{"id":4391,"date":"2026-10-15T11:50:00","date_gmt":"2026-10-15T03:50:00","guid":{"rendered":"https:\/\/www.andelutech.com\/?p=4391"},"modified":"2026-10-15T16:09:11","modified_gmt":"2026-10-15T08:09:11","slug":"what-limits-the-practical-use-of-accelerometers-and-gyroscopes-in-dynamic-systems","status":"publish","type":"post","link":"https:\/\/www.andelutech.com\/fa\/what-limits-the-practical-use-of-accelerometers-and-gyroscopes-in-dynamic-systems\/","title":{"rendered":"What Limits the Practical Use of Accelerometers and Gyroscopes in Dynamic Systems"},"content":{"rendered":"

An accelerometer <\/strong><\/a> and gyroscope may have good static error figures, but when moving a platform, these figures do not necessarily translate well. The full measurement chain must be considered: sensor dynamics, vibration, mounting, sampling rate, temperature, calibration, and estimator. The estimator can calculate attitude or position from the specific force and angular rate information from the sensors. When choosing an IMU, the engineer\u2019s main concern is not the smallest bias figure for a particular sensor, but rather the total error of the full measurement chain for the entire mission in different environments.<\/p>\n

\"What<\/figure>\n

Why Dynamic Motion Exposes Hidden Sensor Limits<\/strong><\/h2>\n

For strapdown systems, accelerometers measure specific force while gyroscopes measure angular rate. Although small errors grow rapidly, a constant accelerometer bias only causes error in estimated velocity, while its effect on position error grows roughly with time squared. Similarly, a constant bias in a gyroscope causes the estimated gravity vector to be tilted by the leaked gravity, which then overwhelms the horizontal acceleration signal. Static calibration of accelerometers usually determines offset, scale factor, nonlinearity, misalignment, and cross-talk between axes. But it does not account for, for example, fast vibrations, thermal effects, or all axes being moved simultaneously.<\/p>\n

The mechanical limit of MEMS parts is mostly defined by the mechanical design of the part. A capacitive accelerometer consists of a proof mass. A vibratory gyroscope detects the Coriolis force. All these designs have resonances and damping, need to be driven, and can be affected by packaging stress and by the interface electronics. Mode matching can increase the sensitivity of a gyroscope. But it also makes the part dependent on frequency control and temperature. To increase the bandwidth by designing drive and sense axes separately lowers the sensitivity and needs very quiet electronics.<\/p>\n

The Parameters That Set the Usable Envelope<\/strong><\/h2>\n\n\n\n\n\n\n\n\n
Parameter<\/td>\nDynamic consequence<\/td>\nSelection test<\/td>\n<\/tr>\n
Range and overload<\/td>\nSaturation can clip peak values, negatively impact subsequent integrations. Survival of a fiber does not guarantee valid data.<\/td>\nSet the largest credible rate, acceleration, and shock with margin.<\/td>\n<\/tr>\n
Bandwidth and phase<\/td>\nLow bandwidth renders motion poorly and adds lag. High bandwidth renders noise and vibration poorly.<\/td>\nAmplitude and phase must match the control or navigation band.<\/td>\n<\/tr>\n
Noise and bias<\/td>\nWhite noise has the property of averaging out. Bias instability and random walk have a tendency to build up over time.<\/td>\nApply Allan deviation and mission-duration error growth instead of using one RMS value.<\/td>\n<\/tr>\n
Scale factor and axes<\/td>\nTemperature dependent gain, nonlinearity and cross-axis sensitivity transform true motion into constant error.<\/td>\nCalibrate across axes, rates, acceleration levels, and temperature.<\/td>\n<\/tr>\n
Sampling and filtering<\/td>\nEnergy that is out of band for a particular signal ends up in the signal\u2019s band. Timing skew affects multi-axis motion in unexpected ways.<\/td>\nAnalog input: Check for anti-alias filtering, accurate timestamping, low latency and correct sample synchronization.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Vibration Creates Errors That Filtering Cannot Always Remove<\/strong><\/h2>\n

