TY - JOUR
T1 - James-stein state filtering algorithms
AU - Manton, Jonathan H.
AU - Krishnamurthy, Vikram
AU - Poor, H. Vincent
N1 - Funding Information:
Manuscript received January 27, 1997; revised November 13, 1997. This work was supported by the Australian Telecommunication and Engineering Research Board, the Cooperative Research Centre for Sensor Signal and Information Processing, an Australian Research Council large grant, the Cooperative Research Centre for Sensor Signal and Information Processing, and the U.S. Office of Naval Research under Grant N00014-G4-1-0115. The associate editor coordinating the review of this paper and approving it for publication was Prof. Chi Chung Ko.
PY - 1998
Y1 - 1998
N2 - In 1961, James and Stein discovered a remarkable estimator that dominates the maximum-likelihood estimate of the mean of a p-variate normal distribution, provided the dimension p is greater than two. This paper extends the James-Stein estimator and highlights benefits of applying these extensions to adaptive signal processing problems. The main contribution of this paper is the derivation of the James-Stein state filter (JSSF), which is a robust version of the Kaiman filter. The JSSF is designed for situations where the parameters of the state-space evolution model are not known with any certainty. In deriving the JSSF, we derive several other results. We first derive a James-Stein estimator for estimating the regression parameter in a linear regression. A recursive implementation, which we call the James-Stein recursive least squares (JS-RLS) algorithm, is derived. The resulting estimate, although biased, has a smaller mean-square error than the traditional RLS algorithm. Finally, several heuristic algorithms are presented, including a James-Stein version of the Yule-Walker equations for AR parameter estimation.
AB - In 1961, James and Stein discovered a remarkable estimator that dominates the maximum-likelihood estimate of the mean of a p-variate normal distribution, provided the dimension p is greater than two. This paper extends the James-Stein estimator and highlights benefits of applying these extensions to adaptive signal processing problems. The main contribution of this paper is the derivation of the James-Stein state filter (JSSF), which is a robust version of the Kaiman filter. The JSSF is designed for situations where the parameters of the state-space evolution model are not known with any certainty. In deriving the JSSF, we derive several other results. We first derive a James-Stein estimator for estimating the regression parameter in a linear regression. A recursive implementation, which we call the James-Stein recursive least squares (JS-RLS) algorithm, is derived. The resulting estimate, although biased, has a smaller mean-square error than the traditional RLS algorithm. Finally, several heuristic algorithms are presented, including a James-Stein version of the Yule-Walker equations for AR parameter estimation.
KW - James-stein estimation
KW - Kaiman filter
KW - Maximum-likelihood estimation
KW - Minimax estimation
KW - Recursive least squares
KW - Robust filtering
KW - Yule-walker equations
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U2 - 10.1109/78.709532
DO - 10.1109/78.709532
M3 - Article
AN - SCOPUS:0032165961
SN - 1053-587X
VL - 46
SP - 2431
EP - 2447
JO - IEEE Transactions on Signal Processing
JF - IEEE Transactions on Signal Processing
IS - 9
ER -