  In this study, we generalize a problem of sampling a scalar Gauss Markov
Process, namely, the Ornstein-Uhlenbeck (OU) process, where the samples are
sent to a remote estimator and the estimator makes a causal estimate of the
observed realtime signal. In recent years, the problem is solved for stable OU
processes. We present solutions for the optimal sampling policy that exhibits a
smaller estimation error for both stable and unstable cases of the OU process
along with a special case when the OU process turns to a Wiener process. The
obtained optimal sampling policy is a threshold policy. However, the thresholds
are different for all three cases. Later, we consider additional noise with the
sample when the sampling decision is made beforehand. The estimator utilizes
noisy samples to make an estimate of the current signal value. The mean-square
error (mse) is changed from previous due to noise and the additional term in
the mse is solved which provides performance upper bound and room for a
pursuing further investigation on this problem to find an optimal sampling
strategy that minimizes the estimation error when the observed samples are
noisy. Numerical results show performance degradation caused by the additive
noise.