Vibration outside the useful range can be even larger than the average amplitude of motion. A second-order nonlinearity can even convert an alternating signal into a constant value \u2013 this is called vibration rectification error. The error is structure-dependent and \u2013 as opposed to linear errors \u2013 converted frequency-dependent, especially near resonance. A digital low-pass filter does not correct for errors that have already been converted within the sensor. Also, the vibration can cause a gyro to report a constant error in angular rate due to structural asymmetry, capacitive nonlinearity, and poor common-mode rejection.<\/p>\n

Resonance and Mechanical Survivability Are Different Limits<\/strong><\/h3>\n

The electrical bandwidth of the output is shown here, but the proof mass is subjected to the full mechanical input. Energy above the output bandwidth can cause the system to resonate, hit a mechanical stop, or increase cyclic stress. This energy may not always show up clearly in the data from a single test, but it can cause a unit to survive a single large shock event and then drift or fail under lower amplitude and ongoing vibration. Mechanical shock testing looks at peak acceleration, pulse shape, and length. Vibration testing looks at frequency content, RMS amplitude, dwell time, and fatigue. When specifying, ask for the unit\u2019s operational accuracy as well as its survival limits. The latter only gives a measure of the device\u2019s ability to survive a test without damage.<\/p>\n

However, the performance of a sensor can also be limited by the mounting. A flexible mounting bracket can introduce additional resonances, base bending, or axis rotation that the sensor picks up from the machine. The same ISO 5348:2021 also treats the mounting of vibration sensors as a contribution to the measurement uncertainty. Here torque, alignment, transverse motion, and cable effects are treated. We qualify the complete installed assembly by means of sine tests and random vibration tests. A test of the sensor alone is not considered to be sufficient.<\/p>\n

Temperature and Aging Defeat Room Temperature Numbers<\/strong><\/h2>\n

Bias, scale factor, alignment, and resonant frequency can shift with temperature. A calibration table can then lock in a \u201cthermal link\u201d that remains stable. However, rapid thermal gradients can create significant lags between package temperature and sensing element temperature. In addition to packaging stress, shifts in bonding, humidity, fatigue, and repeated shock can also shift the calibration point. The 2024 reliability review noted that studies of combined mechanical and thermal stresses are less mature than single stress studies. Environmental qualification of pressure sensors therefore should cover the sensor\u2019s operating temperature as well as temperature cycling, vibration, shock, and a post-test accuracy test. While a high shock rating is often touted as a key sensor characteristic, it says little about long-term vibration reliability.<\/p>\n

Sensor Fusion Helps but Does Not Remove Observability Limits<\/strong><\/h2>\n

Accelerometers and gyroscopes can be combined for attitude estimation. Gyroscopes measure short periods of high rotation rate. Low-frequency roll and pitch can be corrected with the gravity vector. As the period of long vehicle acceleration extends, it is not possible to consider all accelerometer readings as gravity. Other external sources of information such as GNSS, odometry, magnetometers, vision and known motion can improve observability. Each of these sources introduces some delay, occasional outages, interference, and other model assumptions. The Kalman filter reduces the variance of the estimation only if the noise model, time stamping, coordinate reference frames, and the motion model are accurate.<\/p>\n

Fast Multi-Axis Motion Adds Coning and Sculling Errors<\/strong><\/h3>\n

A dynamic platform rarely turns or moves about one axis alone. When angular-rate samples integrate as if rotations commute, small sequential turns create coning error. Rotation and specific force together create sculling error in velocity updates. Raising the output rate helps only if internal sampling, delta-angle and delta-velocity formation, synchronization, and compensation keep the true motion. A high serial baud rate does not confirm high usable sensor bandwidth. Procurement specs should separate mechanical sensing bandwidth, internal sampling rate, digital filter response, output data rate, group delay, and timestamp accuracy.<\/p>\n

\"What<\/figure>\n

Common Engineering Fixes and Their Boundaries<\/strong><\/h2>\n

Filtering and Oversampling<\/strong><\/h3>\n

Note that analog anti-alias filters must reduce energy before it is sampled by the ADC. Once energy has been folded into the passband of a digital filter, it cannot be removed. Oversampling allows for the design of much better filters for a given amount of noise, and reduces quantization error. However, it does not address issues of saturation, non-linear rectification, structural resonance, or temperature-dependent bias. In addition, heavy low-pass filtering of a signal adds group delay to the signal. In a stabilization loop, this reduces the phase margin, potentially turning a quiet signal into a less stable platform. Thus, the choice of filter must consider both its ability to reduce noise and its effect on the closed-loop response.<\/p>\n

