On the performance of Kalman filtering with intermittent observations: a geometric approach with fractals

Authors:
Andrea Censi
Affiliations:
Control & Dynamical Systems department, California Institute of Technology, Pasadena, CA
Venue:
ACC'09 Proceedings of the 2009 conference on American Control Conference
Year:
2009

Citing 3
Cited 1

Kalman filtering with random coefficients and contractions

SIAM Journal on Control and Optimization
Stability of Kalman filtering with Markovian packet losses

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Probabilistic performance of state estimation across a lossy network

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Stochastic Comparison, Boundedness, Weak Convergence, and Ergodicity of a Random Riccati Equation with Markovian Binary Switching

SIAM Journal on Control and Optimization

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Abstract

This paper describes the stationary distribution of the a-posteriori covariance matrix of a Kalman filter when the availability of measurements is subject to random phenomena such as lossy network links. If a certain non-overlapping condition is satisfied, the distribution has a fractal nature, and there exists a closed-form expression for the cdf, which is a singular function. If the condition is not satisfied, deciding whether the cdf is singular or not, even in the scalar case, is at least as hard as some open problems in measure and number theory.