Moving Horizon Estimation for Integrated Navigation Filtering

Abstract This paper presents a nonlinear numerical observer for accurate position, velocity and attitude (PVA) estimation including the accelerometer bias and gyro bias estimation. The Moving Horizon Observer (MHO) processes the accelerometer, gyroscope and magnetometer measurements from the Inertial Measurement Unit (IMU) and the position and velocity measurements from the Global Navigation Satellite System (GNSS). The nonlinear measurement equations with the rotation matrix, expressed through the quaternion parametrization, in combination with the state-space rigid body kinematic model of translational and rotational motion is the subject of optimization defined on a receding data window. The gradient-based trust-region method is applied to solve the MHO's nonlinear least-squares criterion. The MHO is tesed off-line in the numerical experiment involving the experimental flight data from a light fixed-wing aircraft. This study demonstrates the quality of the MHO computations with the comparison of the reference filter, the multiplicative Extended Kalman Filter (EKF).

[1]  Tor Arne Johansen,et al.  Nonlinear observer for GNSS-aided inertial navigation with quaternion-based attitude estimation , 2013, 2013 American Control Conference.

[2]  James B. Rawlings,et al.  Critical Evaluation of Extended Kalman Filtering and Moving-Horizon Estimation , 2005 .

[3]  Tor Arne Johansen,et al.  Moving horizon observer with regularisation for detectable systems without persistence of excitation , 2011, Int. J. Control.

[4]  B. Hofmann-Wellenhof,et al.  Global Positioning System , 1992 .

[5]  M. Psiaki.  Attitude-Determination Filtering via Extended Quaternion Estimation , 2000 .

[6]  D. Y. Hsu.  Comparison of four gravity models , 1996, Proceedings of Position, Location and Navigation Symposium - PLANS '96.

[7]  F. Markley,et al.  Unscented Filtering for Spacecraft Attitude Estimation , 2003 .

[8]  G. Wahba.  A Least Squares Estimate of Satellite Attitude , 1965 .

[9]  I. Bar-Itzhack.  REQUEST: A Recursive QUEST Algorithm for Sequential Attitude Determination , 1996 .

[10]  J. Crassidis,et al.  Particle Filtering for Sequential Spacecraft Attitude Estimation , 2004 .

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

[12]  Jan Swevers,et al.  Spacecraft Attitude Estimation and Sensor Calibration Using Moving Horizon Estimation , 2013 .

[13]  Esmat Bekir.  Introduction to Modern Navigation Systems , 2007 .

[14]  Joanna C. Hinks,et al.  Numerical Solution of a Generalized Wahba Problem for a Spinning Spacecraft , 2011 .

[15]  M. Shuster,et al.  Three-axis attitude determination from vector observations , 1981 .

[16]  E. Glenn Lightsey,et al.  Sequential Optimal Attitude Recursion Filter , 2010 .

[17]  Giorgio Battistelli,et al.  Moving-horizon state estimation for nonlinear discrete-time systems: New stability results and approximation schemes , 2008, Autom..

[18]  David Q. Mayne,et al.  Constrained state estimation for nonlinear discrete-time systems: stability and moving horizon approximations , 2003, IEEE Trans. Autom. Control..

[19]  Marcello R. Napolitano,et al.  Sensitivity Analysis of Extended and Unscented Kalman Filters for Attitude Estimation , 2013, J. Aerosp. Inf. Syst..

[20]  John L. Crassidis,et al.  Survey of nonlinear attitude estimation methods , 2007 .

[21]  Stephen J. Wright,et al.  Numerical Optimization , 2018, Fundamental Statistical Inference.

[22]  F. Landis Markley,et al.  Kalman Filter for Spinning Spacecraft Attitude Estimation , 2007 .

[23]  E. J. Lefferts,et al.  Kalman Filtering for Spacecraft Attitude Estimation , 1982 .

[24]  Yaakov Oshman,et al.  Adaptive Particle Filtering for Spacecraft Attitude Estimation from Vector Observations , 2009 .