EE 570 Location and Navigation Theory Practice Navigation

EE 570: Location and Navigation: Theory & Practice Navigation Sensors and INS Mechanization Tuesday 12 Feb 2013 NMT EE 570: Location and Navigation: Theory & Practice Slide 1 of 19

Navigation Sensors and INS Mechanization Inertial Sensors • As the name implies inertial sensors measure motion wrt an inertial frame § Advantages: Self-contained & non-reliant on external fields (e. g. EM radiation, Earth’s magnetic field, …) § Disadvantages: Typically rate measurements & expensive • Accelerometers measure linear acceleration § Actually measure specific force, typically, in the body frame • Gyroscopes measure angular velocity § Most gyroscopes measure angular speed, typically, in the body frame Tuesday 12 Feb 2013 NMT EE 570: Location and Navigation: Theory & Practice Slide 2 of 19

Navigation Sensors and INS Mechanization Inertial Sensors - Accelerometer Inertial Sensors Accelerometers Pendulous Mass Closed loop Open loop Tuesday 12 Feb 2013 Gyroscopes Vibratory Closed loop Open loop NMT EE 570: Location and Navigation: Theory & Practice Slide 3 of 19

Navigation Sensors and INS Mechanization Inertial Sensors - Gyroscope Inertial Sensors Accelerometers Gyroscopes Tuesday 12 Feb 2013 NMT EE 570: Location and Navigation: Theory & Practice magnetohydrodynamic Conductive fluid based Interferometer Microelectromechanical Resonator Hemispherical Resonator Gyro Coriolis Effect Fiber Optic Gyro DTG Mech Suspension Magnetic Suspension Fluid Suspension Floated Sagnac Effect Ring Laser Gyro Rotating Mass Slide 4 of 19

Navigation Sensors and INS Mechanization Inertial Sensors – Accelerometer: Pendulous Mass b Reaction force Acceleration due to gravity k spring Mass damper displacement (x) • Sense axis Tuesday 12 Feb 2013 NMT EE 570: Location and Navigation: Theory & Practice Slide 5 of 19

Navigation Sensors and INS Mechanization Inertial Sensors – Accelerometer: Pendulous Mass • Closed-loop version generates a force to null the displacement § Can improve linearity and measurement range Tuesday 12 Feb 2013 NMT EE 570: Location and Navigation: Theory & Practice Slide 6 of 19

Navigation Sensors and INS Mechanization Inertial Sensors – Accelerometer: Pendulous Mass • Pendulous Accelerometer § Closed loop configuration Improved linearity Sensitive axis o Figure: Clipp (2006) Tuesday 12 Feb 2013 NMT EE 570: Location and Navigation: Theory & Practice Slide 7 of 19

Navigation Sensors and INS Mechanization Inertial Sensors – Accelerometer: Vibratory • Vibratory accelerometers Sensitive axis § Vibrating Beam Accelerometers (VBA) § Acceleration causes a change in resonance frequency Mass Tuesday 12 Feb 2013 NMT EE 570: Location and Navigation: Theory & Practice Slide 8 of 19

Navigation Sensors and INS Mechanization Inertial Sensors - Accelerometer: Vibratory • MEMS Accelerometers www. ett. bme. hu/memsedu Tuesday 12 Feb 2013 NMT EE 570: Location and Navigation: Theory & Practice Slide 9 of 19

Navigation Sensors and INS Mechanization Inertial Sensors - Accelerometer: Vibratory • MEMS Accelerometers § Spring and mass from silicon and add fingers make a variable differential capacitor § Change in displacement => change in capacitance SENSOR AT REST SENSOR ACCELERATING SPRING APPLIED ACCELERATION MASS FIXED Tuesday 12 Feb 2013 ANCHOR TO SUBSTRATE CS 1 < CS 2 NMT EE 570: Location and Navigation: Theory & Practice Slide 10 of 19

