Heading and Attitude Determination System with Low-cost IMU Embedded Inside One of Multiple Antennas
Nikolay Vasilyuk, Mikhail Vorobiev, and Dmitry Tokarev, Topcon Positioning Systems, LLC, Russia
Location: Big Sur
To measure the attitude of a moving vehicle with the aid of GNSS system, at least two fixed antennas must be used and coordinates of these antennas must be given in the body frame of this vehicle. A GNSS system, which contains only two antennas, can measure only two attitude angles of three Euler angles. The third unmeasurable angle is the rotation angle around the base vector connecting phase centers of both antennas. This angle can be obtained either using a third antenna or by including an inertial measurement unit into the system and then coupling the inertial and GNSS measurements with the aid of Kalman filter. In addition, the usage of the IMU allows extrapolating the position, velocity and attitude of the vehicle during the short-time loss of the GNSS signal, for example, when the vehicle passes near or under various obstacles (towers, bridges, etc).
The attitude of the base vector of the two-antenna GNSS receiver is determined by coherent processing of satellite signals received by both antennas in a common time scale. To implement the coherent signal processing, one of the antennas is assigned to the main antenna (master antenna), and the second to the auxiliary one (slave antenna). It is assumed that the initial point of the base vector lies in the phase center of the master antenna, and its terminal point is in the phase center of the slave antenna. The choice of the master and slave antennas is arbitrary, but must be done before the system starts to work. Coherent processing consists in measuring the path differences between the phases of each GNSS signal received by the master and slave antennas simultaneously. Since these differential phase measurements are obtained from the signals received by closely spaced antennas, no additional information is required for their processing. Thus, GNSS measurements of the angular coordinates of the base vector can be obtained in “stand-alone” receiver’s operation mode. All simultaneously measured path differences are collected in a common observation vector, which uses to calculate the angular coordinates of the base vector with the aid the iterative least-squares method. These angular coordinates always contain the heading angle of the vehicle. The type of the second angle - the roll angle or the pitch angle depends on the geometry of the pair of antennas.
For proper IMU and GNSS measurements coupling, it is necessary to ensure the stability of preset coordinates of the phase centers of both antennas relative to the IMU axes. This task may be significantly simplified if the low-cost IMU is placed directly inside the master antenna, near its phase center. In this case, only the constant orientation of the base vector relative to IMU axes must be provided. This orientation calibrated during system manufacturing or after it is installed on the vehicle. To simplify the cabling structure of the installed system, measurements from the IMU inside the master antenna are transmitted directly to the GNSS receiver via the RF cable together with the GNSS signal received by this antenna. For the transmission of digital information from the IMU over the RF cable, frequency shift keying of the low-frequency carrier is used, which allows separating IMU and GNSS signals in frequency and eliminating their mutual distortion. This solution allows the installation of new antennas with embedded IMU on vehicles with dual-antennas GNSS heading sensors without changing the already existing cabling.
The coupling of GNSS and IMU (inside the master antenna) measurements is performed using the widely known extended Kalman filter. The state vector of the Kalman filter includes sixteen parameters - four coefficients of vehicle’s attitude quaternion, three components of speed vector , three spatial coordinates and six estimates of sensors zeros biases - three for gyroscopes and three for accelerometers. The filter’s observation vector contains eight parameters - six components of the spatial position and the speed vectors of the master antenna's phase center, respectively, and two angular coordinates of the base vector.
The tests of the described system were carried out on vehicles of various types and under different conditions. This system was installed on the roof of the car, for testing under urban conditions. It was used on an excavator, to measure the heading of the boom and cabin and compensate for the loss of the GNSS signal when the excavator’s boom was raised. It was mounted on the doser’s blade, to measure its orientation under hard shocks and vibrations. The distance between the antennas (the length of the base vector) in all experiments varied from 15 cm to 50 cm, the GNSS receiver's operating modes - stand alone, DGPS, RTK-fix. The RMS of the measurement of the heading angle was better than [0.1/(length of base vector, m)] degrees. This accuracy in determining the orientation was maintained for 60 seconds without any GNSS signal if its loss occurred in the steady-state mode of Kalman filter.
Conclusions: in all cases, the system showed itself as a reliable and precise tool for measuring the position, velocity and 3D orientation of a moving vehicle regardless of the mode of operation of the GNSS receiver (stand alone, DGPS, RTK-fix) and with a predictable dependence on the distance between the antennas. This system is able to provide accurate estimates of the instantaneous attitude of the vehicle in poor GNSS conditions, which are characterized by the deterioration or complete loss of the GNSS signal. The attitude measurement system with integrated low-cost IMU can be installed without additional costs for any vehicle that uses a two-antenna heading measurement system. Installation of such a system does not require reworking the existing layout of antenna RF cables.