Zero-error target tracking with limited communication

Tracking Markov targets in binary sensor networks: Source coding and large deviation limits on the required number of queries

“…Suppose that the area is partitioned into a number of non-overlapping regions each corresponds to one sensor which can detect the target in that region free of error. More detailed description of this tracking system is given in [8]. We assume that the target movement in different regions (states) is a Markov process, hence the random variable as the position of target in different regions over time represents a Markov source.…”

“…But when large number of sensors are involved practical problem in implementing this algorithm and also energy saving considerations favour a tracking method based on query by the tracker from the network [8]. In each query, the tracker asks a selected set of sensors if any of those sensors has detected the target at a specified time index.…”

“…A target, with a given transition probability matrix is trackable if almost surely the tracker can get the right target track history at some time index , and this event happens infinitely often. Bounds on the maximum allowed query rate for trackability have been obtained in [8]. There, it is shown that a necessary rate for trackability is ≥ and a sufficient rate is ≥ + 1, where represents the entropy rate of the Markov target position.…”

“…However, the nodes of the tree generated at step of THM code is used for query at time , but at most C level down, and the remaining will be backlogged for the next time step. This is possible due to the time stamp of queries in the query mechanism explained above (see [8] for a detailed explanation of query mechanism), a query at time may be about the symbol −1 or the time before that.…”

“…For transition probabilities being integer powers of (1/2) the Huffman code length satisfies (8). For general transition probability, however the maximum code length satisfies (( , )) ≤ − log , + 1…”