Design of an Integrated GPS/Gyroscope-Free INS Sungsu Park Chin-Woo Tan California PATH University of California, Berke

1. Design of an Integrated GPS/Gyroscope-Free INS Sungsu Park Chin-Woo Tan California PATH University of California, Berkeley

2. Outline • Introduction • GF-IMU Kinematics • Identification and Compensation of GF-IMU Errors • GF-INS Kinematics • GF-INS Error Dynamics • GPS-Aided GF-INS • Simulation Results • Conclusions

3. Introduction • Gyro-based Inertial Measurement Unit (IMU) : • - 3Accelerometers to sense linear acceleration • - 3(Rate) Gyroscopes to sense angular velocity • Gyro-Free Inertial Measurement Unit (GF-IMU) : • - Accelerometersonly to compute linear + angular motion • - An order cheaper than Gyro-based IMU • Micro-Electro-Mechanical System(MEMS) Accelerometers: • - lower cost: an order cheaper than MEMS gyroscopes • - less physical constraints that inhabit precision

4. Introduction • Key Feasibility Result for GF-IMU • Given any 6 accelerometers “arbitrarily” located and • oriented, one can compute the linear and angular motion of • a rigid body using a simple algorithm, with the 6 • accelerometer measurements as inputs to the algorithm. • Simplicity of the Algorithm • - General motion equations Angular rate of body relative to inertial frame Force per unit mass on body frame

5. Introduction - A Cube-shaped GF-IMU - Any other GF-IMU: Cube-shaped GF-IMU + Algebraic compensation • Performance depends on specific vehicle dynamics • Rapid response to angular motion • GF-IMU (dis)advantages • GF-IMU aided by an external reference

6. . . . 3 6 . . 5 . 2 4 2L 1 GF-IMU Kinematics • A Cube-shaped GF-IMU:

7. GF-IMU Kinematics Cube GF-IMU 3-axis Gyroscopes 3-axis Accelerometers

8. GF-IMU Kinematics Any Feasible GF-IMU equivalent

9. GF-IMU Error Sources Accelerometer Errors Configuration Errors bias scale factor error noise location errors orientation errors GF-IMU 3-axis Gyroscopes 3-axis Accelerometers

10. GF-IMU Error Sources - Sensitivity • actual motion: (depends only on angular motion) (motion dependent) in-plane deviation angle out of plane deviation angle

11. GF-IMU Error Sources Erroneous Accelerometer Equations Location Errors Cube GF-IMU+location error

12. GF-IMU Error Sources Orientation Errors Cube GF-IMU+orientation error in-plane deviation angle out of plane deviation angle

13. 5 6 4 3 2 1 Identification of Deterministic Errors Identification of scale factor errors (sj), deterministic bias (bj), and orientation errors ( ) • Six cases of stationary alignment of GF-IMU

14. Identification (Cont’d) Identification of scale factor errors (sj), deterministic bias (bj), and orientation errors ( ) • Bias (bj) : • Orientation errors: • Scale factor errors (sj) : • weighting matrix

15. 4 4 5 5 6 6 Identification (Cont’d) Identification of location errors ( ) • Three cases of constant rotational motion of GF-IMU (assuming that scale factor errors and bias are compensated)

16. Identification (Cont’d) Identification of location errors ( ) • location errors :  inverse matrix exists unless

17. Experimental Setup A six-accelerometer gyro-free IMU IMU on a rate table

18. Noise Resolution • Accelerometers: Ex. ADXL105 • Angular acceleration: Ex. L=10cm; ADXL105 • Angular rate uncertainty growth: Ex. L=10cm; ADXL105 • Specific force: Ex. L=10cm; ADXL105

19. GF-INS Kinematics • Velocity Differential Equation (linear motion): • Attitude Differential Equation (angular motion): • Specific Force and Angular Rate Motion Equations:

20. GF-INS Error Dynamics • - uncompensated accelerometer deterministic errors ( ) • - uncompensated location errors ( ) • uncompensated orientation errors ( ) • - accelerometer noise ( ) Conventional Process for INS Error Dynamics GF-IMU • Error growth rate:

21. GF-INS Error Dynamics • 48th-state Error Model: uncompensated location uncompensated bias tilt angle position uncompensated orientation velocity angular rate • 18th-state Error Model (Kalman filter equation): Time-varying lumped bias

22. Comparison of KF Equations • Gyro-Free INS Error Model: • Conventional INS Error Model:

23. GPS-Aided GF-INS GF-INS Algorithms Compensator for GF-IMU error Kalman Filter GPS Correction

24. Simulation Example - dynamics: cylindrical motion • initial conditions: - simulation time: 1 min • final conditions: - cube length: - location errors:

25. Simulation Results GF-INS alone with compensated

26. Simulation Results GF-INS alone with compensated

27. Simulation Results GPS/GF-INS (GPS time=1sec, GPS latency=0.1sec)

28. Simulation Results GPS/GF-INS (GPS time=1sec, GPS latency=0.1sec)

29. Simulation Results (accuracy) GPS/GF-INS (GPS time=1sec, GPS latency=0.1sec)

30. Simulation Results GPS/GF-INS (GPS time=2sec, GPS latency=0.1sec)

31. Simulation Results GPS/GF-INS (GPS time=2sec, GPS latency=0.1sec)

32. Simulation Results GPS/GF-INS (GPS time=2sec, GPS latency=0.1sec)

33. Conclusions • Gyro-Free INS • - cheaper Inertial Navigation System (INS) • - errors diverge faster than conventional INS • GF-INS: • Conventional INS: • - performance depends on the specific vehicle dynamics • - ideal for rapid changes in angular motion • (e.g. motorcycle dynamics)

34. Conclusions • GF-IMU Error Compensator • - providing unified computational framework for • any feasible GF-IMU • - reducing performance sensitivity to vehicle dynamics • Integration with GPS • - stable and cm-accurate position estimates • Implementation of GPS/GF-INS Algorithms in QNX • for in-vehicle tests