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Linear Bayesian Estimators

# Linear Bayesian Estimators - Detection and...

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Unformatted text preview: Detection and Estimation (Spring, 2009) Linear Bayesian Estimators NCTU EE P.1 Linear Bayesian Estimators ~ Linear MMSE Estimator 9 The optimal Bayesian estimators are difficult to determine in closed form, and in practice too computationally intensive to implement. 9 We consider the class of all linear (actually affine) estimators of the form and choose the weighting coefficients a n ’s to minimize the Bayesian MSE Linear minimum mean square error (LMMSE) estimator Remark: a N is added to allow for nonzero means of x and θ . Let a = [a a 1 … a N-1 ] T , we have Detection & Estimation (Spring, 2009) Linear Bayesian Estimators NCTU EE P.2 Remarks: 1. The LMMSE estimator is identical in form to the MMSE estimator for jointly Gaussian x and θ . 2. If the means of θ and x are zero, 3. All that is required to determine the LMMSE estimator are the first two moments of p( x , θ ). ~ Geometrical Interpretations Here we assume that θ and x are zero mean. If not, we can always define the zero mean random variables θ ’ = θ- E( θ ) and x ’ = x – E( x ). Now, we wish to find the a n ’s so that minimizes Detection & Estimation (Spring, 2009) Linear Bayesian Estimators NCTU EE P.3 We define the inner product between two random variables x and y as...
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Linear Bayesian Estimators - Detection and...

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