Nonlinear Observer for Tightly Coupled Integration of Pseudorange and Inertial Measurements

A global nonlinear algebraic transform of nonlinear pseudorange measurement equations enables navigation solutions based on a globally valid linear time-varying measurement model. Using an interconnection of a nonlinear attitude observer and a translational motion observer based on pseudorange and range-range measurements, a tightly coupled integrated aided inertial navigation system is designed. The attitude observer uses a proper acceleration estimate from the translational motion observer as a reference vector for the accelerometer measurement. This leads to a feedback interconnection that is shown to be globally exponentially stable under some conditions on the tuning parameters. The model transformation has eliminated the information about a certain nonlinear relationship that exists among the measurements. While this enables the global solution to be found, it also leads to loss of estimation accuracy when there is measurement noise. In order to recover close-to-optimal (minimum variance) estimates, the observer estimates are only used to generate a locally linearized time-varying model that is subsequently employed by a Kalman filter, without loss of global convergence.

[1]  F. Markley.  Attitude Error Representations for Kalman Filtering , 2003 .

[2]  Carlos Silvestre,et al.  Position and Velocity USBL/IMU Sensor-based Navigation Filter , 2011 .

[3]  Tor Arne Johansen,et al.  Nonlinear observer for inertial navigation aided by pseudo-range and range-rate measurements , 2015, 2015 European Control Conference (ECC).

[4]  Carlos Silvestre,et al.  Sensor‐Based Long Baseline Navigation: Observability Analysis and Filter Design , 2014 .

[5]  P. Groves.  Principles of GNSS, Inertial, and Multi-Sensor Integrated Navigation Systems , 2007 .

[6]  P. Olver.  Nonlinear Systems , 2013 .

[7]  Tor Arne Johansen,et al.  Attitude Estimation Using Biased Gyro and Vector Measurements With Time-Varying Reference Vectors , 2012, IEEE Transactions on Automatic Control.

[8]  Pedro Batista.  GES Long Baseline Navigation With Unknown Sound Velocity and Discrete-Time Range Measurements , 2015, IEEE Trans. Control. Syst. Technol..

[9]  Itzhack Y. Bar-Itzhack,et al.  Recursive Attitude Determination from Vector Observations: Direction Cosine Matrix Identification , 1984 .

[10]  Richard A. Brown,et al.  Introduction to random signals and applied kalman filtering (3rd ed , 2012 .

[11]  Graham C. Goodwin,et al.  Three-stage filter for position estimation using pseudorange measurements , 2016, IEEE Transactions on Aerospace and Electronic Systems.

[12]  R. E. Kalman,et al.  New Results in Linear Filtering and Prediction Theory , 1961 .

[13]  K. Radio,et al.  An Algebraic Solution of the GPS Equations , 1985 .

[14]  Timothy W. McLain,et al.  Small Unmanned Aircraft: Theory and Practice , 2012 .

[15]  J. Chaffee,et al.  On the exact solutions of pseudorange equations , 1994 .

[16]  Tor Arne Johansen,et al.  Globally exponentially stable attitude and gyro bias estimation with application to GNSS/INS integration , 2015, Autom..

[17]  B. Anderson.  Stability properties of Kalman-Bucy filters , 1971 .

[18]  Jay A. Farrell,et al.  Aided Navigation: GPS with High Rate Sensors , 2008 .

[19]  Carlos Silvestre,et al.  Sensor-Based Globally Asymptotically Stable Filters for Attitude Estimation: Analysis, Design, and Performance Evaluation , 2012, IEEE Transactions on Automatic Control.