rel="nofollow" href="#ulink_649f9b26-22c7-561e-bd7e-c3c3cfa60133">Figure 38.2.
The clock error states evolve according to
Figure 38.2 Clock error states dynamics model.
Source: Z. Kassas, Analysis and synthesis of collaborative opportunistic navigation systems, Ph.D. Dissertation, The University of Texas at Austin, USA, May 2014. Reproduced with permission of Z. Kassas (University of Texas at Austin).
where the elements of
Discretizing the dynamics (Eq. (38.1)) at a sampling interval T yields the discrete‐time‐equivalent model
where
Table 38.2 Typical h0 and h−2 values for different OCXOs [36]
Source: J. Curran, G. Lachapelle, and C. Murphy, “Digital GNSS PLL design conditioned on thermal and oscillator phase noise,” IEEE Transactions on Aerospace and Electronic Systems, vol. 48, no. 1, pp. 180–196, January 2012.
| h 0 | h −2 |
|---|---|
| 2.6 × 10−22 | 4.0 × 10−26 |
| 8.0 × 10−20 | 4.0 × 10−23 |
| 3.4 × 10−22 | 1.3 × 10−24 |
38.4 Navigation Frameworks in Cellular Environments
BTS positions can be readily obtained via several methods, for example, (i) from cellular BTS databases (if available) or (ii) by deploying multiple mapping receivers with knowledge of their own states, estimating the position states of the BTSs for a sufficiently long period of time [37–39]. These estimates are physically verifiable via surveying or satellite images. Unlike BTS positions, which are static, the clock error states are stochastic and dynamic, as discussed in Section 38.3, and are difficult to verify.
Estimating the BTSs’ states can be achieved via two frameworks:
Mapper/NavigatorThis framework comprises (i) receiver(s) with knowledge of their own states, referred to as mapper(s), making measurements on ambient BTSs (e.g. pseudorange and carrier phase). The mappers’ role is to estimate the cellular BTSs’ states. (ii) A receiver with no knowledge of its own states, referred to as the navigator, making measurements on the same ambient BTSs to estimate its own states, while receiving estimates of the BTSs’ states from the mappers.
Radio SLAMIn this framework, the receiver maps the BTSs simultaneously with localizing itself in the radio environment.
To make the estimation problems associated with the above frameworks observable, certain a priori knowledge about the BTSs’ or receiver’s states must be satisfied [27, 40–42]. For simplicity, a planar environment will be assumed, with the receiver and BTS three‐dimensional (3D) position states appropriately projected onto such a planar environment. The state of the receiver is defined as
where
