Optimum Semi-codeless Carrier Phase Tracking of L2

GPS satellites transmit spread spectrum signals on L1 and L2 at 1575.42 and 1227.6 MHz, respectively. The Coarse/Acquisition (C/A) code and the precision (P) code modulate the L1 signal. The L2 signal is modulated by the P-code only. GPS receivers measure the carrier and code phases of the L1 and L2 signals from a number of GPS satellites to compute the position of the receiver and the time at which the measurements are collected. To prevent spoofing of the military P-code signals, an encrypted code, called the W code, which is not available to civilian users, is modulated by the Department of Defense with the publicly known P code on both L1 and L2 to provide the anti-spoofing Y-code. Since L2, unlike L1, does not have the C/A code, its access is denied to all users without knowledge of the W-code. This has severe impacts on survey, carrier phase differential, and kinematic users who need rapid carrier phase ambiguity resolution that requires the difference frequency between L1 and L2 (the so-called Widelane Frequency). The widelane frequency has a wavelength that is 4.5 times larger than L1. Without knowledge of the Y-code, one has to apply a codeless or a semi-codeless technique for the reconstruction of the L2 carrier phase. Most receivers utilize a hybrid technique. The L1 carrier is recovered after C/A code correlation, and the L2 carrier is reconstructed without knowledge of the Y or W codes. There are four known techniques that have been published in the past: squaring, cross-correlation, P-code aided L2 squaring, and Z-tracking. Because of the lack of knowledge of the W code, these techniques perform significantly worse (14 to 31 dB at a typical L2 C/No) than an ideal phase lock loop. This paper presents five additional techniques that can be used to reconstruct the L2 carrier without knowledge of the W-code. These five techniques are: 1) Code-aided L2 Costas loop with W-Bit integrate and dump arm filtering; 2) P-code aided L1, L2 Cross Correlation; 3) Soft decision Z-tracking; 4) Optimum L2 demodulation motivated by maximum a posteriori (MAP) estimation theory; and 5) Linear approximation of the MAP approach. The first three techniques are modification of existing techniques, with improved performance. Techniques 4 and 5 are optimum and near optimum techniques based on statistical estimation theory. A detailed derivation of the MAP approach is given. Also presented is a detailed comparison of the squaring losses of the various L2 recovery techniques as functions of received L2 C/No's. The performance of the MAP technique and its linear approximation is shown to be at least 3 dB better than all techniques published previously. In addition, it is analytically shown that the MAP approach provides the minimum squaring loss that is possible, and represents an upper bound of achievable performance for L2 carrier recovery without knowledge of the W-code. Computer simulation results agree with theory.