  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.
