We examine the problem of distributed estimation when only one sensor can take a measurement per time step. The measurements are then exchanged among the sensors. The problem is motivated by the use of sonar range-finders used by the vehicles on the Caltech Multi-Vehicle Wireless Testbed. We solve for the optimal recursive estimation algorithm when the sensor switching schedule is given. Then we investigate several approaches for determining an optimal sensor switching strategy. We see that this problem involves searching a tree in general and propose and analyze two strategies for pruning the tree to keep the computation limited. The first is a sliding window strategy motivated by the Viterbi algorithm, and the second one uses thresholding. We also study a technique that employs choosing the sensors randomly from a probability distribution which can then be optimized. The performance of the algorithms are illustrated with the help of numerical examples
