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State Estimation for Discrete Linear Systems with Additive Laplace Noise

  • Author(s): Duong, Nhattrieu Chan
  • Advisor(s): Speyer, Jason L
  • et al.

State estimators are developed for discrete linear systems with scalar additive Laplace process and measurement noises and their properties are analyzed. For the scalar case, an analytic recursive estimator is presented, along with detailed analysis of its behavior with respect to noise parameters. In addition, a one-step model predictive controller is developed. Using an objective function with 1-norm control and terminal state costs, the expectation of the objective function with respect to the conditional probability density function is determined by using the computational structure developed for the estimator. Numerical simulations for both the estimator and one-step controller are presented to demonstrate their unique behavior, including robustness to noise spikes in the measurements. For the general vector system, update and propagation algorithms as well as a method for computing moments in closed form using characteristic functions are presented. An explicit state estimator is developed for the two-state case, and a numerical example is presented to demonstrate the algorithms and the unique properties of Laplace estimators.

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