By Bruck R.H.

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38). 26) that the covariance matrix of the observed process is always symmetric:

4 for details>. On the other hand it is possible to derive squareroot-free versions of the Givens reduction. 10]. 12]. 3. Efficient implementation of the Givens reduction. The quantities X(j,k) and Q(k,j) need to be stored twice to avoid overwriting. The desired matrix R' arises in X through rotations. As the computation of the orthogonal matrix Q is not a part of the recursion, its computation remains optional. This algorithm involves division. Whenever the divisor is small, set c =1 and s =0 (identity rotor) FOR k = 1, 2, .

Windowing algorithms, however, can also be important for the recursive updating of a covariance matrix in order to reduce the influence of incoming data points when the process vector length L is small for fast tracking. This leads to the problem of recursive windowing. Recursive windowing algorithms operate on the lag sequence rather than on the sequence of process samples. 8 Recursive Windowing Algorithms 29 where W = [W(O), w(1), w(2), ... 52) is an appropriate window function. 52) is a nonrecursive formulation of the windowing problem.