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In this study, we generalize a problem of sampling a scalar Gauss MarkovProcess, namely, the Ornstein-Uhlenbeck (OU) process, where the samples aresent to a remote estimator and the estimator makes a causal estimate of theobserved realtime signal. In recent years, the problem is solved for stable OUprocesses. We present solutions for the optimal sampling policy that exhibits asmaller estimation error for both stable and unstable cases of the OU processalong with a special case when the OU process turns to a Wiener process. Theobtained optimal sampling policy is a threshold policy. However, the thresholdsare different for all three cases. Later, we consider additional noise with thesample when the sampling decision is made beforehand. The estimator utilizesnoisy samples to make an estimate of the current signal value. The mean-squareerror (mse) is changed from previous due to noise and the additional term inthe mse is solved which provides performance upper bound and room for apursuing further investigation on this problem to find an optimal samplingstrategy that minimizes the estimation error when the observed samples arenoisy. Numerical results show performance degradation caused by the additivenoise.

Performance Bounds for Sampling and Remote Estimation of Gauss-Markov Processes over a Noisy Channel with Random Delay