GPS Based Attitude Determination with Statistical and Deterministic Baseline A Priori Information

P. Jurkowski, P. Henkel, C. Guenther

Abstract:	Attitude determination with carrier phase measurements is becoming increasingly popular for maritime and automobile navigation. However, multipath, frequent loss of lock, cycle slips and severe clock drifts prevent reliable integer ambiguity resolution especially for low-cost GNSS receivers. The reliability of carrier phase ambiguity resolution can be improved by a few methods: One option is the use of some baseline a priori information to reduce the integer search space. This a priori information can be given either in a deterministic or stochastic (Jurkowski [1], Jurkowski et al. [2], Henkel et al. [3]) form. Another option is the use of multi-frequency linear combinations, which increase the wavelength to noise ratio and, thereby, reduce the number of grid points within the search space volume. A third option is the use of state space models, which exploit the inertia of the vehicles and can be efficiently implemented by recursive least-squares estimation/ Kalman Filtering. Finally, one can include additional measurements from inertial sensors and/ or further antennas, and perform an on-board calibration of double difference measurements. In this paper, a method is proposed that uses precise carrier phases for attitude determination without the need of ambiguity resolution: First, a synchronization of double difference measurements is performed by computing a range correction based on the satellite movement within the receiver differential clock offset time. Secondly, if the receiver is moving on a straight path, a linear least- squares fitting of a sequence of absolute code-based position solutions gives an estimate of the path direction and, thus, an on-board calibration of double difference measurements can be even performed with the help of the base-line length, pitch and roll angle a priori information and satellite-receiver direction vectors. The calibrated carrier phases can then be coasted without the need of ambiguity resolution. The observed accuracy is 0.5?/ baseline length, i.e. 0.5? for a baseline length of 1 m an 0.005? for a baseline length of 100 m. The proposed algorithm was tested with real measurements from two low-cost, single frequency u-blox LEA 6T receivers mounted on the roof of a car and compared with the high precision INS/GPS coupled navigation system iTraceRT-F400 of iMAR as a reference sensor. The measurement results show that our kinematic calibration of the double difference phases provides a heading accuracy that is sufficient for most applications. Secondly, a Maximum Likelihood (ML) and Maximum A posteriori Probability (MAP) estimation of ambiguities and baselines is proposed. These estimators find the optimum trade-off between an estimator that minimizes only the range residuals (e.g. unconstrained LAMBDA) and one which minimizes only the distance to the a priori information. The Gaussian a priori knowledge of the baseline length, pitch, roll and yaw angles serves as a soft constraint, i.e. it gives a certain preference direction but allows some uncertainties in the a priori knowledge. Consequently, the development of methods for their reliable resolution has received a lot of attraction during the last years. Approaches include the coupling of GNSS and INS measurements, the use of multi-frequency linear combinations to increase the ambiguity discrimination [4, 5, 6], the introduction of a priori knowledge [7, 2], and the use of multi-antenna systems. Ambiguity resolution uses the code and carrier phase measurements as provided by the delay locked loop and phase locked loop. Note that the integer search is not discussed in this paper as it is described in detail in [8, 9, 10].
Published in:	Proceedings of the 2012 International Technical Meeting of The Institute of Navigation January 30 - 1, 2012 Marriott Newport Beach Hotel & Spa Newport Beach, CA
Pages:	1164 - 1213
Cite this article:	Jurkowski, P., Henkel, P., Guenther, C., "GPS Based Attitude Determination with Statistical and Deterministic Baseline A Priori Information," Proceedings of the 2012 International Technical Meeting of The Institute of Navigation, Newport Beach, CA, January 2012, pp. 1164-1213.
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