Recursive least squares filtering algorithms with systolic array architectures: a geometrical approach
This dissertation presents a geometrical derivation of recursive least squares algorithms for general space-time (multi-channel) filtering. These algorithms are recursive in both the time index and filter order, as well as having a simple systolic array architecture. Thus, by taking advantage of concurrent processing, these algorithms obtain a high throughput and are therefore suitable for real-time least squares filtering. The derivation is based upon developing fundamental order and time update theorems for various vectors in a pseudonorm space, where the pseudonorm determines the least squares criterion. The use of a pseudonorm instead of a true norm leads to a simplified derivation of a time-update theorem. This time update theorem is derived for a sliding memory, exponentially weighted pseudonorm, and is therefore a generalization of a previously derived theorem used in the derivation of the least squares lattice algorithm. However, unlike the least squares lattice algorithm, the order update theorem makes no assumption concerning the time shift properties of the input data, and therefore the general space-time filtering problem is solved without the need of matrix manipulation.
- Research Organization:
- California Univ., Los Angeles (USA)
- OSTI ID:
- 5868829
- Country of Publication:
- United States
- Language:
- English
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