Estimation theory concerns the inference of parameters that characterize a signal from measured data. In this lesson you will be introduced to the parameter estimation problem and simple metrics for characterizing the quality of an estimator. These metrics are used to compare competing estimators and guide the search for good estimators in general. You will […]
Introduction to Signal Estimation and Detection Theory
Parameter estimation is the problem of using data to estimate one or more unknown quantities in a model for the signal. This requires finding a function of the data that gives a good quality estimate of the parameter of interest. In this lesson you will learn about the two common criteria used to design estimators: […]
The maximum likelihood criterion for parameter estimation is simple to write down, but more complex to apply. In this lesson you will learn how to find the maximum likelihood estimate for three different estimation problems. These examples teach you techniques you can use to solve your own maximum likelihood estimation problems.
Detection theory is synonymous with hypothesis testing. The goal is to decide which of several candidate signal models produced the observed data. This is a fundamental and widespread problem in signal processing. Examples include determining whether an aircraft is present in a radar return and whether cancer is present in an image of tissue. In […]
The likelihood ratio test is one of the few tests that are guaranteed to be optimal – that is, no other test can improve on the performance of the likelihood ratio test. In this lesson you will learn when the likelihood ratio test is applicable and how to form the likelihood ratio. An example illustrates […]
The generalized likelihood ratio test (GLRT) extends the likelihood ratio principle to scenarios in which the likelihood ratio test is not applicable. The GLRT is a principled method for obtaining a good test when optimal tests do not exist. In this lesson you will learn how to obtain the GLRT. An example illustrates application of […]