  This paper investigates the problem of estimating biases affecting relative
state measurements in a sensor network. Each sensor measures the relative
states of its neighbors and this measurement is corrupted by a constant bias.
We analyse under what conditions on the network topology and the maximum number
of biased sensors the biases can be correctly estimated. We show that for
non-bipartite graphs the biases can always be determined even when all the
sensors are corrupted, while for bipartite graphs more than half of the sensors
should be unbiased to ensure the correctness of the bias estimation. If the
biases are heterogeneous, then the number of unbiased sensors can be reduced to
two. Based on these conditions, we propose some algorithms to estimate the
biases.
