Kalman Filtering in Non-Gaussian Model Errors: A New Perspective [Tips & Tricks]

It is well known that the optimality of the Kalman filter relies on the Gaussian distribution of process and observation model errors, which in many situations is well justified [1]-[3]. However, this optimality is useless in applications where the distribution assumptions of the model errors do not hold in practice. Even minor deviations from the assumed (or nominal) distribution may cause the Kalman filter's performance to drastically degrade or completely break down. In particular, when dealing with perceptually important signals, such as speech, image, medical, campaign, and ocean engineering, measurements have confirmed the presence of non-Gaussian impulsive (heavy-tailed) and Laplace noises [4]. Therefore, the classical Kalman filter, which is derived under the nominal Gaussian probability model, is biased and even fails in such situations.