By Professor Charles K. Chui, Dr. Guanrong Chen (auth.)
This booklet provides an intensive dialogue of the mathematical thought of Kalman filtering. The filtering equations are derived in a sequence of hassle-free steps permitting the optimality of the method to be understood. It presents a accomplished therapy of assorted significant themes in Kalman-filtering concept, together with uncorrelated and correlated noise, coloured noise, steady-state idea, nonlinear platforms, structures identity, numerical algorithms, and real-time purposes. a chain of difficulties for the scholar, including a whole set of strategies, also are integrated. the fashion of the ebook is casual, and the maths straight forward yet rigorous, making it obtainable to all people with a minimum wisdom of linear algebra and platforms concept. during this moment variation, as well as a few minor corrections and up-dating, the part on real-time process identity has been multiplied and a quick creation to wavelet research integrated.
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Extra resources for Kalman Filtering: with Real-Time Applications
Sample text
Assume that the object is traveling at a constant velocity w with random N(O, q), so that the range d satisfies the difdisturbance ference equation e,. , dk+l = dk + h(wk + ek). d and is contaminated with noise 7J where 7J"' N(O, r), so that Assume that the initial target range is d0 which is independent of ~k and 7Jk, and that {~k} and {77k} are also independent (cf. 2). Derive a Kalman filtering algorithm as a rangeestimator for this radar tracking system. Exercises radar 47 Fig. 2. 8. A linear stochastic system for radar tracking can be described as follows.
We define the "inner product" (x, w} to be the n x q matrix 34 3. Orthogonal Projection and Kalman Filter (x, w) = Cov(x, w) = E(x- E(x))(w- E(w)) T. Let llwllq be the positive square root of (w, w). That is, llwllq is a non-negative definite q x q matrix with llwll; = llwllqllwll; = (w, w). Similarly, let llxlln be the positive square root of (x, x). Now, let w 0 ,···,wr be random q-vectors and consider the "linear span": Y(wo,···,wr) r ={y: y = L Piwi, P0 , · • ·, Pr. n x q constant matrices } .
Let v be a given data vector and y = h + H v, where his determined by the condition E(y) = E(x), so that y is uniquely determined by the constant matrix H. If x* is one of the y 's such that trllx- x*ll! 6).
