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Monday, January 15, 2024
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-07and 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.
If you want to purchase an IMU, please contact our relevant personnel.
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
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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Question 1: What is the resolution of atilt 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.
Question4: 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.
A :1. In order to avoid strong magnetic interference, please be more than 0.5 meters away from the magnetic field source;
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-Modbusfor 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.
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. If you want to learn about or purchase IMU, please contact our relevant personnel.
An accelerometer is an instrument used to measure the linear acceleration of an object. It integrates the acceleration within a certain period of time to obtain the speed of the object under measurement, and integrates the speed to obtain the displacement of the object under measurement. The net acceleration or force of the system over time is gravity, and an accelerometer can also be used to measure the static Angle of tilt or tilt. The quartz flexible accelerometer is one of the representative products of the accelerometer, and adopts high-quality quartz crystal, which can realize high precision acceleration measurement, and has 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.
Applications in the aerospace field
Quartz vibration beam accelerometers can be used to measure the body vibration and flight state of aircraft in order to better estimate the life of aircraft and maintenance costs. In addition, the quartz vibration beam accelerometer can also be used in the development of pilot helmets to ensure that it can smoothly adapt to aerodynamic changes, and thus ensure the safety of the pilot. For example, ER-QA-03A has a zero-bias stability of 10-50μg, a scale factor repeatability of 15-50 PPM, and a second-order nonlinearity of 10-30μg/g2, which is often the best choice for high-performance, aerospace applications.
Applications in oil drilling
Quartz flexible accelerometer is one of the many accelerometers with relatively simple structure, high performance-to-volume ratio and performance-to-price ratio, especially in the high temperature environment of drilling and logging. It is one of the few accelerometers in China that has been verified by a lot of actual underground work experience, and has high temperature and high reliability product characteristics. The ER-QA-03D is designed for the drilling sector and is capable of shock resistance of 0.5ms at 500-1000g in an operating environment of -55 to 180 ° C.
If you want to know more about quartz accelerometers or purchase, please contact me through the following ways:
IMU is used to measure the angular velocity and acceleration of objects. The accuracy of the IMU determines the accuracy of its measurement data and has an important impact on the deception detection algorithm. Global navigation satellite system (GNSS)/inertial navigation system (INS) tightly integrated navigation system usually uses the original observation information (such as pseudorange, pseudorange rate, Doppler, etc.) output by GNSS as Measurements. INS is an inertial navigation system, a system that uses IMU measurement data for navigation. The optimal state estimator of the system is obtained through fusion filtering by the Kalman filter and the measurement values output by the inertial measurement unit in the INS. The tight combination mode has become a hot spot in the current research on GNSS/INS integrated navigation technology due to its moderate calculation amount and good navigation performance.
For civilian satellite navigation signals with an open signal system, forwarding deception and generative deception methods can be used; however, for authorization signals with unknown pseudo codes, forwarding deception and interference can be used, so the accuracy and security of navigation and positioning are seriously threatened. . Deception detection in integrated navigation systems is an important way to improve the reliability of integrated navigation systems. Among them, commonly used innovation-based deception detection methods include snapshot deception detection method and continuous deception detection method. It is difficult to detect ramp-type pseudorange spoofing using the snapshot spoofing detection method, but the detection effect for step-type spoofing is much better. The continuous spoofing detection method can effectively detect the slope spoofing problem, but the longer the window, the longer the calculation time.
The impact of different IMU accuracy on the tight combination anti-spoofing interference algorithm will be analyzed below. Firstly, the GNSS/INS tight combination model and spoofing interference model are explained. Secondly, the impact of the propagation error of IMUs with different performances on the pseudorange prediction value and the mean value of innovation detection amount under the short-time uniform linear error propagation model is analyzed. Finally, experiments were conducted to verify the impact of different precision INS on the tight combination deception detection algorithm.
1 GNSS/INS tight combination model and deception interference model
1.1 GNSS/INS compact combination model
The GNSS/INS compact combination structure model is shown in Figure 1. Based on the receiver position velocity output by the INS and the satellite position velocity obtained from the GNSS satellite ephemeris, the combined system can more accurately predict the pseudorange and Doppler frequency shift of the GNSS signal, and these pseudoranges and pseudorange rates The difference between the predicted value and the actual GNSS measurement value forms the Kalman filter observation value. The observation value can be corrected for the INS positioning and speed results through the Kalman filter system.
