# Opportunistic In-Flight INS Alignment Using LEO Satellites and a Rotatory IMU Platform
## 1 Introduction
As it has been proved that in GPS-challenge environments the attitude error will diverge continuously, signals of opportunity could be a great alternative for INS augmentation. The alignment and online calibration using rotation and other innovative methods was considered and implemented in the following articles. In some methods, by increasing the coupling among the estimated states and measurements, the filter's convergence speed could improve; moreover, it was accepted that the rotation vector-based method can have faster convergence parameters than the Euler angle-based method [15; 16]. Regarding in-flight calibration with a rotatory IMU platform, establishing an excessive-cost IMU structure with the ability to rotate accurately in each of the three axes is necessary. However, some works have been done with single- or dual-axis rotation [17; 18]. These methods are related to the observability rank of the error model of the system. Several in-flight alignment methods of INS/GNSS integration systems have also been investigated in [19; 20]. The articles could correct the orientation results and the INS errors, which may be caused by misalignment or vibrations. Numerous INS alignments have also been presented to estimate and compensate the INS errors using measurements from satellites. For instance, in [21], The INS calibration results improved using the pseudorange measurements of GPS satellites. The article claims an efficiency in estimating the INS/GPS errors using differential phase pseudorange measurements. Additionally, the IMU-rotation method could enhance the navigation results even in GPS-denied environments. All these works show the possibility of INSonline calibration using multiple LEO satellites. Apart from that, the IMU rotation also has an acceptable background in GNSS-challenge environments [22]. So far, various methods of the coarse and fine alignments have been presented based on the swing IMU platform. Swing is a kind of disturbance situation, which mostly affects the orientation variation. In [23; 24; 25], some swing-based INS alignment systems were presented to correct the effect of disturbance. Although the self-alignment was proved theoretically, the accuracy is completely dependent on the gravitational apparent motion vectors. Some researchers have studied the periodical IMU motions in a complete rotation cycle with a special amount of angular rate [26; 27]. These rotation cycles also could be simulated by a sine function. Despite its requirement to an expensive and complex motion platform, the estimated bias states can significantly calibrate the misalignment effects [28]. A novel rotation innovation was presented in [29] to solve the needs of expensive platforms by mounting the IMU on the wheels of a ground vehicle. In the presented article, a navigation system and an error model of the IMU were designed. An in-flight calibration method was implemented using a master-slave system augmented by a rotatory IMU platform followed by an optimized dual-axis rotation algorithm. The slave EKF estimates the states of the dynamic antenna mounted on a vehicle using the Doppler positioning method, and the master system is a regular INS. Additionally, for alignment and bounding the errors of the estimation, as well as reaching the maximum observability, a dual-axis rotation sequence was simulated as an IMU actuator. In fact, the novelty is in combining the LEO-SOP measurements with an IMU-rotating method, which leads to decrease the estimated errors and calculates more reliable and robust navigation data. The article also presents new features regarding the experiment and the duration. In the experimental results, two different tests were designed. The accuracy and robustness of the algorithm was validated with two trajectories on air and on the ground. The robustness is discussed in different time slots of the flight experiment. The main structure of this article is organized as follows.