Temperature Compensation and Calibration<\/strong><\/h3>\n

Calibration at multiple temperatures allows for the determination of bias, scale factor, and axis coupling coefficients over a given range. Repeatability of results is key. Deviations such as hysteresis, warm-up shift, thermal gradients, mechanical stress, and aging can cause different output for the same package temperature. One temperature sensor does not make all sensing elements. Compensation models need to be trained and tested on different thermal cycles. It is better to state the residual error instead of the pre-compensation drift.<\/p>\n

Isolation and Redundant Sensors<\/strong><\/h3>\n

Isolation using elastomeric or mechanical components can also reduce high-frequency vibration. However, such systems can have their own resonance, damping variation with temperature, and alignment shift. In some cases, the isolated band of vibration may overlap with that which needs to be transmitted to control a process. To improve the signal-to-noise ratio of uncorrelated noise sources such as these, sensor arrays can average the signals. However, even seemingly identical temperature sensors, physical mounting, clocks, and vibration transducers have shared inputs that create correlated errors which do not average out. Thus, true redundancy requires not only physical but also statistical independence between sensors, adding more than just more sensors.<\/p>\n

Industry Pain Points in Real Deployments<\/strong><\/h2>\n

While MEMS<\/strong><\/a> have shrunk in size, decreased in power, increased in integration, and improved their nominal performance, the failures in the field continue to concentrate at the interfaces between disciplines. A mechanical engineer may specify a survival vibration level without establishing any accuracy limits. A control engineer may assume a fixed latency, whilst the firmware engineer modifying the filters of a sensor has forgotten to update the relevant calibration data. A navigation engineer tunes a stochastic model on the basis of short stationary test data. The test of an inertial sensor by means of the Allan deviation does not identify the type of noise present, be it white, bias, or random-walk, but rather expresses this type of noise in terms of the relevant slopes, over a test duration and within a given thermal stability. It is not a test to be performed in dynamic or environmental testing.<\/p>\n

A second aspect for the comparison of typical values is how two sensors with the same nominal bias instability can behave differently after power cycling or between different production lots. Even sensors with the same nominal bias instability can react differently under temperature influence or under vibration. The average time, bandwidth, filter settings, as well as definitions of the specifications, can differ a lot. Even IEEE terms and test standards for sensor evaluation do not help enough. A compliance matrix which maps every limit to the corresponding test case, sample population, and acceptance test criterion is still necessary for the buyer.<\/p>\n

A Practical Selection Method<\/strong><\/h2>\n

Start with a mission-level error budget. Specify the smallest signal, largest credible transient, useful frequency band, allowed phase delay, unaided duration, thermal profile, vibration spectrum, mounting stiffness, interface, and calibration interval. Convert bias instability, angle random walk, velocity random walk, scale-factor error, and axis misalignment into attitude, velocity, or control error over that mission. IEEE 1780-2022 provides a framework for writing an IMU specification, while IEEE 1293-2018 and IEEE 952-2020 define disciplined test concepts for accelerometers and fiber-optic gyroscopes.<\/p>\n

Test the full chain and record all raw data, including temperature, time-stamps, filter settings, firmware version, calibration constants, and installation orientation. Compare results from static multi-position test to those obtained from rate-table, vibration-table, and real-motion tests. Set the range with sufficient headroom to avoid clipping but not so high as to waste resolution. Select a bandwidth that matches the required motion spectrum and allows control of phase margin. Do not select the highest number available.<\/p>\n

Selection Priorities by Application<\/strong><\/h2>\n

When selecting sensors for stabilization, prioritize rate range, bandwidth, phase response, vibration sensitivity, latency, and synchronization. For short GNSS outages, measure bias repeatability, thermal behavior, scale factor, and aiding latency. For condition monitoring, define the diagnostic frequency bands and mounting method and test noise density, cross-axis rejection, and anti-alias filter performance. For applications in drilling, mining, or near engines, also consider the combined effect of temperature, shock, continuous vibration, sealing, and connectors, and weigh against accuracy at room temperature. It\u2019s wise to set your priorities before asking vendors for quotes.<\/p>\n

