Key Points Product: Pure Inertial Navigation System (INS) Based on IMU Key Features: Components: Uses MEMS accelerometers and gyroscopes for real-time measurement of acceleration and angular velocity. Function: Integrates initial position and attitude data with IMU measurements to calculate real-time position and attitude. Applications: Ideal for indoor navigation, aerospace, autonomous systems, and robotics. Challenges: Addresses sensor errors, cumulative drift, and dynamic environment impacts with calibration and filtering methods. Conclusion: Provides precise positioning in challenging environments, with robust performance when combined with auxiliary positioning systems like GPS.   MEMS gyroscope is dependent on Coriolis force sensitive angular velocity, and its control system is divided into drive mode control loop and detection mode control loop. Only by ensuring the real-time tracking of drive mode vibration amplitude and resonant frequency can the detection channel demodulation obtain accurate input angular velocity information. This paper will analyze the driving mode control loop of MEMS gyro from many aspects. Drive modal control loop model The vibration displacement of the MEMS gyroscope drive mode is converted into capacitance change through the comb capacitor detection structure, and then the capacitance is converted into the voltage signal characterizing the gyroscope drive displacement through the ring diode circuit. After that, the signal will enter two branches respectively, one signal through the automatic gain control (AGC) module to achieve amplitude control, one signal through the phase locked loop (PLL) module to achieve phase control. In the AGC module, the amplitude of the drive displacement signal is first demodulated by multiplication and low-pass filter, and then the amplitude is controlled at the set reference value through the PI link and the control signal of the drive amplitude is output. The reference signal used for multiplication demodulation in the PLL module is orthogonal to the demodulation reference signal used in the AGC module. After the signal passes through the PLL module, the driving resonant frequency of the gyroscope can be tracked. The output of the module is the control signal of the driving phase. The two control signals are multiplied to generate the gyroscope drive voltage, which is applied to the drive comb and converted into electrostatic driving force to drive the gyroscope drive mode, so as to form a closed-loop control loop of the gyroscope drive mode. Figure 1 shows the drive mode control loop of a MEMS gyroscope. Figure 1. MEMS gyroscope drive mode control structure block diagram Drive modal transfer function According to the dynamic equation of the driving mode of the vibrating MEMS gyroscope, the continuous domain transfer function can be obtained by Laplace transform: Where, mx is the equivalent mass of the gyroscope drive mode, ωx=√kx/mx is the resonant frequency of the drive mode, and Qx = mxωx/cx is the quality factor of the drive mode. Displacement-capacitance conversion link According to the analysis of the detection capacitance of the comb teeth, the displacement-capacitance conversion link is linear when the edge effect is ignored, and the gain of the differential capacitance changing with the displacement can be expressed as: Where, nx is the number of active combs driven by gyroscopic mode, ε0 is the vacuum dielectric constant, hx is the thickness of the driving detection combs, lx is the overlap length of the driving detection active and fixed combs at rest, and dx is the distance between the teeth. Capacitance-voltage conversion link The capacitor-voltage conversion circuit used in this paper is a ring diode circuit, and its schematic diagram is shown in Figure 2. Figure 2 Schematic diagram of ring diode circuit In the figure, C1 and C2 are gyroscope differential detection capacitors, C3 and C4 are demodulation capacitors, and Vca are square wave amplitudes. The working principle is: when the square wave is in the positive half cycle, the diode D2 and D4 are switched on, then the capacitor C1 charges C4 and C2 charges C3; When the square wave is in positive half period, the diodes D1 and D3 are switched on, then the capacitor C1 discharges to C3 and C2 discharges to C4. In this way, after several square wave cycles, the voltage on the demodulated capacitors C3 and C4 will stabilize. Its voltage expression is: For the silicon micromechanical gyroscope studied in this paper, its static capacitance is in the order of several pF, and the capacitance variation is less than 0.5pF, while the demodulation capacitance used in the circuit is in the order of 100 pF, so there are CC0》∆C and C2》∆C2, and the capacitor voltage conversion gain is obtained by simplified formula: Where, Kpa is the amplification factor of the differential amplifier, C0 is the demodulation capacitance, C is the static capacitance of the detection capacitance, Vca is the carrier amplitude, and VD is the on-voltage drop of the diode. Capacitance-voltage conversion link Phase control is an important part of MEMS gyroscope drive control. The phase-locked loop technology can track the frequency change of the input signal in its captured frequency band and lock the phase shift. Therefore, this paper uses the phase-locked loop technology to enter the phase control of the gyroscope, and its basic structure block diagram is shown in Figure 3. Figure. 3 Block diagram of the basic structure of PLL PLL is a negative feedback phase automatic regulation system, its working principle can be summarized as follows: The external input signal ui(t) and the feedback signal uo(t) output of the VCO are input to the phase discriminator at the same time to complete the phase comparison of the two signals, and the output end of the phase discriminator outputs an error voltage signal ud(t) reflecting the phase difference θe(t) of the two signals; The signal through the loop filter will filter out the high-frequency components and noise, get a voltage control oscillator uc(t), the voltage control oscillator will adjust the frequency of the output signal according to this control voltage, so that it gradually closer to the frequency of the input signal, and the final output signal uo(t), When the frequency of ui(t) is equal to uo(t) or a stable value, the loop reaches a locked state. Automatic gain control Automatic gain control (AGC) is a closed-loop negative feedback system with amplitude control, which, combined with phase-locked