The discussion turns now to what might be called Kalman ®lter engineering, which is that body of applicable knowledge that has evolved through practical experience in the use and misuse of the Kalman ®lter. The material of the previous two chapters (extended Kalman ®ltering and square-root ®ltering) has also evolved in this way and is part of the same general subject. | Kalman Filtering Theory and Practice Using MATLAB Second Edition Mohinder S. Grewal Angus P. Andrews Copyright 2001 John Wiley Sons Inc. ISBNs 0-471-39254-5 Hardback 0-471-26638-8 Electronic 7 Practical Considerations The time has come the Walrus said To talk of many things Of shoes and ships and sealing wax Of cabbages and kings And why the sea is boiling hot And whether pigs have wings. From The Walrus and the Carpenter in Through the Looking Glass 1872 Lewis Carroll Charles Lutwidge Dodgson 1832-1898 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 extended Kalman filtering and square-root 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. 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. 270 DETECTING AND CORRECTING ANOMALOUS BEHAVIOR 271 3. Detection and rejection of anomalous sensor data. The inverse of the matrix HPlD R characterizes the probability distribution of the innovation z Hx and may be used to test for exogenous measurement errors such as those resulting from sensor or transmission malfunctions. 4. Statistical design of sensor and estimation systems. The covariance equations of the Kalman filter provide an analytical basis for the predictive
