Inertial Measurement Unit Error Calibration

The inertial measurement unit (IMU) is an inertial measurement device composed of a three-axis accelerometer, a three-axis gyroscope, and a three-axis magnetic sensor. It is mainly used to measure the angular rate, acceleration, and magnetic heading of the aircraft’s three degrees of freedom. The navigation-grade MEMS IMU independently developed by ERICCO can independently seek north. It adopts MEMS design and system integration methods. This product has the advantages of light weight, small size, low cost, and high reliability, and has been widely used in military and civilian fields.

The measurement accuracy of the inertial measurement unit is not only related to the detection accuracy of the inertial measurement component itself, but also to the processing technology and installation accuracy. Therefore, the research on the calibration and error compensation of the inertial measurement unit is of great significance.

The calibration methods of the IMU mainly include the traditional multi-position and angular rate calibration method based on the turntable and the on-site multi-position calibration method. Based on the position calibration method, a gyro calibration method that eliminates the north misalignment is given. The traditional calibration method is based on a high-precision turntable, and the calibration process is very complicated. On-site calibration can not only reduce the workload, but also effectively improve the calibration accuracy. Another calibration method is to combine the traditional static multi-position and rate calibration method and propose a 6-position calibration method based on a dual-axis rotating mechanism. This method is more convenient to solve the scaling factor and installation error, but it has a few steps when solving the constant drift. More cumbersome.

Next, the error sources of the IMU unit will be analyzed. An improved calibration method based on accelerometer and gyroscope is proposed. To understand this improved calibration method, we need to first understand the error model and calibration method of the inertial measurement unit. It will be further introduced from the accelerometer and gyroscope.

1.Inertial measurement unit error model

As shown in Figure 1, OXnYnZn is the orthogonal coordinate system, OXbYbZb is the coordinate system of the inertial measurement unit, and the three axes of the ideal gyroscope and accelerometer are respectively installed on three orthogonal surfaces to form a right-handed coordinate system. However, due to the working principles and structures of gyroscopes and accelerometers, as well as integrated manufacturing and installation, the input coordinate axes of the accelerometer and gyroscope in the inertial measurement unit cannot be orthogonal, and there are 6 orthogonal coordinate systems. Installation error angles θxy, θxz, θyx, θyz, θzx, θzy. The purpose of sensor calibration is to compensate for the calibration factor between the output value and the measured value, to compensate for the zero offset error, and to compensate for the installation coupling error caused by machining accuracy, assembly technology, etc.

                                             Figure 1. Installation error angle in non-normal coordinate system

1.1Gyro error model

The gyro output data is affected by the orthogonality of the coordinate system, installation accuracy and ambient temperature, which will cause changes in the gyro’s zero bias, scale factor, installation error angle and noise. Therefore, the gyro’s output model is. Therefore, the gyro’s output model is One part is the measured angular velocity vector of the sensitive axis, and the other part is the real angular velocity vector, which will include a linear scale factor, a non-orthogonal matrix, a constant drift (zero bias), and a gyro noise error. Considering that it has a small impact on the calibration results, the noise is ignored. The impact of errors on calibration. Let K = I + Sω + Nω, then the formula can be expressed as:

Among them, Kyx and Kzx are the coupling coefficients of the installation error angles θxy and θxz of the sensitive axis xg. Kxy and Kzy are the coupling coefficients of the installation error angles θyx and θyz of the sensitive axis yg. Kxz and Kyz are the coupling coefficients of the installation error angles θzx and θzy of the sensitive axis zg. Coupling coefficients, Kxx, Kyy, Kzz are the calibration coefficients of the sensitive axes xg, yg, zg, Dωx, Dωy, Dωz are the constant drift (zero bias) of the gyro sensitive axes xg, yg, zg.

