MEMS-IMU error analysis

MEMS-IMU has many advantages over traditional IMUs, such as small size, low cost, low power consumption and high integration. MEMS IMU is widely used in the military field, such as tactical guided weapons. In recent years, the application scope of MEMS-IMU in the civilian field has been continuously expanded, such as drones, underwater equipment, car navigation, etc. At present, the performance indicators of MEMS inertial sensors at home and abroad cannot meet the requirements of inertial navigation. The performance indicators of the most advanced MEMS gyroscopes can only reach the tactical level, and they are easily interfered in the actual working environment, reducing the output accuracy. MEMS accelerometer performance is also inferior to traditional quartz accelerometers. This chapter will comprehensively analyze various errors and compensation solutions of MEMS-IMU.

The following table shows the main indicators for judging gyroscope performance. Different grades have different accuracy levels.

The errors of MEMS-IMU mainly include errors of MEMS sensors and MEMS-IMU integration errors. The errors of MEMS IMU will be analyzed in detail from these two aspects below.

1.MEMS inertial sensor error analysis

1.1 Zero offset

The bias errors of MEMS accelerometers and MEMS gyroscopes mainly include bias, bias stability and bias repeatability. Zero-bias repeatability and zero-bias can be eliminated through initial alignment. Zero-bias stability refers to the degree of drift of its output angular velocity or acceleration over time under a certain input. This is related to the structure, design and external environment of the MEMS sensor.

1.2 Scale factor error

Since MEMS gyroscopes and MEMS accelerometers convert signals between signals through a scale factor, the error in the scale factor will directly affect the output error of the MEMS accelerometer and MEMS gyroscope. The error of the scale factor is divided into temperature drift and nonlinear error. It is difficult to measure the relationship between the scale factor and temperature through experimental testing for MEMS accelerometers, because centrifuges generally do not have temperature control devices, while MEMS gyroscopes can be temperature controlled. The relationship between the scale factor and temperature was measured using the turntable.

1.3 Non-sensitive axis coupling error

The non-sensitive axis coupling error refers to the error output caused by the non-orthogonality of the sensor structure itself when there is input on the non-sensitive axis. The non-sensitive axis mutual coupling error can be expressed by Equation

                                                                    Formula1：Insensitive axis mutual coupling error1-1

Among them, VX, VY, and VZ represent the output voltages of the x, y, and z-axis sensors, Input is the external input, and K is the mutual coupling error coefficient. It can be seen that the expression of the coupling error of the MEMS accelerometer and the MEMS gyro is the same as the installation error expression of the IMU can be processed together.

1.4 Acceleration sensitivity

The acceleration sensitivity of the MEMS gyroscope refers to the output of the MEMS gyroscope’s sensitive acceleration, which is an error term with a large impact. Because most MEMS gyroscopes are based on mechanical vibration, they may be affected by acceleration, especially in working environments with large accelerations. For example, when the acceleration of the carrier is 20g and the duration is 10s, when the acceleration sensitivity is 0.05 (° /s)/g, the angle error produced by this is approximately 10°. Such a large angle error has a great impact on the MEMS-IMU attitude solution, so acceleration sensitivity is an error term that cannot be ignored.

1.5 Random noise

The random noise of the structure and the random noise of the circuit are the main components of the random noise of the MEMS inertial sensor. The random noise of the structure is mainly mechanical thermal noise. The random noise of the circuit includes the thermal noise of the circuit, 1/f noise, shot noise and g-r. Noise, etc., the biggest impact on the performance of MEMS sensors is mechanical thermal noise and circuit thermal noise, which are the main research objects.

Brown’s force is the source of mechanical thermal noise. Its principle is that gas molecules or liquid molecules produce random collisions with mechanical particles. This effect directly affects the sensitivity and resolution of the MEMS sensor and increases the random noise during measurement. Because the structure of the MEMS sensor is on the micron or even nanoscale, the impact of molecular motion cannot be ignored.

