ionospheric error compensation described above, the P-code (DS-modulated by the data bit stream similarly to C/A-code) is transmitted on both frequencies L1 and L2, quadrature multiplexing of C/A and P signals being used on L1 with 3 dB stronger C/ A-signal. In its turn, the L2 intensity is 3 dB lower than that of L1. The structure of the P-code is described in open GPS documents. It is formed as a symbol-wise modulo 2 sum of two very long binary sequences differing in length by 37 chips. The resulting period of the sequence thus formed is around 266 days. The non-overlapping 7-day (6:187104 1012 chips) segments of this sequence are used as P-codes for different satellites. The USA Department of Defense commissioned the designers of GPS to make provision for strict limitation of access to the P-code, reckoning that unauthorized usage of it may be hazardous to national security. Encryption of the P-code is realized by its modulo 2 summation with a masking or key W-code, whose structure is secret. The resulting Y-code possesses excellent cracking resistance (see Example 3.3.1).

11.2.3 Signal processing

The basic operations of a single-frequency (L1) GPS receiver are very conventional for any DS spread spectrum system. After a coarse acquisition of a satellite C/A-signal (see Sections 8.2 and 8.3), aided when possible by a priori knowledge of satellite locations, the code delay-lock loop (Section 8.4) is locked and starts to output a sequence of estimations of a satellite pseudo-range. Typically, modern GPS receivers include a set of channels processing in parallel the C/A-signals of all visible satellites. On finishing the search for the last used satellite, the receiver is ready to produce the user’s coordinates, which is a steady-state process lasting for as long as the user wishes.

The authorized receiver repeats the same operations for the P-codes of both carriers, spending only a little time on searching the signals, since the data frame available from the L1 signal contains a special handover word which facilitates setting the local generator of the P-code to an appropriate initial state.

In many modern GPS receivers these basic operations are supplemented or replaced by a variety of others pursuing improvements of accuracy, speeding up of the initial fixing time, consumer convenience etc. For example, additional accuracy may be gained by measuring pseudo-ranges via integration of the carrier frequency of the received signal. The instantaneous Doppler frequency shift is proportional to the radial speed of the satellite relative to a user. Hence, the integral of the Doppler frequency over some period is proportional to variation of the satellite–user distance over this time interval. Having started from the point with precisely known coordinates, the receiver may further position itself via integrals of instantaneous frequencies of visible satellites, i.e. their current accumulated ranges. Moreover, methods of ambiguity resolution exist, making possible positioning through frequency integrals even without initialization at a known point [117,118].

Another hugely popular operational technique is so-called differential or relative positioning, the idea of which is as follows. Let one GPS receiver be set up at the reference site (base) with precisely known coordinates. Then comparing pre-computed satellite ranges with the measured ones, the base receiver can find systematic errors (biases) inserted by system imperfection. Let another receiver be placed at a remote

point with unknown coordinates. If the baseline, i.e. the distance between the base and remote receivers, is not very long (e.g. within tens of kilometres) the systematic errors at the base and remote sites are strongly correlated, so the remote receiver may subtract biases estimated by a base receiver from measured ranges, improving their accuracy. Of course, such system modification should contain a communication link providing delivery of base-receiver data to the remote receivers. A vast number of reference sites are now arranged all over the world, transmitting differential corrections via FM stations, broadcasting satellites, radio beacons, cellular radio, Internet etc. [117,118].

11.2.4 Accuracy

The originally planned precision of C/A-code GPS positioning was set up around 100 m in the horizontal and 156 m in the vertical directions, the probability of keeping errors within these limits being 95%. Analogous figures for the P-code fixing were 16 m and 23 m, respectively. However, numerous advanced receiver structures developed by manufacturers have exhibited much better precision even without involving the P-code. This became a matter of anxiety for the US institutions responsible for national security, and in 1990 a selective availability mode was introduced, distorting satellite-transmitted ephemeris and timing and thereby deliberately corrupting positioning accuracy. During the subsequent decade, however, differential navigation, which eliminates these types of errors almost entirely, gained great popularity, so the selective availability mode turned out to be pointless in practice and was terminated in 2000. Nowadays a wide spectrum of offers is characteristic of the GPS equipment market, with proclaimed accuracies ranging from tens of metres to several millimetres and better.

11.2.5 GLONASS and GNSS

The Russian space-based navigation system GLONASS has many common features with GPS. Its space segment consists of 24 satellites located in 3 nearly circular orbits with nominal sidereal period 11 hours 15 minutes and 64.8 inclination to the equator. Again, two frequencies L1 and L2 (respectively in the 1.5 and 1.2 GHz bands) are used to provide ionospheric correction, with C/A-code transmitted on L1 and P-code transmitted on both carriers. Current ephemeris and other relevant data encoded by Hamming code and properly arranged into subframes and frames are superimposed onto ranging codes in a DS manner and transmitted by satellites at the rate 50 bps. A control segment provides continuous monitoring of satellites, computation/prediction of their orbit parameters and uploading them to the satellite onboard memory.

The substantial difference between GLONASS and GPS is that all satellites transmit the same C/A-code, which is a binary m-sequence of length N ¼ 511 with real-time period 1 ms. Distinguishing individual satellite signals is possible due to the small mutual carrier offsets between them, transforming the common C/A code into an ensemble of frequency-offset replicas of the m-sequence, as described in Section 7.5.1. In order to save bandwidth antipodal satellites of the same orbit (which are never seen by a user simultaneously) employ the same frequency offset.