Kalman Filtering, 4th Edition

Chapter 9Practical Considerations

The classical (more accurately, old-fashioned) view is that a mathematical problem is solved if the solution is expressed by a formula. It is not a trivial matter, however, to substitute numbers in a formula¹.

9.1 Chapter Focus

The discussion turns now to what might be called Kalman filter engineering, which is that body of applicable knowledge that has evolved through practical experience in the use and misuse of the Kalman filter. The material of the previous two chapters (square-root and nonlinear filtering) has also evolved in this way and is part of the same general subject. Here, however, the discussion includes many more matters of practice than nonlinearities and finite-precision arithmetic.

9.1.1 Main Points to Be Covered

1. Roundoff Errors are Not the Only Causes for the Failure of the Kalman Filter to Achieve Its Theoretical Performance. There are diagnostic methods for identifying causes and remedies for other common patterns of misbehavior.
2. Prefiltering to Reduce Computational Requirements. If the dynamics of the measured variables are “slow” relative to the sampling rate, then a simple prefilter can reduce the overall computational requirements without sacrificing performance.
3. Detection and Rejection of Anomalous Sensor Data. The inverse of the matrix () characterizes the probability distribution of the innovation and may be used ...