Optimal Intermittent Particle Filter

TL;DR

This paper develops and compares three optimal intermittent particle filtering strategies that allocate measurement times to minimize mean square error, using stochastic programming, offline, and online approaches, with practical approximations and algorithms.

Contribution

It introduces three novel optimal measurement scheduling methods for particle filtering, incorporating stochastic, offline, and online decision frameworks, with practical approximation techniques.

Findings

Stochastic program filter outperforms online and offline filters in mean square error.

Particle filter approximations enable practical implementation of optimal measurement strategies.

Performance demonstrated on tumor motion and benchmark models.

Abstract

The problem of the optimal allocation (in the expected mean square error sense) of a measurement budget for particle filtering is addressed. We propose three different optimal intermittent filters, whose optimality criteria depend on the information available at the time of decision making. For the first, the stochastic program filter, the measurement times are given by a policy that determines whether a measurement should be taken based on the measurements already acquired. The second, called the offline filter, determines all measurement times at once by solving a combinatorial optimization program before any measurement acquisition. For the third one, which we call online filter, each time a new measurement is received, the next measurement time is recomputed to take all the information that is then available into account. We prove that in terms of expected mean square error, the stochastic program filter outperforms the online filter, which itself outperforms the offline filter. However, these filters are generally intractable. For this reason, the filter estimate is approximated by a particle filter. Moreover, the mean square error is approximated using a Monte-Carlo approach, and different optimization algorithms are compared to approximately solve the combinatorial programs (a random trial algorithm, greedy forward and backward algorithms, a simulated annealing algorithm, and a genetic algorithm). Finally, the performance of the proposed methods is illustrated on two examples: a tumor motion model and a common benchmark for particle filtering.