For capacitive MEMS inertial sensors, the equivalent Brown noise acceleration is

                                                                    Formula2：Equivalent Brown noise acceleration1-2

                                                                                                Formula3： 1-3 

 

Circuit thermal noise refers to the irregular thermal movement of carriers in a conductor when the temperature is above zero. Due to this irregular thermal movement, the current in the circuit deviates from the average fluctuation, resulting in voltage fluctuations. The power spectrum distribution of this thermal noise is

                                                                 Formula4： The power spectrum of thermal noise1-4

Among them, R is the resistance of the conductor. From the above formula, we can know that the power spectrum of random noise is constant in the entire frequency band. However, the noise can be suppressed through low-pass filtering to prevent it from spreading in the form of integrals in navigation and positioning.

2.MEMS-IMU integrated error analysis

Sensor mounting non-orthogonality errors and lever-arm effect errors are the main components of MEMS-IMU integration errors.

2.1 Sensor installation error

The sensor installation error of MEMS-IMU is mainly due to the non-orthogonality of the MEMS-IMU shell, the sensor installation error and the non-orthogonality of the sensor itself. As shown below.

 where xByBzB is the reference orthogonal coordinate system, xyz is the coordinate system of the gyroscope group or accelerometer group, θij (i, j=x, y, z) represents the installation error angle, where i represents the measurement axis, j represents the measurement axis around j The installation error angle caused by shaft rotation is positive in counterclockwise direction. The transformation from the reference coordinate system to the axis coordinate system is as follows.

 

The form is consistent with the formula (1-1) and does not need to be distinguished. The installation error of the MEMS gyroscope can be evaluated using the turntable test method. Given different rotational speeds, the installation error angle parameters can be obtained by measuring the output at different rotational speeds. The static tumbling test method can be used to evaluate the installation error of the MEMS accelerometer, and the installation error angle parameters of the MEMS accelerometer can be solved by measuring the output at multiple positions.

2.2 Lever arm effect error

Since the sensor of the combined MEMS-IMU is installed separately, when the carrier rotates around a certain rotation axis, the sensor will be subject to additional centrifugal acceleration and tangential acceleration, resulting in output errors of the MEMS accelerometer and MEMS gyroscope. The error is related to the rotation angular rate. Directly proportional.

 

3 Calibration

According to the above calibration method, the single-axis turntable can be used to complete the angular rate calibration experiment and position calibration of the MEMS gyroscope and MEMS accelerometer, and solve the various error coefficients in the error model. The experimental platform is shown in the figure, and the performance indicators of the experimental platform as follows.

4 Calibration method verification

Use the obtained error coefficients to compensate the MEMS gyroscope and MEMS accelerometer, then install the MEMS-IMU on the turntable with the Z-axis facing upward and fix it, and control the temperature of the turntable to rise from -40° to 80°, and then from 80° ° drops to -40°, collect the output data of MEMS-IMU respectively and save them. Use MATLAB to draw the saved data into a graph, and the results are shown in the figure below.

   

                                                   Comparison of data before and after MEMS IMU compensation

As can be seen from the data before and after X-axis compensation in the figure above, the maximum output error of the gyro before compensation reached 0.025°/s, and after compensation it was reduced to 0.02°/s, and it can also be seen from the figure that the error is increasing. The data at 0.01°/s-0.025°/s is significantly reduced, and the errors in the Y and Z axes are also reduced. This shows that the calibration method in this article is feasible.

Summarize

Analyze various error sources of MEMS-IMU, including device errors and integration errors. Based on the main error sources of MEMS gyroscopes and MEMS accelerometers, corresponding error models were established, a calibration experimental plan was designed, and the calibration experimental plan was experimentally verified, confirming that the given calibration method is feasible and can improve MEMS-IMU measurement accuracy. Regarding the accuracy of MEMS IMU, I have to say that the MEMS IMU independently developed by ERICCO has high accuracy, small size, light weight and low power consumption. For example, the gyroscopes and accelerometers in ER-MIMU01 and ER-MIMU-02 are also more accurate. Strict measures have also been taken for the error calibration of the IMU.