1.2 Accelerometer error model

The accelerometer output data is affected by the orthogonality of the axis system in the coordinate system, installation accuracy and ambient temperature, which will cause changes in the accelerometer’s zero bias, scale factor, installation error angle and noise, so the output model of the accelerometer is part of Measure the acceleration vector for the sensitive axis, and part of it is the true specific force vector, which will include nonlinear scaling factors, non-orthogonal matrix constant drift (zero bias), and gyro noise errors. Considering that it has a small impact on the calibration results, the noise is ignored The impact of errors on measurement results. Let C = I + Sa + Na, then the formula can be expressed as:

Among them, Cyx and Czx are the coupling coefficients of the installation error angles θxy and θxz of the sensitive axis xg. Cxy and Czy are the coupling coefficients of the installation error angles θyx and θyz of the sensitive axis yg. Cxz and Cyz are the coupling coefficients of the installation error angles θzx and θzy of the sensitive axis zg. Coupling coefficient, Cxx, Cyy, Czz are the calibration coefficients of the sensitive axes xg, yg, zg, Dax, Day, Daz are the constant drift (zero bias) of the accelerometer’s sensitive axes xg, yg, zg.

2.Calibration of inertial measurement unit

2.1 Gyro calibration method

The scale factor and installation error of the gyroscope can be calibrated by the multi-position method. In order to minimize the calibration state, make the sensitive axis of the gyroscope point east or west during initial calibration, then the component of the earth’s rotation rate in this axis is zero. Based on this principle, 4 states are selected from 24 states for gyro calibration. Rotate the inertial measurement unit to four different positions as shown in the figure below, record the output data of the three axial gyroscopes in sequence, and calibrate the zero bias, scale factor and installation error of the gyroscope.

2.2 Accelerometer calibration method

In its natural state, the accelerometer is not affected by any external force or angular velocity input except the acceleration of gravity and the rotation of the earth. The accelerometer calibration adopts the static multi-position calibration method. The IMU is rotated to 6 different positions as shown in the figure below, and the three-axis accelerometer output data output at each position is recorded in turn, and the zero bias and scale of the accelerometer are calibrated. factors and installation errors.

This article proposes a calibration method for low-cost inertial measurement unit zero bias, scale factor and installation error angle, which simplifies the calibration process and improves calibration efficiency. The calibration method was applied to the inertial measurement unit, which met the expected test requirements and verified the correctness and effectiveness of the compensation method. A scale factor temperature model and a zero-bias temperature model can be established to further improve the accuracy of calibration. The ER-MIMU-01 and ER-MIMU02 independently developed by our company (ERICCO) are calibrated using the above calibration method, which effectively improves the accuracy of the product. If you want to learn about and purchase IMU, please contact our technical staff.

The Advantages and Disadvantages of the Transmission Mode of Tilt Sensor

In today's industrial and commercial environment, tilt sensors are increasingly used to measure and monitor the tilt angle of equipment or structures. Depending on the data transmission method, inclination sensors can be divided into wired and wireless types. In this article, we'll delve into both types of tilt sensors, including the pros and cons, and how to choose the best solution for your specific needs.

1. Wired tilt sensor

Wired inclination sensor built-in high performance MCU built-in algorithm, through a high oversampling rate, improve the high frequency characteristics of the data, through the data filtering algorithm to remove unreasonable accidental error data, Kalman filter algorithm for higher precision data processing, suitable for monitoring the structure deformation monitoring field with high monitoring frequency requirements. Wired inclination sensors usually use RS485 bus or other similar bus protocols to transmit inclination signals. RS485 is a serial communication protocol widely used in the field of industrial automation, which has the advantages of noise suppression and high signal quality. ER-TS-3160VO is a linear inclination sensor with an accuracy of 0.01°, its cable standard length is 1.5m, and it can output RS232 at the same time, RS485 can be customized, the measurement range can reach 0~±180°, and the impact vibration resistance is strong.

The main advantage of the wired inclination sensor is that the signal stability is high, and the signal quality is not easy to be disturbed because of the wired transmission mode. In addition, wired sensors have a long service life, lower maintenance costs, and a lower failure rate. However, this sensor also has some disadvantages, such as the need to lay cables, high requirements for the field environment, may exist in some application scenarios wiring difficulties.

