Instantaneous estimation of attitude from GNSS

Abstract

The use of the Global Navigation Satellite System (GNSS) is widely spread from position determination to attitude determination of a platform in space. This system offers time invariant estimation position. Another thing that can be an advantage is that the flexibility to operate the GNSS receiver variants, from the low-cost until the high-performance GNSS receivers. In terms of attitude determination application at least three receivers are required to determine three spatial axes, where the cost-effective GNSS attitude determination systems can be constructed with today’s receiver technology. At the moment, however, algorithms are lacking which are fast and efficient enough to estimate the position angles without delay. For this reason, the present work deals with the development of algorithms for the attitude determination in space of a platform under the help of the "GNSS" Global Positioning System (GPS). The investigation through this work is classified into three sequential parts: The first part is the estimation of the optimal configuration of baseline array as well as the estimation of the integer ambiguity of carrier phase differences. The estimated integer ambiguity is then used to estimate the high precision baseline coordinates. The second part is to estimate the attitude of the platform in space by means of quaternion using batch process, and the last part is to improve the algorithm using a recursive algorithm for the kinematic application purpose. The precise attitude determination about three spatial axes is possible if at least three GNSS receivers with fixed baselines are used in particular array configurations. Assuming that the basic lengths of the baselines are known apriori, the attitude angles can be calculated via the combination of carrier phase and pseudorange observations. Since the carrier of the GPS signal is propagated in short-wave form, the measured phase differences are ambiguous. The multiples of the GPS signal phases together with the baseline lengths are therefore estimated and improved in a first step with the aid of the a priori baseline lengths information. The multiple-baseline float solution estimation method is used. However, the approach does not provide optimal results. Therefore, an alternative algorithm for the float solution is presented, which estimates the float solution by using the so-called the gradient based iterative method of the least-squares. It shows that method is able to give convergent estimate parameter. It is also shown here that the proposed method outperforms the conventional iterative least-squares in terms of iteration number and computational time. For instantaneous applications, the Least-squares AMBiguity Decorrelation Adjustment (LAMBDA) method is not optimal for fixing the integer multiples of the carrier phase differences for several baseline lengths. In addition, this method requires a high computational effort as soon as a larger number of baseline lines enter into the calculation. An improvement in this work is utilising the partial LAMBDA method, which only uses a subset of the integer multiples to be determined. This algorithm improves the determination of integer multiples and precise calculation of the baseline lengths. The advantages of this algorithm are discussed, and it is empirically demonstrated that the ambiguities are better resolved. Furthermore, the estimation of the attitude angles with the aid of quaternions is theoretically improved and analysed. Two processing strategies are investigated: the least-squares method and the Kalman Filter (KF) method. For the static case, the least-squares is applied and tested. Simulations show that the developed gradient based iterative method of the least-squares provides better estimates than the conventional adjustment methods. It is also shown that the number of iterations required is less and the computational time is reduced. This algorithm is not useful for kinematic applications where a fast sequence of results is required. A modified Extended Kalman Filter (EKF)-Like algorithm is used for kinematic applications. Experiments show that with this algorithm more stable quaternions can be calculated with fewer outliers than when they are determined by the least-squares method. All newly developed algorithms are theoretically analysed and subjected to extensive simulations and experimental kinematic tests in the field.