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IEEE 1293 2018:2019 Edition

IEEE 1293 2018:2019 Edition

$105.08

IEEE Standard Specification Format Guide and Test Procedure for Linear Single-Axis, Nongyroscopic Accelerometers

Published By Publication Date Number of Pages
IEEE 2019 271
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Revision Standard – Active. The specification and test requirements for a linear, single-axis, nongyroscopic accelerometer for use in inertial navigation, guidance, and leveling systems are defined. A standard specification guide and a compilation of recommended test procedures for such accelerometers are provided. Informative annexes are given on the various types of such accelerometers (force or pendulous torque rebalance with analog or digital output, vibrating beam, and micromechanical) and error effects, on filtering, noise, and transient analysis techniques, and on calibration and modeling techniques (multipoint tumble analysis, vibration and shock test analyses, and geophysical effects in inertial instrument testing).

PDF Catalog

PDF Pages PDF Title
1 IEEE Std 1293-2018 Front Cover
2 Title Page
3 Abstract/Keywords
4 Important Notices and Disclaimers Concerning IEEE Standards Documents
7 Participants
9 Introduction
11 Contents
15 1. Overview
1.1 Scope
1.2 Purpose
1.3 Document structure
16 2. Normative references
Part I—Specification format
3. Overview
3.1 Scope
17 3.2 Purpose
4. Applicable documents
18 4.1 Specifications
4.1.1 Government
4.1.2 Industry/technical
4.1.3 Company
4.2 Standards
4.2.1 Government
4.2.2 Industry/technical
4.2.3 Company
4.3 Drawings
4.3.1 Government
4.3.2 Industry/technical
4.3.3 Company
4.4 Bulletins
4.4.1 Government
4.4.2 Industry/technical
4.4.3 Company
4.5 Other publications
5. Requirements
5.1 Description
21 5.2 General requirements
5.2.1 Precedence
5.2.2 Deliverables
22 5.2.3 Other
5.3 Performance
5.3.1 General
5.3.2 Input range
23 5.3.3 Overload capacity
5.3.4 Accelerometer temperature
5.3.4.1 Operating temperature
5.3.4.2 Temperature sensor
5.3.5 Scale factor
5.3.5.1 Absolute value
24 5.3.5.2 Asymmetry
5.3.5.3 Short-term stability
5.3.5.4 Long-term stability
25 5.3.5.5 Repeatability
5.3.5.6 Sensitivity
5.3.6 Nonlinearity
26 5.3.7 Bias
5.3.7.1 Absolute value
5.3.7.2 Asymmetry
5.3.7.3 Short-term stability
5.3.7.4 Long-term stability
27 5.3.7.5 Repeatability
5.3.7.6 Sensitivity
5.3.8 IA misalignment
5.3.8.1 About pendulous axis (PA)
5.3.8.2 About output axis (OA)
28 5.3.8.3 Short-term stability
5.3.8.4 Long-term stability
5.3.8.5 Repeatability
5.3.8.6 Sensitivity
29 5.3.9 Temperature model and temperature hysteresis
5.3.9.1 Temperature-controlled operation
5.3.9.2 Non–temperature-controlled operation
30 5.3.10 Cross-axis nonlinearity
5.3.11 Cross coupling
5.3.12 Warm-up time
5.3.13 Acceleration threshold
5.3.14 Acceleration resolution
31 5.3.15 Acceleration dead band
5.3.15.1 Force-rebalance dead band
5.3.15.2 Vibrating beam accelerometer (VBA) frequency lock
5.3.15.3 VBA activity dips
5.3.16 Repeatability across shut-down or nonoperational environment
5.3.17 Turn-on hysteresis
5.3.18 Inversion transient
32 5.3.19 Velocity storage
