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IEEE Information Theory Workshop 2010 (ITW 2010)
A continuous-time finite-power process with distribution is observed through an AWGN channel, at a given signal-to-noise ratio (SNR), and is estimated by an estimator that would have minimized the mean-square error if the process had distribution . We show that the causal filtering mean-square error (MSE) achieved at SNR level snr is equal to the average value of the noncausal (smoothing) MSE achieved with a channel whose SNR is chosen uniformly distributed between 0 and snr. Emerging as thedoi:10.1109/itwksps.2010.5503172 fatcat:7cfsuvkmezexbkz5j464bdblv4