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Application of IMU in UAV Flight Control System

Nowadays, with the development of chip, artificial intelligence and big data technology, UAV has begun the trend of intelligence, terminal and clustering. A large number of professional talents in automation, mechanical electronics, information engineering and microelectronics have been invested in UAV research and development. In a few years, UAVs have flown from military applications far away from people’s vision to ordinary people’s homes. It is undeniable that the development of flight control technology is the biggest driver of UAV changes in this decade.

Flight control is the abbreviation of flight control system, which can be regarded as the brain of aircraft. The flight control system is mainly used for flight attitude control and navigation. For flight control, it is necessary to know the current status of the aircraft, such as three-dimensional position, three-dimensional velocity, three-dimensional acceleration, three-axis angle and three-axis angular velocity. There are 15 states in total. The current flight control system uses an IMU, also known as inertial measurement unit, which is composed of three-axis gyroscope, three-axis accelerometer, three-axis geomagnetic sensor and barometer. So what is a three-axis gyroscope, a three-axis accelerometer, a three-axis geomagnetic sensor, and a barometer? What role do they play in the aircraft? What are the three axes?

The three axes of the three-axis gyroscope, three-axis accelerometer and three-axis geomagnetic sensor refer to the left and right of the aircraft, and the vertical up and down in the front and back directions, which are generally represented by XYZ. The left and right directions in the aircraft are called roll, the front and rear directions in the aircraft are called pitch, and the vertical direction is the Z axis. It is difficult for a gyroscope to stand on the ground when it does not rotate. Only when it rotates, it will stand on the ground. This is the gyro effect. According to the gyro effect, smart people invented a gyroscope. The earliest gyroscope was a high-speed rotating gyroscope, which was fixed in a frame through three flexible axes. No matter how the outer frame rotates, the high-speed rotating gyroscope in the middle always maintains a posture. The data such as the degree of rotation of the external frame can be calculated through the sensors on the three axes.

Because of its high cost and complex mechanical structure, it is now replaced by the electronic gyroscope. The advantages of the electronic gyroscope are low cost, small size and light weight, only a few grams, and its stability and accuracy are higher than those of the mechanical gyroscope. Speaking of this, you will understand the role of gyroscope in flight control. It is used to measure the inclination of the three XYZ axes.

So what does the three-axis accelerometer do? It was just said that the three-axis gyroscope is the three axes of XYZ. Now it goes without saying that the three-axis accelerometer is also the three axes of XYZ. When we start driving, we will feel a thrust behind us. This thrust is acceleration. Acceleration is the ratio of speed change to the time of occurrence of this change. It is a physical quantity describing the speed of object change. Every second power of meter. For example, when a car is stopped, its acceleration is 0. After starting, it takes 10 seconds from 0 meters per second to 10 meters per second. This is the acceleration of the car, If the vehicle travels at a speed of 10 meters per second, its acceleration is 0. Similarly, if it decelerates for 10 seconds, from 10 meters per second to 5 meters per second, its acceleration is negative. The three-axis accelerometer is used to measure the acceleration of the three axes of the aircraft XYZ.

Our daily travel is based on landmarks or memories to find our own direction. The geomagnetic sensor is a geomagnetic sensor, which is an electronic compass. It can let the aircraft know its flight direction, nose direction, and find the position of the mission and home. The barometer is used to measure the atmospheric pressure at the current position. It is known that the higher the altitude, the lower the pressure. This is why people have plateau reactions after arriving at the plateau. The barometer obtains the current altitude by measuring the pressure at different positions and calculating the pressure difference. This is the whole IMU inertial measurement unit. It plays a role in the aircraft to sense the change of the aircraft attitude, such as whether the aircraft is currently leaning forward or left and right, What is the role of the most basic attitude data, such as nose orientation and altitude, in flight control?

