The subject is also closely related to recent "social learning" models that have been attracting attention in the social sciences. In the latter models, sensors/agents make decisions that are best in a local (myopic/selfish) sense. In contrast, the papers below correspond to an "engineering" perspective whereby each sensor makes a decision that will be most beneficial for the overall system objective.
Work along the engineering and the social science strands does have some interesting points of contact. For example, any negative (or impossibility) results on the engineering version of a problem, readily implies the same negative results for a social learning formulation involving selfish/myopic agents. Furthermore, one strand can borrow mathematical techniques from the other.
A 1993 survey with a unified treatment of the subject (from the engineering perspective) can be found in:
If the measurements at each sensor are conditionally independent (conditional on any hypothesis), there is a lot to say:
W. P. Tay and J. N. Tsitsiklis, "The Value of Feedback for Decentralized Detection in Large Sensor Networks", Proceedings of the IEEE International Symposium on Wireless Pervasive Computing (ISWPC 2011), Hong Kong, China, February 2011.
O. P. Kreidl, J. N. Tsitsiklis, and S. Zoumpoulis, "On Decentralized Detection with Partial Information Sharing among Sensors", IEEE Transactions on Signal Processing, Vol. 59, No. 4, 2011, pp. 1759-1765.
W. P. Tay, J. N. Tsitsiklis, and M. Z. Win, "Bayesian Detection in Bounded Height Tree Networks", IEEE Transactions on Signal Processing, Vol. 57, No. 10, October 2009, pp. 4042-4051.
W. P. Tay and J. N. Tsitsiklis, "Error Exponents for Decentralized Detection in Tree Networks," in Networked Sensing Information and Control, V. Saligrama (Ed.), Springer Verlag, 2008, pp. 73-92.
W. P. Tay, J. N. Tsitsiklis, and M. Z. Win, "On the Impact of Node Failures and Unreliable Communications in Dense Sensor Networks", IEEE Transactions on Signal processing, Vol. 56, No. 6, June 2008, pp. 2535-2546.
W. P. Tay, J. N. Tsitsiklis, and M. Z. Win, "On the Sub-exponential Decay of Detection Error Probabilities in Long Tandems", IEEE Transactions on Information Theory, Vol. 54, No. 10, October 2008, pp. 4767-4771.
W. P. Tay, J. N. Tsitsiklis, and M. Z. Win, "Data Fusion Trees for Detection: Does Architecture Matter?", IEEE Transactions on Information Theory, Vol. 54, No. 9, September 2008, pp. 4155-4168.
W. P. Tay, J. N. Tsitsiklis, and M. Z. Win, "Asymptotic Performance of a Censoring Sensor Network ,'' IEEE Transactions on Information Theory, Vol. 53, No. 11, pp. 4191-4209, November 2007.
W.W. Irving and J.N. Tsitsiklis, "Some Properties of Optimal Thresholds in Decentralized Detection", IEEE Transactions on Automatic Control, Vol. 39, No. 4, April 1994, pp. 835-838.J.N. Tsitsiklis, "Extremal Properties of Likelihood-Ratio Quantizers", IEEE Transactions on Communications, Vol. 41, No. 4, 1993, pp. 550-558. G. Polychronopoulos and J.N. Tsitsiklis, "Explicit Solutions for some Simple Decentralized Detection Problems", IEEE Transactions on Aerospace and Electronic Systems, Vol. 26, 1990, pp. 282-291. J.N. Tsitsiklis, "Decentralized Detection by a Large Number of Sensors", Mathematics of Control, Signals and Systems, Vol. 1, No. 2, 1988, pp. 167-182.
This is an alternative model whereby each sensor keeps revising its estimate of an unknown quantity by forming each time, and communicating the optimal estimate (given the currently available information) to its neighbors.
J.N. Tsitsiklis and M. Athans, "Convergence and Asymptotic Agreement in Distributed Decision Problems", IEEE Transactions on Automatic Control, Vol. 29, No. 1, 1984, pp. 42-50.
Agent 1 knows x, agent 2 knows y. They want to compute a function f(x,y). How much do they need to communicate? This formulation captures much of the essence of the data fusion problem:
Unfortunately, the problem is NP-complete, in general:
But for specific types of functions f, progress is possible. When x and y are continuous variables, calculating the communication complexity may involve tools from algebraic or differential geometry:
In another variant, agent 1 knows a convex function g(.), agent 2 knows a convex function h(.) and they want optimize f(.)+g(.) within some accuracy epsilon: