EE 570: Location and Navigation

Transcription

1 EE 570: Location and Navigation Sensor Technology Stephen Bruder 1 Aly El-Osery 2 1 Electrical and Computer Engineering Department, Embry-Riddle Aeronautical Univesity Prescott, Arizona, USA 2 Electrical Engineering Department, New Mexico Tech Socorro, New Mexico, USA February 26, 2014 Stephen Bruder, Aly El-Osery (ERAU,NMT) EE 570: Location and Navigation February 26, / 14

2 Terminology Accuracy: Proximity of the measurement to the true value Precision: 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 Probability density Digital Output Reference value Accuracy Precision 4/8 8/8 LSB Full Scale value Stephen Bruder, Aly El-Osery (ERAU,NMT) EE 570: Location and Navigation February 26, / 14

3 Accuracy vs Precision Stephen Bruder, Aly El-Osery (ERAU,NMT) EE 570: Location and Navigation February 26, / 14

4 Inertial Sensors Bias Errors Bias often the most critical error Fixed Bias b FB Deterministic in nature and can be addressed by calibration Often modeled as a function of temperature Bias Stability b BS Varies from run-to-run as a random constant Bias Instability b BI In-run bias drift typically modeled as random walk Bias Errors f = b a,fb + b a,bi + b a,bs = b a ω = b g,fb + b g,bi + b g,bs = b g Stephen Bruder, Aly El-Osery (ERAU,NMT) EE 570: Location and Navigation February 26, / 14

5 Inertial Sensors Scale Factor Errors Fixed scale factor error Deterministic in nature and can be addressed by calibration Often modeled as a function of temperature Scale Factor Stability s a (accel) or s g (gyro) Varies from run-to-run as a random constant Typically given in parts-per-million (ppm) Scale Factor Errors f = s a f ω = s g ω output Measured 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 True input Stephen Bruder, Aly El-Osery (ERAU,NMT) EE 570: Location and Navigation February 26, / 14

6 Inertial Sensors Misalignment Refers to the angular difference between the ideal sense axis alignment and true sense axis vector a deterministic quantity typically given in milliradians f z = m a,zx f x + m a,zy f y ω z = m g,zx ω x + m g,zy ω y Combining misalignment & scale factor s a,x m a,xy m a,xz f x f = m a,yx s a,y m a,yz f y = M a f b ib m a,zx m a,zy s a,z f z Stephen Bruder, Aly El-Osery (ERAU,NMT) EE 570: Location and Navigation February 26, / 14

7 Inertial Sensors 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 Stephen Bruder, Aly El-Osery (ERAU,NMT) EE 570: Location and Navigation February 26, / 14

8 Inertial Sensors Other Noise Sources Typically characterized as additive in nature May have a compound form white noise Gyros: white noise in rate Angle Random Walk (ARW) Accels: white noise in accel Velocity Random Walk (VRW) Quantization noise May be due to LSB resolution in ADC s Flicker noise Colored noise Stephen Bruder, Aly El-Osery (ERAU,NMT) EE 570: Location and Navigation February 26, / 14

9 Inertial Sensors Gyro Specific Errors G-sensitivity The gyro may be sensitive to acceleration Primarily due to device mass assymetry Mostly in Coriolis-based devices (MEMS) ω b ib = G g f b ib a G 2 -Sensitivity Anisoelastic effects Due to products of orthogonal forces Stephen Bruder, Aly El-Osery (ERAU,NMT) EE 570: Location and Navigation February 26, / 14

10 Inertial Sensors Accel Specific Errors Axis Offset The accel may be mounted at a lever-arm distance from the center of the Inertial Measurement Unit (IMU) Leads to an ω 2 r type effect f x = ω 2 y x +ω 2 z x = ( ω 2 y + ω 2 z ) x Stephen Bruder, Aly El-Osery (ERAU,NMT) EE 570: Location and Navigation February 26, / 14

11 Inertial Sensors Sensor Models Accelerometer model f b ib = f b ib + f b ib = b a + (I + M a ) f b ib + w a (1) Gyro Model ω b ib = ω b ib + ω b ib = b g + (I + M g ) ω b ib + G g f b ib + w g (2) Typically, each measures along a signle sense axis requiring three of each to measure the 3-tupple vector Stephen Bruder, Aly El-Osery (ERAU,NMT) EE 570: Location and Navigation February 26, / 14

12 Current Accel Application Areas Stephen Bruder, Aly El-Osery (ERAU,NMT) EE 570: Location and Navigation February 26, / 14

13 Current Gyro Application Areas Stephen Bruder, Aly El-Osery (ERAU,NMT) EE 570: Location and Navigation February 26, / 14

14 Grades, Performance and Cost Different Grades of inertial sensors Cost as a function of performance and technology Stephen Bruder, Aly El-Osery (ERAU,NMT) EE 570: Location and Navigation February 26, / 14