Improved Single-Satellite Direct Position Determination Method via Real-Valued Space-Time Subspace Data Fusion

‍ ‍Direct position determination of radiation sources is an unpowered localization technique that estimates the position of radiation sources directly from the raw sampled signals. Direct localization of fixed radiation sources on the Earth’s surface using a single satellite has significant research value due to its high positioning accuracy and strong flexibility. However， traditional spatial subspace data fusion methods used for direct localization lack sufficient utilization of Doppler information， leading to inadequate positioning performance in single-satellite direct localization scenarios. Existing space-time subspace data fusion methods have improved positioning performance in such scenarios， but they still suffer from poor accuracy and resolution under low signal-to-noise ratio conditions. To address these issues， this study proposes an improved single-satellite direct localization method based on real-valued space-time subspace data fusion， enabling direct localization of multiple radiation sources with known elevation. First， the study establishes a space-time signal model based on the WGS-84 Earth ellipsoid model， incorporating both the arrival angles and Doppler frequencies， effectively utilizing the Doppler frequency shift information caused by the satellite’s relative high-speed motion with respect to the radiation sources. Subsequently， this study introduces the Toeplitz matrix adjustment method to block-adjust the covariance matrix of the received signals in the space-time signal model. Forward-backward smoothing and space-time subspace unitary transformation techniques are employed to obtain a real-valued space-time subspace. Subsequently， this paper combines space-time subspace data from multiple time slots to construct the cost function for localization and designs a numerator function based on the feature space concept to improve the cost function. The radiation source’s position is then estimated using a grid search method. Simulation results demonstrate that the proposed method outperforms the multiple signal classification （MUSIC） direct localization method， minimum variance distortionless response （MVDR） direct localization method， maximum likelihood （ML） direct localization method， and unitary space-time subspace data fusion （U-ST-SDF） method in low signal-to-noise ratio conditions， exhibiting superior positioning performance.