Collective detection (CD) is a technique for signal acquisition and direct positioning in weak signal environments. It is implemented by searching the position and time domain to maximize the CD cost function. The conventional CD method suffers from high computation complexity because the cost function is multi-dimensional and non-convex. The precision of the time parameter is much lower than that of the position parameters, which lead the computation burden much heavier. In order to reduce the clock bias search space, the relationship of the propagation time error, the user position error, the clock bias error, and the positions of the satellites are presented. Based on the relationships, two search schemes are proposed to reduce the search space. Computation complexity comparison between the proposed schemes and the original CD method is provided. Simulations are also presented to validate the proposed method. Results show that the proposed scheme I and II can be implemented with at least 1 and 2 strong signals respectively and can reduce the search space dramatically.
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