2. Wireless tilt sensor

Wireless inclination sensors have become more and more popular in recent years, and common wireless inclination sensors include NB-IoT wireless inclination sensors and LORO wireless inclination sensors. These sensors transmit tilt signals via wireless communication technology without cable connections, making them highly flexible.

The main advantages of wireless tilt sensors are their flexibility and convenience. Since no wiring is required, the sensor can be easily installed anywhere it is needed, without considering the laying of cables. In addition, wireless sensors also have the advantages of high mobility, easy expansion and maintenance. However, wireless sensors also have some disadvantages, such as signal quality may be affected by radio interference, and signal stability and reliability may not be as good as wired sensors. ER-TS-12200-Modbus is a high-precision tilt sensor using Bluetooth and ZigBee wireless transmission technology of the internet of things, eliminating the complicated wiring and noise interference caused by long cable transmission, using lithium battery power supply, good long-term stability, zero drift, can automatically enter low-power sleep mode, get rid of the dependence on the use of environment.

Generally speaking, the mass of the building structure is huge, and the rate of change of inclination is relatively small, and there is a development process. The sampling frequency of conventional structural health monitoring is not high, and once a day can meet the requirements. In this case, the choice of the wireless inclination sensors with its own battery is the most appropriate, and the installation is very convenient.

3. How to choose the most suitable tilt sensor for you

When choosing an inclination sensor, you need to consider the following factors:

(1) Application scenarios: Different application scenarios have different requirements for sensors. For example, in some scenarios where long-term stability measurements are required, wired sensors may be preferred; Some use cases, such as house monitoring, basically have 220V mains power in the field, and low cost wired tilt sensors can be used. Of course, for monitoring scenarios with high acquisition frequency requirements, choosing a wired inclination sensor is a wise choice. In scenarios that require flexible deployment, easy scaling and maintenance, wireless sensors may be more suitable.

(2) Signal quality: For some application scenarios that require high-precision measurement, such as precision equipment monitoring or large-scale structure monitoring, it is necessary to choose a wired sensor with higher signal quality. For some application scenarios with low precision requirements, such as logistics and transportation, agricultural monitoring, etc., wireless sensors may be enough to meet the needs.

(3) Cost and maintenance: For some application scenarios that require a large number of sensors to be deployed, such as large-scale facility monitoring or logistics tracking, the deployment and maintenance cost of wireless sensors may be lower. For some cost-sensitive scenarios, such as small device monitoring or small structure monitoring, the cost of wired sensors may be lower.

(4) Durability and reliability: For some scenarios that require long-term continuous operation, such as equipment monitoring and fault warning systems in petrochemical, electric power and other fields, it is necessary to choose wired sensors with higher durability and reliability. For some scenarios that require portable and temporary use, such as construction sites, agricultural monitoring, etc., wireless sensors will be more suitable.

In short, when choosing an inclination sensor, it is necessary to choose according to actual needs and specific scenarios. Both wired and wireless sensors have their own advantages and scope of application. Only by fully understanding the characteristics and application scenarios of various sensors can we make the most appropriate choice.

A tactical grade inertial measurement device

Today, microelectromechanical systems (MEMS) inertial sensors and inertial systems have become an indispensable development direction for future navigation technology. MEMS technology is widely used due to its advantages such as small size, light weight, low power consumption, low cost, and impact resistance. At present, the development of MEMS inertial technology is relatively mature. It forms a combined system with auxiliary systems such as gyroscopes and accelerometers to provide suitable solutions for most navigation applications. The inertial measurement unit developed by Ericco is divided into MEMS IMU and FOG IMU. MEMS inertial measurement units are divided into tactical grade and navigation grade. Navigation-grade IMUs can seek north independently, while tactical-grade inertial measurement units can rely on magnetometers or GNSS to find north. Below we will introduce and recommend an ERICCO tactical grade IMU.

Next, we mainly learn about a new inertial measurement unit — ERICCO INERTIAL SYSTEM tactical-grade inertial measurement unit: ER-MIMU03 (high-precision navigation/stability control MEMS IMU).

