Real-time GNSS attitude determination by a direct approach with efficiency and robustness

Abstract

Estimating attitude directly from multi-antenna carrier phase measurements is known as the direct approach of global navigation satellite system attitude determination. Without the process of resolving baseline vectors in advance, this approach makes full use of raw observations. However, the known baseline constraints would be missing when the least squares method is used in the direct approach, of which the corresponding model contains no baseline parameter. The constraint information is important for real-time ambiguity resolution. Therefore, we propose using an adaptively robust Kalman filter for the direct approach, in which the predicted attitude plays the role of an attitude constraint. An observation model parameterized by the multiplicative quaternion error vector and the integer ambiguities is derived, accompanied with a state model consisting of the quaternion error vector, the ambiguities and the angular rate. Since the state vector contains three different types of parameters, the filter uses an adaptive matrix consisting of different adaptive factors instead of a single factor. The factor of the quaternion error vector is determined by a three-section function containing the ratio value from the ratio-test of ambiguity resolution. The factors of the ambiguities are calculated by the detected cycle slip. The equivalent weight matrix of the filtering can resist the influence of outliers in harsh environment. By the direct approach with the proposed adaptively robust filtering, the accuracy of the float solution and the variance-covariance matrix are significantly improved, and the ambiguity can be efficiently searched and fixed using the standard least-squares ambiguity decorrelation adjustment method. The proposed algorithm is suitable for real-time applications since no time-consuming and complex searching of ambiguity resolution is required. Finally, the efficiency and robustness of the algorithm is validated by a field test.