Introduction to Random Signals and Applied Kalman Filtering with Matlab Exercises and Solutions, Volume 1In this updated edition the main thrust is on applied Kalman filtering. Chapters 1-3 provide a minimal background in random process theory and the response of linear systems to random inputs. The following chapter is devoted to Wiener filtering and the remainder of the text deals with various facets of Kalman filtering with emphasis on applications. Starred problems at the end of each chapter are computer exercises. The authors believe that programming the equations and analyzing the results of specific examples is the best way to obtain the insight that is essential in engineering work. |
Contents
A Review | 1 |
The Discrete Kalman Filter StateSpace Modeling | 5 |
Mathematical Description of Random Signals | 72 |
Copyright | |
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algorithm amplitude analysis applications assume autocorrelation function average bandlimited block diagram Chapter component computed Consider constant convergence correlation corresponding covariance matrix crosscorrelation defined deterministic differential equation discrete error covariance example Figure Fourier transform frequency fx(x Gauss-Markov process given by Eq independent inertial initial conditions input integral interval joint probability Kalman filter linear MATLAB mean mean-square error mean-square value measurement noise Navigation normal random variables Note obtained output P₁ parameters periodogram power spectral density probability density function problem process X(t pseudorange random process Random Signals recursive reference result S(jw sample realizations sample space satellite scalar Section sequence shown in Fig smoothing solution spectral density function spectral function stationary statistically independent steady-state step suboptimal t₁ t₂ Table theory trajectory transfer function unity update usual variance vector velocity voltage white noise Wiener Wiener filter Wiener process X₁ yield zero zero-mean