RECURSIVE PARTITIONING ESTIMATION (CONTROL)

CHING-FU GAU, Purdue University

Abstract

The partitioned solutions for adaptive control, estimation, identification, and associated Riccati equation solutions were developed by Lainiotis and his co-workers. In this work, the Recursive Partitioning Algorithm (RPA), a recursive version of Lainiotis' Generalized Partitioned Algorithm (GPA) is presented. The interpretation of RPA as a combination of a nominal Kalman filter for the partial initial condition and a recursive least-squares estimator for smoothing the remaining portion of a total initial condition gives great intuitive insight into the partitioned solutions of Lainiotis. The Parallel Partitioning Algorithm (PPA) is then presented to unify various partitioning approaches for optimal linear estimation. This procedure allows the process noise to be partitioned into two parts. The resulting algorithms based on the PPA retained a two-part partitioning structure which consists of two nested suboptimal kalman filters. The applications of RPA are presented, including a fast computational approach in optimal linear estimation, a dependent partitioning of initial condition, a multipartitioning of the initial condition, a decomposed parameter estimator, smoothing algorithms, change of initial condition for filtered and smoothed estimates, and a fixed-interval process-noise partitioning algorithm. In addition, the PPA is applied to obtain a decoupled bias-filtering algorithm for randomly time-varying bias system, a Q-adaptive estimator, and unknown function estimator, a decentralized optimal filter for large inter-connected system, and a two-stage filtering solutions which include partitioning of measurement noise. A unique two-filter approach to the problem of tracking of maneuvering targets is presented, which facilitates the switch between different filters. Finally, the applications to a multi-rate and a simplified filter are presented.

Degree

Ph.D.

Subject Area

Aerospace materials

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