Constrained total least-square solution for GPS compass attitude determination

Abstract

GPS compass attitude determination problem has been solved by using least-square (LS) approach conventionally. However, in this problem carrier phase measurement noises affect both system matrix and observation vector and total least-square (TLS) technique, which is a generalized least-square method to solve an over-determined set of equations whose coefficients are noisy, is more appropriate for this problem. By using the relationship between the carrier phase noise and the resulting baseline displacement vector error, the system matrix error and the observation vector error are shown to be linear correlated, and this relationship is utilized to formulate the problem as a constrained total least-square (CTLS) problem. Iterative technique based on Newton’s method is utilized to solve for the unknown initial baseline vector in the resulting nonlinear optimization problem. An integrity check criterion is proposed to determine if the estimated integer ambiguities have converged to the true values. Simulation results show that the CTLS solution converges faster and has smaller error than LS solution.