By Shankar Sastry

This quantity surveys the most important effects and methods of research within the box of adaptive keep watch over. concentrating on linear, non-stop time, single-input, single-output platforms, the authors provide a transparent, conceptual presentation of adaptive tools, permitting a serious evaluate of those innovations and suggesting avenues of extra improvement. 1989 variation

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If strict inequality holds, measuring RV Z decreases our uncertainty about the unknown RV X. 40) The PDF fX/Z (x/z) is normal with conditional mean X/Z and conditional covariance PX/Z . It is important to note that X/Z depends on the value of Z, but that covariance PX/Z is independent of the value of Z. Thus, PX/Z can be computed before we take any measurements. It is not diﬃcult to redo this example for the case of nonorthogonal X and V. See the problems. 41) a. Express PX/Z and X/Z in terms of K.

Sequence σk is decreasing, indicating that each measurement ˆk . 2 31 Sequential Maximum-Likelihood Estimation Let us generalize our results by deriving a sequential maximum-likelihood estimator. 102) where X ∈ Rn , Z ∈ Rp , V ∈ Rp , V ∼ N (0, R), and |R| = 0. Recall that “maximum likelihood” implies ignorance of any statistics of X. 102 explicitly in terms of the components of vectors as hT1 v1 z1 T v2 z2 h 2 .. = . X + .. . .. zp vp hTp where hTi is the ith row of H and suppose that R = diag{σi2 }.

Thus, X is deterministic and Z is stochastic. pdf 20/7/2007 12:35 20 Optimal and Robust Estimation The conditional PDF of Z given the unknown X, fZ/X (z/X), contains information about X, and if it can be computed, then X may be estimated according to the maximum-likelihood estimation criterion, which can be stated ˆ ML is as follows: Given a measurement Z, the maximum-likelihood estimate X the value of X which maximizes fZ/X , the likelihood that X resulted in the observed Z. The PDF fZ/X is a likelihood function.