At Andelu<\/strong><\/a>, our portfolio includes: accelerometers, MEMS IMUs, fiber-optic gyroscopes, dynamically tuned gyroscopes as well as complete integrated navigation systems. This wide choice of sensors allows matching the error budget of each component. For instance, the ADL-MIMU-01 is a three-axis MEMS accelerometer + gyroscope sensor that outputs on RS422. The published data provides separate figures for bias instability, angular random walk, accelerometer bias stability, bandwidth, temperature drift, as well as resistance to vibration and shock. When selecting a sensor, apply the same care as when choosing a component. Ask for guaranteed values as well as for test conditions, and provide evidence of the sensor being used in a given system.<\/p>\n

Engineering Conclusion<\/strong><\/h2>\n

There are several practical limitations to the use of accelerometers and gyroscopes. They can be defined by the intersection of a number of limiting factors including dynamic range, bandwidth, noise, thermal drift, sensitivity to vibration, assembly, sampling rate, and the underlying assumptions made by the estimator. As has been noted previously, no amount of clever algorithmization can recover from sensor clipping or non-linear bias with respect to vibration. The design of a robust system therefore links each sensor\u2019s specification to a specific error, qualifies the assembled system under a number of different stresses, and maintains traceable configuration data throughout its service life.<\/p>\n

References<\/strong><\/h2>\n

[1] IEEE 1780-2022, IEEE Standard for Specifying Inertial Measurement Units.<\/p>\n

[2] IEEE 1293-2018: IEEE Standard Specification Format Guide and Test Procedure for Linear Single-Axis Nongyroscopic Accelerometers.<\/p>\n

[3] IEEE 952-2020, IEEE Standard for Specifying and Testing Single-Axis Interferometric Fiber Optic Gyros.<\/p>\n

[4] ISO 5348:2021 Mechanical vibration and shock – Mechanical mounting of accelerometers.<\/p>\n

[5] Chen et al., Reliability of MEMS inertial devices in mechanical and thermal environments: A review, Heliyon 10 (2024), e27481.<\/p>\n

[6] Frequency-Dependent Vibration Rectification Error in Area-Variation-Based Capacitive MEMS Accelerometers, Micromachines 15 (2024), 65.<\/p>\n

[7] El-Sheimy, Hou and Niu, \u201cAnalysis and Modeling of Inertial Sensors Using Allan Variance\u201d, IEEE Transactions on Instrumentation and Measurement, Vol. 57, No. 1, 2008, pp. 140-149.<\/p>\n

[8] Andelu, High Accuracy North-Seeking MEMS IMU ADL-MIMU-01, product specification.<\/p>\n

[9] Andelu technical references: Inertial Sensor Technologies; Inertial Navigation Error and Calibration; Environmental Reliability and Testing.<\/p>\n","protected":false},"excerpt":{"rendered":"

Dynamic motion exposes errors missed by static specifications; this guide covers vibration, sampling, temperature, calibration, and estimation limits.<\/p>","protected":false},"author":1,"featured_media":4390,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[44],"tags":[],"class_list":["post-4391","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-industry-news"],"_links":{"self":[{"href":"https:\/\/www.andelutech.com\/fa\/wp-json\/wp\/v2\/posts\/4391","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.andelutech.com\/fa\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.andelutech.com\/fa\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.andelutech.com\/fa\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.andelutech.com\/fa\/wp-json\/wp\/v2\/comments?post=4391"}],"version-history":[{"count":3,"href":"https:\/\/www.andelutech.com\/fa\/wp-json\/wp\/v2\/posts\/4391\/revisions"}],"predecessor-version":[{"id":4394,"href":"https:\/\/www.andelutech.com\/fa\/wp-json\/wp\/v2\/posts\/4391\/revisions\/4394"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.andelutech.com\/fa\/wp-json\/wp\/v2\/media\/4390"}],"wp:attachment":[{"href":"https:\/\/www.andelutech.com\/fa\/wp-json\/wp\/v2\/media?parent=4391"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.andelutech.com\/fa\/wp-json\/wp\/v2\/categories?post=4391"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.andelutech.com\/fa\/wp-json\/wp\/v2\/tags?post=4391"}],"curies":[{"name":"\u0648\u0631\u062f\u067e\u0631\u0633","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}