Student's t Kalman Smoother

We propose a new nonlinear outlier-robust Kalman smoother, which we call T-Robust. The smoother finds the maximum {\it a posteriori} likelihood (MAP) solutions for statistical models with heavy tailed observation noise. Specifically, the T-Robust Kalman smoother assumes a Gaussian process model and Student's t observation model. It compares favorably to the recently developed $\ell_1$-Robust smoother - it performs as well as the $\ell_1$-Robust on several simulated examples and even better when the level of contamination is high or contaminating errors come from the uniform distribution. The T-Robust smoother was also used to construct a smoothed fit for a nonlinear underwater tracking application without data removal in the presence of large outliers. The number of arithmetic operations required by the smoother grows linearly with the number of time points $N$.