Fault Tolerance in a Multisensor Environment

Replicating sensors is desirable not only to tolerate sensor failures but also to increase the expected accuracy of the ensemble of replicated sensors beyond that obtainable with a single one. Such replication is used in a multisensor environment or in a distributed sensor network. We model a continuous valued sensor as an interval of real numbers containing the physical value of interest. Given n sensors of which at most f of them can su er arbitrary failures, we present an e cient O(n log n) fault tolerant algorithm whose output is reliable, that is, guaranteed to contain the correct value at all times, and is fairly accurate when f < n=2. The output of the algorithm could be a single interval or a set of intervals depending on the nature of the multisensor environment. This algorithm can be used not only to detect all the possible faulty sensors but to detect all sets (combinations) of possibly faulty sensors. We prove the following results pertaining to the possibly faulty sensors pointed out by the algorithm: 1) The number of sets each containing f possibly faulty sensors is at most (f+1). 2) The number of possibly faulty sensors pointed to by the algorithm is at most 2f . 3) The number of sets each containing f or fewer faulty sensors is at most (2f + 1). These results help narrow down the search to detect faulty sensors and to bound the number of intervals needed to construct an accurate and reliable \abstract sensor".