جبران‌سازي خطاهاي سرعت و موقعيت يك سيستم ناوبري تلفيقي اينرسي/سماوي به‌كمك هموارسازي، فيلتر كالمن درجه دوم

Velocity and position compensation in an integrated inertial/celestial navigation system by implementing, smoothing and unscented Kalman filter

هدف مقاله‌ي حاضر جبران خطاي سرعت و موقعيتي است كه در ابتداي عملكرد حساسه‌ي ستاره‌نگر در يك سيستم ناوبري تلفيقي اينرسي/سماوي وجود دارد. اين دو سيستم ناوبري به‌وسيله‌ي فيلتر كالمن درجه دوم تلفيق شده‌اند. به‌منظور حل دقيق معادلات ناوبري، از الگوريتم انتگرال‌گيري ديجيتال استفاده شده است. به‌علاوه، به‌منظور كاهش بار محاسباتي، در تمامي مراحل ناوبري و تلفيق از كواترنيون‌ها استفاده شده است. با استفاده از معادلات غيرخطي و به‌كارگيري هموار‌سازي و پسروي، وضعيت اوليه و باياس شتاب‌سنج‌ها با دقت زياد تخمين زده شده است. افزون بر اين، در حين پسروي و هموارسازي، وضعيت وسيله در لحظات پيشين به دقت تخمين زده مي‌شود. در ادامه، با انجام يك ناوبري موازي جديد، كه براساس وضعيت برآورد شده‌ي لحظات پيشين و جبران‌سازي باياس شتاب‌سنج‌ها صورت مي‌گيرد، خطاهاي سرعت و موقعيت جبران مي‌شود. در انتها با انجام شبيه‌سازي براي يك ماهواره‌بر، روش ناوبري ارايه‌شده بررسي شده است.

In this paper, the purpose is to compensate the errors of velocity and position, existing at the starting time of star sensor work in an integrated inertial/celestial navigation system. In an inertial navigation system, there exists attitude error at launch moment. Moreover, while integrating gyros and accelerometers outputs, errors grow in estimation of attitude, velocity, and position on vehicle. On the other hand, because of earth’s atmosphere effects, celestial navigation cannot be implemented for a while after launch moment. Then, pure inertial navigation is carried out at this interval. Consequently, large errors of velocity and position exist at starting time of integration. The estimation and integration are carried out using unscented Kalman filter through which current attitude and the gyros fixed bias can be estimated accurately. To precise integration, nonlinear navigation equations have been used and propagated implementing an accurate discretization method. Moreover, in all sequences of navigation and estimation, quaternions have been used to deal with attitude. This will reduce computation costs and immunize integrated system from singularity. Since quaternions have their own vector space, some considerations are applied to estimation procedure which includes sigma point’s calculation, propagation, and calculating mean and covariance. On the other hand, velocity and position errors are not observable in an integrated inertial/celestial navigation system. Then, in this paper, using nonlinear navigation equations and implementing back-propagation and smoothing, initial attitude and accelerometers fixed bias are estimated accurately. In addition, the vehicles attitude is acquired at prior time steps while back-propagating. By carrying out a new parallel navigation based on vehicles attitude at prior moments and taking out gyros and accelerometers fixed biases, velocity and position errors are compensated. To demonstrate the validity and performance of the proposed method, navigation of a LEO launch vehicle has been simulated. Results admit great compensations in velocity and position errors.