Navigation Sensors and INS Mechanization Inertial Sensors – Gyroscopes: Rotating Mass • Rotating Mass Gyros § Conservation of Angular Momentum § The spinning mass will resist change in its angular momentum § Angular momentum o H = I (Inertia * Angular velocity) § By placing the gyro in a pair of frictionless gimbals it is free to maintain its inertial spin axis § By placing an index on the x-gimbal axes and y-gimbal axis two degrees of orientational motion can be measured Tuesday 12 Feb 2013 NMT EE 570: Location and Navigation: Theory & Practice Slide 11 of 19

Navigation Sensors and INS Mechanization Inertial Sensors – Gyroscopes: Rotating Mass • Rotating Mass Gyros o – = H t) o Disk is spinning about z-axis Apply a torque about the x-axis Results in precession about the y-axis dt H(t+d o H(t) § Precession z y Precession rate ( ) Tuesday 12 Feb 2013 NMT EE 570: Location and Navigation: Theory & Practice x Slide 12 of 19

Navigation Sensors and INS Mechanization Inertial Sensors – Gyroscopes: Sagnac Effect Gyros • Fiber Optical Gyro (FOG) § Basic idea is that light travels at a constant speed § If rotated (orthogonal to the plane) one path length becomes longer and the other shorter § This is known as the Sagnac effect § Measuring path length change (over a dt) allows to be measured R itt m ns a Tr Tuesday 12 Feb 2013 NMT EE 570: Location and Navigation: Theory & Practice er De te cto r Slide 13 of 19

Navigation Sensors and INS Mechanization Inertial Sensors - Gyroscopes: Sagnac Effect Gyros • Fiber Optical Gyro (FOG) itte Tr m ans itt m s an Tr Splitter er r De te cto r r cto NMT EE 570: Location and Navigation: Theory & Practice r R R te Tuesday 12 Feb 2013 De § Measure the time difference betw the CW and CCW paths § CW transit time = t. CW § CCW transit time = t. CCW § LCW = 2 R+R t. CW = ct. CW § LCCW = 2 R-R t. CCW = ct. CCW § t. CW = 2 R/(c-R ) § t. CCW= 2 R/(c+R ) § With N turns § Phase Slide 14 of 19

Navigation Sensors and INS Mechanization Inertial Sensors - Gyroscopes: Sagnac Effect Gyros • Ring Laser Gyro § A helium-neon laser produces two light beams, one traveling in the CW direction and the other in the CCW direction § When rotating o o o The wavelength in dir of rotation increases (decrease in freq) The wavelength in opposite dir decreases (increase in freq) Similarly, it can be shown that Tuesday 12 Feb 2013 NMT EE 570: Location and Navigation: Theory & Practice Slide 15 of 19

Navigation Sensors and INS Mechanization Inertial Sensors - Gyroscopes: Coriolis Effect • Vibratory Coriolis Angular Rate Sensor § Virtually all MEMS gyros are based on this effect Li ne ar m ot io n Tuesday 12 Feb 2013 NMT EE 570: Location and Navigation: Theory & Practice Slide 16 of 19

Navigation Sensors and INS Mechanization Inertial Sensors - Gyroscopes: Coriolis Effect • Basic Planar Vibratory Gyro Tuesday 12 Feb 2013 NMT EE 570: Location and Navigation: Theory & Practice Slide 17 of 19

Navigation Sensors and INS Mechanization Inertial Sensors - Gyroscopes: Coriolis Effect • In plane sensing (left) • Out of plane sensing (right) www. ett. bme. hu/memsedu Tuesday 12 Feb 2013 NMT EE 570: Location and Navigation: Theory & Practice Slide 18 of 19

Navigation Sensors and INS Mechanization Inertial Sensors - Summary • Accelerometers § Measure specific force of the body frame wrt the inertial frame in the body frame coordinates o Need to subtract the acceleration due to gravity to obtain the motion induced quantity § In general, all points on a rigid body do NOT experience the same linear velocity • Gyroscopes § Measure the inertial angular velocity o Essentially, the rate of change of orientation § All points on a rigid body experience the same angular velocity Tuesday 12 Feb 2013 NMT EE 570: Location and Navigation: Theory & Practice Slide 19 of 19