EE 570: Location and Navigation: Theory & Practice

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1 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

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

2 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

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

4 Inertial Sensor Modeling Error Sources Bias Often the most critical error source Fixed Bias o Deterministic in nature and can be addressed by calibration o Often modeled as a function of temperature Bias Stability b FB o Varies from run-to-run as a random constant Bias Instability b BS b BI b b b o In-run bias drift Typically modeled as a random walk b static FB BS dynamic f ba, BI ba, FB ba, BS ba bg, BI bg, FB bg, BS bg b BI 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

Inertial Sensor Modeling Error Sources Output Scale Factor Fixed Scale Factor Error o Deterministic in nature and can be addressed by calibration o Often modeled as a function of temperature Scale

5 Inertial Sensor Modeling Error Sources Output Scale Factor Fixed Scale Factor Error o Deterministic in nature and can be addressed by calibration o Often modeled as a function of temperature Scale Factor Stability s a (accel) or s g (gyro) o Varies from run-to-run as a random constant o Typically given in parts-per-million (ppm) f s f sg a 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 s a Ref: Park, 04 Scale Factor Error Input Thursday 14 Feb 2013 NMT EE 570: Location and Navigation: Theory & Practice Slide 5 of 14

6 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 fz ma, zx f x ma, zy f y z mg, zx x mg, zy y Normalized z-sense axis Combining Misalignment & Scale Factor b z s m m f f m s m f M f m m s f a, x a, xy a, xz x b a, yx a, y a, yz y a ib a, zx a, zy a, z z m zy m zx b y b x Thursday 14 Feb 2013 NMT EE 570: Location and Navigation: Theory & Practice Slide 6 of 14

7 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

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:

8 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

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

10 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 f x x x x y z y z z y x Thursday 14 Feb 2013 NMT EE 570: Location and Navigation: Theory & Practice Slide 10 of 14

11 Inertial Sensor Modeling Sensor Models Accelerometer model f f f b I M f w b b b b ib ib ib a a ib a Gyro Model b I M G f w b b b b b ib ib ib g g ib g ib g 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

12 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

13 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

Tutorial, Norwegian Space Centre, 2008.06.

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

IMU06WP. What is the IMU06?

IMU06WP. What is the IMU06? IMU06 What is the IMU06? The IMU06 is a compact 6 degree of freedom inertial measurement unit. It provides 3 axis acceleration (maximum 10G) and angular velocities (maximum 300 degrees/s) on both CAN and