The most basic function of flight control is to control the balance of an aircraft when flying in the air, which is measured by IMU, sense the current inclination data of the aircraft and compile it into an electronic signal through the compiler. The signal is transmitted to the microcontroller inside the flight control through the new time of the signal. The microcontroller is responsible for the calculation. According to the current data of the aircraft, it calculates a compensation direction and angle, and then compiles the compensation data into an electronic signal, It is transmitted to the steering gear or motor. The motor or steering gear is executing the command to complete the compensation action. Then the sensor senses that the aircraft is stable, and sends the real-time data to the microcontroller again. The microcontroller will stop the compensation signal, which forms a cycle. Most flight controls are basically 10HZ internal cycles, that is, 10 refreshes per second.

This is the most basic function application of IMU in the flight control system. Without this function, once an angle is tilted, the aircraft will quickly lose balance and cause a crash.

Ericco’s MEMS IMU ER-MIMU-03 and ER-MIMU-04, ER-MIMU-07 and ER-MIMU-08 have built-in high-precision advanced MEMS gyroscopes and high-performance accelerometers, which can measure linear acceleration and angular velocity of rotation from three directions, and obtain carrier attitude, velocity and displacement information through analysis. They are specially designed for high-performance applications of inertial navigation equipment such as UAV flight control. Provides excellent stability in the temperature range of – 45° C to 80° C. The advanced gyro sensor design suppresses the linear acceleration effect of shock and vibration, enabling ER-MIMU-04, ER-MIMU-07 and ER-MIMU-08 to operate in harsh environments.

In addition to the application of ERICCO’s MEMS products in UAVs, its popularity in oil drilling, mining and other application markets is also growing. MEMS technology is developing into a huge industry. Just like the great changes brought to mankind by the microelectronics industry and computer industry in the past 20 years, MEMS has also bred a profound technological change, which has had a new round of impact on human society. 

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Application of Tilt Sensor in the Settlement of Railway Track Subgrade

The tilt sensor can be well applied in the remote automatic monitoring system of subgrade settlement.

In order to ensure the high-speed and healthy development of railway, the remote automatic monitoring system of subgrade settlement based on laser measurement, advanced sensing and wireless network technology is developed. The monitoring system includes four sub-systems: automatic measurement of surface settlement by laser, simultaneous automatic measurement of subgrade stratified settlement and lateral displacement, automatic measurement of subgrade lateral profile settlement, data acquisition and wireless transmission. Automatic measurement of surface settlement is achieved by laser measurement and automatic calibration technology: simultaneous automatic measurement of subgrade stratified settlement and lateral displacement is achieved by Hall sensor, laser ranging and dip angle transmission sensor realization: The automatic measurement of subgrade transverse profile settlement is achieved by the tilt sensor driven by the main and slave motors. The monitoring system has been verified by laboratory and designed by engineering, and has been tested in a station of high-speed railway.

The ER-TS-12200-Modbus tilt sensor can be well applied in the control system, so as to realize real-time monitoring of the overall settlement of the subgrade, local settlement and the settlement of different layers in the section, and transmit the output signal of the tilt sensor to the computer through wireless transmission or various wired networks. Then the received data is processed, analyzed and stored by computer software.

If you want to learn more about MEMS tilt sensors or buy tilt sensors

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What sensors are inside the IMU and how do they work?

Inertial measurement units typically consist of three different types of sensors. The first type of sensor is an accelerometer, which measures acceleration, or the rate at which an object accelerates or decelerates. While there are many different sensor technologies for accelerometers, by far the most common for wearable applications is MEMS (microelectromechanical systems). MEMS are sensor systems composed of electrical and mechanical components, typically etched from micron-sized silicon.

