GNSS based techniques allow a highly accurate attitude determination when using carrier-phase measurements. This paper describes a technique for attitude determination of a vehicle using GNSS carrier-phase measurements from multiple antennas and baselines.
Nghiên cứu khoa học công nghệ ROBUST ATTITUDE DETERMINATION USING MULTIPLE ANTENNAS GNSS CARRIER-PHASE MEASUREMENT FOR UAV APPLICATIONS Nguyen Huu Trung1*, Nguyen Minh Duc1, Thai Trung Kien2 Abstract: GNSS based techniques allow a highly accurate attitude determination when using carrier-phase measurements This paper describes a technique for attitude determination of a vehicle using GNSS carrier-phase measurements from multiple antennas and baselines Real time attitude determination is required for a number of applications such as UAV controller design This system is essential for real time vehicle navigation, guidance and control applications The attitude determination system is based on RTK differential GNSS algorithm that estimates body frame baselines formed from multiple antennas, solves the ambiguity and attitude iteratively every epoch to give robust solutionand projects them onto a local horizontal plane The Monte Carlo simulations were performed to verify effectiveness of the proposed model Key words: Attitude determination, UAV, Integer ambiguity, RTK, GNSS INTRODUCTION In recent years, the use of the GNSS for attitude determination has become well known, as it provides advantages over other methods [1] Attitude determination by differential carrier-phase GNSS has been studied extensively, and has resulted in numerous publications The traditional GNSS attitude system requires at least three or four satellites to give attitude solution This depends on whether line bias is known and depends on a continuous, integrated carrier-phase measurements from multiple antennas [2] Heading and pitch angles can be determined using only two antennas The attitude determination consisted of two main steps The first step is to calculate the vector between the antennas using differential solution techniques, and then calculate the attitude parameters Calculating the vector can be done by pseudo range or by phase measurements For accurate applications, the vector is calculated using carrier-phase measurements and solving integer ambiguity The attitude determination system is based on differential algorithms that estimate three or more baselines The attitude information is derived by projecting these baselines onto a local horizontal plane [3] GNSS based attitude system processes code and carrier-phase observations to estimate baselines, which are then used to estimate the attitude angles [4] Any interruption of signal leads to reinitialize the attitude calculation process This interruption is considered as cycle slip of the calculation A new integerambiguity search is initialized in the attitude computation algorithm caused by a cycle slip This is always susceptible to error, especially if the signals are noisy [5] In this paper, we propose the attitude estimation algorithmby solving the ambiguity iteratively every epochin order to prevent interruption, give robust attitude solution for UAV applications The rest of the paper is organized as follows In the next section, we present GNSS attitude determination system model Section presents simulation Tạp chí Nghiên cứu KH&CN quân sự, Số Đặc san CNTT, 12 - 2017 83 Công nghệ thông tin results Concluding remarks and directions for further researches are mentioned in the last section GNSS ATTITUDE DETERMINATION 2.1 GNSS Attitude Determination principle An attitude determination