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Research Papers

Nonlinear Observer for Tightly Integrated Inertial Navigation Aided by Pseudo-Range Measurements

[+] Author and Article Information
Tor A. Johansen

Department Engineering Cybernetics,
Center for Autonomous Marine Operations
and Systems (NTNU-AMOS),
Norwegian University of Science
and Technology,
Trondheim 7491, Norway
e-mail: tor.arne.johansen@itk.ntnu.no

Jakob M. Hansen

Department Engineering Cybernetics,
Center for Autonomous Marine Operations
and Systems (NTNU-AMOS),
Norwegian University of Science and Technology,
Trondheim 7491, Norway

Thor I. Fossen

Department Engineering Cybernetics,
Center for Autonomous Marine Operations
and Systems (NTNU-AMOS),
Norwegian University of Science
and Technology,
Trondheim 7491, Norway
e-mail: thor.fossen@ntnu.no

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received March 5, 2015; final manuscript received August 7, 2016; published online October 17, 2016. Assoc. Editor: Jingang Yi.

J. Dyn. Sys., Meas., Control 139(1), 011007 (Oct 17, 2016) (10 pages) Paper No: DS-15-1088; doi: 10.1115/1.4034496 History: Received March 05, 2015; Revised August 07, 2016

A modular nonlinear observer for inertial navigation aided by pseudo-range measurements is designed and analyzed. The attitude observer is based on a recent nonlinear complementary filter that uses magnetometer and accelerometer vector measurements to correct the quaternion attitude estimate driven by gyro measurements, including gyro bias estimation. A tightly integrated translational motion observer is driven by accelerometer measurements, employs the attitude estimates, and makes corrections using the pseudo-range and range-rate measurements. It estimates position, range bias errors, velocity and specific force in an earth-fixed Cartesian coordinate frame, where the specific force estimate is used as a reference vector for the accelerometer measurements in 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 the attitude observer initialization and local region of attraction with respect to translational motion observer initialization. The latter is due to linearization of the range measurement equations that is underlying the selection of injection gains by solving a Riccati equation. In typical applications, the pseudo-range 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 practical limitation of the approach for many applications. Advantages of the proposed nonlinear observer are low computational complexity and a solid theoretical foundation.

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Figures

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Fig. 1

Observer block diagram

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Fig. 2

Trajectory of the unmanned aerial vehicle (UAV)

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Fig. 3

Position estimation errors of nonlinear observer (red), nonlinear observer with ARE (black), and MEKF (blue). The RTK solution is used as reference.

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Fig. 4

Estimated attitude of nonlinear observer (red), nonlinear observer with ARE (black), and MEKF (blue)

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