I am trying to estimate the clean form of a time series, $u(t)$ that is corrupted by additive White Gaussian noise $w(t)$ at a particular SNR. The received signal is:
$$y(t) = u(t) + w(t)$$
- My first choice was to apply MLE or OLS since the gaussianity would yield an optimal estimate. But I don't know which terms would go into the pseodiinverse component: $u_{est} = y*pinv(\cdot)$ ?
Is OLS the correct approach or is there any other technique?
- I thought of applying state-space estimators such as Kalman filtering but I do not understand how the design matrices would be applicable here. Is there a simpler technique?