Maximum likelihood parameter estimation of dynamic systems by heuristic swarm search

As a method of estimating the parameters of statistical models in statistics, maximum likelihood (ML) method has gained much attention and been popularly applied to a variety of fields. In the subjects of information, control, as well as system science and engineering, it is usually exploited to estimate the parameters of diverse linear dynamic systems. The tough task of estimating ML parameters of diverse linear dynamic systems can be attributed to a constrained optimization problem. In an effort to solve the constrained optimization problem effectively, we first use the ML method to address the statistical modelling of ML parameter estimation of general linear dynamic systems. Then we present a novel heuristic particle swarm search algorithm called sliding mode controlling particle swarm optimization (SMCPSO) algorithm. In SMCPSO, we introduce a sliding mode controller (SMC) into standard particle swarm optimization (SPSO). The SMC is intentionally placed between the particle position and the global best particle position so as to improve the particles' position information. It ameliorates the exploration and exploitation search abilities of the particles. Thereafter, SMCPSO is exploited to solve the problem of the ML parameter estimation of a given linear dynamic system together with SPSO, recursive ML generalized least squares (RMLGLS) method, and recursive ML least squares (RMLLS) algorithm. The simulation results demonstrate that SMCPSO is an effective approach and superior to other three approaches in estimating the ML parameters of the linear dynamic system.