URTSFRLS: An LEO Positioning Method for Large Measurement Errors and High GDOP

In pseudorange positioning using Low Earth Orbit satellites, the Least Squares (LS) method suffers from degraded positioning accuracy and solution instability under the coupled influence of large measurement errors and a large Geometric Dilution of Precision. To address this problem, this paper proposes an Unscented Rauch-Tung-Striebel Fractional-order Regularization Least Squares (URTSFRLS) algorithm. The URTSFRLS algorithm employs the unscented transform to approximate the mean and covariance of the pseudorange vector, thereby improving linearization accuracy. Meanwhile, the URTSFRLS algorithm performs information fusion through backward smoothing and forward filtering to mitigate the effect of LS solutions falling into local extrema. Furthermore, following the idea of fractional-order regularization, regularization terms and fractional-order terms are introduced into the objective function of the LS positioning solution, alleviating the numerical ill-conditioning. Simulation results demonstrate that the URTSFRLS algorithm enhances both positioning accuracy and solution stability by improving linearization accuracy, mitigating LS trapping in local extrema, and alleviating ill-conditioning.