Positioning System Signals

In this paper, a new algorithm is developed for attitude estimation using Global Positioning System (GPS) signals. The new algorithm is based on a predictive filtering scheme designed for spacecraft without rate measuring devices. The major advantage of this new algorithm over traditional Kalman filter approaches is that the model error is not assumed to represented by an unbiased Gaussian noise process with known covariance, but instead is determined during the estimation process. This is achieved by simultaneously solving system optimality conditions and an output error constraint. This approach is well suited for GPS attitude estimation since some error sources that contribute to attitude inaccuracy, such as signal multipath, are known to be nonGaussian processes. Also, the predictive filter scheme can use either GPS signals or vector observations or a combination of both for attitude estimation, so that performance characteristics can be maintained during periods of GPS attitude sensor outage. The performance of the new algorithm is tested using flight data from the REX-II spacecraft. Results are shown using the predictive filter to estimate the attitude from both GPS signals and magnetometer measurements, and comparing that solution to a magnetometer-only based solution. Results using the new estimation algorithm indicate that GPS-based solutions are verified to within 2 degrees using the magnetometer cross-check for the REX-II spacecraft. GPS attitude accuracy of better than 1 degree is expected per axis, but cannot be reliably proven due to inaccuracies in the magnetic field model. Introduction The concept of using phase difference measurements from GPS receivers for three-axis attitude determination has been successfully proven on many systems in the past [1-3]. However, to this date only a handful of these experiments have been tested on spacecraft. One of the first space-based applications was flown on the RADCAL (RADar CALibration) spacecraft [4], which demonstrated GPS attitude determination using post-processed measurements. To obtain maximum GPS visibility, and to reduce signal interference due to multipath reflection, GPS patch antennas were placed on the top surface of the spacecraft bus. Although the antenna baselines were short for attitude determination, attitude accuracy of about 2 degrees per axis 3σ was achieved for a 0.67 meter antenna separation. Another experiment, Crista-SPAS [5], provided the first on-orbit demonstration of real-time attitude determination. The spacecraft contained an accurate gyro reference, but the coordinate frame alignment was not measured relative to the GPS attitude reference frame, which means that discrepancies between the two reference frames might account for slightly different measurements from the two systems. Over the course of the experiment the two sets of attitude solutions agreed to within 2 degrees, which is thought to be within the alignment tolerance of the two