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Extensions of the Optimum Linear Filter
GaussMarkov Processes and Stochastic
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accept Jf algorithms of Table approach approximate assume Bayes risk Chap computed conditional density conditional-mean consider continuous cost function covariance covariance matrix decision theory defined definition density function derivation determine developed discrete discussion equivalent error variance error-variance estimation algorithms estimation problem estimation theory Example filter algorithms fixed-point smoothing Fokker-Planck equation foregoing equation given by Eq independent initial condition input Kalman filter likelihood ratio test MAP estimate matrix inversion lemma maximum a posteriori maximum likelihood estimate mean and variance measurement noise message and observation message model minimum variance estimate miss probabilities notation observation model obtain optimum estimate parameter prior statistics probability density pseudo Bayes estimator random processes relation samples become dense scalar signal smoothing algorithms solution spectral density stationary stochastic differential equations stochastic processes sufficient statistic theorem threshold unbiased variance equation vector white-noise Wiener process zero zero-mean