00073 Ì669057b99e1a32461d685010d9b1f0

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Hembree & Zimmer

FigurÄ™ 11. Adaptiye Filter Weights (true gain = 0.7).

Notation for Sensitiyity Analysis

Given the form of the adaptive Kalman filter, as presented in the last section, we would now like to examine its sensitivities. In particular, we examine the implications of discretizing across the unknown parameters. How many discrete values are needed? What is the impact of assigning prior probabilities? How does it compare to the Kalman filter constructed from complete knowledge?

In order to explore these issues, we need to modify our notation as follows. We have a state-space model of the process that actually generates the measured data, or the truth model, given by

=<D^rxr.i+wr

yf = H^rxf +vf

where wf ~ N(o,Qf), vf ~N(o,Rf), and xj