Whenever the MEMS accelerometer experiences acceleration, the proof mass also experiences that acceleration. An etched spring set resists this acceleration. Using Hooke’s law (spring force is proportional to the distance the spring is compressed) and Newton’s second law (force is proportional to acceleration), check that the distance a mass moves is proportional to the acceleration it experiences (see figure below). This movement is sensed using the electrical properties of capacitance, which is related to the distance between two conductors. A set of electronics is then able to measure the change in capacitance, calibrate the signal, and further process it to give acceleration.

The second type of sensor in an Inertial measurement unitis a gyroscope, which measures angular velocity, or the speed and direction of an object’s rotation or spin. Gyroscopes also typically use MEMS technology, although they are more complex than MEMS accelerometers. The main physical phenomenon used in gyroscopes is the Coriolis effect, which describes the forces involved when an object moves in a rotating reference frame.

MEMS gyroscopes have masses that reciprocate at a constant frequency. During the rotation of the gyroscope, due to the Coriolis effect, the mass will induce a force perpendicular to the direction of the reciprocating motion. This force is counteracted by an etched spring and sensed by a capacitive sensing arm such as an accelerometer. Signal processing electronics then process the change in capacitance relative to the reciprocating motion of the resonant mass (see figure below).

The final sensor commonly found in Inertial measurement units is a magnetometer, which measures the strength of a magnetic field and acts somewhat like a digital compass. Most magnetometers use the Hall effect to measure magnetic field strength. The basic premise of a magnetometer is that electrons moving in a conductor are deflected by the magnetic field to which the conductor is exposed. When charges pass through a conducting plate in a magnetic field, the magnetic field deflects the electrons to one side of the conducting plate. As more negative charge builds up on one side of the plate and more positive charge builds up on the other side of the plate, there is a measurable voltage between the two sides of the plate that is proportional to the strength of the magnetic field.

The current status and classification of IMU

Generally,Inertial measurement units on the market are divided into laser IMUs, fiber optic IMUs, and MEMS IMUs. Laser IMU has high cost, high precision, and large size. It is widely used in the military. It is a technology for positioning moving objects and guiding them to their destination safely, accurately, and economically. Fiber optic IMUs are medium in cost, large in size, and relatively medium in accuracy. MEMS generally refers to micron systems of 1um to 100um, or systems with outline dimensions on the millimeter level and component sizes on the order of microns. MEMS-IMU is an inertial measurement unit based on MEMS technology. It is divided into tactical grade and navigation grade, with low precision and small size. Several high-precision, small size, light weight, low cost, and high-performance MESM IMUs have recently appeared on the market. For example, Ericco’s newly developed tactical-grade ER-MIMU03 and ER-MIMU07 and navigation-grade ER-MIMU01 and ER-MIMU05 are small in size, light in weight, low in cost, high in performance, and use high-performance north seeking. Among them, the MEMS gyroscope (ER-MG2–100), can reach 0.1°/h. The accuracy is more accurate than the lowest-precision IMUs of many large companies, and can better reflect its high performance in complex environments.

This article explains how the Inertial measurement unit works and how it works. I hope you have a general understanding of IMU. If you want to know more information, you can find useful content in “More technical questions”. If you are interested in IMU related products, you can click “Products in Articles”.

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Tilt sensor, Tilt Switch&Other Common Problems in Installation and Use Process

 

Question 1: What is the resolution of a tilt sensor?

A: It refers to the smallest change to be measured that can be detected and distinguished by the tilt sensor within the measurement range.

Question 2: What is precision?

A: Accuracy refers to the actual angle and tilt sensor measurement angle multiple times (＞24 times) root mean square value error of the measurement.

Question 3: How can the sensor be installed to ensure its best accuracy?

A: During installation, the sensor mounting surface should be kept parallel to the target of the measured surface, and the influence of dynamic and acceleration on the sensor should be reduced. The product can be installed horizontally or vertically, and the vertical installation is suitable for single-axis tilt sensor, which is suitable for measuring range < The 60-degree product is installed horizontally, and the front of the sensor is marked with X and Y direction indication stickers, which can be referred to when installing.

