Introduction

In this chapter we will discuss a few important topics that have not been addressed in preceding chapters. Although a Kalman filter can be built that gives the correct theoretical answers, we often want to see if those answers are useful for a particular application. The first section will address this issue by investigating how filter performance can degrade if there is too much measurement noise. In preceding chapters of this text, most of the examples were for cases in which there were hundreds of measurements. In the second section we will investigate how the performance of a polynomial Kalman filter behaves as a function of filter order (i.e., number of states in filter) when only a few measurements are available. Filter divergence is fairly easy to recognize in a simulation where we have access to the true states in our model of the real world. We will demonstrate in the third section that the filter residual and its theoretical bounds can also be used as an indication of whether or not the filter is working properly outside the world of simulation (i.e., the world in which the truth is not available). In the fourth section we will show that a Kalman filter can be built even if some states are unobservable. Because the filter will appear to work, we will then demonstrate some practical tests that can be used to detect that the estimates obtained from the unobservable states are worthless. Finally, in the last section we will...