March 10, 2008
Daniel Choukroun
Title: Conditionally-Linear Optimal Filtering with Application to Jump-Linear Systems
A general discrete-time dynamical not necessarily linear system with additive not necessarily Gaussian noises is considered and the problem of estimating the unknown states using the past history of the known states is addressed. The proposed approach is based on the concept of conditionally-orthogonal projection, where the conditional expectation operator given the known states' history, rather than the unconditional expectation, is used to define orthogonality. This approach, called conditionally-linear approach, is a direct extension of the standard linear filtering approach, and is more adequate than the latter for on-line implementation since it allows for the filter gains to be function of the incoming observations. In the case of an underlying discretization of a continuous-time system with Gaussian additive measurement noises, the proposed discrete-time algorithm is formally shown to be asymptotically equivalent to the continuous-time optimal non-linear filter, when the discretization step is very small. For conditionally-Gaussian systems, this filter coincides with the standard conditionally-Gaussian filter. The advantage of the conditionally-linear filter over the standard linear filter is analyzed and illustrated when applied to identification of a constant discrete parameter.
The mode estimation problem for special classes of jump systems is investigated in discrete-time. Assuming a non-linear dynamics and full information for the continuous states, a mode estimator is developed based on the conditionally-linear approach. This suboptimal filter is compared with the optimal algorithm (Wonham filter) on a simple numerical example via Monte-Carlo simulations, which confirms the asymptotic optimal behavior of the proposed filter in the case of Gaussian observation noises. A local convergence analysis for the equivalent continuous-time algorithm is proposed for the case of a static mode, which yields an intuitive criterion for observability. In a case of partial information on the continuous states of jump-linear systems, which cannot be handled using Wonham filter, a finite-dimensional mode estimator is developed in the framework of conditionally-linear filtering. As a numerical example, the problem of gyro failure detection from accurate spacecraft attitude measurements is considered and the filter performances are illustrated via extensive Monte-Carlo simulations.
Short Bio: Daniel Choukroun received the B.Sc. (summa cum laude), M.Sc., and Ph.D. degrees in Aerospace Engineering from TECHNION - Israel Institute of Technology, Haifa, Israel, in 1997, 2000, and 2003, respectively. He also hold the title "Engineer Under Instruction" from ENAC - the Ecole Nationale de l'Aviation Civile, Toulouse, France, in 1994. From 1998 to 2003, he was a Teaching and Research Assistant in the field of Automatic Control at TECHNION, where he received the Miriam and Aaron Gutwirth Special Excellency Award for achievement in research. From 2003 to 2006, he has been a Postdoctoral Fellow at UCLA - University of California at Los Angeles, working in the department of Mechanical and Aerospace Engineering. Since 2006, Dr Choukroun is Lecturer in the department of Mechanical Engineering at BEN-GURION University of the Negev, Beer Sheva, Israel. His research interests are in stochastic optimal estimation and control with applications to aerospace systems.