Question 4: What does offset mean in analog output sensors?

A: Zero bias voltage, if you customize the 0~5V output, then the zero position voltage output 2.5V.

Question 5: The larger the measurement range of the inclination sensor, does it determine the better and more expensive the product?

A: Can not be understood in this way, relatively speaking, the size of the range and the accuracy will be inversely proportional, the smaller the range, the higher the accuracy, the price is not directly related to the range.

Question 6: How can the visual value be less than the actual measured value (especially for the tilt alarm of the platform monitored by the tilt switch, the old-fashioned alarm)?

A: There may be an installation angle when the tilt switch is installed, and at this time, the tilt switch has an initial angle, so that the actual application will appear larger than the visual angle, and an alarm will occur.

Question 7: How can the visual angle of an electronic compass be greater than the measured angle?

Answer: Because the two axes of the inclination measurement are the most sensitive, when the inclination direction is not aligned with the measurement axis, the actual value will be greater than the measured value, which can also be understood as a projection.

Question 8: Which direction does the single-axis and dual-axis measurement of the tilt sensor refer to?

A: The double axis can measure the rollover (X direction) and pitch angle (Y direction), while the single axis can only measure the rollover angle or pitch angle when selecting the horizontal installation. If the single axis can only measure the rollover angle when selecting the vertical installation, the pitch angle is not optional.

Question 9: Do your products work well in harsh industrial environments?

A: At present, our products are used in various industrial control fields, including underground non-underground mining machinery, underwater machinery, Antarctic survey, oil drilling, etc., and the work is very stable.

Question 10: How to understand course accuracy?

A: The course accuracy refers to the root-mean-square error, not a random error, and to compensate for the influence of the surrounding static magnetic field, and the magnetic inclination should not be greater than 75 degrees of the value.

Question 11: In actual use, the electronic compass can not reach the nominal accuracy, especially in the measurement of the presence of pitch angle and roll angle.

A: Generally, the environment at the time of calibration is different from that at the time of use, so the calibration failure cannot guarantee the established indicators. If there is no tilt or roll in the rotation of the electronic compass during calibration, but there is a tilt and roll phenomenon in actual use, so this calibration is not effect.

Question 12: Axis alignment problem during installation of electronic compass?

A: The north point on the mounting surface of the electronic compass can be at a certain angle with the axis of the mounted body, which can be solidified into the memory body in the device through the setting software of the electronic compass for normal use to correct the output value.

Question 13: Electronic compass installation precautions?

A :1. In order to avoid strong magnetic interference, please be more than 0.5 meters away from the magnetic field source;

2. If there is magnetic field interference of other supporting products around the installation, it is recommended to calibrate the device before using it. For details about the calibration method, see the calibration instructions in the product manual or consult technical support.

In Summary:

Question 5 we mentioned above: Does the larger the measurement range of the tilt sensor determine the better and more expensive the product?

A: Can not be understood in this way, relatively speaking, the size of the range and the accuracy will be inversely proportional, the smaller the range, the higher the accuracy, the price is not directly related to the range.

Let’s take these two wireless tilt sensors as an example, the measuring range of ER-TS-12200-Modbus is ±30°, the measuring range is very small, but its accuracy reaches 0.001°. Small range but high precision.

We use this product ER-TS-32600-Modbus for comparison. Its range is ±90°, which is larger than the above product, but its accuracy is only 0.01°. It can be seen that the range size and accuracy are indeed inversely proportional.

Customers in the use of the process may encounter some common problems, these problems are often consulted by customers in the past, in order to avoid causing unnecessary trouble to customers, Ericco listed here with the majority of customers and peers to share our experience. 

