Fisher Information Matrix and the Cramér–Rao Lower Bound

In the parameter estimation problems—including position estimation—the amount of information about the observations coming from underlying probability distribution—sample data—can be obtained. The information is in the form of a matrix known as the Fisher Information Matrix (FIM) and can be assessed using the Cramér-Rao Lower Bound (CRLB) technique, helping in choosing the set of observations that results in acceptable or high accuracy of the estimated parameters. The CRLB technique is based on quantifying the amount of information about the estimated position vector that is contained in a particular set of observations. This chapter provides brief and sufficient mathematical descriptions of each of the topics at hand C++ implementations using the standard and Eigen libraries, with explanations.