# Opportunistic In-Flight INS Alignment Using LEO Satellites and a Rotatory IMU Platform
## 1 Introduction  
In recent years, many loosely and tightly coupled integrations of the inertial navigation system (INS) and the global navigation satellite system (GNSS) have been used and implemented in ground and air navigation applications in many studies [1, 2, 3]. Various kinds of signals of opportunity (SOP) are being used in many navigation algorithms. To compare several augmented navigation methods, there are distinct factors to choose a proper SOP: the number of transmitters, the distance, and the global coverage [4]. The signals of opportunity (SOP) transmitted by several low Earth orbit (LEO) satellites became more popular in recent years as a reliable alternative in GNSS-denied environments. Various LEO constellations such as Iridium-Next, Orbcomm, and Globalstar are transmitting on their downlink mode in a wide range of frequencies and amplitudes. The close distance of LEO satellites to the surface of the Earth made it possible to track their Doppler shiftswhile passing through a static or dynamic receiver. The pseudorange rate measurements obtained from the LEO receivers could be a consistent source of measurements instead of the pseudoranges of the GNSS satellites in blocking situations or inaccessible places. Many researchers have concentrated on positioning solutions using Doppler measurements of the LEO satellites. Designing single- and multi-constellation LEO signal receivers was the first step to provide these Doppler measurements. The receiver architecture introduced in [5; 6] could acquire and track the phase and the Doppler measurements of the acquired signal from various LEO constellations. The receiver utilizes the power spectral density (PSD) analysis in order to detect and acquire the transmitted signals. Several parameters of the receiver-like sampling frequency, the center frequency, the window size, and the peak threshold could be defined depending on the downlink specification of each LEO constellation. The receiver's tracking block consists of a numerically controlled oscillator (NCO), a first-order loop filter, and a phase detector. This block is able to track Doppler shifts of different channels of one or multiple constellations. INS/SOP integrations [7], SOP-based collaborative navigation [8], and distributed SOP-aided INS [9] were investigated and discussed. The Doppler positioning method with LEO satellites was also used to estimate the trajectory of an unmanned aerial vehicle (UAV) or a ground vehicle (GV). In [10], the messaging bursts of Iridium-Next satellites were used to estimate their Doppler shift. Later, the states of a flight vehicle were extracted using a least-squares estimator. The paging channels of Iridium-Next satellites with acceptable coverage and powerful amplitude made the Iridium constellation more prevalent. Opportunistic navigation for various applications using single or multiple overhead Iridium satellites has been long reviewed and presented [11; 12; 13]. These articles are mostly based on designing an extended Kalman filter (EKF) with a nonlinear pseudorange rate measurement model. The positioning accuracy was obtained in short-term experiments. Additionally, using multi-constellation LEO satellites combining the Doppler measurements of Orbcomm and Iridium satellites is articled in [14]. Authors could estimate the location of a stationary receiver with an accuracy of less than 30 m.  
The alignment is one of the most important stages of the navigation system and the validity and the reliability of the results are dependent on the accuracy of the alignment in every navigation system. The main goal of the work presented in this article was not only implementing the dynamic alignment and obtaining the attitude of inertial measurement unit (IMU) related to the navigation reference frame but also increasing the error estimation results by means of increasing the observability rank of the error model.