# Integrated GNSS/IMU-Gyrocompass with Rotating IMU. Development and Test Results
## 3 Materials
### Integrated GNSS/IMU Gyrocompass Structure and Features  
The integrated GNSS/IMU gyrocompass comprises two satellite antennas, IMU and a computing unit installed on a rotating foundation providing rotation about the vertical axis \(Z_{b}\). Data can also be received from external sensors of the object linear velocity and altitude (depth). The antenna module contains two antennas with two satellite navigation receivers receiving GNSS signals with code division (GPS) and frequency division (GLONASS) and using a common  
Figure 3: Appearance of integrated GNSS/IMU gyrocompass (**a**) and its prototype GNSS compass include rotating antenna unit (**b**), and reference frames bound with them: b-frame \(X_{b}Y_{b}Z_{b}\) and s-frame \(X_{s}Y_{s}Z_{s}\). clock. The clock frequency stability is better than \(10^{-6}\). It should be emphasized that instead of MEMS gyros traditionally applied in existing GNSS compasses the IMU contains three more accurate small-sized tactical grade open loop FOGs (CJSC Fizoptika, Russia) [36] with drift instability of 6-30\({}^{\circ}\)/h. Bias instability of the employed accelerometers is estimated to be 0.001 g. 3D model of the developed integrated GNSS/IMU gyrocompass is shown in Figure 3a. Major distinctive features of the developed integrated GNSS/IMU gyrocompass include rotating antenna unit and IMU installed on a common foundation, common clock, and attitude determination method using phase measurements from two antennas. Rotation of antenna baseline excludes rather complicated search algorithms to estimate phase ambiguity and improves heading accuracy because the observed satellites are located in elevation and azimuth zones effective for heading determination for a much longer time [9]. Due to rotation of antenna module the direction of antenna baseline with respect to satellite direction is changing, which critically reduces the error and provides heading solution by observing the signals of only one satellite. IMU rotation creates the required dynamics and makes it possible to decompose the gyro error model and effectively estimate its components if GNSS data are available. Selection of the motion law is a separate problem not covered in the paper. It should be only noted that angular displacement is realized using an original optimal algorithm effective in terms of minimizing the errors of GNSS/IMU gyrocompass. Optimization of rotation parameters is detailed in [31]. These features (rotation and using IMU on tactical grade FOGs) allow downsizing the system, with its overall dimensions being \(\partial 400\times 270\) mm. The proposed distance between the antennas' phase centers is 0.36 m. The majority of existing GNSS/IMU compasses have larger dimensions and antenna baseline of 0.7-1.5 m, which is required to obtain the heading solution accurate to 0.5-1\({}^{\circ}\)(3\(\sigma\)) [37; 38]. INS and GNSS data are integrated via extended Kalman filter (EKF) described in Section 4.4 using a tightly coupled scheme [18; 35]. As raw data for joint processing we use pseudorange \(\rho^{i}\), radial velocity \(\dot{\rho}^{i}\), and single difference of carrier phase \(\Delta\phi^{i}\) received by the spaced antennas for each observed i-th satellite. The available measurements are processed using so-called invariant scheme, i.e., based on complementary filter. Thus, in filtering described further, the measurement errors are estimated by using differential measurements [39; 40]. The data sources used in this study are INS, satellite receivers, and external sensors of linear velocity and altitude (depth) in case of satellite signal outage. Note that phase measurements are processed using their single differences, which allows getting heading updates by signals from only one satellite. Then to eliminate error in phase single differences arising due to various receiver clock errors of two antennas, two satellite navigation receivers with a common external clock are applied [35].