Inertial navigation systems
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The document discusses inertial measurement units (IMUs), detailing their components including accelerometers and gyroscopes that measure linear and angular motion in three dimensions. It explains how accelerations are integrated to determine velocity and position, and outlines the key errors and calibration methods necessary for accurate measurements. Applications of IMUs span various fields such as navigation, robotics, and aircraft tracking.
Inertial navigation systems
- 1. AHRS By: Vikas Kumar Sinha 07/02/19 1
- 2. An inertial measurement unit (IMU) measures linear and angular motion in three dimensions without external reference. The IMU consists of two orthogonal sensor triads, one consisting of three accelerometers, the other of three gyroscopes 07/02/19 2
- 3. Fig 1: Inertial measurement unit 07/02/19 3
- 4. Fig 2: The body and global frames of reference. 07/02/19 4
- 5. • If we can measure the acceleration of a vehicle we can • integrate the acceleration to get velocity • integrate the velocity to get position • Then, assuming that we know the initial position and velocity we can determine the position of the vehicle at ant time t. Formula: ..(1) 07/02/19 5
- 7. The three axes of the aircraft are: The roll axis which is roughly parallel to the line joining the nose and the tail Positive angle: right wing down The pitch axis which is roughly parallel to the line joining the wingtips Positive angle: nose up The yaw axis is vertical Positive angle: nose to the right 07/02/19 7
- 8. Accelerometers are defined as acceleration sensors that measure the non-gravitational linear acceleration along their sensitive axis. F=M*A …(2) F=K*X …(3) Where: F= force M= mass A =acceleration X= displacement 07/02/19 8
- 9. Applications Motion, vibration, blast, shock wave In this way X α A ………(4) Fig 4: basic sturcture of accelerometer 07/02/19 9
- 11. A gyroscope is a device for measuring of maintaining orientation based on the principle of angular momentum(rotation momentum) Fig: 6 07/02/19 11
- 12. Uses Coriolis effect using vibrating elements ▪ Fc -Force m -mass w -angular velocity v –velocity Fig: 7 07/02/19 12
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- 17. ….(5) ….(6) Where: a = true specific force vector ω = body frame rotation rate vector b = bias vector S = scale factor matrix N = non-orthogonality error matrix η = non-deterministic accelerometer errors 07/02/19 17
- 18. Six Position Static Test Rotation Rate Test Thermal Test Multi-Position Calibration Method Modified Multi-Position Calibration Method Allan Variance approach 07/02/19 18
- 20. ….(9) the ideal accelerations would be measured as: …(10) 07/02/19 20
- 21. design matrix (A) for the least squares …(11) The raw output of the sensors (in volts) constitutes the matrix U: …(12) 07/02/19 21
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- 23. Using the least squares method as follows: …(14) 07/02/19 23
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- 26. General calibration model as below for accelerometer : …(17) By using the same methodology, we can derive the general model for the gyros as: …(18) Where ωe is the true Earth rotation rate. 07/02/19 26
- 27. Rotation matrix: , Ry …(19) The non-orthogonality of the z axis can be expressed by two consecutive rotations; rotation about the x axis by θzx and about the y axis by θzy. …(20) 07/02/19 27
- 28. ... (21) The accelerometers on the IMU axes sense the following values: . .. ..(22) 07/02/19 28
- 29. Inclusion of the major errors, bias and scale factor error, into the IMU data is done by the equation below: ..(23) Where Ya , b, a ,s IMU observation, bias and scale factor error, respectively, for the accelerometer and i = x, y and z. 07/02/19 29
- 30. The observation equations for the accelerometer sensors on the IMU axis triad will be obtained as below: ….(24) 07/02/19 30
- 31. The true values for the specific force vector components are found as: (26) 07/02/19 31
- 32. Navigation Use in quadcopter Tracking Robotics Aircraft 07/02/19 32
- 33. We estimate the value of bias, scale and non-orthogonality errors. By using these methods we will get an error less IMU sensor. 07/02/19 33
- 34. To evaluate the contribution of the calibration and stochastic error modeling with thermal compensation Investigation of a general model including both deterministic and stochastic noise terms 07/02/19 34
- 35. P. Aggarwal, Z. Syed, X. Niu, and N. El-Sheimy, "A standard testing and calibration procedure for low cost MEMS inertial sensors and units," Journal of navigation, vol. 61, pp. 323- 336, 2008. W. Fong, S. Ong, and A. Nee, "Methods for in-field user calibration of an inertial measurement unit without external equipment," Measurement Science and Technology, vol. 19, p. 085202, 2008 S. Nassar, “Improving the inertial navigation system (INS) error model for INS and INS/DGPS applications” University of Calgary, Department of Geomatics Engineering, 2003. 07/02/19 35