Fast Particle Filters and Their Applications to Adaptive Control in Change-Point ARX Models and Robotics

Abstract

handle parameter jumps is to apply carefully designed on-line change detection algorithms to segment the data. Another approach, called AFMM (adaptive forgetting through multiple models), is to use Bayesian updating formulas to calculate the posterior probability of each member in a family of models locating the change-points. To keep a fixed number of such models at every stage, the model with the lowest posterior probability is deleted while that with the highest posterior probability gives birth to a new model by allowing for a possible change-point from it. The fast particle filters introduced by Chen & Lai (2007) enable them to develop a much more precise implementation of the Bayesian approach than AFMM, with little increase in computational cost, and to come up with more efficient adaptive control schemes, as shown in Section 3. Another area where particle filters have been recognized to offer promising solutions to important and difficult control problems is probabilistic robotics. Section 4 provides a brief summary of the applications of particle filters to estimate the position and orientation of a robot in an unknown environment from sensor measurements. It also reviews previous work and ongoing work on using these particle filters to tackle the difficult stochastic control problems in robotics. The stochastic models in Sections 3 and 4 are special cases of hidden Markov models. Section 2 gives a brief introduction to hidden Markov models and particle filters, which are sequential estimates of the hidden states by using Monte Carlo methods that involve sequential importance sampling and resampling. The basic idea underlying these sequential Monte Carlo filters is to represent the posterior distribution of the hidden state at time t given the observations up to time t by a large number of simulated samples ("particles"). Simulating a large number of samples, however, makes the Monte Carlo approach impractical for on-line identification and control applications. We show in Section 3 that by choosing appropriate resampling schemes and proposal distributions for importance sampling, we can arrive at good approximations to the optimal filter by using a manageable number (as small as 50) of simulated samples for on-line identification and adaptive control. This point is discussed further in Section 5 where we consider related issues and give some concluding remarks.