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The way I've always seen a Kalman filter is as a recursive least squares fitter, but instead of being run on the same input until convergence, it is run one ste
by mgaunard 5y ago
The way I've always seen a Kalman filter is as a recursive least squares fitter, but instead of being run on the same input until convergence, it is run one step on every new sample of ever-changing inputs, in effect leading to a smoothing fitter.
For some reason I rarely see it being described as such.
- nextaccountic 5y agoWhat's the "recursive" part? It's like the difference between IIR and FIR?
- gugagore 5y agoThat is an astute connection. The "recursive" part is that you do not need to keep all the history of observations and actions (often denoted y and u. in control theory). You can summarize the past with sufficient statistics (the mean and the variance for linear quadratic gaussian (LQG) problems). You could imagine keeping all of the data and fitting a model to that. For LQG problems, you can use dynamic programming [1] to solve the problem faster. You could alternatively imagine keeping a finite window of data and fitting a model to that. That filter would have a finite impulse response. [1] https://en.wikipedia.org/wiki/Dynamic_programming https://en.wikipedia.org/wiki/Dynamic_programming btw that term kind of means two things, and this is a situation in which the two meanings overlap.
- ephimetheus 5y agoWe also use it for fitting charged particle tracks in high energy physics experiments. Here, we’re iteratively incorporating measurements along the trajectory, finally arriving at basically a least squares fit result, after a backward smoothing pass.