Maximum likelihood estimation of liner signal parameters for Poisson processes

The estimation of linear signal parameters is studied under the hypothesis of independently Poisson distributed measurements. A simple interactive maximum-likelihood estimator (MLE) is derived and is optimized for rapid convergence. It is shown to be statistically optimal in the sense of providing unbiased and minimum variance estimates. Experimental conditions are identified where MLE results in significant performance improvement when compared to conventional linear least-squares (LLS).>