From Wiener to Kalman filter
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Date
2025-02-20
Authors
Αναγνωστάκη, Ιωάννα
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Abstract
The Kalman filter has been widely recognized as an optimal solution for tracking, data prediction, and visual motion analysis. Designed to minimize mean squared error, the filter can also be derived using maximum likelihood statistics. Its performance is evaluated using a cost or loss function, with the objective being to minimize this function.
Before introducing the Kalman filter, the Wiener filter is described as an optimal finite impulse response (FIR) filter in terms of minimizing mean squared error. Its solution shares many similarities with the Kalman filter. In essence, it utilizes both the autocorrelation and cross-correlation of the received signal with the original data to determine the filter's impulse response.
However, the Kalman filter offers several advantages over the Wiener filter. Notably, it eliminates the need to compute the filter’s impulse response, which is often challenging for numerical calculations. Kalman formulated his filter using state-space techniques, allowing it to function as a smoother, filter, or predictor—unlike Wiener’s approach. The predictive capability of the Kalman filter has been widely applied to tracking, visual motion tasks, and navigation problems, many of which are discussed in this work.
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Keywords
Wiener filter, Kalman filter, Prediction, Tracking, Adaptive systems