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the overall State estimate is obtained by summation across the individual weighted estimates.

Application of the DBAF to SPC

We have demonstrated the equivalence between the Kalman filter, based on the state-space equations for a scalar random walk buried in white noise, and the most common SPC estimation procedures. The Bayesian adaptive filter described above is applied to that model in this section. There are four parameters, in the state-space equations, O, H, Q, and R, that need to be specified. Based on [2], these are specified as O = H = 1, w_t~ N( 0,    ), and

v,~vV(0, <j\) and we also assume w and v to be uncorrelated.

Everything has been specified except for the two variance terms, a²w and a]. For our application of the DBAF we will assume that one of them is known, namely o\, and that the other is unknown and must be estimated from the data. We feel that this is not too restrictive an assumption for the following reasons. First of all, in most applications, it is much easier to get a handle on the white noise error source than it is to understand the autocorrelation. Quite often, much of the white noise contribution is due to short term repeatability

measurement -►

Figurę 6. DBAF Structure.