I am wondering what approach is more accurate for estimating parameters between two different models of exponentially decaying signal data.
The signal decays very rapidly and only a few samples can be acquired, i.e., a maximum of 8 over several milliseconds.
The signals are acquired by a phased array of sensors and processed into a signal magnitude (sum of squares) from complex phase data.
As a result of the operation, the (zero-centered) gaussian noise from each sensor then becomes non-gaussian and a non-zero positive value. i.e., the exponential decaying magnitude signal does not go to zero.
My understanding is that the noise distribution follows a noncentral chi distribution. This simplifies to a Central Chi distribution if the mean signal is zero (Rice and Rayleigh distributions are special simplified cases where number of sensors = 2).
With that background, what model is more accurate for parameter estimates? 1) A simple exponential decay but truncating or censoring data below a certain signal threshold.
2) An exponential decay model which takes into account the noise model and the bias introduced. The data is not truncated or censored. Essentially being a maximum likelihood estimator.
Knowing that exponential decay parameter estimation is an extremely ill-posed inverse problem. I would like to know what thoughts there are on these two approaches.