New convergence bounds for Bayes estimators

Using some recently derived spectral expressions for distance measures between vector Gaussian stationary processes, upper bounds are given for the mean-square-error performance of the Bayes estimate of a parameter on the basis of vector Gaussian observations. The result is directly applicable to evaluating the performance of certain adaptive estimation schemes and to finite-state Markov chain systems.

[1]  Edward A. Patrick,et al.  On unsupervised estimation algorithms , 1970, IEEE Trans. Inf. Theory.

[2]  D. Magill.  Optimal adaptive estimation of sampled stochastic processes , 1965 .

[3]  D. Lainiotis.  Optimal adaptive estimation: Structure and parameter adaptation , 1970 .

[4]  J. Spragins,et al.  A note on the iterative application of Bayes' rule , 1965, IEEE Trans. Inf. Theory.

[5]  Stanley C. Fralick,et al.  Learning to recognize patterns without a teacher , 1967, IEEE Trans. Inf. Theory.

[6]  Edison Tse,et al.  A Quantitative Measure of Identifiability , 1978, IEEE Transactions on Systems, Man, and Cybernetics.

[7]  A. Haddad,et al.  Robust state estimation in uncertain systems: Combined detection-estimation with incremental MSE criterion , 1976 .

[8]  A. Haddad,et al.  Robust state estimation in uncertain systems: Combined detection estimation with incremental MSE criterion , 1976, 1976 IEEE Conference on Decision and Control including the 15th Symposium on Adaptive Processes.

[9]  E. Tse,et al.  On the identifiability of parameters , 1971, CDC 1971.

[10]  Demetrios Kazakos,et al.  The Bhattacharyya distance and detection between Markov chains , 1978, IEEE Trans. Inf. Theory.

[11]  A. Willsky,et al.  The stochastic control of the F-8C aircraft using the multiple model adaptive control (MMAC) method , 1975, 1975 IEEE Conference on Decision and Control including the 14th Symposium on Adaptive Processes.

[12]  Louis A. Liporace,et al.  Variance of Bayes estimates , 1971, IEEE Trans. Inf. Theory.

[13]  T. Kailath.  The Divergence and Bhattacharyya Distance Measures in Signal Selection , 1967 .

[14]  T. Kailath.  The innovations approach to detection and estimation theory , 1970 .

[15]  J.B. Moore,et al.  Performance bounds for adaptive estimation , 1976, Proceedings of the IEEE.

[16]  P. Papantoni-Kazakos,et al.  Spectral distance measures between Gaussian processes , 1980, ICASSP.

[17]  D. Lainiotis.  Optimal adaptive estimation: Structure and parameter adaption , 1971 .

[18]  D. Lainiotis,et al.  Recursive algorithm for the calculation of the adaptive Kalman filter weighting coefficients , 1969 .

[19]  R. Hawkes,et al.  Performance of Bayesian parameter estimators for linear signal models , 1976 .