The Global Positioning System: A Shared National Asset (1995)
Chapter: DISCUSSION
12.6 dB is more than adequate for detection, which means that the ratio of signal voltage-to-noise is 4.3. If the detection threshold were conservatively set at three times the noise there would only be a 1-three sigma, or about 1 percent probability of false detection.
If a receiver is implemented with a parallel search capability of 1,000 correlation channels, a full search over 1 second of delay could be accomplished in 10 seconds based on the equation below.1
(107 chips)(0.001 correlation channel sec/chip search)/(1,000 correlation channel)
= 10 seconds.
This assumes that the signal Doppler is known to about 1,000 Hz, which corresponds to about 200 m/second, or 720 km/hr.
Current Technology (500,000 Gate ASIC)
The search time would be reduced by a factor of 5, to 2 seconds. Using the same procedure as above, if a receiver is implemented with a parallel search capability of 5,000 correlation channels, a full search over 1 second of delay could be accomplished in
(107 chips)(0.001 correlation channels sec/chip search)/(5,000 correlation channel)
=2 seconds.
Again, this assumes that the signal Doppler is known to 1,000 Hz, which corresponds to about 200 m/second, or 720 km/hr.
Discussion
For both cases, modest assumptions about receiver capabilities have been made. Time keeping accurate to 1 second is within the range of a wristwatch-level oscillator over a day or so. Most platforms can estimate their velocity to 720 km/hr. If the velocity and time are not known to this level, additional multiples of the 10- or 2-second search would be required. Once the first satellite is acquired, the receiver clock can be fixed to about 0.01 second, so searches for additional satellites can be done sequentially taking about 0.1 second each. We have also assumed that the receiver has on-board ephemerides for the satellites to allow position solutions immediately following acquisition of the first four satellites. If there are no on board ephemerides, it takes about 30 seconds to receive all five ephemeris subframes, so 30 seconds should be added to obtain a time-to-first-fix.
