Statistical Signal Processing in Engineering

10Numerical Analysis and Montecarlo Simulations

Estimators are compared according to their performance, and numerical simulations are often the preferred method to better evaluate that performance in the range of interest, in addition to CRB or any sensitivity analysis in the neighborhood of the true solution. The benefits of performance analysis by simulation are several, such as:

• analysis of the accuracy of the estimation method compared to any analytical bound (e.g., comparison with CRB);
• evaluation of accuracy when the model is non‐linear and threshold effects might appear in the estimator due to the extrema‐search method (typical for small or large noise);
• analysis of robustness for any deviation from model assumptions;
• analysis of implementation method and any sub‐optimal choice (e.g., signal quantization).

Montecarlo simulations are based on three main building blocks that are encoded here in MATLAB® (Figure 10.1): signal generation, estimation, and performance analysis. The signal is generated by simulating the generation mechanism with a random number generator that has a pdf that is as the one specified by the model itself (or any deviation, if this is the aspect of interest):

Figure 10.1 Typical Montecarlo simulations.

For the kth realization of the signal, the ...