Figure1 GNSS/INS tight combination diagram
In filters used with INS, the state vector is usually not the estimated state. In order to reduce the impact of linearization error, the error state vector is usually selected. According to the characteristics of the tight combination mode, a total of 17 states, including position error, velocity error, attitude error, gyroscope bias, accelerometer bias, clock error and clock drift, are selected as the error state vector. In closed-loop Kalman filtering, the error estimate obtained by filtering is fed back in each iteration to correct the system itself, making the Kalman filtering state tend to zero in the process. In open-loop Kalman filtering, since there is no feedback, the state value will gradually become larger as time goes by. Therefore, closed-loop Kalman filtering is commonly used in integrated navigation.
When performing closed-loop Kalman filtering, the observation value and the observation innovation are the same. Therefore, there are
1.2 Deception and interference model
The mathematical model of pseudorange deception based on GNSS measurements can be expressed as
The code phase delay can be specifically expressed as
If a=0,b≠0, it means step pseudorange spoofing; if a≠0,b=0, it means slope pseudorange spoofing.
2 Impact of IMU accuracy on spoofing detection algorithm
2.1 Deception detection algorithm
The higher the accuracy of the IMU, the more accurate its measurement data, and the higher the accuracy of the deception detection algorithm. The accuracy of the IMU determines the response speed of the deception detection algorithm. For a Kalman filter, the measured innovation vector is shown in equation (4), which is the difference between the actual observation vector and the one-step prediction vector , that is
The innovation vector can indicate whether the measurement is consistent with the estimate, and its size is determined by the measurement error and the accuracy of the system model. When the accuracy of the system model is high, the Kalman filter information can represent the actual measurement error. The covariance of the innovation is the sum of the values converted into the measurement space by the measurement noise covariance and the error covariance of the state estimate, that is
Smaller, slowly building up deviations between measurements and state estimates can be identified by a statistical test consisting of the latest N measurements. N is the “detection window”. When N is 1, it is snapshot deception detection, and when N is greater than 1, it is continuous deception detection. Chi-square test is often used in the innovation deception detection algorithm, and the innovation test statistic is constructed as
2.2 The impact of INS error propagation on observation information
IMU accuracy is usually characterized by bias and random noise. The bias error term exists in all accelerometers and gyroscopes. In most cases, the bias error term is the main component of all errors in inertial instruments; in addition, it is affected by a variety of Effect of Error Sources,All inertial sensors exhibit random noise.
In the GNSS/INS combined system, since the output results of GNSS and INS must be fused and filtered every interval, when considering the impact of IMU accuracy on new information, the error propagation model of INS can be equivalent to a short-time uniform straight line Error propagation. The speed error is the integral of the acceleration error. The speed and position errors caused by the constant acceleration deviation are
The measured specific force can be approximated as the opposite value of acceleration when moving at a uniform speed on a horizontal plane for a short period of time. Then the position and velocity errors caused by the gyro bias can be simply expressed as
In the formula, is the acceleration due to gravity. In addition, in a well-designed system, the inertial sensor noise will be the largest noise source, which can be obtained from the inertial navigation error variance or the time update covariance matrix of the Kalman filter. In order to quantify the relationship between inertial navigation error and time, if the one-sided power spectral density of accelerometer noise is , then the standard deviation of the velocity error and position error caused by the noise is
In the same way, the standard deviation of the speed error and position error caused by noise is
The IMU accuracy reference for different performance levels is shown in Table 1.
Table 1 IMU accuracy reference for different performance levels
According to the IMU performance parameters shown in Table 1, calculate the pseudorange prediction error caused by INS error propagation at different state propagation intervals. Because the satellite velocity position at k can be obtained from the GNSS satellite ephemeris, assuming that the receiver position is accurately known, then The projection of the position error caused by the INS in the line of sight direction of the receiver and satellite is the pseudorange prediction value error. Consider the situation with the largest error, that is, we have
The calculation of propagation errors under different levels of IMU and different error propagation times is shown in Table 2.
Table 2 Pseudorange error
Therefore, the observation value error caused by the IMU accuracy not only increases as the IMU accuracy decreases, but also increases as the error propagation time increases. Since each iteration of the closed-loop Kalman filter corrects the system itself, the INS error propagation time in integrated navigation is the state propagation interval of the Kalman filter, that is, the observation value error caused by the IMU accuracy increases as the Kalman filter state propagation interval increases. And increase.