5.3.19.1 Normal operation
5.3.19.2 Over-range operation
5.3.19.3 Across power interrupt
5.3.20 Noise
33 5.3.21 Frequency response
5.3.22 Vibration-induced errors
5.3.23 Self-test scale factor
5.3.24 Pickoff characteristics
5.3.24.1 Pickoff excitation
34 5.3.24.2 Scale factor
5.3.24.3 Phase/polarity
5.3.24.4 Electrical null
5.3.24.5 Output limits
5.3.24.6 Output impedance
5.3.24.7 Frequency response
35 5.3.25 Reference constants
5.3.26 Torquer polarity
5.3.27 Sensor transfer function
36 5.3.28 Proof-mass elastic restraint
5.3.29 [Analog, Pulse-rebalance] capture-loop electronics
5.3.29.1 Capture-loop input characteristics
5.3.29.2 Capture-loop frequency response
37 5.3.29.3 Capture-loop output characteristics
39 5.3.29.4 Command input(s)
5.3.29.5 Clock reference
5.4 Mechanical requirements
5.4.1 Exterior surfaces
5.4.2 Dimensions
40 5.4.3 Identification of product
5.4.4 Sensor axes
42 5.4.5 Weight or mass
43 5.4.6 Seal
5.5 Electrical and magnetic requirements
5.5.1 Electrical interface
5.5.1.1 Torquer or forcer characteristics
5.5.1.2 Pickoff characteristics
44 5.5.1.3 Heater characteristics
5.5.1.4 Temperature sensor characteristics
5.5.1.5 Self-test torquer or forcer characteristics
46 5.5.2 Electromagnetic interference/compatibility
5.5.3 Insulation resistance
5.5.4 Dielectric strength
5.5.5 Magnetic leakage
47 5.6 Environmental requirements
5.6.1 Nonoperating environment
5.6.1.1 Temperature
5.6.1.2 Thermal shock
5.6.1.3 Vibration
5.6.1.4 Mechanical shock
5.6.1.5 Pressure
5.6.1.6 Humidity
5.6.1.7 Magnetic induction
48 5.6.1.8 Nuclear radiation
5.6.1.9 Other nonoperating environments
5.6.1.10 Storage life
5.6.2 Operating environment
5.6.2.1 Temperature (high and low)
5.6.2.2 Thermal shock
5.6.2.3 Other thermal conditions
49 5.6.2.4 Vibration
5.6.2.5 Mechanical shock
5.6.2.6 Acceleration
5.6.2.7 Pressure
5.6.2.8 Humidity
5.6.2.9 Acoustic noise
5.6.2.10 Magnetic induction
5.6.2.11 Nuclear radiation
5.6.2.12 Other operating environments
50 5.6.2.13 Operating life
5.6.3 Dormancy environment
5.7 Reliability
5.7.1 Reliability program
5.7.2 Mean time between failure (MTBF)
6. Quality assurance
51 6.1 Classification of tests
53 6.2 Acceptance tests
54 6.2.1 Individual tests
6.2.2 Sampling plan and tests
6.2.2.1 Sampling plan
6.2.2.2 Sampling tests
55 6.2.3 Rejection and retest
6.2.4 Defects in accepted items
6.3 Qualification tests
6.3.1 Qualification test samples
6.3.2 List of qualification tests
6.4 Reliability tests
56 6.5 Test conditions and equipment
6.6 Test methods
6.6.1 Test setup
6.6.1.1 Nonoperating test setup
6.6.1.2 Operating test setup
6.6.2 Accelerometer nonoperating tests
6.6.2.1 Examination of product
6.6.2.2 Weight or mass
6.6.2.3 Impedance
6.6.2.4 Dielectric strength
6.6.2.5 Insulation resistance
6.6.2.6 Seal
6.6.2.7 Temperature sensor characteristics
6.6.3 Accelerometer operating tests
6.6.3.1 Functional checkout
6.6.3.2 Noise
6.6.3.3 Inversion transient
6.6.3.4 Four-point tumble
57 6.6.3.5 Static multipoint
6.6.3.6 Threshold, resolution, and dead band
6.6.3.7 Warm-up time
6.6.3.8 Short-term stability
6.6.3.9 Long-term stability
6.6.3.10 Repeatability
6.6.3.11 Sensitivity
