Maximum likelihood estimates of linear dynamic systems

1965/08/01 by H. E. RAUCH, Herbert E. Rauch, F. TUNG +3 · 1,950 citations
Computer Science · Engineering · Mathematics · #Applied mathematics #Control Systems and Identification #Fault Detection and Control Systems #Mathematics #Maximum likelihood #Statistics #Target Tracking and Data Fusion in Sensor Networks

paper · doi:10.2514/3.3166

published in AIAA Journal 3(8), 1445-1450 (American Institute of Aeronautics and Astronautics)

openalex publication_date 1965/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

This paper considers the problem of estimating the states of linear dynamic systems in the presence of additive Gaussian noise. Difference equations relating the estimates for the problems of filtering and smoothing are derived as well as a similar set of equations relating the covariance of the errors. The derivation is based on the method of maximum likelihood and depends primarily on the simple manipulation of the probability density functions. The solutions are in a form easily mechanized on a digital computer. A numerical example is included to show the advantage of smoothing in reducing the errors in estimation. In the Appendix the results for discrete systems are formally extended to continuous systems.

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