alt="equation"/>

      where is a discrete‐time zero‐mean white noise sequence with covariance Q = diag [Q_pv, Q_clk]. Defining and to be the power spectral densities of the acceleration in the x− and y− directions, Q_pv and Q_clk are given by

where and correspond to the receiver’s and the i‐th BTS clock process noise covariances, respectively, specified in Eq. (38.2). Formulations of other more sophisticated radio SLAM scenarios are discussed in [27, 29, 41].

      Note that in many practical situations, the receiver is coupled with an inertial measurement unit (IMU), which can be used instead of the statistical model to propagate the estimator’s state between measurement updates from BTSs [44, 45]. This is discussed in more detail in Section 38.9.

38.5 Navigation with Cellular CDMA Signals

      To establish and maintain a connection between cellular CDMA BTSs and the UE, each BTS broadcasts comprehensive timing and identification information. Such information could be utilized for PNT. The sequences transmitted on the forward link channel, that is, from BTS to UE, are known. Therefore, by correlating the received cellular CDMA signal with a locally generated sequence, the receiver can estimate the TOA and produce a pseudorange measurement. This technique is used in GPS. With enough pseudorange measurements and knowing the states of the BTSs, the receiver can localize itself within the cellular CDMA environment.

      This section is organized as follows. Section 38.5.1 provides an overview of the modulation process of the forward link channel. Section 38.5.2 presents a receiver architecture for producing navigation observables from received cellular CDMA signals. Section 38.5.3 analyzes the precision of the cellular CDMA pseudorange observable. Section 38.5.4 shows experimental results for ground and aerial vehicles navigating with cellular CDMA signals.

      38.5.1 Forward Link Signal Structure

      Cellular CDMA networks employ orthogonal and maximal‐length pseudorandom noise (PN) sequences in order to enable multiplexing over the same channel. In a cellular CDMA communication system, 64 logical channels are multiplexed on the forward link channel: a pilot channel, a sync channel, 7 paging channels, and 55 traffic channels [46]. The following sections discuss the modulation process of the forward link and give an overview of the pilot, sync, and paging channels from which timing and positioning information can be extracted. Models of the transmitted and received signals are also given.

      38.5.1.1 Modulation of Forward Link CDMA Signals

The data transmitted on the forward link channel in cellular CDMA systems is modulated through quadrature phase shift keying (QPSK) and then spread using direct‐sequence CDMA (DS‐CDMA). However, for the channels of interest from which positioning and timing information is extracted, the in‐phase and quadrature components, I and Q, respectively, carry the same message m(t) as shown in Figure 38.4. The spreading sequences c_I and c_Q, called the short code, are maximal‐length PN sequences that are generated using 15 linear feedback shift registers (LFSRs). Hence, the length of c_I and c_Q is 2¹⁵ − 1 = 32, 767 chips at a chipping rate of 1.2288 Mcps [47]. The characteristic polynomials of the short code I and Q components, P_I(D) and P_Q(D), are given by

      where D is the delay operator. It is worth noting that an extra zero is added after the occurrence of 14 consecutive zeros to make the length of the short code a power of two.

In order to distinguish the received data from different BTSs, each station uses a shifted version of the PN codes. This shift is an integer multiple of 64 chips, and this integer multiple, which is unique for each BTS, is known as the pilot offset. The cross‐correlation of the same PN sequence with different pilot offsets can be shown to be negligible [46]. Each individual logical channel is spread by a unique 64‐chip Walsh code [48]. Therefore, at most 64 logical channels can be multiplexed at each BTS. Spreading by the short code enables multiple access for BTSs over the same carrier frequency, while orthogonal spreading by the Walsh codes enables multiple access for users over the same BTS. The CDMA signal is then filtered using a digital pulse shaping filter that limits the bandwidth of the transmitted CDMA signal according to the cdma2000 standard. The signal is finally modulated by the carrier frequency ω_c to produce s(t).

Figure 38.4 Forward link modulator (Khalife et al. [18]).

      Source: Reproduced with permission of IEEE.

      38.5.1.2 Pilot Channel

      The message transmitted by the pilot channel is a constant stream of binary zeros and is spread by Walsh code zero, which also consists of 64 binary zeros. Therefore, the modulated pilot signal is nothing but the short code, which can be utilized by the receiver to detect the presence of a CDMA signal and then track it. The fact that the pilot signal is data‐less allows for longer integration time. The receiver can differentiate between the BTSs based on their pilot offsets.

      38.5.1.3 Sync Channel

The sync channel is used to provide time and frame synchronization to the receiver. Cellular CDMA networks typically use GPS as the reference timing source, and the BTS sends the system time to the receiver over the sync channel [49]. Other information such as the pilot PN offset and the long code state are also provided on the sync channel [47]. The long code is a PN sequence and is used to spread the reverse link signal (i.e. UE to BTS) and the paging channel message. The long code has a chip rate of 1.2288 Mcps and is generated using 42 LFSRs. The outputs of the registers are masked and modulo‐two added together to form the long code. The latter has a period of more than 41 days; hence, the states of the 42 LFSRs and the mask are transmitted to the receiver so that it can readily achieve long code synchronization. The sync message encoding before transmission is shown in Figure

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