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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 is the position vector of the receiver, δt_r is the receiver’s clock bias, and c is the speed of light. Similarly, the state of the i‐th BTS is defined as , where is the position vector of the i‐th BTS, and is its clock bias. The pseudorange measurement to the i‐th BTS, ρ_i, can be expressed as

(38.3)

where and v_i is the measurement noise, which is modeled as a zero‐mean Gaussian random variable with variance [27]. The following sections outline the calculations associated with each navigation framework assuming pseudorange measurements from cellular towers. Frameworks with carrier phase measurements are discussed in [43].