A Generic Observer Design for Inertial Navigation Systems Using an LTV Framework

Abstract: This paper addresses the problem of accurate pose estimation-position, velocity, and orientation-of a rigid body using an Inertial Measurement Unit (IMU) in combination with generic exteroceptive measurements. By reformulating the vehicle's dynamics and measurement models within a linear time-varying (LTV) framework, we enable the application of a linear Kalman filter, significantly simplifying observer design for inertial navigation systems (INS). A key strength of this approach lies in its generality: rather than relying on specific measurement modalities, our framework accommodates a broad class of exteroceptive measurements. To illustrate its effectiveness, we conduct a uniform observability (UO) analysis for two fundamental benchmark cases-GPS-aided INS and landmark-aided INS-deriving sufficient conditions that guarantee the global uniform exponential stability of the proposed filter. Simulations for both applications confirm the versatility and robustness of our approach.