Analytical Fault Detection and Isolation Algorithms Based on Rotation Matrices for a Three Axis Stabilized Satellite

This paper presents fault detection and isolation (FDI) algorithms for attitude determination system (ADS) of a satellite including a sun sensor and a magnetometer. The suggested methodology is based on derivation of all possible rotations between reference and body frames and computation of Euler angles by them. Using the resulted Euler angles, some variance measures have been derived that offer a solution for analytical model-free fault detection mechanism. Consequently, when significant variations occur in these variances a fault occurrence is declared. It is shown that by properly categorizing the Euler angles computation methods, not only the faulty sensors but also their faulty components could be isolated. Based on the mentioned feature, four steps of fault isolation have been proposed. In the first step, fault occurrence in only one component of a sensor is isolated. In the second step, two faults in two different sensors are investigated. In the third step, two faults in one sensor are evaluated that means a high level of failure in the sensor. Finally, if fault does not belong to the above categories, it means that more than 50% damage has been occurred in the ADS hardware. Through extensive simulation studies, the desired performance and accuracy of the outlined methods have been demonstrated.
Ovaj rad prikazuje detekciju pogreške i izolacijske algoritme za sustav određivanja stanja satelita uključujući sunčani senzor i magnetometar. Predložena metodologija temelji se određivanju svih mogućih rotacija među referentnim i stvarnim koordinatnim sustavima i Eulerovim kutevima među njima. Koristeći Eulerove kutove dobivene su varijance pomoću kojih se dobiva rješenje za analitičku detekciju pogreške bez korištenja modela. U slučaju značajnih promjena varijance detektirana je pogreška. Pokazano je da se prikladnim kategoriziranjem izračuna Eulerovih kuteva uz pogreške senzora može i izolirati komponenta senzora koja je uzrokovala pogreku. Na temelju toga predlažu se četiri koraka izolacije pogreške. U prvom koraku, izolirano je postojanje pogreške u samo jednom senzoru. U drugom koraku, istražuju se dvije pogreške u dva različita senzora. U trećem koraku, promatraju se dvije pogreške u jednom senzoru što će značiti visoku razimu pogreške u senzoru. Konačno, ukoliko pogreška ne pripada niti jednoj od navedenih kategorija, to znači da je prisutno oštećenje opreme veće od 50%. Kroz opsežne simulacije prikazano je željeno ponašanje i točnost navedene metode.