Theoretically the Kalman Filter is an estimator for what is called the linear-quadratic problem, which is the problem of estimating the instantaneous ``state'' (a concept that will be made more precise in the next chapter) of a linear dynamic system perturbed by white noiseÐby using measurements linearly related to the state but corrupted by white noise. The resulting estimator is statistically optimal with respect to any quadratic function of estimation error | Kalman Filtering Theory and Practice Using KblTKlB 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 1 General Information . the things of this world cannot be made known without mathematics. Roger Bacon 1220-1292 Opus Majus transl. R. Burke 1928 ON KALMAN FILTERING First of All What Is a Kalman Filter Theoretically the Kalman Filter is an estimator for what is called the linear-quadratic problem which is the problem of estimating the instantaneous state a concept that will be made more precise in the next chapter of a linear dynamic system perturbed by white noise by using measurements linearly related to the state but corrupted by white noise. The resulting estimator is statistically optimal with respect to any quadratic function of estimation error. Practically it is certainly one of the greater discoveries in the history of statistical estimation theory and possibly the greatest discovery in the twentieth century. It has enabled humankind to do many things that could not have been done without it and it has become as indispensable as silicon in the makeup of many electronic systems. Its most immediate applications have been for the control of complex dynamic systems such as continuous manufacturing processes aircraft ships or spacecraft. To control a dynamic system you must first know what it is doing. For these applications it is not always possible or desirable to measure every variable that you want to control and the Kalman filter provides a means for inferring the missing information from indirect and noisy measurements. The Kalman filter is also used for predicting the likely future courses of dynamic systems that people are not likely to control such as the flow of rivers during flood the trajectories of celestial bodies or the prices of traded commodities. From a practical standpoint these are the perspectives that this book will present 1 2 GENERAL .
