# Accuracy of exponential decay parameter estimates comparing different models

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.

• If anybody could help answer this...I would be greatly appreciative. – esd100 Dec 7 '16 at 21:28
• It might help if you write out the underlying "correct" model you believe is going on. (You can use MathJax.) This might be relevant for the "noise" distribution? – GeoMatt22 Dec 29 '16 at 0:20
• My understanding is that in a local region, the noise distribution is en.m.wikipedia.org/wiki/Noncentral_chi_distribution. Globally, the noise distribution is not homoscedastic. – esd100 Dec 29 '16 at 0:29
• Well, is almost been a full year since I asked this question. I guess no one in the statistics community has enough knowledge to answer this. – esd100 May 27 '17 at 20:24