ERICCO launches tactical-grade inertial measurement unit (IMU): ER-MIMU03 uses high-quality and reliable MEMS accelerometer and gyroscope. Equipped with three-axis precision gyroscopes of (complement code) numerical temperature, angle, accelerometer hexadecimal temperature, acceleration hexadecimal complement); It can also output floating point dimensionless values of gyroscope and accelerometer data processed by underlying calculations. ). The IMU has a built-in acceleration sensor and gyroscope, which can measure linear acceleration and rotational angular velocity in three directions, and obtain the attitude, speed and displacement information of the carrier through analysis. Applications for this tactical-grade IMU include azimuth, attitude, position measurement and maintenance in GNSS-assisted INS. Heading, pitch, roll measurement in UAV AHRS Robot control and control of autonomous machines, UAV directional stabilization and control of satellite antenna pointing, target tracking system Guidance, navigation and control attitude and attitude IMU orientation in tactical MEMS weapon systems Corner retention and positioning. Motion survey and maintenance of MRU and other application areas.

The high-precision navigation/stability control MEMS IMU integrates a three-axis MEMS accelerometer and a three-axis MEMS gyroscope in a unique redundant design that maximizes performance while reducing device size.

In terms of performance specifications, the high-precision navigation/stability control MEMS IMU has excellent gyroscopes and accelerometers. The gyroscope has a bias instability of 0.3°/h. Achieve long-term dead reckoning and maintain excellent heading performance. The MEMS sensor in ER-MIMU03 has extremely low vibration correction errors and can withstand high vibration environments up to 6.06g.

With extremely low gyroscope bias instability, the navigation performance of the high-precision navigation/stability control MEMS IMU can work normally when GNSS is interfered with or has no signal. This tactical-grade IMU has relatively high accuracy compared to tactical-grade IMUs from other peer companies. If you want to purchase our IMU, please contact our relevant personnel.

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Advantages of Fiber Optic North Seekers in Mining

The fiber optic gyro north seeker is an inertial product with a gyroscope as its core component. Fiber optic gyroscope is a kind of gyroscope with simple structure and easy to be mass-produced. Its development is based on low-loss optical fibers and small and reliable semiconductor light sources. It is an interferometer composed of optical fibers and is a static gyroscope. Its main advantages are: ① It uses solid-state devices, no moving parts, and the instrument is firm and stable. ②Long continuous working time. ③Long life, low power consumption, stable and reliable signal. It is precisely because of the advantages of fiber optic gyroscopes that are different from other traditional gyroscopes that many domestic and foreign research institutions attach great importance to the development of fiber optic gyroscope north seekers. Therefore, it has a broad application market and high research value.

Determining the north direction is an important parameter during the mining process and is also an important guarantee for the normal operation of the project. The underground conditions are complex and changeable, and magnetic field interference has a great impact on the project. The fiber optic gyro north seeker has strong anti-interference ability and a large measurement range, making it suitable for mining operations.

Ericco Company has a low-cost three-axis fiber optic north seeker, which is mainly used in mining. It not only uses a closed-loop fiber optic gyroscope as the core component, but is more suitable for customers with limited budgets. https://www.ericcointernational.com/north-finders/fiber-optic-gyro-north-finder/er-fiber-optic-gyro-north-finder-for-mining.html

If you are interested in fiber optic gyro north finder, you can discuss it with us.Contact information:

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What is the Principle of Inertial Measurement Unit?

Introduction to IMU

An inertial measurement unit is a device that measures the three-axis angular velocity and acceleration of an object. In a narrow sense, an IMU is equipped with gyroscopes and accelerometers on three orthogonal axes, with a total of 6 degrees of freedom, to measure the angular velocity and acceleration of objects in three-dimensional space. This is what we know as a "6-axis IMU"; in a broad sense, The IMU can add a magnetometer to the accelerometer and gyroscope, forming a "9-axis IMU".

 

Accelerometer: detects acceleration signals of three independent axes of the carrier coordinate system;

Gyroscope: detects the angular velocity signal of the carrier relative to the navigation coordinate system;

Magnetometer: Use algorithms such as Kalman or complementary filtering to provide users with absolute reference pitch angles, roll angles and heading angles.