system (ADS) is a system that defines the orientation of a moving vehicle The attitude is defined by three angles including yaw, pitch, roll of the body frame to a system frame typically defined in reference to the horizonal plane [6] Figure Vector Diagram for attitude determination The fundamental concept of GNSS Attitude Determination (GAD) is shown in Figure The measurement of the phase of the GNSS signal carrier allows to determine the baselines of the antennas in the body reference frame Baselines areused to calculate the attitude of the vehicle by coordinates transformation Figure Double difference model The single or doubwn coordinate while the input parameters in Earth-Centered-Earth-Fixed (ECEF) coordinate The rotation matrix of the ECEF coordinates to the local coordinates is expressed as: − − = − (20) Where and are the geodetic latitude and the longitude of the receiver position By using the and the receiver position in the ECEF coordinates, the position in the ECEF coordinates can be transformed to the position in the local coordinates as: = ( − ) (21) SIMULATION RESULTS An attitude determination system for simulation based on multiple antennas GNSS carrier-phase measurement method consists of two configuration The first configuration for fixed-wing UAVs uses four antennas to receive the GNSS signals placed on the middle of the tail, on the wings and on the nose as shown in Figure and the second configuration uses four antenna with antenna places as shown in Figure for quadrotor UAVs The simulationparameters and the calculated baselines between antennas as shown on the Table Table Simulation parameters Antenna configuration Parameters Unit Fixed-wing Quadrotor UAVs UAVs GNSS Signal GPS-L1 GPS-L1 Sampling frequency Hz 1 Measurement method C/A code/ C/A code/ Carrier-phase Carrier-phase Number of epochs 100-500 500 Prime distance between antennas m 5 (d) Integer ambiguity resolution LAMBDA LAMBDA Carrier-phase accuracy m 0.001 0.001 Monte-Carlo Q 200 200 Baseline calculations d1=d2=2.0751d d1=d2=d d3=1.5206d d3=1.414d d23=d13=2.236d d23=d13=d 88 N H Trung, N M Duc, T T Kien, “Robust attitude determination … UAV applications.” Nghiên cứu khoa học công nghệ The attitude solution is derived from unaided, single-epoch, single-frequency GNSS observations at L1 frequency The simulation collected GPS-L1 data for 500 epochs at 1Hz sampling We consider the single-frequency case because it is of interest for many aerospace applications, where limits on weight and power consumption must often be respected Using multiple baselines and after the optimal integer ambiguity set is known for all the baselines, the attitude angles are obtained The simulation results are presented in Figure (a-b), Figure (a-b) The performance is good with high accuracy shown in Table As represented in Table and in Figure 6, 7, the yaw angle gives the best performance because of the influence of the Up coordinate which is more effected by noise than the East and North coordinates in both pitch and roll angles Table Standard errors of attitude determination simulation for Fixed-wing UAVs by code-phase and carrier-phase measurement Test Epochs Attitude 100 Yaw; Roll; Pitch 200 Yaw; Roll; Pitch 300 Yaw; Roll; Pitch 400 Yaw; Roll; Pitch 500 Yaw; Roll; Pitch Fixed-wing UAVs, Std Errors (degree) Code-phase Carrier-phase 0.165; 0.329; 0.242 0.0041; 0.0077; 0.0058 0.391; 0.406; 0.787 0.0042; 0.0084; 0.0066 0.448; 0.599; 0.630 0.0044; 0.0094; 0.0070 0.419; 0.648; 0.812 0.0046; 0.0100; 0.0071 0.386; 0.600; 0.750 0.0048; 0.0108; 0.0071 Figure Four-antenna configuration in multiple antennas