SINGLE-EPOCH, SINGLE-FREQUENCY, STANDALONE FULL ATTITUDE DETERMINATION: EXPERIMENTAL RESULTS

Attitude determination is the problem of estimating the orientation of an object with respect to a frame of reference. There exist a large number of sensors which can provide a platform attitude, such as gyroscopes, horizon scanners, horizon crossing indicators, sun sensors, star tracker, magnetometers. Already in the early years of the GPS utilization, it was proposed that the baseline observations obtained with two GPS antennae could be used as another valid instrument to perform attitude determination [1]. Although the precision of the GNSS measurements might be less accurate compared to some of the other available sensors, its use presents several advantages: it is driftless, it is virtually maintenance-free (depending only on an external source, the GNSS constellation), and it does not need any ground reference. In order to obtain accurate measurements of a platform attitude, the GNSS carrier phase observations must be employed, for which sub-degree precisions in the angles estimation are achieved with baselines lengths shorter than a meter. However, the carrier phase observations are inherently affected by an ambiguity, which must be resolved in order to exploit the better precision of the phase observations with respect to the code observations. The integer ambiguity fixing process is therefore the key for an accurate GNSS-based attitude estimation. In this paper we will make use of the LAMBDA (Least Squares Ambiguity Decorrelation Adjustment) algorithm, an optimal Integer Least Squares (ILS) estimator introduced in [2]. This method is based on a decorrelation of the ambiguities prior to the search for the least-square minimizer, via a transformation that maintains the integerness of the parameters. The LAMBDA method is mathematically rigorous ([3], [4]), it has been successfully tested in a wide set of tests (see for example [5], [6]) and it has been theoretically demonstrated to be optimal in the sense of maximizing the probability of correct integer estimation [7]. This algorithm has recently been extended to accommodate those applications where the baseline length is fixed: in [8] the new Baseline Constrained LAMBDA method was introduced. A description of the two algorithms will be presented, stressing how the LAMBDA has been modified in order to exploit the constraint on the baseline. The use of the a-priori knowledge over the baseline length in the ambiguity fixing process has the effect of strengthening the underlying GNSS model: this positively affects the ability of fixing the correct ambiguity vector, as was shown in [9]. Once the integer ambiguities have been resolved, the precise baseline solutions can be used to determine the attitude of the platform. In this contribution, experimental results will be shown, examining the improvement in the capacity of fixing the correct integer vector when using the baseline constrained LAMBDA algorithm for attitude determination in the most challenging environment, the single-epoch, single-frequency, GNSS-only processing. The method will be tested using two dataset collected at a static reference station and onboard an aircraft.