Due to Federal Communications Commission (FCC) requirements for identifying mobile phone location, vendors are beginning to incorporate global positioning system (GPS) receivers into their handsets.  This is an assisted form of GPS where the host base station provides key search parameter information to the handset such that the GPS satellite search and subsequent delay measurement becomes significantly less computationally extensive for the handset.  In the code-division multiple access (CDMA) context, the messaging between the base station and the handset to support the assisted GPS (AGPS) is documented in “Position Determination Service Standards for Dual Mode Spread Spectrum Systems,” TIA/EIA/IS-801-1, published by the Telecommunications Industry Association (TIA). 
In order for mobile location to be successfully based on AGPS, it is necessary that the GPS receiver in the handset unit have significantly higher sensitivity than is nominally required in a typical stand alone GPS unit.  The reason is that the handset unit is usually oriented in positions or in locations that are not favorable for GPS signal reception.  Hence a signal to noise ratio (SNR) sensitivity target is typically around 17 dB-Hz.  Given that the GPS Coarse/Acquisition (C/A) L1 band which is typically used for mobile position location has a bandwidth of about 2 MHz, this implies that the input raw GPS, prior to processing, is more than 40 dB below the thermal noise floor. 
There is also a significant push to drive the cost of the overall handset down which limits the quantity of the processing which can be done on the received GPS signals to extract them from the noise.  This also limits the quality of the various radio frequency (RF) oscillator components used in the handset's receiver.  Consequently, it can be expected that there will be some additional local oscillator (LO) noise that needs to be compensated for.  Notably, there is no closed automatic frequency correction (AFC) loop possible during the GPS measurement as the input SNR is too low.  The lack of AFC, and the use of low cost, low power, RF LO components, implies that there will Inevitably be a significant finite offset, drift, and some instability associated with the LO down conversion frequency. 
The C/A signal from a GPS SV (space vehicle) is a DS-SS (direct sequence spread spectrum) with a chip rate of 1.023 Mcps.  It is modulated as binary phase shift keying (BPSK) on a 1.574 GHz carrier.  The GPS receiver correlates the received signal with a locally generated DS-SS code signal.  In the AGPS scheme, traditional DS-SS correlation is also done.  However, detailed information regarding the doppler shift of the SV GPS signal and code offset is available from the host base station (BS) which significantly reduces the search and detection effort.  Nevertheless, the mobile GPS receiver is still required to determine the code delay and doppler to a finer resolution than that available from the host BS such that mobile location is possible. 
Based on standard assumptions regarding the noise in the GPS signal channel, the optimum receiver would correlate the signal in a coherent fashion over an integration time period that is sufficiently long to provide about 11 dB SNR at the correlator output.  This will typically provide an adequate probability of detection with a reasonable false alarm rate.  However, in the case of a mobile GPS receiver, due to the instability of the RF LO and the uncertainly of the SV doppler, the coherent integration epoch needs to be limited.  Also valid GPS readings are still required even if the user does not hold the receiver steady.  Hence, typically the coherent integration time is limited to 10 msec or less.  As the available coherent integration epoch is not sufficient to obtain the sensitivity required, non-coherent summations of sequential coherent correlation.  Integration outputs are used.  However, non-coherent processing is a very inefficient means of further enhancing the SNR of a signal as it discards certain known statistical aspects of the signal. 
Various examples of the use of Viterbi algorithms for phase trajectory determinations are known.  For example U.S. Pat.  No.  6,477,208 to Huff teaches a method and apparatus for processing a received digitally-modulated carrier signal to coherently demodulate a signal utilizing a composite trellis diagram.  However, the method of Huff is only applicable to cases of discrete jumps in phase based on specific modulations.  When using a continuous, free running oscillator, the phase steps are continuous in time.  Huff does not teach a method for approximating these phase steps.