The use of multiple GPS sensors provides the conceptual framework for novel techniques for reducing the minimum signal strength required by a GPS assistance system to acquire and accurately track GPS satellites at or near the horizon. A strong signal attenuation system for synthesizing GPS satellite-specific I/F signals, enabling more efficient and effective acquisition of GPS satellites, is disclosed, comprising N+1 reference GPS sensors, each with an omni-directional antenna and front end, for down converting composite GPS satellite signals, and strong signal suppression (SSS) means for synthesizing, from the I/F signals produced by the N+1 reference GPS sensors, a set of one or more I/F signals (corresponding to a set of designated satellites), each with at least N of the strongest potentially-interfering satellite signals suppressed.