6.6.3.12 Temperature model calibration and temperature hysteresis
6.6.3.13 Velocity storage across power interrupt
6.6.3.14 Centrifuge input range and overload capacity
6.6.3.15 Precision centrifuge
6.6.3.16 Frequency response
6.6.3.17 Vibration calibration (nonlinear terms)
6.6.3.18 Vibration and shock calibration (scale factor and bias)
6.6.3.19 Performance through and across environment
6.6.3.20 Velocity storage in normal and over-range shock
6.6.3.21 Slew calibration
6.6.3.22 Magnetic leakage
6.6.4 Electromagnetically torqued pendulous accelerometer tests
6.6.4.1 Pickoff characteristics
6.6.4.2 Torquer and self-test torquer polarity
6.6.4.3 Open-loop frequency response
6.6.4.4 Pickoff scale factor and pendulum elastic restraint
6.6.4.5 Turn-on hysteresis
6.6.4.6 Self-test torquer scale factor
6.6.4.7 Velocity storage—Open-loop test
6.6.4.8 Velocity storage—Pulse-torque steady-state operation
6.6.5 VBA tests
58 6.6.5.1 VBA frequency lock
6.6.5.2 VBA activity dips
6.6.6 Micromechanical accelerometer tests
6.6.6.1 Wafer level tests
6.6.6.2 Proof-mass suspension resonant frequency
6.6.6.3 Proof-mass freedom
6.6.6.4 Pickoff and torquer electrode capacitor values
6.6.6.5 Pickoff scale factor
6.6.6.6 Flexure elastic restraint
6.6.7 Life tests
6.6.7.1 Life—Storage or dormant
6.6.7.2 Life—Operating
6.6.8 Reliability tests
6.6.8.1 Laboratory reliability test
6.6.8.2 Field reliability experience
6.6.9 Environmental tests
6.6.9.1 Vibration
6.6.9.2 Mechanical shock
6.6.9.3 Acceleration
6.6.9.4 Angular acceleration and spin
6.6.9.5 Temperature (high, low)
6.6.9.6 Thermal shock
6.6.9.7 Thermal radiation
6.6.9.8 Pressure (high, low)
6.6.9.9 Acoustic noise
6.6.9.10 Electromagnetic interference
6.6.9.11 Electromagnetic susceptibility
6.6.9.12 Magnetic induction
59 6.6.9.13 Fungus
6.6.9.14 Humidity
6.6.9.15 Salt spray
6.6.9.16 Sand and dust
6.6.9.17 Nuclear radiation
6.7 Data submittal
7. Preparation for delivery
8. Notes
8.1 Intended use
8.2 Ordering data
8.3 Model equation
64 Part II—Test procedure
9. Test procedure overview
10. Description
11. Test conditions and equipment
11.1 Standard test conditions
11.1.1 Ambient environment
11.1.1.1 Atmospheric conditions
11.1.1.2 Magnetic induction
11.1.1.3 Vibration
11.1.1.4 Other conditions
65 11.1.2 Installation requirements
11.1.2.1 Mechanical conditions
11.1.2.2 Operating temperature
66 11.1.2.3 Electrical interconnections
11.2 Test equipment
11.2.1 General requirements
67 11.2.2 Description of test equipment
11.2.2.1 General equipment
11.2.2.2 Accelerometer-specific equipment
68 11.2.2.3 Dividing head and mounting fixture
11.2.2.4 Vibration and shock equipment
11.2.2.5 Centrifuge
69 11.2.2.6 Environmental chambers
12. Test procedure
12.1 Test setup
12.1.1 Nonoperating test setup
12.1.2 Operating test setup
12.1.2.1 Interconnections
12.1.2.2 OA rotation mounting position
70 12.1.2.3 PA rotation mounting position
12.2 Accelerometer nonoperating tests
12.2.1 Examination of product
12.2.2 Weight or mass
12.2.3 Impedance
71 12.2.3.1 Purpose
12.2.3.2 Test equipment
12.2.3.3 Test setup
12.2.3.4 Test procedure
12.2.3.5 Test results
72 12.2.4 Dielectric strength
12.2.4.1 Purpose
12.2.4.2 Test equipment
