Abstract
The problem of optimal filtering consists in determining the filter coefficients w opt through the normal equations solution in the Wiener stochastic or the Yule–Walker deterministic form. In practice this is achieved by inverting the correlation matrix R or its estimate R xx . Formally, the problem is simple. Basically, however, this inversion is most often of ill-posed nature. The classical matrix inversion approaches are not robust and in certain applications cannot be implemented. In fact, most of the adaptive signal processing problems concern the computational cost and robustness of the estimation algorithms.
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Notes
- 1.
The foundations for deconvolution and time-series analysis were largely laid by Norbert Wiener. The book [2] was based on work Wiener had done during World War II but that had been classified at the time. Some of the early attempts to apply these theories were in the fields of weather forecasting and economics.
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Uncini, A. (2015). Linear Prediction and Recursive Order Algorithms. In: Fundamentals of Adaptive Signal Processing. Signals and Communication Technology. Springer, Cham. https://doi.org/10.1007/978-3-319-02807-1_8
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DOI: https://doi.org/10.1007/978-3-319-02807-1_8
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