GNSS carrier-phase measurement method for fixed-wing UAVs Tạp chí Nghiên cứu KH&CN quân sự, Số Đặc san CNTT, 12 - 2017 89 Công nghệ thông tin Figure Four-antenna configuration in multiple antennas GNSS carrier-phase measurement method for quadrotor UAVs Roll [deg] Pitch [deg] Yaw [deg] Mean=38.5068 Std=0.3568 52.45 52.02 51.59 51.16 50.73 28.13 27.14 26.15 25.16 24.17 -37.79 -38.35 -38.91 -39.47 -40.04 50 100 150 200 250 300 350 400 Epoch Mean=13.0827 Std=0.9109 450 500 550 50 100 150 200 250 300 350 400 Epoch Mean=-51.9820 Std=0.5906 450 500 550 50 100 150 200 250 450 500 550 300 350 Epoch 400 (a) 90 N H Trung, N M Duc, T T Kien, “Robust attitude determination … UAV applications.” Nghiên cứu khoa học công nghệ Pitch [deg] Yaw [deg] Mean=37.9511 Std=0.0051 50.97 50.96 50.95 50.94 50.93 24.70 24.68 24.67 24.65 24.64 Roll [deg] -40.10 -40.11 -40.12 -40.14 -40.15 50 100 150 200 250 300 350 400 Epoch Mean=11.6691 Std=0.0116 450 500 550 50 100 150 200 250 300 350 400 Epoch Mean=-53.1234 Std=0.0072 450 500 550 50 100 150 200 250 450 500 550 300 Epoch 350 400 (b) Figure Fixed-wing configuration, Single epoch, GPS-L1, code-phase measurement (a), carrier-phase measurement (b), d=5m Roll [deg] Pitch [deg] Yaw [deg] Mean=38.5529 Std=0.3717 52.45 52.02 51.59 51.16 50.73 28.13 27.14 26.15 25.16 24.17 -37.79 -38.35 -38.91 -39.47 -40.04 50 100 150 200 250 300 350 Epoch Mean=13.1919 Std=0.9661 400 450 50 100 150 200 400 450 50 100 150 200 400 450 250 300 350 Epoch Mean=-52.1095 Std=0.5746 250 Epoch 300 350 (a) Tạp chí Nghiên cứu KH&CN quân sự, Số Đặc san CNTT, 12 - 2017 91 Công nghệ thông tin Roll [deg] Pitch [deg] Yaw [deg] Mean=38.7647 Std=0.0053 51.78 51.77 51.76 51.76 51.75 26.31 26.30 26.28 26.26 26.25 -39.05 -39.06 -39.07 -39.09 -39.10 50 100 150 200 250 300 350 Epoch Mean=13.2821 Std=0.0115 400 450 50 100 150 200 400 450 50 100 150 200 400 450 250 300 350 Epoch Mean=-52.0753 Std=0.0075 250 Epoch 300 350 (b) Figure Quadrotor configuration, Single epoch, GPS-L1, code-phase measurement (a), carrier-phase measurement (b), d=5m CONCLUSIONS This paper has presented a system model and algorithm for attitude determination of a vehicle using simultaneous GNSS carrier-phase measurements from multiple antennas This system which uses multiple antennas for attitude determination is a high-bandwidth, accurate means of determining three-axis attitude for guidance and control applications The results of this ongoing research have shown that it is possible to achieve reality and reliability and a certain attitude solution precision based-on MATLAB simulations In the next research, we increase the robustness of GNSS system by coupling it with an INS system by robust filter to minimize the maximum error of a sensor signal due to any possible disturbance, without making assumptions about the interferences in the system for such applications that work in rugged environment Acknowledgement: The authors would like to thank the Ministry of Science and Technology has supported under the project number ĐT.ĐL.01/02-2016 92 N H Trung, N M Duc, T T Kien, “Robust attitude determination … UAV applications.” Nghiên cứu khoa học công nghệ REFERENCES [1] Gabriele Giorgi; Peter J G Teunissen, “Low-Complexity Instantaneous Ambiguity Resolution with the Affine-Constrained GNSS Attitude Model”, IEEE Transactions on Aerospace and Electronic Systems, Volume: 49, Issue: 3, pp: 1745 - 1759, 2013, DOI: 10.1109/TAES.2013.6558017 [2] Alireza A Ardalan; Mohammad-HadiRezvani, “An iterative method for attitude determination based on misaligned GNSS baselines”, IEEE Transactions on Aerospace and Electronic