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Keynote Lecture Series Archive

Fall, 2026

The Multivariate Cauchy Estimator

Jason L. Speyer

Distinguished Professor, Ronald and Valerie Sugar Endowed Professor of Engineering
Mechanical and Aerospace Engineering Department
UCLA
Los Angeles, CA

The multivariate Cauchy estimator (MCE) provides an exact Bayesian filtering framework for discrete-time linear dynamic systems subject to additive Cauchy process and measurement noise, a direct analog to the Gaussian-based Kalman filter. For an n-dimensional system (n>1), applying Bayes’ rule directly in the state domain fails to yield a recursive, closed-form conditional probability density function (cpdf). However, propagating the cpdf’s characteristic function (the Fourier transform of the cpdf) produces the same analytic function through measurement updates and dynamic propagations, establishing the MCE as the only estimator derived in the characteristic function spectral domain and, alongside the Kalman filter, the only known filter with exact recursive analytic properties. Because heavy-tailed Cauchy distributions process measurement updates through nonlinear operations, the MCE can model asymmetric and multimodal state distributions that are impossible under the linear-Gaussian framework. The development of computationally efficient numerical methodologies now enables real-time application of this theory to complex engineering systems. When compared against the Extended Kalman Filter (EKF), numerical evaluations of the Extended MCE (EMCE) demonstrate superior performance and robustness in handling system parameter uncertainty within Gaussian simulations, suppressing severe impulsive radar noise in missile tracking, and estimating the position, velocity, and atmospheric density of Very Low Earth Orbit (VLEO) satellites operating in impulsive atmospheric environments.

Jason Speyer, professor at UCLA.Jason L. Speyer received the B.S. in aeronautics and astronautics from MIT, Cambridge and the Ph.D. in applied mathematics from Harvard University, Cambridge, MA. He was awarded an Honorary Doctorate from the Technion in 2013. He is the Ronald and Valerie Sugar Distinguished Professor in the Mechanical and Aerospace Engineering Department and the Electrical and Computer Engineering Department, UCLA. He coauthored, with W. H. Chung, Stochastic Processes, Estimation, and Control (SIAM, 2008), and coauthored, with D. H. Jacobson, Primer on Optimal Control Theory (SIAM, 2010). He served as Associate Editor for Technical Notes and Correspondence (1975–1976) and Stochastic Control (1978–1979), IEEE Transactions on Automatic Control, for AIAA Journal of Guidance and Control (1977–1978), and for Journal of Optimization Theory and Applications (1981-present). He is a fellow of the IEEE, an Honorary fellow of the AIAA, and was awarded the AIAA Mechanics and Control of Flight Award, AIAA Dryden Lectureship in Research, Air Force Exceptional Civilian Decoration (1991 and 2001), IEEE Third Millennium Medal, AIAA Guidance, Navigation, and Control Award, Richard E. Bellman Control Heritage Award, and membership in the National Academy of Engineering.

Wednesday, October 14, 2026
3:30 PM
Seaver Science Library, Room 202 (SSL 202)

 

hosts: Ronney/Madni

Published on August 2nd, 2017Last updated on October 9th, 2026