James-Stein state filtering algorithms

نویسندگان

  • Jonathan H. Manton
  • Vikram Krishnamurthy
  • H. Vincent Poor
چکیده

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 Kalman 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.

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عنوان ژورنال:
  • IEEE Trans. Signal Processing

دوره 46  شماره 

صفحات  -

تاریخ انتشار 1998