Precise UAV Navigation with Cellular Carrier Phase Measurements
Joe Khalife and Zak (Zaher) M. Kassas, University of California, Riverside
Signals of opportunity (SOPs) have shown their potential as an alternative navigation source to global navigation satellite systems (GNSS) in GNSS-challenged environments, e.g., in- doors, deep urban environments, and environments under intentional jamming and spoofing. Such signals include AM/FM radio signals , iridium satellite signals , cellular signals , digital television signals , and Wi-Fi signals . A number of experimental studies have demonstrated receiver localization and timing via SOPs on both ground vehicles and unmanned aerial vehicles (UAVs) [6, 7, 8, 9, 10].
Cellular signals, particularly code-division multiple access (CDMA) and long term evolution (LTE), are among the most attractive SOP candidates for navigation. These signals are abundant, received at a much higher power than GNSS signals, offer a favorable horizontal geometry, and are free to use. However, several challenges arise when using cellular signals for navigation, most notably the unavailability of: (1) appropriate signal models for optimal extraction of states and parameters of interest for navigation purposes, (2) published receiver architectures that are capable of producing navigation observables, and (3) rigorous error budgets and performance analyses under different error models. Recent research in navigation using SOPs addressed the first two challenges for cellular CDMA and LTE signals [8, 9, 11]. In order to deal with the unknown, dynamic, and stochastic nature of SOP clock errors, a mapping receiver was employed by  to estimate the SOP clock errors and share the estimates with the navigating receiver. Subsequently, errors inherent to cellular CDMA systems that are not harmful for communication purposes, but would severely degrade the navigation performance were detected in this mapper/navigator framework [12, 13]. These errors were characterized for code phase-based cellular pseudorange measurements.
Recently, the relative stability of cellular CDMA base transceiver station (BTS) clocks was characterized, revealing the potential for using cellular CDMA signals exclusively for precise navigation, without the need for a mapping receiver . This paper presents a comprehensive framework for precise UAV navigation with standalone cellular CDMA signals using carrier phase measurements. To this end, this paper: (1) models the relative stability of neighboring BTS clocks with cellular carrier phase measurements, (2) proposes a framework for mapping BTSs and navigating with cellular carrier phase, and (3) characterizes the mapping and navigation performances as a function of the relative BTS clock stability.
One important challenge to overcome when navigating with cellular signals is the unknown nature of the BTS positions and clock error states (namely, the bias and drift). Since cellular BTSs are spatially stationary, their positions may be mapped prior to using them for navigation. This can be achieved in one of several ways: (1) using the framework developed in , (2) through access to a BTS position database, or (3) via satellite imagery (e.g., Google Earth). Subsequently, it is reasonable to assume that the BTS positions are known. However, as mentioned earlier, BTS clocks are dynamic and stochastic and must be continuously estimated. If the receiver is navigating with cellular signals with unknown BTS clock errors, a dynamic estimator, such as an extended Kalman filter (EKF), must be employed to estimate for the BTS clock states. It was noted in  that while BTS clocks may not be perfectly synchronized to GPS, their clock bias is dominated by a common term. Motivated by these findings, the cellular carrier phase measurement is re-parameterized to leverage the relative stability of neighboring BTS clocks. The resulting pseudorange model consists of the sum of the true range, a common clock error term, the deviation from the common clock term, and the measurement noise. Preliminary experimental data indicate that the deviations from the common clock terms are stable processes, implying that these deviations will have bounded variances. This paper makes three contributions which are discussed next.
The first contribution is to rigorously model the deviations of the BTS clocks from the common term. System identification techniques are used to model these deviations as stochastic dynamic processes and sufficient statistics of the process noise will be identified. Moreover, experimental results over long periods of time validating the identified models will be presented. Next, the paper discusses how to estimate these statistics on-the-fly when the receiver has access to GNSS signals.
The second contribution is to optimally incorporate these models into static and dynamic estimators for mapping cellular BTSs and for navigating. The static estimator leverages the stable dynamics of these deviations and inflates the measurement noise covariance by the steady-state covariance of these deviations. Although this method is suboptimal, it allows the receiver to navigate without the help of a mapper, while using a simple estimator. Next, mapping BTSs and navigating using cellular carrier phase signals is discussed in an EKF framework. This method also alleviates the need of a mapper and optimally fuses cellular carrier phase measurements with the deviation models derived in the first part of the paper.
The third contribution is to characterize the mapping and navigating performance of the proposed framework with various a priori knowledge scenarios and for the static and dynamic estimators. In the first scenario, a receiver that has knowledge of its position and clock error states for a given period of time enters an unknown cellular SOP environment. Subsequently, the receiver characterizes the BTS clock deviations on-the-fly. At some point in time, the receiver loses access to GNSS and subsequently starts navigating exclusively using cellular signals. The expected navigation performance is characterized as a function of the statistics of the process noise driving the clock deviations. In the second scenario, the receiver does not have initial access to its position and clock error states, and therefore assumes a BTS clock deviation model that is not necessarily true. This will inherently introduce a model mismatch in the receiver’s estimator. The paper will analyze the effect of model mismatch between the true statistics of the process noise of the BTS clock deviations and the statistics assumed by the receiver on the navigation solution.
The clock deviation models will be validated experimentally. To this end, a universal software radio peripheral (USRP) will be used to simultaneously collect cellular CDMA and GPS signals over a period of 24 hours. The USRP will be driven by a GPS-disciplined oven-controlled crystal oscillator (OCXO) to obtain an accurate reading on the clock bias of neighboring BTSs. The cellular CDMA signals will then be processed, yielding carrier phase measurements that will be used to calculate the clock biases of neighboring BTSs. The mapping and navigation frameworks will also be validated experimentally. Therefore, a UAV will be equipped with a USRP and a cellular antenna to collect cellular CDMA signals. Experimental results for navigating with cellular CDMA carrier phase measurements from five BTSs over more than 3 Km and for more than 5 minutes demonstrate a total position root-mean-squared error (RMSE) of less than 1.2 m.
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