Abstract: The integrated navigation system including an all-time star tracker and a strap-down inertial navigation system with the advantages of high precision and strong autonomy has been extensively applied in fields such as planes, drones and vessels. During the long-term operation of the integrated Inertial Navigation System (INS), the change in force and heat leads to the drift of the installing matrix, affecting the accuracy of the INS. Moreover, the all-time star tracker influenced by the background light in the sky usually has a small Field of View and can only observe one star at a time, therefore unable to directly estimate the installing matrix according to one star chart. A new method is presented for the estimation of attitude matrixes in real time based on the Levernberg-Marquart (L-M) algorithm. Taking advantage of the attitude measurement values of the INS, this approach transfers the observed star vectors at different times to the same time in a unified coordinate system, thereby constructing a cost function relating the observation vector errors of multiple observation stars and the corresponding navigation star vectors in the least square sense. After that, the L-M algorithm with adaptive step size is used for the iterative solution, obtaining the on-line real-time change in the installing matrix. Experimental data show that the pointing accuracy of single stars projecting onto the INS is twice as high as that before using this method and has an estimation time shorter than 5 ms, meeting the engineering requirements for this kind of integrated INS.

Key words: starlight navigation, integrated navigation algorithms, L-M algorithm, installing matrix, online estimation