Toward massive satellite signals of opportunity positioning: Challenges, methods, and experiments

In a research article recently published in Space: Science & Technology, researchers from Chinese Academy of Military Science, Tsinghua University, and Beihang University together work on how to figure out an applicable receiver position from the signals transmitted by anonymous satellites with unknown emission time and present their recent progress on SSOOP.

First, authors summarize the challenges to be solved to achieve a best SSOOP. The downlink beam of a communications satellite can be either wide or directional. As illustrated in Fig. 1, the downlink beam patterns of satellites can be divided into single wide beam, satellite fixed multiple beams, user fixed multiple beams, and hybrid beams. All the satellite signals, from either a wide beam or a directional beam, can potentially be used for SSOOP. Certain signals include the satellite ID, beam ID, and even the satellite’s rough position. Theses frames are called “key frames” for identifying a satellite in SSOOP. The challenges to be solved to achieve a best SSOOP can be summarized as follows:

• Satellite orbit prediction: Obtaining the position P_k^s,i and the velocity V_k^s,i of the ith satellite at a given epoch k when the satellites are non-GNSS, noncooperative satellites.
• Signal processing for measurements: Signal processing to obtain a best measurement z_kⁱ of the ith satellite, thus to construct equations for frequency difference of arrival (FDoA).
• Machine learning for satellite identification: Identifying that current received satellite signal is transmitted by the given ith non-GNSS, noncooperative satellite of a given constellation. Since the format of the key frames is not known, a machine learning framework is required to analyze the large volumes of received data from the key frames and identify the bits that contain the satellite’s ID.
• Working out user position: Working out the state of the user by solving the state evolution and the measurement equation. In many cases, it means to combine satellite measurements with other sources of PNT. For example, the user velocity V_u = [v_x^u, v_y^u, v_z^u] can be first determined by an odometer and a direction finder, and then the user position can be worked out by Doppler measurements.

Then, a set of methods for SSOOP are proposed, including orbit predication, signal processing for measurements, machine learning for satellite identification, and different modes of user positioning. The orbit prediction flow based on empirical accelerations is shown Fig. 2. The orbit determination results and the deterministic dynamic models are used via a reduced dynamics batch least square process to obtain initial states and the empirical accelerations. Empirical accelerations are then modeled using a Fourier series through a fitting process. The initial states, the deterministic dynamic models, and the empirical accelerations in Fourier series are used together to do orbit extrapolation for orbit predication results. The non-GNSS satellite signal processing for measurements involves signal acquisition and Doppler estimation. Signal acquisition process is to capture the key frames in non-GNSS satellite signals and Fig. 3 gives a general flow for signal detection. The coarse Doppler can be estimated by searching the peak amplitude of a fast Fourier transform before match filtering. Satellite identification is done by some reference nodes that have known positions. Satellite identification process is to find the unique bits that do not change over time in the key frame for a given satellite, which is also called satellite ID. The user positioning mode can be divided into standalone mode and differential mode. In standalone mode, a user node has no common view of any satellite signals with any reference nodes. It just receives satellite signals and the reference information about the satellites’ orbits to work out a position. In differential mode of positioning, a reference node and the user node are roughly time-synchronized, and they simultaneously receive the key frames transmitted by non-GNSS satellites. The reference node communicates key frame information to the user node for positioning. The differential mode of positioning is more accurate than the standalone mode in terms of positioning precision and more robust.

Finally, an IRIDIUM SSOOP receiver prototype is designed for verifying the proposed methods and tested for corroborating the analysis. The receiver prototype receives the signals from broadcast channels, the ring alert channel, and message channels of the IRIDIUM mobile communication satellite system to figure out its own position. The hardware of the IRIDIUM SSOOP receiver prototype is given in Fig. 4. As is shown, a GNSS active antenna is redesigned to support IRIDIUM signal reception. A commercial-off-the-shell (COTS) software-defined radio (SDR) platform (from http://www.sdrai.cn) was used for running the signal processing and positioning algorithms, and a laptop computer is used for running host software that display the final results. The SDR platform has an SDR front end to receive IRIDIUM signals, a Xilinx Zynq 7045 FPGA for computation, and a USB 3.0 port and Ethernet for interfacing with the host computer. As for algorithm implementation, the signal processing flow given in Fig. 3 is used and implemented by the programmable logic part of the Zynq 7045 FPGA To acquire the incoming IRIDIUM signal burst. For Doppler frequency estimation, a whole frame-based estimation algorithm is adopted. For figuring out user position, a three-dimensional (3D) Doppler positioning algorithm is used. Both the Doppler estimation algorithm and the Doppler positioning algorithm are implemented by the programmable system of the Zynq 7045 FPGA of Fig. 4. The performance of the IRIDIUM SSOOP receiver prototype is given in Fig. 8. The receiver can uniquely identify passing IRIDIUM satellites and showed a standalone mode CEP ≈ 892 m and a differential mode CEP ≈ 40 m in the stationary tests. The test results indicate that the TLE orbit prediction error is the main source of user positioning error. In future, for improved SSOOP positioning, private orbit determination and prediction, either by active or passive observations, is required to improve the precision of orbit prediction.