MLE and CRB for Some Selected Cases
Umberto Spagnolini · 2017
In this chapter, the maximum likelihood estimation (MLE) and the Cramer-Rao bound (CRB) are evaluated for some of the most common models and applications. The ML estimation of the amplitude and delay follows from the log-likelihood function. The frequency estimation is from minimization of the log-likelihood metric. The estimation of the time of delay (ToD) is informative on the position of the target. The estimate of the logistic regression parameters reduces to a non-linear optimization that needs to be solved by numerical methods. Furthermore, from the inspection of the CRB, some methods are revised such as the common usage of numerical histograms. Bin-width can be optimized and this needs to account for a metric for probability density function (pdf) estimation. An optimized bin-width follows as a second step after a uniform bin-spacing histogram. This chapter also focuses to gain insight into histogram design.