Constructive synchronous observer design for inertial navigation with delayed GNSS measurements

Inertial Navigation Systems (INS) estimate a vehicle’s navigation states (attitude, velocity, and position) by combining measurements from an Inertial Measurement Unit (IMU) with other supporting sensors, typically including a Global Navigation Satellite System (GNSS) and a magnetometer. Recent nonlinear observer designs for INS provide powerful stability guarantees but do not account for some of the real-world challenges of INS. One of the key challenges is to account for the time-delay characteristic of GNSS measurements. This paper addresses this question by extending recent work on synchronous observer design for INS. The delayed GNSS measurements are related to the state at the current time using recursively-computable delay matrices, and this is used to design correction terms that leads to almost-globally asymptotic and locally exponential stability of the error. Simulation results verify the proposed observer and show that the compensation of time-delay is key to both transient and steady-state performance.