Laplace Estimator for Linear Scalar Systems

Uncertainties in many physical systems have impulsive properties poorly modeled by Gaussian distributions. Building on work to develop Cauchy estimators, a Laplace estimator is explored as another heavier-tailed alternative. For a scalar discrete linear system with additive Laplace-distributed process and measurement noises, the unnormalized conditional pdf is recursively and analytically propagated and updated, and its structure is presented. The conditional mean and variance of the Laplace estimator after one update are examined and compared to those of the Cauchy estimator and Kalman filter. Additionally, a 50-step numerical example is presented to demonstrate its superior performance to the Kalman filter in the presence of outliers.