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Session C6: Terrestrial Signals of Opportunity-Based Navigation Systems

Low-SWaP GNSS-Denied Navigation Using LTE Signals of Opportunity with B-Spline Trajectory Estimation
Tyler Sweat, Michael Rice, Willie K. Harrison, and Randal W. Beard, Brigham Young University

Unmanned aerial vehicles rely heavily on accurate positional information from GNSS for autonomous missions. However, GNSS signals are vulnerable to jamming, and dead-reckoning with only inertial measurements quickly leads to drift, leaving the UAV without accurate positional information. To mitigate these limitations, recent work has focused on exploiting signals of opportunity, such as LTE cellular signals, for navigation.
In this paper, we present a method to generate navigation observables from terrestrial cellular signals using a low-cost, low-SWaP software defined radio. Given the hardware constraints, our approach differs from that of other leading signal-of-opportunity navigation research (e.g. Kassas). We extract the change in signal propagation time from a cell tower to the receiver, which we term a differential pseudorange. This differential pseudorange represents the range change between successive observations, capturing differential position changes over time. We combine these differential pseudorange measurements with inertial measurements to estimate the UAV’s trajectory. Since the LTE-based measurements are not synchronized with the IMU data, we use a moving horizon estimation technique and exploit the differential flatness of the system to model the state and input of the system with a low-order B-Spline of the flat output trajectory. This approach manages the asynchronous nature of the data effectively, and allows for the estimation of clock off-set and scaling parameters.
Differential Pseudorange
For this project, we are using the ADALM-PLUTO software-defined radio to receive LTE signals. This SDR has a maximum tunable channel bandwidth of 56 MHz which means only one LTE signal carrier frequency can be listened to at a time. Other LTE signal-of-opportunity navigation methods receive signals from many cells across a wide bandwidth to determine pseudorange measurements from the receiver to each cell. Given the limitations of the low-SWaP, low-cost SDR, we present an alternative approach. The receiver listens for a detected frame from a new cell and saves the frame start time to be used as a reference for subsequent frames. The reference time can be broken into the time of transmission from the cell tower plus the time of flight from the cell tower to the receiver. Without knowing the time of transmission for a frame, we can’t solve for the time of flight. As part of the LTE standard, cells transmit a frame every 10 ms. The start time of each frame after the reference can be broken down into the time of transmission for the reference frame plus an integer multiple of 10 ms plus the time-of-flight between the cell tower and the receiver’s new position. Taking the difference between the current and reference frame start times leaves the integer multiple of 10 ms plus a difference between the current and reference propagation times. We can easily remove the integer multiple of 10 ms by using the mod function. As the cell tower is in a fixed location, a change in propagation time between the current frame and the reference frame indicates a change in position for the receiver relative to the cell tower. We call this measurement the differential pseudorange.
Moving Horizon Estimation using B-Splines
We will assume that the mobile platform carrying the SDR is differentially flat. The history of the flat output trajectory over a look-behind window is represented by a B-Spline of an appropriate degree of continuity. Since B-Splines have closed-form derivatives, it is straightforward to relate the IMU data with functions of the position and derivative of the B-spline. We define a minimization problem, optimizing spline control points to reduce the error over a window of differential pseudorange and IMU measurements. The continuous nature of B-Splines accommodates asynchronous and out-of-sequence measurements, and clock mismatches. Since the B-spline control points affect only localized segments, the optimization can be performed in an efficient manner.
Hardware Limitations
One challenge of using low-cost SDRs is the instability of the reference clock, which affects the tuned carrier frequency and sampling rate. The standard oscillator in the ADALM-PLUTO SDR has a stability of 25 ppm, introducing timing errors. To address this, we developed a custom reference oscillator with a 0.05 ppm stability, improving timing accuracy and reducing oscillator-induced errors in the trajectory estimation.
Current Progress
We have implemented digital signal processing techniques to extract differential pseudorange measurements using the selected hardware. Fusion of IMU and differential pseudorange data using the B-Spline estimator has been tested in simulation. Ongoing work includes flight tests for real-world validation, using RTK-GPS data as ground truth.
Results
Preliminary simulation results indicate that the B-Spline estimator achieves an RMSE of about 11.5 m when using only IMU data. Incorporating differential pseudoranges improves the RMSE to about 2.1 m. The final submission will include flight test results with ground truth RTK-GPS data and estimated trajectories. We will evaluate two scenarios: (1) known LTE cell tower locations, and (2) unknown tower locations that require estimation.
In contrast to traditional LTE-based navigation methods requiring high-precision hardware, this study demonstrates an effective alternative with low-SWaP equipment. This approach offers a feasible starting point for further exploration of LTE signals of opportunity in navigation applications.

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