IMU self-calibration based on factorization

Inertial Measurement Units (IMUs) are critical sensor systems in many applications, including navigation, robotics, motion science, and autonomous driving. The IMU consists of an accelerometer and a gyroscope, which are used to measure the acceleration and angular velocity of an object, thereby providing attitude and position information of the object. However, IMUs often have errors due to manufacturing and environmental factors, which affect their measurement accuracy. Therefore, the IMU needs to be calibrated to eliminate these errors.

This paper proposes an IMU self-calibration method based on factorization. The method includes steps such as sensor calibration, initial alignment, data preprocessing, motion compensation, fusion algorithm, attitude solution and error correction. This method enables self-calibration without the use of external measurement equipment, greatly reducing the complexity and cost of calibration.

1. Sensor calibration
Sensor calibration is the first step in the calibration process. The purpose is to determine the static parameters of each sensor in the IMU, such as sensitivity and bias. This step usually needs to be performed in a laboratory environment by applying known acceleration and angular velocity and comparing the sensor measurement results with the actual values to obtain the calibration parameters of the sensor.

2. Initial alignment
Initial alignment is an important step in the calibration process, its purpose is to determine the initial attitude and position of the IMU. In this step, the IMU is fixed in a reference coordinate system with known position and attitude, and its measurement data is then recorded. By comparing these measured data with known reference data, the IMU's initial attitude and position information can be calculated.

 

 

3. Data preprocessing
The purpose of data preprocessing is to remove noise and outliers to improve the accuracy of the calibration process. This may include filtering algorithms, such as Kalman filters or low-pass filters, to reduce the effects of noise. In addition, the identification and removal of outliers is also an important part of data preprocessing.

4. Motion compensation
Motion compensation is an important step in the calibration process, aiming to improve the accuracy of the IMU by identifying and compensating for the dynamic effects of objects in motion. These effects may include the Earth's gravitational acceleration and the Coriolis force, among others. Methods to compensate for these effects often include using fusion algorithms to fuse IMU data with external sensor data such as GPS or magnetometers.

5. Fusion algorithm
Fusion algorithm is the process of fusing multiple sensor data together to obtain more accurate attitude and position information. Common fusion algorithms include Kalman filter and extended Kalman filter. These algorithms can optimize the fusion of data based on the characteristics and accuracy of different sensors, thereby improving the measurement accuracy of the IMU.

6. Attitude calculation
Attitude calculation is the process of calculating the attitude of an object based on the measurement data of the IMU. In this process, quaternions or rotation matrices are usually used to represent the attitude of the object. Attitude calculation methods include accelerometer- and gyroscope-based data fusion and the use of additional sensor data (such as magnetometers) for attitude correction.

7. Error correction
Error correction is the process of eliminating or reducing IMU errors during calibration. These errors may include sensor sensitivity errors, bias errors, cross-coupling errors, etc. Error correction methods include self-calibration algorithms based on factorization and iterative optimization using known motion patterns. Through these methods, the measurement accuracy of the IMU can be significantly improved and the impact of errors can be reduced.

Summarize
The IMU self-calibration method based on factorization mainly includes the following steps:
1. Use the original data of IMU for error modeling;
2. Factorize the error model and identify error factors;
3. Correct the error factor through algorithm optimization or hardware compensation;
4. Use the corrected data to recalibrate the IMU to improve its measurement accuracy.

Compared with other traditional IMU calibration methods, the factorization-based self-calibration method has the following advantages:
1. Multiple error factors can be automatically identified and corrected, while traditional methods can usually only calibrate a single error;
2. No additional calibration equipment or complex environmental settings are required, reducing calibration costs and time;
3. Calibration parameters can be dynamically adjusted according to actual conditions, improving the flexibility and accuracy of calibration.

Domestic company ERICCO has been committed to the research of inertial products. For IMU, we not only have optical fiber IMU, but also MEMS IMU. We also have our own advantageous products: ER-MIMU01, ER-MIMU05, and ER-MIMU02, which have the characteristics of high precision, low power consumption, light weight, and small size. The most important thing is that the navigation-level one does not need a magnetometer and can find north independently.
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