 

The 9-axis sensor with added magnetometer is also called AHRS (Attitude and Heading Reference System). Because the heading angle has a reference to the geomagnetic field, it will not drift. However, the geomagnetic field is very weak and is often interfered by surrounding objects with magnetic fields. The more orthogonal the magnetic field and gravity field are, the better the attitude measurement effect will be. That is to say, if the magnetic field and gravity field are parallel, such as the geomagnetic north and south poles, AHRS cannot be used.

How an accelerometer works

An accelerometer is a sensor that measures acceleration. Accelerometers manufactured by traditional mechanical processing methods are large in size, mass, and cost, and their applications are greatly limited. With the development of Micro Electro Mechanical System (Micro Electro Mechanical System) technology, the development of micro accelerometers has been regarded as a priority project for the productization of Micro Electro Mechanical Systems at home and abroad. Compared with ordinary accelerometers, microaccelerometers have many advantages: small size, light weight, low cost, low power consumption, good reliability, etc. It can be widely used in aerospace, automotive industry, industrial automation and robotics and other fields, and has broad application prospects.

The essence of an accelerometer is to detect force rather than acceleration, that is, the detection device of the accelerometer captures the inertial force that causes acceleration, and then Newton's second law can be used to obtain the acceleration value. The measuring principle can be represented by a simple mass, spring and indicator.

The accelerometer adopts the "Northeast Sky" coordinate system (ENU): g = (0, 0, −9.81) T g= (0, 0, -9.81)^T g= (0, 0, −9.81) T.

 

An accelerometer is a sensor that measures acceleration. It usually consists of mass block, damper, elastic element, sensitive element and adjustment circuit. During the acceleration process, the sensor uses Newton's second law to obtain the acceleration value by measuring the inertial force exerted on the mass block. The structure includes a silicon diaphragm, an upper cover, and a lower cover. The diaphragm is between the upper cover and the lower cover and is bonded together. One-dimensional or two-dimensional nanomaterials, gold electrodes and leads are distributed on the diaphragm, and a pressure welding process is used to lead out the leads. Depending on the sensor sensitive components, common acceleration sensors include capacitive, piezoresistive, piezoelectric, etc.

How gyroscopes work

When a particle moves in a straight line relative to the inertial system, its trajectory is a curve relative to the rotating system due to its own inertia. Based on the rotation system, we believe that there is a force driving the movement trajectory of the particle to form a curve. The Coriolis force is a description of this deflection, expressed as:

That is to say, when the linear motion is placed in a rotating system, the linear trajectory will deviate. In fact, the linear motion problem is not affected by a force. The establishment of such a virtual force is called the Coriolis force.

Therefore, we select two objects in the gyroscope. They are in constant motion, and the phase difference of their movements is -180 degrees. That is, the two mass blocks move in opposite directions but have the same size. The Coriolis forces they generate are opposite, thus forcing the two corresponding capacitor plates to move, resulting in a differential change in capacitance. The change in capacitance is proportional to the angular velocity of rotation. The change in rotation angle can be obtained from the capacitance.

The measurement accuracy of the IMU is mainly determined by the gyroscope used, so the gyroscope is the core component of the navigation system.

How a magnetometer works

A magnetometer is a device that uses the earth's magnetic field to determine the North Pole. The magnetometer can provide data on the magnetic field experienced by the device in each of the XYZ axes. The relevant data is then imported into the microcontroller's processor to provide the heading angle related to the magnetic north pole. This information can be used to detect geographical orientation. The magnetometer uses three mutually perpendicular magnetoresistive sensors. The sensor in each axis detects the strength of the geomagnetic field in that direction.

The picture above shows an alloy material with a crystal structure. They are very sensitive to external magnetic fields, and changes in the strength of the magnetic field will cause changes in the resistance value of the magnetoresistive sensor.

 

The above article briefly describes the principle of IMU. The MEMS IMU developed by ERICCO has the advantages of low cost, low consumption, high performance and light weight. It is very popular among customers. If you want to buy an IMU, please contact our professionals.

