The class of all stable unbiased state estimators
Systems & Control Letters
Trade-offs in linear filter design
Automatica (Journal of IFAC)
Multivariable Feedback Design
Fundamental Limitations in Filtering Control
Fundamental Limitations in Filtering Control
Frequency Domain Properties of Scalar and Multivariable Feedback Systems
Frequency Domain Properties of Scalar and Multivariable Feedback Systems
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This paper examines fundamental limitations in performance which apply to linear filtering problems associated with multivariable systems having as many inputs as outputs. The results of this paper quantify unavoidable limitations in the sensitivity of state estimates to process and measurement disturbances, as represented by the maximum singular values of the relevant transfer matrices. These limitations result from interpolation constraints imposed by open right half-plane poles and zeros in the transfer matrices linking process noise and output noise with state estimates. Using the Poisson integral inequality, this paper shows how sensitivity limitations and tradeoffs in multivariable filtering problems are intimately related to the directionality properties of the open right half-plane poles and zeros in these transfer matrices.