Laplace estimation for scalar linear systems. (October 2022) - Duong, Nhattrieu C.; Speyer, Jason L.; Idan, Moshe
Abstract: Uncertainties in many physical systems have impulsive properties poorly modeled by Gaussian distributions. Refocusing previous work, an estimator is derived for a scalar discrete-time linear system with additive Laplace measurement and process noises. The a priori and a posteriori conditional probability density functions (pdf) of the state given a measurement sequence are propagated recursively and in closed form, and the a posteriori conditional mean and variance are derived analytically from the conditional pdf. A simulation for an estimator is presented, demonstrating marked resilience to large, un-modeled spikes in the measurements.