On Some Alternatives to Kalman Filtering
In a Dynamic Linear Model, the weighted least-squares approach is known to yield the Kalman filter equations. On the other hand, it is also known that any least-squares solution might adversely be affected by undetected model errors. After having previously derived “robust Kalman filters” — which are resistant against multiple scale errors — as one possible remedy, we now develop the so-called “look-ahead filters” which use some of the future observations for the update and can therefore operate only in almost real-time. It will be shown that this new class of filters turns out to be everywhere superior over Kalman filtering (in the Mean Square Error sense), and that some of the modified Kalman filters — including Salychev’s “wave algorithm” — belong to this class indeed.
KeywordsGlobal Position System Kalman Filter Linear Prediction Dispersion Matrix Dynamic Linear Model
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