Mmse

Why is being jointly WSS important in signal estimation with LMMSE estimator?

Why is being jointly WSS important in signal estimation with LMMSE estimator?
  1. How do you calculate MMSE estimator?
  2. What is LMMSE?

How do you calculate MMSE estimator?

The linear MMSE estimator of the random variable X, given that we have observed Y, is given by ˆXL=Cov(X,Y)Var(Y)(Y−EY)+EX=ρσXσY(Y−EY)+EX. The estimation error, defined as ˜X=X−ˆXL, satisfies the orthogonality principle: E[˜X]=0,Cov(˜X,Y)=E[˜XY]=0.

What is LMMSE?

The linear minimum MSE estimator (LMMSE) estimator is: ̂θ = ̂AT x = ΣθxΣ−1. xx x. 2 Orthogonality Principle.

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