access icon free GNSS attitude determination method through vectorisation approach

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° 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°.

Inspec keywords: vectors; Newton method; satellite navigation; covariance matrices; nonlinear functions; least squares approximations

Other keywords: RMSE; baseline vector estimation; visible satellites; least-squares method; estimation error extraction; direction cosine matrix; roll-pitch-yaw angle estimation; global navigation satellite system carrier signals; vectorisation approach; standard-deviation; Gibbs vector; GNSS attitude determination method; root mean squared error; analytical approach; error attitude; variance covariance matrix; estimated free matrix; Gauss-Newton iteration algorithm; carrier measurements; DCM estimate extration; measurement model; nonlinear function

Subjects: Radionavigation and direction finding; Interpolation and function approximation (numerical analysis); Nonlinear and functional equations (numerical analysis)

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