The Application of Accelerometer in Aircraft

 The accelerometer uses high quality quartz crystals to achieve high precision acceleration measurement with extremely high reliability and stability. Its special flexible construction enables it to adapt to high acceleration applications under various environmental conditions, such as high temperature, high pressure and high vibration environments.

Accelerometers are an important part of aircraft, which can help control the attitude and stability of aircraft, helicopters, drones, etc. Accelerometer technology can detect the acceleration of the position to find out whether other aircraft are running over the aircraft, so that the aircraft can correct the deviation in time and maintain stability.

The attitude indication system on the aircraft mainly refers to the instrument system that accurately measures and indicates the attitude of the aircraft, which provides the pitch Angle, roll Angle and yaw Angle for the pilot and other on-board electronic products (such as flight guidance system, automatic flight control system and radar, etc.). The traditional attitude indication system is mainly composed of horizon instrument aircraft, turning instrument and sidering-slip instrument, with large size, cumbersome structure and weak accuracy. The digital attitude indication system widely used today uses high-precision gyro and accelerometer, with greatly improved accuracy. However, because the traditional high-precision gyro has weak overload carrying capacity, large size and expensive price, its application scenario is greatly limited. The Ericco accelerometer ER-QA-01A, specially designed for aviation applications, is not only small in size but also has a bias repeatability of 10μg, a proportional coefficient repeatability of 10 PPM, and a Class II nonlinear repeatability of 10μg/g². The high precision navigation MEMS gyroscope ER-MG2-300/400 is capable of meeting the measurement range of ±400°/s, 0.05°°/hr bias instability and 0.025°/√hr Angle random walk, in addition to the strict requirements for accuracy and carrier space size in the aviation field, compared to other products of the same type. Or other advantages.

The principle of the angular accelerometer is similar to that of an accelerometer. Its outer box is mounted on a rotating object. Due to the angular acceleration, a tangential dynamic load is generated on the reference mass, and a signal proportional to the magnitude of the tangential acceleration or the angular acceleration can be output. With different measured moving objects and measurement requirements, accelerometers have various principles and implementations. For example, on the aircraft, there are gyro accelerometers designed according to the gyro principle.

Measure the acceleration of the carrier line. An accelerometer that measures aircraft overload is one of the first aircraft instruments to be applied. Accelerometers are also commonly used on aircraft to monitor engine failure and fatigue damage of aircraft structures. Accelerometers are important tools for investigating flutter and fatigue life of aircraft in flight tests of various types of aircraft. In a flight control system, an accelerometer is an important dynamic characteristic correction element. In inertial navigation systems, a high-precision accelerometer is one of the most basic sensitive components. The accelerometers used in different occasions vary greatly in performance. A high-precision inertial navigation system requires the resolution of the accelerometer to be as high as 0.001 g, but the range is not large; an accelerometer for measuring an aircraft overload may require a 10 g range, and the accuracy The demand is not high.

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Which Indicators Affect the Installation and Measurement Accuracy of tilt sensor

 

Tilt sensor accuracy

Tilt sensor is used to measure the object relative to the horizontal tilt angle, in the platform leveling, mechanical manufacturing, safety protection, precision measurement and many other fields have a wide range of applications, manufacturers are also many, but the market face of the accuracy of the inclination sensor understanding is unclear or even biased.

First define the accuracy of the tilt sensor: accuracy refers to the error between the angle measured by the sensor and the true angle. This error is usually defined as the mean square error. That is, the root mean square value between the results of multiple measurements and the true value.

Indicators that affect accuracy

We take the tilt sensor of the acceleration sensing principle as an example. The acceleration sensor converts the component of gravity acceleration measured on the sensitive axis of the acceleration sensor into angle data, that is, the inclination value and the acceleration value are sinusoidal.

Where g represents the gravitational acceleration, a represents the inclination value measured by the acceleration sensor, and α is the inclination angle.

