Kalman Filter Varying dT and consequences
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Would the convergence theory of (E/)KF still hold if we change the dT each iteration (non-constant sampling rate of a given sensor) ? Since the A and H matrices are normally dT-dependent, this dT variation requires mainly changing these matrices at each iteration, depending on current dT. Technically, this is easy, but is it allowed from the theoretical point of view? For instance, the measurement space dimension (number of rows in H) should be approximately identical to the moving-average of the normalised innovations squared. I have noticed that this condition is not fulfilled when the dT is varying with high variance. Could it be related to some missing normalisation required in this case?
John Petersen on 28 Jul 2014
Edited: John Petersen on 28 Jul 2014
The conditions of stability for a Kalman filter is that the system is stochastically observable and controllable. So non-constant sampling should usually not affect the stability. I have not experienced any stability problems with varying sample rates. Incidentally, a bad choice of sampling rate can make a cyclical state unobservable and therefore divergent.