Nonlinear Observer for Inertial Navigation Aided by Pseudo-Range and Range-Rate Measurements

Range measurement systems are commonly based on measuring time-of-flight of signals encoded in electromagnetic or acoustic waves. This leads to so-called pseudo range measurements due systematic errors such receiver clock synchronization error and uncertain wave propagation speed. Inertial navigation aided by pseudo-range measurements is addressed. A modular nonlinear observer is designed and analyzed. The attitude observer is based on a recent nonlinear complementary filter, and includes a gyro bias estimation. The translational motion observer includes the estimation of position, range bias errors (such as receiver clock bias), velocity and specific force, where the latter is used as a reference vector by the attitude observer. The exponential stability of the feedback interconnection of the two observers is analyzed and found to have a semiglobal region of attraction with respect to attitude observer initialization, and local region of attraction with respect to translational motion observer initialization. The latter is due to linearization of the pseudo-range and range rate measurement equations that is underlying the selection of injection gains using a time varying Riccati equation. In typical applications the pseudo-range and range-rate equations admit an explicit algebraic solution that can be easily computed and used to accurately initialize the position and velocity estimates. Hence, the limited region of attraction is not seen as a limitation of the approach. Advantages of the proposed nonlinear observer include low computational complexity and a solid theoretical foundation.