12.2.4.3 Test setup
12.2.4.4 Test procedure
12.2.4.5 Test results
12.2.5 Insulation resistance
12.2.5.1 Purpose
12.2.5.2 Test equipment
12.2.5.3 Test setup
73 12.2.5.4 Test procedure
12.2.5.5 Test results
12.2.6 Seal
12.2.6.1 Purpose
12.2.6.2 Test equipment
12.2.6.3 Test setup
12.2.6.4 Test procedure
74 12.2.6.5 Test results
12.2.7 Temperature sensor characteristics
12.2.7.1 Purpose
12.2.7.2 Test equipment
12.2.7.3 Test setup
12.2.7.4 Test procedure
75 12.2.7.5 Test results
12.3 Accelerometer operating tests
76 12.3.1 Functional checkout
12.3.1.1 Purpose
12.3.1.2 Test equipment
12.3.1.3 Test setup
12.3.1.4 Test procedure
12.3.1.5 Test results
12.3.2 Noise
12.3.2.1 Purpose
77 12.3.2.2 Test equipment
12.3.2.3 Test setup
12.3.2.4 Test procedure
78 12.3.2.5 Test results
12.3.3 Inversion transient
12.3.3.1 Purpose
79 12.3.3.2 Test equipment
12.3.3.3 Test setup
12.3.3.4 Test procedure
12.3.3.5 Test results
12.3.4 Four-point tumble
80 12.3.4.1 Purpose
12.3.4.2 Test equipment
12.3.4.3 Test setup
12.3.4.4 Test procedure
81 12.3.4.5 Test results
12.3.5 Static multipoint
12.3.5.1 Purpose
12.3.5.2 Test equipment
82 12.3.5.3 Test setup mounting position 1
12.3.5.4 Test procedure mounting position 1
12.3.5.5 Test setup mounting position 2
12.3.5.6 Test procedure mounting position 2
12.3.5.7 Test results
84 12.3.6 Threshold, resolution, and dead band
12.3.6.1 Purpose
12.3.6.2 Test equipment
12.3.6.3 Test setup
12.3.6.4 Test procedures
85 12.3.6.5 Test results
12.3.7 Warm-up time
12.3.7.1 Purpose
86 12.3.7.2 Test equipment
12.3.7.3 Test setup
12.3.7.4 Test procedure
12.3.7.5 Test results
12.3.8 Short-term stability
12.3.8.1 Purpose
12.3.8.2 Test equipment
12.3.8.3 Test setup
87 12.3.8.4 Test procedure
12.3.8.5 Test results
12.3.9 Long-term stability
12.3.9.1 Purpose
12.3.9.2 Test equipment
12.3.9.3 Test setup
12.3.9.4 Test procedure
88 12.3.9.5 Test results
12.3.10 Repeatability
12.3.10.1 Purpose
12.3.10.2 Test equipment
12.3.10.3 Test setup
12.3.10.4 Test procedure
12.3.10.5 Test results
89 12.3.11 Sensitivity
12.3.11.1 Purpose
12.3.11.2 Test equipment
12.3.11.3 Test setup
12.3.11.4 Test procedure
90 12.3.11.5 Test results
91 12.3.12 Temperature model calibration and temperature hysteresis
12.3.12.1 Purpose
12.3.12.2 Test equipment
12.3.12.3 Test setup
12.3.12.4 Test procedure
12.3.12.5 Test results
92 12.3.13 Velocity storage across power interrupt
12.3.13.1 Purpose
12.3.13.2 Test equipment
12.3.13.3 Test setup
93 12.3.13.4 Test procedure
12.3.13.5 Test results
94 12.3.14 Centrifuge input range and overload capacity
12.3.14.1 Purpose
12.3.14.2 Test equipment
12.3.14.3 Test setup mounting position A
12.3.14.4 Test procedure mounting position A
12.3.14.5 Test setup mounting position B
95 12.3.14.6 Test procedure mounting position B
12.3.14.7 Test results
12.3.15 Precision centrifuge
12.3.15.1 Purpose
12.3.15.2 Test equipment
12.3.15.3 Test setup mounting position A
12.3.15.4 Test procedure mounting position A
96 12.3.15.5 Test setup mounting position B
12.3.15.6 Test procedure mounting position B
12.3.15.7 Test results
12.3.16 Frequency response
12.3.16.1 Purpose
97 12.3.16.2 Test equipment
12.3.16.3 Test setup
