Description
The Fast Kalman filter applies only to systems with sparse matrices (Lange, 2001), since HWB is an inversion method to solve sparse linear equations (Wolf, 1978).
The ordinary Kalman filter is optimal for general systems. However, an optimal Kalman filter is probably stable only if Kalman's observability and controllability conditions are also satisfied (Kalman, 1960). These conditions are challenging to continuously maintain for a large system which means that even an optimal Kalman filter may diverge towards false solutions. Fortunately, the stability of an optimal Kalman filter can be controlled by monitoring its error variances if these can be reliably estimated. Their precise computation is, however, much more demanding than the optimal filtering itself but the FKF method may provide the required speed-up also in this respect.
Read more about this topic: Fast Kalman Filter
Famous quotes containing the word description:
“I was here first introduced to Joe.... He was a good-looking Indian, twenty-four years old, apparently of unmixed blood, short and stout, with a broad face and reddish complexion, and eyes, methinks, narrower and more turned up at the outer corners than ours, answering to the description of his race. Besides his underclothing, he wore a red flannel shirt, woolen pants, and a black Kossuth hat, the ordinary dress of the lumberman, and, to a considerable extent, of the Penobscot Indian.”
—Henry David Thoreau (1817–1862)
“A sound mind in a sound body, is a short, but full description of a happy state in this World: he that has these two, has little more to wish for; and he that wants either of them, will be little the better for anything else.”
—John Locke (1632–1704)
“The Sage of Toronto ... spent several decades marveling at the numerous freedoms created by a “global village” instantly and effortlessly accessible to all. Villages, unlike towns, have always been ruled by conformism, isolation, petty surveillance, boredom and repetitive malicious gossip about the same families. Which is a precise enough description of the global spectacle’s present vulgarity.”
—Guy Debord (b. 1931)