Resumen
With the emergence of numerous low Earth orbit (LEO) satellite constellations such as Iridium-Next, Globalstar, Orbcomm, Starlink, and OneWeb, the idea of considering their downlink signals as a source of pseudorange and pseudorange rate measurements has become incredibly attractive to the community. LEO satellites could be a reliable alternative for environments or situations in which the global navigation satellite system (GNSS) is blocked or inaccessible. In this article, we present a novel in-flight alignment method for a strapdown inertial navigation system (SINS) using Doppler shift measurements obtained from single or multi-constellation LEO satellites and a rotation technique applied on the inertial measurement unit (IMU). Firstly, a regular Doppler positioning algorithm based on the extended Kalman filter (EKF) calculates states of the receiver. This system is considered as a slave block. In parallel, a master INS estimates the position, velocity, and attitude of the system. Secondly, the linearized state space model of the INS errors is formulated. The alignment model accounts for obtaining the errors of the INS by a Kalman filter. The measurements of this system are the difference in the outputs from the master and slave systems. Thirdly, as the observability rank of the system is not sufficient for estimating all the parameters, a discrete dual-axis IMU rotation sequence was simulated. By increasing the observability rank of the system, all the states were estimated. Two experiments were performed with different overhead satellites and numbers of constellations: one for a ground vehicle and another for a small flight vehicle. Finally, the results showed a significant improvement compared to stand-alone INS and the regular Doppler positioning method. The error of the ground test reached around 26 m. This error for the flight test was demonstrated in different time intervals from the starting point of the trajectory. The proposed method showed a 180% accuracy improvement compared to the Doppler positioning method for up to 4.5 min after blocking the GNSS.