When using integrated navigation information to detect spoofing interference, it is usually assumed that the output of the INS within the state propagation interval is relatively accurate; however, due to the influence of IMU accuracy, the pseudorange error caused by the INS is close to or even exceeds that caused by spoofing interference at the same time. When the pseudorange deviates, the results obtained by innovation detection will become unreliable. It can be seen from the analysis in Section 1.1 that when there is an INS propagation error at time , the observation vector is also an observation innovation vector in the closed-loop correction, and the pseudorange observation part can be expressed as
The principle of innovation deception detection is to take advantage of the fact that innovation obeys a zero-mean Gaussian distribution when there is no deception interference, and obeys a Gaussian distribution with a non-zero mean when there is deception interference. However, if the pseudorange deviation caused by IMU accuracy is large, it will destroy the characteristics of the zero-mean distribution of innovations, thereby affecting the deception detection algorithm.
It can be seen that when using innovation for deception detection, there are requirements for IMU performance, that is, the total deviation of the observation value caused by the IMU within the detection window cannot exceed the detection threshold of the innovation deception detection algorithm.
3 Experiment and result analysis
3.1 Experimental design
In order to compare the impact of different IMU accuracy on deception detection algorithms, it is considered that the observation value error caused by IMU accuracy not only increases with the decrease of IMU accuracy, but also increases with the increase of Kalman filter state propagation interval and detection window length. Large, experiments are mainly designed from the following aspects:
(Experiment 1) Apply the same ramp-type deception, and analyze and compare the impact of different precision INS on the deception detection algorithm within the same state propagation interval.
Figure 2 Detection situation at different IMU accuracy
(Experiment 2) Apply the same ramp-type spoofing to analyze and compare the impact of lower-precision INS propagation intervals in different states on the spoofing detection algorithm.
Figure 3 Detection situation at different state propagation intervals
(Experiment 3) Apply the same ramp-type spoofing, and analyze and compare the effects of spoofing detection algorithms with different detection windows on low-precision INS and the same state propagation interval.
Figure 4 Detection conditions in different windows
Combining the results of the three experiments, it can be seen that IMU accuracy will indeed affect the detection effect of the deception detection algorithm. When using consumer-grade IMUs, the impact will be greater, and it may even cause the deception detection algorithm to fail. Specifically, when there is no interference from spoofing, the spoofing detection statistics are still affected by the error caused by the IMU accuracy, causing the spoofing detection statistics to exceed the threshold. And experiments show that the impact of low-precision IMU can be reduced by adjusting the Kalman filter state propagation interval and the detection window of the spoofing detection algorithm.
Summarize
Through theoretical derivation and simulation experiments, this paper comparatively analyzes the impact of different IMU accuracy on the tight combination anti-spoofing algorithm, and experimentally analyzes the effects of two factors: the Kalman filter state propagation interval and the detection window of the spoofing detection algorithm. The results show that the influence of different IMU accuracies on pseudorange estimates causes the innovation detection amount to no longer be zero mean when there is no spoofing interference. The use of innovation-based spoofing detection algorithms has requirements for IMU accuracy. With the detection probability and Kalman As the filtering state propagation interval increases, the requirements for IMU accuracy increase.
Specifically:
1) IMU accuracy does affect the detection effect of the deception detection algorithm, and consumer-grade IMUs can cause false alarms in the chi-square deception detection algorithm.
2) Under the condition that the state propagation interval of the Kalman filter is less than or equal to 0.1 s and the detection window used is equal to 1, the false alarm problem of the chi-square deception detection algorithm caused by the consumer-level IMU is solved, but when there is a detection greater than 50 s extension.
Then the domestic company ERICCO independently develops IMU, which is divided into navigation level and tactical level. Navigation-level ER-MIMU01 and ER-MIMU05 can independently seek north. Other IMUs only need to add GNSS and magnetometers to the IMU to independently seek north. They also have a wide range of applications. For example, ER-MIMU03 and ER-MIMU07 can be used in drones. This product has a built-in acceleration sensor and gyroscope, which can measure linear acceleration and rotational angular velocity in three directions, and obtain the carrier’s velocity through analysis. Attitude, velocity and displacement information enable precise positioning.
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