98 12.3.16.4 Test procedure
12.3.16.5 Test results
12.3.17 Vibration calibration (nonlinear terms)
12.3.17.1 Purpose
12.3.17.2 Test equipment
99 12.3.17.3 Test setup
12.3.17.4 Test procedure
100 12.3.17.5 Test results
12.3.18 Vibration and shock calibration (scale factor and bias)
12.3.18.1 Purpose
12.3.18.2 Test equipment
12.3.18.3 Test setup
101 12.3.18.4 Test procedure
12.3.18.5 Test results
12.3.19 Performance through and across environment
12.3.19.1 Purpose
102 12.3.19.2 Test equipment
12.3.19.3 Test setup
12.3.19.4 Test procedure
12.3.19.5 Test results
12.3.20 Velocity storage in normal and over-range shock
12.3.20.1 Purpose
103 12.3.20.2 Test equipment
12.3.20.3 Test setup
12.3.20.4 Test procedure
104 12.3.20.5 Test results
12.3.21 Slew calibration
12.3.21.1 Purpose
12.3.21.2 Test equipment
12.3.21.3 Test setup
12.3.21.4 Test procedure
12.3.21.5 Test results
105 12.3.22 Magnetic leakage
12.3.22.1 Purpose
12.3.22.2 Test equipment
12.3.22.3 Test setup
12.3.22.4 Test procedure
12.3.22.5 Test results
106 12.4 Electromagnetically torqued pendulous accelerometer tests
12.4.1 Pickoff characteristics
12.4.1.1 Purpose
12.4.1.2 Test equipment
12.4.1.3 Test setup
12.4.1.4 Test procedure
107 12.4.1.5 Test results
12.4.2 Torquer and self-test torquer polarity
12.4.2.1 Purpose
12.4.2.2 Test equipment
12.4.2.3 Test setup
12.4.2.4 Test procedure
108 12.4.2.5 Test results
12.4.3 Open-loop frequency response
12.4.3.1 Purpose
12.4.3.2 Test equipment
109 12.4.3.3 Test setup
12.4.3.4 Test procedure
12.4.3.5 Test results
12.4.4 Pickoff scale factor and pendulum elastic restraint
12.4.4.1 Purpose
12.4.4.2 Test equipment
12.4.4.3 Test setup
12.4.4.4 Test procedure
110 12.4.4.5 Test results
12.4.5 Turn-on hysteresis
12.4.5.1 Purpose
111 12.4.5.2 Test equipment
12.4.5.3 Test setup
12.4.5.4 Test procedure
12.4.5.5 Test results
112 12.4.6 Self-test torquer scale factor
12.4.6.1 Purpose
12.4.6.2 Test equipment
12.4.6.3 Test setup
12.4.6.4 Test procedure
12.4.6.5 Test results
113 12.4.7 Velocity storage—Open-loop test
12.4.7.1 Purpose
12.4.7.2 Test equipment
12.4.7.3 Test setup
12.4.7.4 Test procedure
115 12.4.7.5 Test results
12.4.8 Velocity storage-pulse-torqued steady-state operation
12.4.8.1 Purpose
12.4.8.2 Test equipment
12.4.8.3 Test setup
12.4.8.4 Test procedure
12.4.8.5 Test results
116 12.5 VBA tests
12.5.1 VBA frequency lock
12.5.1.1 Purpose
12.5.1.2 Test equipment
12.5.1.3 Test setup
12.5.1.4 Test procedure
12.5.1.5 Test results
117 12.5.2 VBA activity dips
12.5.2.1 Purpose
12.5.2.2 Test equipment
12.5.2.3 Test setup
12.5.2.4 Test procedure
12.5.2.5 Test results
118 12.6 Micromechanical accelerometer tests
12.6.1 Wafer-level tests
12.6.2 Proof-mass suspension resonant frequency
12.6.2.1 Purpose
12.6.2.2 Test equipment
12.6.2.3 Test setup
12.6.2.4 Test procedure
119 12.6.2.5 Test results
12.6.3 Proof-mass freedom
12.6.3.1 Purpose
12.6.3.2 Test equipment
12.6.3.3 Test setup
12.6.3.4 Test procedure
120 12.6.3.5 Test results
12.6.4 Torquer and pickoff electrode capacitor values
12.6.4.1 Purpose
12.6.4.2 Test equipment
12.6.4.3 Test setup
12.6.4.4 Test procedure
12.6.4.5 Test results
121 12.6.5 Pickoff scale factor
