A Probabilistic Perspective on Gaussian Filtering and Smoothing

We present a general probabilistic perspective on Gaussian filtering and smoothing. This allows us to show that common approaches to Gaussian filtering/smoothing can be distinguished solely by their methods of computing/approximating the means and covariances of joint probabilities. This implies that novel filters and smoothers can be derived straightforwardly by providing methods for computing these moments. Based on this insight, we derive the cubature Kalman smoother and propose a novel robust filtering and smoothing algorithm based on Gibbs sampling. Inference in latent variable models is about extracting information about a not directly observable quantity, the latent variable, from noisy observations. Both recursive and batch methods are of interest and referred to as filtering respective smoothing. Filtering and smoothing in latent variable time series models, including hidden Markov models and dynamic systems, have been playing an important role in signal processing, control, and machine learning for decades [12, 15, 3].