Comparison of various static multiple-model estimation algorithms

A static multiple-model (SMM) estimation and decision algorithm has two functions: estimate the state of the system and decide which model is the best representation of the system. This paper concentrates on static multiple-model systems, that is, there is only one mathematical model applicable to a sequence of measurements, that model is one of a number of known possible mathematical models, but which one of these models is applicable is not known. In this paper, the characteristics of both estimation and decision errors of three SMM optimal algorithms are evaluated with a variety of performance measures using a Monte Carlo simulation. The SMM algorithms evaluated include those that are optimal for the following optimization criteria: the minimum mean sum squared estimation error, the joint maximum a posteriori probability, and the most probable model. The performance measures include the root mean sum squared estimation error, the mean root sum squared estimation error, the estimation maximum a posteriori probability density function, and two simultaneous estimation and decision measures of performance. The first three measures of performance correspond to the mean, median, and mode, respectively, of the a posteriori probability density function of the system state conditioned on the measurements. One of these performance measures could be more suitable to a specific system application, while another might be more suitable to a different system. This study address one of the fundamentals of target tracking. It demonstrates that algorithms that are optimal for different criteria exhibit different error characteristics and do not all perform the same for the various performance evaluation measures. As a result, there is no single algorithm that is best for all system applications - different algorithms are suitable for different applications. The results presented in the paper provide insight for the selection and design of different algorithms for different applications.