Ill-conditioned GPS compass attitude determination using regularization approach

A new robust motion-based GPS compass attitude determination method is proposed. For vehicles traveling on horizontal surfaces, ill-conditions in matrix inversion often appears in the attitude determination process when using the least square approach and the proposed method is particularly useful in these situations. As a result, noise in the measurement will be amplified leading to unacceptable results in the singular direction in the traditional least square solution. A regularized least square method based on Tikhonov regularization is proposed in this paper to address this problem. By adding a regularization (penalty) term proportional to the desired solution norm in the system minimization cost function, the original ill-conditioned matrix can be replaced by a better-conditioned one to alleviate the perturbations in the solution and produce a regularized solution to the original problem. An error analysis that compares the errors of least square solution and regularized least square solution based on mean square error criterion is presented. It is shown that with an appropriate choice of regularization parameter, regularized least square method effectively reduces the mean square error when compared with the least square method. An algorithm based on baseline length constraint is proposed to select an optimal regularization parameter for regularization. Simulations and experiments are conducted to verify the validity of the proposed method. The results revealed that the accuracy of the regularized least square solution is better than the traditional least square solution based on mean square error criteria for comparison.