Systems, Volume: 51, Issue: 1, pp: 97 - 107, 2015, DOI: 10.1109/TAES.2014.130070 [3] D Gebre-Egziabher, G H Elkaim, J D Powell, and B W Parkinson, “A gyro-free quaternion based attitude determination system suitable for implementation using low cost sensors,” in Position Location and Navigation Symposium, IEEE 2000, (San Diego, CA), pp 185 –192, 2000 [4] Sang Heon Oh, Dong-Hwan Hwang, Chansik Park and Sang Jeong Lee, “Attitude Determination GPS/INS Integration System Design Using Triple Difference Technique”, Journal ofElectrical Engineering & Technology Vol 7, No 4, pp 615~625, 2012 http://dx.doi.org/10.5370/JEET.2012.7.4.615 [5] Rodrigo Munguía, and Antoni Grau, “A Practical Method for Implementing an Attitude and Heading Reference System, International Journal of Advanced Robotic Systems”, Vol 11:62, 2014, DOI: 10.5772/58463 [6] Li, Y.; Efatmaneshnik, M.; Dempster, A.G “Attitude determination by integration of MEMS inertial sensors and GPS for autonomous agriculture applications” GPS Solut Vol 16, pp: 41–52, 2012 [7] Cong, L.; Li, E.; Qin, H.; Ling, K.V.; Xue, R., “A performance improvement method for low-cost land vehicle GPS/MEMS-INS attitude determination” Sensors, Vol 15, pp: 5722–5746, 2015 [8] Yingdong Yang, Xuchu Mao and Weifeng Tian, “Rotation Matrix Method Based on Ambiguity Function for GNSS Attitude Determination”, Sensors, Vol.16, 841, 2016; doi:10.3390/s16060841 [9] Teunissen, P.J.G., “The LAMBDA method for the GPS compass” Artif Satell., Vol 41, pp: 89–103, 2006 [10] Chang, X.W.; Yang, X.; Zhou, T., “MLAMBDA: A modified LAMBDA method for integer least squares estimation”, J Geod Vol 79, pp: 552–565, 2005 [11] P J G Teunissen, “The affine constrained GNSS attitude model and its multivariate integer least-squares solution”, J Geod,Vol 86, pp:547–563, 2012,DOI 10.1007/s00190-011-0538-z Tạp chí Nghiên cứu KH&CN quân sự, Số Đặc san CNTT, 12 - 2017 93 Cơng nghệ thơng tin TĨM TẮT ĐỊNH VỊ TƯ THẾ BỀN VỮNG BẰNG PHƯƠNG THỨC ĐỊNH VỊ VỆ TINH GNSS ĐA ANTEN DỰA TRÊN CƠ SỞ ĐO PHA SĨNG MANG Hệ thống định vị tồn cầu GNSS cho phép xác định tư xác sử dụng phép đo pha-sóng mang Bài báo mơ tả mơ hình thuật tốn xác định tư đối tượng phương thức định vị vệ tinh GNSS đa anten dựa sở đo pha sóng mang từ nhiều anten đường sở Định vị tư yêu cầu ứng dụng thiết kế điều khiển UAV Hệ thống tảng ứng dụng định vị, dẫn đường điều khiển Hệ thống xác định tư đối tượng dựa thuật toán RTK vi sai xác định đường sở tạo thành từ anten, giải toán số nguyên định vị tư phương pháp lặp theo cụm liệu cho nghiệm bền vững ánh xạ lên mặt phẳng nằm ngang cục Các kết mô theo phương pháp Monte-Carlo điều kiện khác minh chứng hiệu phương pháp đề xuất Từkhóa: Định vị tư thế, UAV, bất định số nguyên, RTK, GNSS Nhận ngày 16 tháng năm 2017 Hoàn thiện ngày 26 tháng 11 năm 2017 Chấp nhận đăng ngày 28 tháng 11 năm 2017 Địa chỉ: Đại học Bách Khoa Hà Nội; Viện CNTT/ Viện KHCNQS * Email: trung.nguyenhuu@hust.edu.vn 94 N H Trung, N M Duc, T T Kien, “Robust attitude determination … UAV applications.” ... RESULTS An attitude determination system for simulation based on multiple antennas GNSS carrier- phase measurement method consists of two configuration The first configuration for fixed-wing UAVs uses... code -phase measurement (a), carrier- phase measurement (b), d=5m CONCLUSIONS This paper has presented a system model and algorithm for attitude determination of a vehicle using simultaneous GNSS carrier- phase. .. carrier- phase measurements from multiple antennas This system which uses multiple antennas for attitude determination is a high-bandwidth, accurate means of determining three-axis attitude for guidance