12.6.5.1 Purpose
12.6.5.2 Test equipment
12.6.5.3 Test setup
12.6.5.4 Test procedure
12.6.5.5 Test results
122 12.6.6 Flexure elastic restraint
12.6.6.1 Purpose
12.6.6.2 Test equipment
12.6.6.3 Test setup
12.6.6.4 Test procedure
12.6.6.5 Test results
12.7 Life tests
12.7.1 Life—Storage or dormant
12.7.1.1 Purpose
123 12.7.1.2 Test equipment
12.7.1.3 Test setup
12.7.1.4 Test procedure
12.7.1.5 Test results
12.7.2 Life—Operating
12.7.2.1 Purpose
12.7.2.2 Test equipment
124 12.7.2.3 Test setup
12.7.2.4 Test procedure
12.7.2.5 Test results
12.8 Reliability tests
12.8.1 Laboratory reliability test
12.8.1.1 Purpose
12.8.1.2 Test equipment
12.8.1.3 Test setup
12.8.1.4 Test procedure
125 12.8.1.5 Test results
12.8.2 Field reliability experience
12.9 Environmental tests
12.9.1 Purpose
12.9.2 Test equipment
12.9.3 Test setup
126 12.9.4 Test procedure
12.9.5 Test results
129 Part III—Accelerometer descriptions
Annex A (informative) Accelerometer dynamic block diagrams
A.1 Introduction
A.2 Open-loop operation
130 A.3 Closed-loop operation
131 A.4 Open-loop operation of closed-loop accelerometer
A.5 Operation with voltage-to-frequency conversion
132 A.6 Operation with digital capture loop
A.7 Accuracy of capture-loop readout
133 Annex B (informative) Digital accelerometers and comments concerning their test methods
B.1 Introduction
B.2 Description of commonly encountered digital output formats
B.2.1 Sample and hold with an analog-to-digital converter
B.2.2 Digitally captured accelerometers
135 B.2.3 Analog accelerometer with a voltage-to-frequency converter
B.2.4 Biased outputs
B.2.5 VBA
B.3 Comments concerning test methods associated with digital instruments
B.3.1 Aliasing
B.3.2 One-count uncertainty and moding
136 B.3.3 Period measurement versus measurement of the number of pulses over a fixed time interval
B.3.4 Measurement of positive and negative pulses provided on separate data lines
B.3.5 Asymmetry
B.3.6 Biased outputs
137 B.3.7 Threshold and resolution (see 12.3.6)
138 Annex C (informative) Characteristics of pendulous accelerometers
C.1 Design principles
C.2 Applications
139 C.3 Error sources
C.3.1 Cross-coupling
141 C.3.2 Effective centers of mass
144 C.3.3 Anisoinertia
C.4 Trade-offs
145 C.5 Environmental effects
C.6 Testing
C.7 Special requirements in the specification
146 C.8 Advantages and disadvantages
147 Annex D (informative) Overview of the characterization and use of the VBA
D.1 Introduction
D.2 Historical background
D.2.1 Early frequency output devices
D.2.2 Vibrating string accelerometer
148 D.3 VBA—Theory of operation
D.3.1 Quartz resonator
149 D.3.2 Single tine resonator
150 D.3.3 Dual tines—Double-ended tuning fork (DETF)
151 D.3.4 Push–pull mechanization
152 D.3.5 Gas damping
D.4 VBA signal processing
D.4.1 Frequency counting
153 D.4.2 Period
D.4.3 Phase processing
154 D.4.4 Dual resonators
D.4.5 Algorithms
156 D.5 VBA error sources
D.5.1 Scale factor stability
D.5.2 Bias stability
D.5.3 Effect of clock errors
157 D.5.4 Quantization noise
D.5.5 Vibration rectification compensation
158 D.5.6 Aliasing
D.5.7 Inversion transients
D.5.8 Dual-pendulum effects
D.5.9 Frequency lock and activity dips
