GPS Satellite Signal Acquisition and Tracking

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Principle: At this moment, there are two sets of global positioning system ( GPS ) services from satellites: SPS ( Standard Positioning Service ) and PPS ( Precise Positioning Service ). SPS is open to all users; PPS is only available to US government and military users. Due to the availability of SPS, people have the chance to use the signal from satellites to do global positioning without charge and restriction. The basic idea is that 4 satellites will send out the signal to the receiver about their positions, heights, and time stamp (x,y,z,t ) of sending signal, then the receiver's position and the time for receiving the signal (X,Y,Z,T ) can be found by

(x1 - X)² + (y1 - Y)² + (z1 - Z)² = c²(t1 - T)²
(x2 - X)² + (y2 - Y)² + (z2 - Z)² = c²(t2 - T)²
(x3 - X)² + (y3 - Y)² + (z3 - Z)² = c²(t3 - T)²
(x3 - X)² + (y3 - Y)² + (z4 - Z)² = c²(t4 - T)²

where c is the velocity of light ( 300,000 km/sec ). And the rest of the work is the signal modulation and date encoding and decoding ( CDMA scheme, Gold pseudorandom noise codes with its generator polynomial ). If Doppler effect and Special Relativity are taken into account, it would be more complicated. Collect the material of GPS and check if you can make any improvement.