outperforms existing robust filters in both accuracy and speed on simulated and real-world GPS data.
Filtering and smoothing algorithms for linear discrete-time state-space models with skew-t-distributed measurement noise are proposed. The algorithms use a variational Bayes based posterior approximation with coupled location and skewness variables to reduce the error caused by the variational approximation. Although the variational update is done suboptimally using an expectation propagation algorithm, our simulations show that the proposed method gives a more accurate approximation of the posterior covariance matrix than an earlier proposed variational algorithm. Consequently, the novel filter and smoother outperform the earlier proposed robust filter and smoother and other existing low-complexity alternatives in accuracy and speed. We present both simulations and tests based on real-world navigation data, in particular GPS data in an urban area, to demonstrate the performance of the novel methods. Moreover, the extension of the proposed algorithms to cover the case where the distribution of the measurement noise is multivariate skew-$t$ is outlined. Finally, the paper presents a study of theoretical performance bounds for the proposed algorithms.