Single-Point Positioning with Altitude Constrains: A Hard Constrain and a Weighted Constrain

Abstract

AbstractAccuracy and robustness of positioning are key factors in modern global navigation satellite system (GNSS) applications. Pseudo ranging Single-Point Positioning (SPP) utilizes the pseudo-range observations from satellites to achieve highly robust meter-level positioning accuracy with a single receiver. However, this precision does not satisfy the requirements of some modern applications. Pre-obtained receiver altitude data is used in this study to develop a new altitude-constrained SPP algorithm for positioning scenarios that require sub-meter accuracy and high robustness. The altitude constraint is first incorporated into the SPP model in the form of a quadratic equality, which expands the existing unconstrained least-squares (LS) algorithm to a quadratic equality constrained one, which is well-suited to positioning scenes where priori altitude information is obtainable. By further considering a priori altitude information with a certain error, the LS algorithm can be improved by taking the altitude and variance of its measurement error as a constraint condition, then constructing a weighted altitude constraint SPP algorithm. Experimental data results are utilized to validate the proposed algorithm. Compared to the traditional unconstrained SPP approach, the positioning performance of the altitude-constrained SPP method is significantly improved to the point of sub-meter level positioning accuracy.KeywordsGlobal navigation satellite systemPseudo-range single-point positioningLeast squares with quadratic equality constraintsAltitude constraint