EE 570 Location and Navigation Theory Practice Navigation

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EE 570: Location and Navigation: Theory & Practice Navigation Sensors and INS Mechanization Thursday

EE 570: Location and Navigation: Theory & Practice Navigation Sensors and INS Mechanization Thursday 14 Feb 2013 NMT EE 570: Location and Navigation: Theory & Practice Slide 1 of 14

Navigation Sensors and INS Mechanization Inertial Sensor Modeling - Terminology • Accuracy: Akin to

Navigation Sensors and INS Mechanization Inertial Sensor Modeling - Terminology • Accuracy: Akin to the mean § Proximity of the measurement to the true value • Precision: Akin to the standard deviation § The consistency with which a measurement can be obtained • Resolution: § The magnitude of the smallest detectable change. • Sensitivity: § The ratio between the change in the output signal to a small change in input physical signal. Slope of the input-output fit line. • Linearity: § The deviation of the output from a "best” straight line fit for a given range of the sensor Thursday 14 Feb 2013 NMT EE 570: Location and Navigation: Theory & Practice Slide 2 of 14

Navigation Sensors and INS Mechanization Inertial Sensor Modeling – Accuracy vs Precision Accurate but

Navigation Sensors and INS Mechanization Inertial Sensor Modeling – Accuracy vs Precision Accurate but not precise Neither accurate nor precise Precise but not accurate Thursday 14 Feb 2013 Both accurate and precise NMT EE 570: Location and Navigation: Theory & Practice Slide 3 of 14

Navigation Sensors and INS Mechanization Inertial Sensor Modeling – Error Sources • Bias –

Navigation Sensors and INS Mechanization Inertial Sensor Modeling – Error Sources • Bias – Often the most critical error source § Fixed Bias o o Deterministic in nature and can be addressed by calibration Often modeled as a function of temperature § Bias Stability o Varies from run-to-run as a random constant § Bias Instability o In-run bias drift – Typically modeled as a random walk Gyro bias errors are a major INS error source Thursday 14 Feb 2013 NMT EE 570: Location and Navigation: Theory & Practice Slide 4 of 14

Navigation Sensors and INS Mechanization Inertial Sensor Modeling – Error Sources • Ref: Park,

Navigation Sensors and INS Mechanization Inertial Sensor Modeling – Error Sources • Ref: Park, 04 Output Scale Factor Error The scale factor represents a linear approximation to the steady-state sensor response over a given input range – True sensor response may have some non-linear characteristics Thursday 14 Feb 2013 NMT EE 570: Location and Navigation: Theory & Practice e d Tru ure s a Me Input Slide 5 of 14

Navigation Sensors and INS Mechanization Inertial Sensor Modeling – Error Sources • Misalignment §

Navigation Sensors and INS Mechanization Inertial Sensor Modeling – Error Sources • Misalignment § Refers to the angular difference between the ideal sense axis alignment and true sense axis vector o A deterministic quantity typically given in milliradians z-se nse a § Combining Misalignment & Scale Factor xis Normalized z-sense axis Thursday 14 Feb 2013 NMT EE 570: Location and Navigation: Theory & Practice Slide 6 of 14

Navigation Sensors and INS Mechanization Inertial Sensor Modeling – Error Sources • Cross-Axis Response

Navigation Sensors and INS Mechanization Inertial Sensor Modeling – Error Sources • Cross-Axis Response § Refers to the sensor output which occurs when the device is presented with a stimulus which is vectorially orthogonal to the sense axis Misalignment and cross-axis response are often difficult to distinguish – Particularly during testing and calibration activities Thursday 14 Feb 2013 NMT EE 570: Location and Navigation: Theory & Practice Slide 7 of 14

Navigation Sensors and INS Mechanization Inertial Sensor Modeling – Error Sources • Other noise

Navigation Sensors and INS Mechanization Inertial Sensor Modeling – Error Sources • Other noise sources § Typically characterized as additive in nature o May have a compound form – White noise » Gyros: White noise in rate Angle random walk » Accels: White noise in accel Velocity random walk – Quantization noise » May be due to LSB resolution in ADC’s – Flicker noise – Colored noise A more detailed discussion of noise will be given at a later date Thursday 14 Feb 2013 NMT EE 570: Location and Navigation: Theory & Practice Slide 8 of 14

Navigation Sensors and INS Mechanization Inertial Sensor Modeling – Error Sources • Gyro Specific

Navigation Sensors and INS Mechanization Inertial Sensor Modeling – Error Sources • Gyro Specific Errors § G-sensitivity o o o The gyro may be sensitive to acceleration Primarily due to device mass assymetry Mostly in Coriolis-based devices (MEMS) § G 2 -Sensitivity o o Anisoelastic effects Due to products of orthogonal forces Thursday 14 Feb 2013 NMT EE 570: Location and Navigation: Theory & Practice Slide 9 of 14

Navigation Sensors and INS Mechanization Inertial Sensor Modeling – Error Sources • Accelerometer Specific

Navigation Sensors and INS Mechanization Inertial Sensor Modeling – Error Sources • Accelerometer Specific Errors § Axis Offset o The accel may be mounted at a leverarm distance from the “center” of the Inertial Measurement Unit (IMU) – Leads to an “ 2 r” type effect Thursday 14 Feb 2013 NMT EE 570: Location and Navigation: Theory & Practice Slide 10 of 14

Navigation Sensors and INS Mechanization Inertial Sensor Modeling – Sensor Models • Accelerometer model

Navigation Sensors and INS Mechanization Inertial Sensor Modeling – Sensor Models • Accelerometer model • Gyro Model • Typically, each measures along a single sense axis requiring three of each to measure the 3 -tupple vector Thursday 14 Feb 2013 NMT EE 570: Location and Navigation: Theory & Practice Slide 11 of 14

Navigation Sensors and INS Mechanization Inertial Sensor Modeling – Applications • Current Accelerometer Application

Navigation Sensors and INS Mechanization Inertial Sensor Modeling – Applications • Current Accelerometer Application Areas Ref: “INS/GPS Technology Trends“ by George T. Schmidt RTO-EN-SET-116(2010 ) Thursday 14 Feb 2013 NMT EE 570: Location and Navigation: Theory & Practice Slide 12 of 14

Navigation Sensors and INS Mechanization Inertial Sensor Modeling – Applications • Current Gyro Application

Navigation Sensors and INS Mechanization Inertial Sensor Modeling – Applications • Current Gyro Application Areas Earth Rate Ref: “INS/GPS Technology Trends“ by George T. Schmidt RTO-EN-SET-116(2010 ) Thursday 14 Feb 2013 NMT EE 570: Location and Navigation: Theory & Practice Slide 13 of 14

Navigation Sensors and INS Mechanization Inertial Sensor Modeling – Applications Different “Grades” of Inertial

Navigation Sensors and INS Mechanization Inertial Sensor Modeling – Applications Different “Grades” of Inertial Sensors Cost as a function of Performance and technology Ref: INS Tutorial, Norwegian Space Centre, 2008. 06. 09 Thursday 14 Feb 2013 NMT EE 570: Location and Navigation: Theory & Practice Slide 14 of 14