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A dynamic estimator, such as an extended Kalman filter (EKF), can be used in the radio SLAM framework for stand‐alone receiver navigation (i.e. without a mapper). Certain a priori knowledge about the BTSs’ and/or receiver’s states must be satisfied to make the radio SLAM estimation problem observable [27, 40–42].

To demonstrate a particular formulation of the radio SLAM framework, consider the simple case where the BTSs’ positions are known. Also, assume the receiver’s initial state vector to be known (e.g. from a GNSS navigation solution). Using the pseudoranges (Eq. (38.3)), the EKF will estimate the state vector composed of the receiver’s position and velocity as well as the difference between the receiver’s clock bias and each BTS and the difference between the receiver’s clock drift and each BTS, specifically

where ; δt_r and are the receiver’s and the i‐th BTS clock bias, respectively; and and are the receiver’s and the i‐th BTS clock drift, respectively.

Assuming the receiver to be moving with velocity random walk dynamics, the system’s dynamics after discretization at a uniform sampling period T can be modeled as

(38.4)

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.