Filter Tuning and Solution Testing

Abstract

Since this is a monograph, there are necessarily subjects that have not been fully covered. Here we wish to amend this to some degree. First, although the science behind the modeling and the mathematics of the Kalman filter have been addressed, there are two issues that, until now, have been neglected. These are the process of “tuning” the Kalman filter, and that of assessing the quality of the solutions. The solution quality is mainly based on testing of the innovations sequence. The innovations sequence is, in essence, a continual observer of the progress of the Kalman filter, since it sequentially compares each new measurement to what the model thinks it will be. As such it carries highly useful information on how the processor can be improved. As a simple example, at the end of the last chapter the model-based localization problem was presented. Here we recall that according to the data, there were five modes. This was known a priori since it was determined by a spatial spectrum of the data taken during the experiment. However, suppose this were not the case. That is, suppose that it were assumed that there were only four modes. In such a case, the spectrum of the innovations sequence would have indicated this by presenting the spatial spectral line of the fifth mode, since it was contained in the data. Speaking more generally, the innovations not only indicated modeling errors, but in many cases it can actually identify the problem.