# The Potential of LEO Satellite-Based Opportunistic Navigation for High Dynamic Applications
## 1 Introduction
In [6], positioning using Iridium signals in forest canopy is demonstrated. Experiments showed a height aided static positioning accuracy of a few hundred meters obtained with 30 min data. In [7], the authors showed that the satellite position accuracy, based on the Simplified Perturbation model (SPG4) fed with Two Line Element (TLE) files, can be as high as 3 km, and the velocity accuracy can be as high as 3 m/s. They showed that the two-body model using the second gravitational zonal coefficient J2 allows for a better satellite positioning, if a good initial satellite position is available. In [8], the authors presented a Doppler-based positioning using Ku-band Starlink signals. A 3D positioning better than 23 m was shown by the experiment in which the TLE epochs were adjusted to cope with the ephemeris errors. In [9], a Multi-Constellation Software-Defined Receiver was designed to measure the Doppler shifts of LEO SV downlink signals. The paper showed by means of the experiment the benefits of the multi-constellation (Orbcomm and Iridium systems) for the positioning. A multi-constellation LEO SV signal receiver was also presented in [10]. The demonstrated positioning accuracy is 22.7 m, obtained by assuming a known altitude of the user, and when up to four LEO SVs were tracked from Iridium and Orbcomm systems. In [11], the Doppler shift is measured on signals with orthogonal frequency-division multiplexing (OFDM) modulation, which is expected for the deployment of future LEO SV. Experiments using new 5G terrestrial radio signals showed an RMSE of 6.45 Hz in the estimation of the Doppler shift. In [12], a carrier phase-based positioning on LEO SV signals was designed. Then a 3D positioning accuracy of 33.5 m was achieved by the experiment using six Starlink SV signals. The synthesis of this existing work shows that the navigation is typically performed based on the Doppler shift measurement, which is a straightforward observable that can be obtained from a radio signal transmitter with a known carrier frequency. A first category of LEO SV-based navigation techniques uses only LEO SV signals. While the positioning is usually standalone, the differential mode involving two observers has also been explored. A second category performs the navigation based on the coupling between LEO SV and an INS (based on gyroscopes and accelerometers). In general, the tight coupling is considered due to the poor availability of the LEO SVs. In both categories, the navigation is either single- or multi-constellation (involving two or more LEO SV systems) and is eventually height-aided. These developments and similar work [13; 14; 15; 16] demonstrated the potential of LEO SV signals for the opportunistic positioning. In this work, we will address the following complementary tasks  
* Evaluate the potential of LEO SV SOP for a high dynamic vehicle with a short-duration mission. The short duration is expected to prevent achieving an optimal navigation performance. * Design a filter measurement model based on magnetometer outputs and LEO SV Doppler shift that allows for observing the position, velocity, attitude, and receiver clock bias and drift. * Use of representative Iridium data for performance simulation. Indeed, the Doppler shift measurements are obtained by processing Iridium-like signals by an Iridium signal-processing tool. These Doppler shift data are more representative than those obtained by simply adding an error distribution to the geometric Doppler shift between a satellite and a user terminal. * Evaluate the performance of attitude estimation in addition to that of positioning. Note that the attitude and especially the roll angle can be used to roll-rate stabilize the vehicle, and in guidance [17]. * Evaluate the influence of the individual error sources on Doppler-based navigation. The errors consist mainly of the satellite position and velocity errors, the satellite clock drift, and thermal noise. * Benchmark the performance of the system against an INS based on a tactical-grade IMU and magnetometers.