Transcription of 1 Discrete-time Kalman filter
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1 Discrete-time Kalman filter
Estimation IIIan ReidHilary Term, 20011 Discrete-time Kalman filterWe ended the first part of this course deriving the Discrete-time Kalman Filter as a recursive Bayes estimator. In this lecture we will go into the filter in more detail, and provide a new derivation forthe Kalman filter, this time based on the idea ofLinear Minimum Variance (LMV) estimation ofdiscrete-time BackgroundThe problem we are seeking to solve is the continual estimation of a set of parameters whose valueschange over time. Updating is achieved by combining a set of observations or measurementsz(t)which contain information about the signal of interestx(t). The role of the estimator is to providean estimate^x(t+ )at some timet+ . If >0we have apredictionfilter, if <0asmoothingfilter and if =0the operation is simply that an estimator is said to beunbiasedif the expectation of its output is the expectation ofthe quantity being estimated,E[^x =E[x.]]
Estimation II Ian Reid Hilary Term, 2001 1 Discrete-time Kalman filter We ended the first part of this course deriving the Discrete-Time Kalman Filter as a recursive Bayes’
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