Precision point positioning with additional baseline vector constraint

Abstract

<jats:title>Abstract</jats:title><jats:p>Traditional precise point positioning (PPP) based on undifferenced ionosphere-free linear combination of observations has many advantages such as high accuracy and easy operation. PPP usually uses the Kalman Filter (KF) to estimate state vector. However, the positioning performance depends on the accuracy of the kinematic model and initial value. The inaccurate kinematic model or initial value will lead to filter performance degradation or even divergence. To overcome this problem, this paper proposes a PPP method with an additional baseline vector constraint, which uses the direction information and length information of the baseline to correct the estimated position of the receiver. By reducing the error covariance matrix of the float solution, the algorithm improves the accuracy of the float solution. By using the collected real GPS static and kinematic data, the performance of the traditional model and the proposed model in this paper are compared. It is shown that the additional baseline vector constraint improves the PPP solution effectively in comparison with that of traditional PPP model. Additionally, the contribution of the additional constraint is up to the accuracy of the prior information.</jats:p>

Retrieving Accurate Precipitable Water Vapor Based on GNSS Multi‐Antenna PPP With an Ocean‐Based Dynamic Experiment

“…where 𝐴𝐴 [Δ𝑋𝑋12 Δ𝑌𝑌12 Δ𝑍𝑍12] 𝑇𝑇 moving−baseline is the baseline vector coordinates from station 1 to 2, which can be precisely determined using GNSS relative positioning with the moving-baseline mode (Takasu, 2013) in a real-time manner. Previous studies use nonlinear constraints of known baseline length or direction, where linearization errors may lead to estimation performance degradation or even divergence, especially for very short baselines (Chen et al, 2020;Guan et al, 2021). By contrast, the baseline vector constraint of Equation 2 presented in this study is more advantageous because it contains full baseline information and is free from any linearization errors.…”

“…The baseline vector constraint can be expressed as: $$${\left[\begin{array}{l}{\Delta }{X}_{12}\\ {\Delta }{Y}_{12}\\ {\Delta }{Z}_{12}\end{array}\right]}_{\mathrm{m}\mathrm{o}\mathrm{v}\mathrm{i}\mathrm{n}\mathrm{g}-\mathrm{b}\mathrm{a}\mathrm{s}\mathrm{e}\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}=\left[\begin{array}{l}{X}_{2}-{X}_{1}\\ {Y}_{2}-{Y}_{1}\\ {Z}_{2}-{Z}_{1}\end{array}\right]$$$ where $${\left[{\Delta }{X}_{12}\,{\Delta }{Y}_{12}\,{\Delta }{Z}_{12}\right]}_{\mathrm{m}\mathrm{o}\mathrm{v}\mathrm{i}\mathrm{n}\mathrm{g}-\mathrm{b}\mathrm{a}\mathrm{s}\mathrm{e}\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}^{T}$$ is the baseline vector coordinates from station 1 to 2, which can be precisely determined using GNSS relative positioning with the moving‐baseline mode (Takasu, 2013) in a real‐time manner. Previous studies use nonlinear constraints of known baseline length or direction, where linearization errors may lead to estimation performance degradation or even divergence, especially for very short baselines (Chen et al., 2020; Guan et al., 2021). By contrast, the baseline vector constraint of Equation presented in this study is more advantageous because it contains full baseline information and is free from any linearization errors.…”

“…Compared to traditional PPP, multi‐antenna PPP can incorporate additional constraints of known baseline vector and common tropospheric delay for closely spaced antennas. By incorporating these constraints, multi‐antenna PPP is expected to shorten the convergence time and improve the accuracy of estimated parameters including positioning coordinates and zenith wet delay (ZWD) (Chen et al., 2020; Guan et al., 2021; Teunissen, 2012).…”