标题：GNSS attitude determination method through vectorisation approach
作者：Chang, Guobin; Xu, Tianhe; Wang, Qianxin; Li, Shengquan; Deng, Kailiang
作者机构：[Chang, Guobin; Wang, Qianxin] China Univ Min & Technol, Sch Environm Sci & Spatial Informat, Xuzhou 221116, Peoples R China.; [Chang, Guobin; Xu, T 更多
通讯作者地址：[Chang, GB]China Univ Min & Technol, Sch Environm Sci & Spatial Informat, Xuzhou 221116, Peoples R China;[Chang, GB]Xian Res Inst Surveying & Mapping, 更多
来源：IET RADAR SONAR AND NAVIGATION
关键词：satellite navigation; vectors; Newton method; covariance matrices; least; squares approximations; nonlinear functions; GNSS attitude determination; method; vectorisation approach; global navigation satellite system; carrier signals; analytical approach; baseline vector estimation;; least-squares method; DCM estimate extration; estimated free matrix;; error attitude; Gibbs vector; measurement model; nonlinear function;; Gauss-Newton iteration algorithm; roll-pitch-yaw angle estimation;; variance covariance matrix; direction cosine matrix; estimation error; extraction; visible satellites; standard-deviation; carrier; measurements; root mean squared error; RMSE
摘要：Determining the attitude using GNSS carrier signals is studied. It features an analytical approach to get an estimate as initial guess for iterative algorithms, in three steps. First, baseline vectors are estimated by least-squares method. Second, the constraint of the direction cosine matrix (DCM) is ignored and the least-squares estimates of its 9 elements are solved. Third, a mathematically feasible DCM estimate is extracted from the above estimated free matrix. An error attitude, formulated using the Gibbs vector, is introduced to relate the previously estimated and the true attitude, and the measurement model becomes a nonlinear function of the Gibbs vector. The Gauss-Newton iteration is employed to solve the least-squares problem with this measurement model. The estimate of the roll-pitch-yaw angles and the variance covariance matrix of their estimation errors are extracted from the final solution. Numerical experiments are conducted. With 3 orthogonally mounted 3-meter baselines, 4 visible satellites, and 5-millimeter standard-deviation of the carrier measurements, the accuracy of the analytical solution can be less than 1 degrees in the root mean squared error (RMSE) sense. The convergence of the iteration is rather fast, the RMSE converges after only one iteration, with the converged RMSE less than 0.1 degrees.