Fast Kalman Filter - Optimum Calibration - Inverse Problem

Inverse Problem

The computing load of the inverse problem of an ordinary Kalman recursion is roughly proportional to the cube of the number of the measurements processed simultaneously, which can always be set to 1 by processing each scalar measurement independently and (if necessary) performing a simple pre-filtering algorithm to de-correlate these measurements.

Even when many measurements are processed simultaneously, it is not unusual that the linear equation system is sparse, because some measurements turn out to be independent of some state or calibration parameters. In Satellite Geodesy problems (Brockmann, 1997), the computing load of the HWB (and FKF) method is only roughly proportional to the square of the number of the state parameters (and not of the measurements whose number may be billions).