6. Statistical Signal Processing

The basic tenets of detection and estimation are presented in this chapter. These topics from statistical inference comprise the field of statistical signal processing and have numerous applications in underwater acoustics. The advantage of characterizing an application as a detection or estimation problem lies in the wealth of solutions that can be found in the statistics literature, along with the associated performance measures. The presentation found in this chapter begins with the performance measures and the techniques used to estimate them from simulated or real data. For estimation applications, the Cramér-Rao lower bound (CRLB) on the variance of unbiased estimators is presented in general and for the common cases of multivariate real and complex Gaussian models. Although the CRLB does not describe the performance achieved by a specific estimator, it characterizes the best achievable performance over all unbiased estimators and is therefore a very useful analysis tool. A number of standard techniques for developing detectors (Neyman-Pearson optimal, uniformly most powerful, locally optimal, generalized likelihood ratio, and Bayesian approaches) and estimators (maximum likelihood, method of moments, Bayesian, and the expectation-maximization algorithm) are then presented along with examples using both standard statistical models and those relevant to applications in underwater acoustics.