The measurement accuracy of the tilt sensor is closely related to the following indicators:

Noise – depends on the core sensitive device’s own characteristics, but at the same time associated with the frequency response, also known as amplitude frequency characteristics. Generally speaking, the higher the frequency response, the greater the noise. Noise determines the resolution of the sensor, and if the angle change is so small that the change is almost submerged in the noise and cannot be resolved, we consider the angle change to be the resolution of the tilt sensor. For example, the ER-TS-12200-Modbus, its resolution is 0.0005°, because its frequency response is not high, the angle change is very small, and the noise is very small.

The zero bias stability depends on the characteristics of the core sensitive device, which means that when the sensor has no angle input (such as absolute horizontal plane), the measured output of the sensor is not zero, and the actual output angle value is zero bias. The effect of zero bias on the accuracy of the sensor is not terrible, because the zero bias can be eliminated by calibration, but the zero bias usually drifts with time and temperature changes, the drift is called the zero bias stability, and this drift is usually difficult to eliminate, so the drift will cause the accuracy to deteriorate.

Nonlinearity – can be corrected later, depending on the number of correction points. The more correction points, the better the nonlinearity. Although the nonlinear can be corrected by the subsequent correction method, the nonlinear also has the phenomenon of drift, and the drift can not be eliminated, resulting in the deterioration of accuracy.

Cross-coupling error – refers to the error caused by coupling to the output signal of the sensor when the sensor applies a certain acceleration perpendicular to its sensitive axis or tilts at a certain angle. For example, for the wireless tilt sensor ER-TS-22800 with a measuring range of ±30° (assuming that the X direction is the inclination direction), when the space is tilted 10° perpendicular to the X direction (at this time, the actual tilt angle of the measured X direction remains unchanged, such as +5°), the output signal of the sensor will cause additional errors due to this 10° tilt. This error is called cross-coupling error. This extra error varies depending on the product. When the cross-coupling error of the inclination sensor is 3%FS(FS: full scale, full range), the additional error generated is 3%x10°=0.3°, and the actual output angle of the sensor is simply estimated to be 5.3°(=5°+0.3°). At this time, even if the nonlinear error of the inclination sensor reaches 0.01°, compared with the cross-coupling error, this nonlinear error can be ignored, that is, as the measurement accuracy of the inclination sensor, the cross-coupling error cannot be counted, otherwise it will cause a large measurement error.

Installation error – When the sensor is installed and measured, the measuring shaft should be reconnected with the sensor’s sensitive shaft. However, in the actual installation and measurement, it is always impossible to accurately match. For example, if the angle between the installation measuring shaft and the sensor’s sensitive shaft is 1 degree, the measured value is the projection of the actual angle change on the sensitive shaft. If the angle change is 30 degrees, the measured value is 30*cos(0.1)=29.995 degrees, the error is 0.005 degrees, so for high-precision applications, it is very important to keep the measurement shaft and the sensor sensitive shaft match.

Repeated measurement accuracy – depends on the core sensitive device’s own characteristics and cannot be improved by subsequent corrective measures.

The effect of temperature on zero point and sensitivity – also includes drift and repeatability of the temperature curve, which depends on the own characteristics of the core sensitive device and cannot be improved by subsequent correction measures. In the case of repeatability, it can be corrected later, depending on the number of correction points (angle points and temperature points). The more correction points, the better the temperature drift accuracy.

Range – Because the relationship between inclination measurement and acceleration is sinusoidal, the angle measurement error and acceleration measurement error meet the following relationship:

Where da is the inclination measurement error and da is the acceleration measurement error. When the range is close to 90 degrees, the acceleration a is close to the gravitational acceleration g, which is close to infinity, so a slight acceleration error causes a large inclination measurement error.

It can be seen that the systematic error of the inclination sensor contains the repeatability of noise zero deviation and temperature drift, which cannot be corrected and compensated, while the random error contains the cross-coupling error of the input axis non-aligned nonlinear temperature linearity which can be corrected

Positive-sum compensation measures to improve. Therefore, the measurement accuracy of the inclination sensor must not be measured only by nonlinearity, and it is necessary to synthesize the systematic error and random error of the sensor.

Therefore, the accuracy error of the inclination sensor should include nonlinearity, repeatability, noise, zero bias drift, zero nonlinear drift and cross-coupling error.