I n attitude determination using the unit quaternion representation, the unit norm constraint results in singularity of thc covariancc matrix using classical filtering methods. To cope with this problem, a constrained filtering method is developcd. In this method, the constraint equations and the state equations are trcated as pscudo-iiieasLireiiient equations, so that they can be processed simultaneously with the rcal measurement equations. To illustrate thc application of the proposed scheme, a sccnario using GPS aiid gyro to pcrform attitudc determination is considcrcd. Software simulations show that the proposed scheme is sound, effcctive, and superior to existing methods.

In this paper, a maximum-likelihood-based (MLbased) filter is proposed for attitude determination via the GPS carrier phase observables. The quaternion representation is adopted here to describe the attitude. Hence, the norm constraint on the quaternion should be considered. The ML estimation with Lagrange multipliers can be used to consider simultaneously the evolution equation and the constraint, and to minimize the error covariance matrix. The attitude determination via GPS carrier phase observables is fulfilled in two steps. The first step is the GPS carrier phase ambiguity resolution. After the integer ambiguities being fixed, the ML-based filter is used to determine the optimal attitude. The advantage of adopting the quaternion as the state vector to describe the kinematic behaviors is that no singular problems arise. To verify our algorithm, the simulation has been conducted. In the simulation, the white noises are added on the carrier phase observables to assess the performance of the proposed method. The body frame is formed by three non-colinear GPS antennae which are mounted on a platform with two aluminum bars representing the baseline vectors. According to the simulation, our method is sound and effective.

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A baseline rotation method is proposed for determining the direction of the baseline vector via Global Positioning System (GPS) carrier phase measurements. The space difference technique is adopted to resolve GPS carrier phase cycle ambiguities. Possible applications include the determination of the aiming directions of artillery rockets and the line of sights of tracking radars, etc. For such armaments, the direction findings are important and the rotating mechanisms are well equipped already. A general baseline vector which can be rotated on a two-degree-of-freedom platform is considered first. The relationship among the baseline vector and the two rotation axes is not known. A sequence of rotations is used to change the configuration of the system to find the direction of the baseline. Under different circumstances such as the cases that some orthogonal conditions among the unknown vectors are given, simplified algorithms are devised. To verify our method, software simulation and hardware experiments have been conducted. The simulation outcomes are used to determine the experimental parameters, such as the length of the baseline, the rotation angles etc. The results of repeated hardware experiments show that the sample standard deviation for the azimuth angle and the elevation angle of the 1.35 m baseline vector are 0.91 deg and 1.23 deg, respectively. The GPS receivers employed are Motorola ONCOREs. The errors of the estimated direction angles induced by the inaccuracy of rotation angles, which are unavoidable due to the imperfectness of the mechanical structure, are analyzed as well. Numerical examples for the error analysis are included.

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