Optimal Designs for Steady-State Kalman Filters
We consider a stationary discrete-time linear process that can be observed by a finite number of sensors. The experimental design for the observations consists of an allocation of available resources to these sensors. We formalize the problem of selecting a design that maximizes the information matrix of the steady-state of the Kalman filter, with respect to a standard optimality criterion, such as D- or A-optimality. This problem generalizes the optimal experimental design problem for a linear regression model with a finite design space and uncorrelated errors. Finally, we show that under natural assumptions, a steady-state optimal design can be computed by semidefinite programming.
KeywordsKalman Filter Linear Matrix Inequality Information Matrix Semidefinite Programming Optimal Design Problem
The research of the second author was supported by the VEGA 1/0163/13 grant of the Slovak Scientific Grant Agency.
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