Robust ` 1 Estimation
نویسنده
چکیده
This paper considers the design of robust`1 estimators based on multiplier theory (which is intimately related to the mixed structured singular value). Speciically, the Popov-Tsypkin multiplier is used to develop an upper bound on an`1 cost function over an uncertainty set. The robust`1 estimation problem is formulated as a parameter optimization problem in which the upper bound is minimized subject to a Riccati equation constraint. A BFGS quasi-Newton continuation algorithm is developed to solve the minimization problem. The algorithm has two stages. The rst stage solves a mixed-norm H 2 =` 1 estimation problem. In particular, it is initialized with a steady-state Kalman lter and by varying a design parameter from 0 to 1, the Kalman lter is deformed to a ` 1 estimator. In the second stage thè 1 estimator is made robust. A numerical example is presented to illustrate the design algorithms. A primary motivation for this work is its potential application to fault detection.
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