Observability Analysis in Navigation Systems with an Underwater Vehicle Application

Precise navigation of autonomous underwater vehicles (AUV) is one of the most important challenges in the realization of distributed and cooperative algorithms for marine applications. We investigate an underwater navigation technology that enables an AUV to compute its trajectory in the presence of unknown currents in real time and simultaneously estimate the currents, using range or distance measurements from a single known location. This approach is potentially useful for small AUVs which have severe volume and power constraints. The main contribution of this work is observability analysis of the proposed navigation system using novel approaches towards uniform observability of linear time-varying (LTV) systems. We utilize the notion of limiting systems in order to address uniform observability of LTV systems. Uniform observability of an LTV system can be studied by assessing finite time observability of its limiting systems. A new definition of uniform observability over a finite interval is introduced in order to address existence of an observer whose estimation error is bounded by an exponentially decaying function on the finite interval. We also show that for a class of LTV systems, uniform observability of a lower dimensional subsystem derived from an LTV system is sufficient for uniform observability of the LTV system. Acknowledgement My deepest gratitude goes to my advisor Dr. Dan Stilwell for his invaluable assistance, guidance, and encouragement in bringing this research work to a successful completion. He showed extraordinary patience and was always available for a friendly advice. I am also grateful to my thesis committee members, Dr. Pushkin Kachroo, for their advise and help. I am grateful to current and past members of the Autonomous Systems and Controls Lab (ASCL) at Virginia Tech. We were a great team and it was a great pleasure knowing them and working with them over all these years. I have acquired a large number of great friends during my years at Virginia Tech. I express my deepest thanks to them, for it was their company and the great moments we shared that kept my spirits high. This is a major milestone in my life and it would not have been possible without love and constant support and encouragement of my parents Shrikant and Anuradha and my wife Amruta. There are innumerable others who were indirectly supportive of my work and I would like to thank all of them from my heart.