A review of efficient applications of genetic algorithms to improve particle filtering optimization problems

Abstract

Particle filtering (PF) is a sequential Monte Carlo method that draws sample (particle) values of state variables of interest to approximate the posterior probability distribution function (PDF) of the state and to infer the true state from this PDF. The values of the state variables that belong to a particle can differ from those of the other particles and the evaluated importance weights of particles can be different as well. Resampling employs a selection process to eliminate low-weight particles and retain high-weight particles that are further used to construct the new prediction PDF (or prior PDF) for drawing particles at the next time step. Genetic algorithms (GAs) help in finding the optimal solution by stochastically identifying new solutions that have higher fitness values. Each solution is treated as an individual: the individuals that have high fitness survive and are allowed to create offspring. The individuals with low fitness are more likely to be eliminated from the population according to the principle of the selection process. Selection is employed in both PF and GAs. However, particles found after the selection process can be left trapped around local maxima of the objective function. We can integrate genetic operations (e.g., crossover and mutation) to find new offspring particles that are expected to have higher weights. We construct the new prediction PDF to draw new particles at the next time step after we obtain offspring particles. This paper reviews and discusses efficient techniques of integrating GAs to enhance the performance of PF. These techniques can open doors into research advances in state prediction and estimation, leading to new insights and innovations.