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A geometric approach to the singular filtering problem

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1 Author(s)
Schumacher, J. ; Centre for Mathematics and Computer Science, Amsterdam, The Netherlands

We consider the least-squares filtering problem for a stationary Gaussian process when the observation is not fully corrupted by white noise, the so-called "singular" case. An optimal estimator is constructed consisting of an integrating part, which is, as in the regular case, computed from a spectral factorization or an equivalent matrix problem, and a differentiating part whose parameters are computed from a single matrix equation. This improves on older results which either work under restrictive assumptions, or describe the solution only as the result of some nested algorithm.

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Automatic Control, IEEE Transactions on  (Volume:30 ,  Issue: 11 )