160 D.6 Related developments
D.6.1 Coriolis rate sensors
D.6.2 Silicon micromachining technology
161 Annex E (informative) VBA resonator frequency as a function of applied acceleration
E.1 Geometry and elastic properties of vibrating beam
162 E.2 Square-root relationship derived from energy considerations
E.2.1 Internal energy of beam
163 E.2.2 Effect of axial force
164 E.2.3 Taylor series expansion for square root expression
165 E.3 Direct frequency versus force relation
166 E.3.1 Vibrating beam partial differential equation
E.3.2 Reduction to ordinary differential equations
167 E.3.3 Solution by separation of variables
168 E.3.4 Application of the boundary conditions
E.3.5 Frequency of beam under no axial load
169 E.3.6 Frequency of beam with axial load
170 E.4 Frequency versus force numerical evaluation
E.4.1 Generation of curve
172 E.4.2 Least-squares fit
E.5 Comparison of fit coefficients and square-root Taylor coefficients
174 Annex F (informative) Micromechanical accelerometers
F.1 Micromachining
F.2 Micromachined silicon accelerometer—flexured-mass configurations
F.2.1 Design features of the piezoresistive flexured-mass accelerometer
175 F.2.2 Design features of the capacitive pickoff and forcer flexured-mass accelerometer
178 F.2.3 Circuit diagrams for capacitive sensing and forcing
F.2.4 Open-loop operation
180 F.2.5 Closed-loop operation
181 F.2.6 Scale-factor, bias, and second-order nonlinearity
182 F.2.7 Performance considerations
184 F.3 Micromachined silicon VBAs
F.3.1 Design features
185 F.3.2 Drive force and position sensing
187 F.3.3 Oscillator drive loop
F.3.4 Error mechanisms
189 Annex G (informative) Outline of error sources in accelerometers
G.1 Introduction
G.2 Sensor characterization by mechanization
190 G.3 Typical sensor characterization by manufacturing process
G.4 Error categories
191 G.5 Sensor physics
193 Part IV—Filtering, noise, and transient analyses
Annex H (informative) Digital filtering
H.1 Types of filtering and decimation
194 H.2 Rectangular filtering
H.3 Triangular filtering
195 H.4 Higher order filtering
196 Annex I (informative) Noise characterization
I.1 Stochastic processes
I.2 Autocorrelation function of a stochastic process
197 I.3 Estimation of the autocorrelation function
198 I.4 Power spectral density (PSD) of a stationary stochastic process
199 I.5 Estimation of the PSD
I.5.1 Continuous data
200 I.5.2 Interpretation of the PSD as a power spectrum
201 I.5.3 Discrete data
203 I.6 Numerical evaluation and plotting of the PSD
204 I.7 Characteristic PSD noise slopes
I.7.1 Deterministic signals
205 I.7.2 White, random walk, and flicker noise
I.7.3 Quantization noise
206 I.7.4 Typical log–log PSD plot
207 I.7.5 Noise specification
208 I.8 Characteristic Allan variance noise slopes
209 I.9 Estimation of Markov noise parameters
I.9.1 Stochastic linear dynamic systems
210 I.9.2 Stochastic linear dynamic system noise models
212 I.9.3 Estimating parameters in stochastic linear dynamic systems
214 Annex J (informative) Characterization of transient behavior
J.1 Types of transient behavior
J.2 Second-order ordinary differential equation transient
