Optimum constellation of multisensors in a circular area based on TDOA

In this paper, the constellation of multisensors based on the time difference of arrival (TDOA) is systematically investigated. First, the probability distribution of the location error is given; after having the relationship between the error ellipsoid volume and the error covariance matrix, the optimal constellation is obtained for the case in which the sensors are constrained in an ellipse area to locate a target in space exact above the central point by use of the minimum error ellipsoid volume criterion. And then taking advantage of the result, the optimal constellation is achieved for the case in which the sensors are constrained in a circular area to locate a target in space with any given coordinate.