# An Improved Single-Epoch Attitude Determination Method for Low-Cost Single-Frequency GNSS Receivers
## 1 Introduction
The MC-LAMBDA method takes both the baseline geometric condition and attitude constraint into consideration; it is still complicated, and a large amount of calculation effort is required. Meanwhile, this method can only use the same common-view satellite pair between the baselines. The adoption of the MC-LAMBDA model will lose some observation information because of the complicated urban environments. Besides, the only means of avoiding a loss of information is to apply the 'ambiguity-graph' strategy, to form the maximum number of double-differenced ambiguities [24; 25; 26]. However, this method is too complicated and has a computational burden. GNSS attitude determination methods include the direct method, the least-square method, Kalman filter-based quaternion method [27], and so on. This paper, directly using the baseline vector to solve the attitude angle, has advantages of a relatively small calculation effort and the need for no prior information. The above discusses some GNSS attitude determination methods, with a special focus on reviewing the ambiguity fixing with a single epoch. However, most GNSS attitude determination experiments are performed with GPS-only observations, and with geodetic quality antennas, or even geodetic receivers. In other words, performance analysis in complex environments, for low-cost vehicle applications, is rare and not convincing [17; 18; 19; 21; 28]. Fortunately, some scholars have proposed that the performance of multi-system single-frequency GNSS receivers is equivalent to that of single-system multi-frequency receivers [29], and also proves that the performance of the GPS/BDS dual system is superior to the GPS-only within the Asia-Pacific region [30]. In terms of attitude determination quality control, [PERSON] et al. proposed an attitude integrity monitoring algorithm [31]. Experiments have shown that the maximum error can be reduced by 2.3\({}^{\circ}\). [PERSON] proposed a quality control method based on affine transformation, when the number of common-view satellites is insufficient [32]. However, investigations concerning attitude quality control for low-cost receivers are still limited. Based on the above discussions, in order to avoid complicated calculations and the lack of common-view satellites for multi-baselines, this paper proposes a combination of multi-baseline, CLAMBDA, and direct method to resolve the attitude angle parameters. In order to further improve the ambiguity fixing success rate for the three-antenna baseline model, given a fixed ambiguity of a baseline in one direction, this paper proposes to obtain the fixed ambiguity solution by searching the attitude angle of the degree of freedom in the other directions, by minimizing the ambiguity objective function globally. At the same time, several test conditions are constructed, based on the known multiple-baseline geometric information in this paper. The proposed method is verified by static experiments, with various baseline lengths and environments, and dynamic experiments in urban environments. The hardware is the consumer-grade Ublox GNSS receiver and patch antenna. The experimental results show that the method can still have good attitude determination performance in a single-frequency single-epoch way under the complex urban environment with low-cost receivers. Moreover, the results show a high success rate, high accuracy, and high reliability.