215 J.3 Exponential, square root, and logarithmic transients
217 J.4 Estimation of transient parameters
218 Part V—Calibration and modeling techniques
Annex K (informative) Calibrating accelerometer model coefficients from static multipoint tumble data
K.1 Multipoint tumble test and analysis procedures
K.1.1 Purpose of multipoint tumble testing
K.1.2 Analysis procedures
219 K.1.3 Setup of dividing head and mounting fixture
K.1.4 Test and data acquisition scenarios
220 K.1.5 Test orientations
222 K.2 Model equation for multipoint tumble analysis
K.2.1 Choice of model coefficients
K.2.2 Estimating model coefficients
223 K.2.3 Single accelerometer model equation
224 K.2.4 Fourier coefficients and parameter correlations
225 K.2.5 Model equation with dual orthogonal accelerometers
227 K.2.6 Magnitude-squared-of-g model equation
228 K.3 Multipoint tumble analysis with a single accelerometer observable
K.3.1 Solving for bias, scale factor, and misalignment
230 K.3.2 Effect of asymmetries
233 K.3.3 Effect of quadratic and cubic acceleration sensitivities
234 K.3.4 Difficulty of estimating quadratic and cubic acceleration sensitivities in a single accelerometer multipoint tumble
K.4 Multipoint tumble analysis with dual orthogonal accelerometer observables
K.4.1 Simultaneous estimation of angle-setting and tilt errors, nonorthogonality, and accelerometer model coefficients
235 K.4.2 Covariance simulation
236 K.5 Multipoint tumble analysis with orthogonal accelerometer magnitude-squared-of-g observable
K.5.1 Comparison with solving for angle-setting errors with individual accelerometer observables
K.5.2 Covariance simulations
237 K.6 Least-squares maximum likelihood estimation
K.6.1 Likelihood function and maximum likelihood estimates
238 K.6.2 Iterative determination of least-squares maximum likelihood estimates
K.6.3 Postfit data residuals
239 K.6.4 Fisher information matrix
240 K.6.5 Cramer-Rao lower bound
241 K.6.6 Covariance of parameter estimates
243 Annex L (informative) Vibration test equipment, test procedures, and analysis techniques
L.1 Test equipment and test fixtures
L.1.1 Mounting fixture
L.1.2 Electrodynamic vibrator
L.1.3 Hydraulic vibrator
244 L.1.4 Vibrator orientation, slip tables, and attachment to floor
245 L.1.5 Measurement and control of vibration
246 L.2 Test scenarios
L.2.1 Vibration tests
247 L.2.2 Shock tests
L.3 Error sources
248 L.4 Test instrumentation and procedures
L.4.1 Data acquisition
249 L.4.2 Test procedures
L.5 General comments on analysis techniques
250 L.6 Calibration of nonlinear coefficients from vibration along different instrument axes
L.6.1 Introduction
L.6.2 Calibration with vertical and horizontal electrodynamic vibrations
254 L.6.3 High-precision calibration with horizontal hydraulic vibrations
258 L.6.4 Error sources
260 L.7 Summary
261 Annex M (informative) Geophysical effects in inertial instruments testing
M.1 Introduction
M.2 Seismic environment
262 M.3 Tilt and azimuth variations
M.4 Effect of lunar–solar earth tides
264 M.5 Effect of ocean tides
265 M.6 Variations in earth rotation
267 Annex N (informative) Bibliography
271 Back Cover

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