A Lower Bound for the Error Covariance of Radio SLAM with Terrestrial Signals of Opportunity

Alexander A. Nguyen, Zeinab Shadram, and Zaher M. Kassas

Abstract: A lower bound for the error covariance of radio simultaneous localization and mapping (SLAM) with terrestrial signals of opportunity (SOPs) is derived. The following problem is considered. An unmanned aerial vehicle (UAV) equipped with an on-board receiver extracts psuedorange measurements from SOP towers with unknown emitter positions and SOP towers with known emitter positions. Each SOP tower contains dynamic, stochastic clock error states (bias and drift). An extended Kalman filter (EKF) is employed to fuse the psuedorange measurements to simultaneously localize the UAV and SOP towers, together with estimating the difference between the receiver’s and each SOP’s clock bias and clock drift terms. It is shown that the so-called radio SLAM base case is observable, in which a UAV with imperfect knowledge about its initial states is navigating in an environment containing one unknown SOP tower and two partially known SOP towers (i.e., towers whose position are known, but clock bias and drift states are unknown). A lower bound on the EKF estimation error covariance matrix is derived and demonstrated numerically. Monte Carlo simulation results are presented demonstrating the derived lower bound for a UAV navigating in a radio SLAM fashion without global navigation satellite systems (GNSS) signals. Experimental results are presented for a UAV with an initial estimate of its position making pseudorange measurements to two partially known and one unknown cellular SOP. The UAV achieves a two-dimensional (2-D) position root-mean squared error (RMSE) of 10.76 m over a trajectory of 600 m.
Published in: Proceedings of the 34th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2021)
September 20 - 24, 2021
Union Station Hotel
St. Louis, Missouri
Pages: 2294 - 2306
Cite this article: Nguyen, Alexander A., Shadram, Zeinab, Kassas, Zaher M., "A Lower Bound for the Error Covariance of Radio SLAM with Terrestrial Signals of Opportunity," Proceedings of the 34th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2021), St. Louis, Missouri, September 2021, pp. 2294-2306.
https://doi.org/10.33012/2021.18100
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