loop, provides amplitude and phase stable vibration for the gyroscope drive mode. Its structure diagram is shown in Figure 4. Figure 4. Automatic gain control structure block diagram The working principle of automatic gain control can be summarized as follows: the signal ui(t) with the gyroscope drive displacement information is input to the amplitude detection link, the drive displacement amplitude signal is extracted by multiplication demodulation, and then the high-frequency component and noise are filtered by low-pass filter; At this time, the signal is a relatively pure DC voltage signal that characterizes the drive displacement, and then controls the signal at the given reference value through a PI link, and outputs the electric signal ua(t) that controls the drive amplitude to complete the amplitude control. Conclusion In this paper, the driving mode control loop of MEMS gyro is introduced, including model, dislock-capacitance conversion, capacitance-voltage conversion, phase-locked loop and automatic gain control. As a manufacturer of MEMS gyro sensor, Micro-Magic Inc has done detailed research on MEMS gyros, and often popularized and shared the relevant knowledge of MEMS gyro. For a deeper understanding of MEMS gyro, you can refer to the parameters of MG-501 and MG1001. If you are interested in more knowledge and products of MEMS, please contact us.   MG502 MEMS Gyroscope MG502      

Key Points Product: Navigation-Grade MEMS Gyroscope Key Features: Components: MEMS gyroscope for precise angular velocity measurement. Function: Provides high-accuracy navigation data with low drift, suitable for long-term and stable navigation. Applications: Ideal for aerospace, tactical missile guidance, marine navigation, and industrial robotics. Performance: Features low bias instability and random drift, offering reliable performance over time. Comparison: Different models (MG-101, MG-401, MG-501) cater to varying accuracy needs, with the MG-101 providing the highest precision. MEMS gyroscope is a kind of inertial sensor for measuring angular velocity or angular displacement. It has a wide application prospect in oil logging, weapon guidance, aerospace, mining, surveying and mapping, industrial robot and consumer electronics. Due to the different accuracy requirements in various fields, MEMS gyroscopes are divided into three levels in the market: navigation level, tactical level and consumer level. This paper will introduce the navigation MEMS gyroscope in detail and compare their parameters. The following will be elaborated from the technical indicators of MEMS gyro, the drift analysis of gyro and the comparison of three navigation-grade MEMS gyro. Technical specifications of MEMS gyroscope The ideal MEMS gyroscope is that the output of its sensitive axis is proportional to the input angular parameters (Angle, angular rate) of the corresponding axis of the carrier under any conditions, and is not sensitive to the angular parameters of its cross axis, nor is it sensitive to any axial non-angular parameters (such as vibration acceleration and linear acceleration). The main technical indicators of MEMS gyroscope are shown in Table 1. Technical indicator Unit Meaning Measuring range (°)/s Effectively sensitive to the range of input angular velocity Zero bias (°)/h The output of a gyroscope when the input rate in the gyroscope is zero. Because the output is different, the equivalent input rate is usually used to represent the same type of product, and the smaller the zero bias, the better; Different models of products, not the smaller the zero bias, the better. Bias repeatability (°)/h(1σ) Under the same conditions and at specified intervals (successive, daily, every other day…) The degree of agreement between the partial values of repeated measurements. Expressed as the standard deviation of each measured offset. Smaller is better for all gyroscopes (evaluate how easy it is to compensate for zero) Zero drift (°)/s The rate of time change of the deviation of the gyroscope output from the ideal output. It contains both stochastic and systematic components and is expressed in terms of the corresponding input angular displacement relative to inertial space in unit time. Scale factor V/(°)/s、mA/(°)/s The ratio of the change in the output to the change in the input to be measured. Bandwidth Hz In the frequency characteristic test of gyroscope, it is stipulated that the frequency range corresponding to the amplitude of the measured amplitude is reduced by 3dB, and the precision of the gyroscope can be improved by sacrificing the bandwidth of the gyroscope. Table 1 Main technical indexes of MEMS gyroscope Drift analysis of gyroscope If there is interference torque in the gyroscope, the rotor shaft will deviate from the original stable reference azimuth and form an error. The deviation Angle of rotor axis relative to inertial space azimuth (or reference azimuth) in unit time is called gyro drift rate. The main index to measure the accuracy of gyroscope is the drift rate. Gyroscopic drift is divided into two categories: one is systematic, the law is known, it causes regular drift, so it can be compensated by computer; The other kind is caused by random factors, which causes random drift. The systematic drift rate is expressed by the angular displacement per unit time, and the random drift rate is expressed by the root mean square value of the angular displacement per unit time or the standard deviation. The approximate range of random drift rates of various types of gyroscopes can be reached at present is shown in Table 2. Gyroscope type Random drift rate/(°)·h-1 Ball bearing gyroscope 10-1 Rotary bearing gyroscope 1-0.1 Liquid float gyroscope 0.01-0.001 Air float gyroscope 0.01-0.001 Dynamically tuned gyroscope 0.01-0.001 Electrostatic gyroscope 0.01-0.0001 Hemispherical resonant gyroscope 0.1-0.01 Ring laser gyroscope 0.01-0.001 Fiber optic gyroscope 1-0.1 Table 2 Random drift rates of various types of gyroscopes   The approximate range of random drift rate of gyro required by various applications is shown in Table 3. The typical index of positioning accuracy of inertial navigation system is 1n mile/h(1n mile=1852m), which requires the gyroscope random drift rate should reach 0.01(°)/h, so the gyroscope with random drift rate of 0.01(°)/h is usually called inertial navigation gyroscope. Application Requirements for random drift rate of gyro/(°)·h-1 Rate gyroscope in flight control system 150-10 Vertical gyroscope in flight control system 30-10 Directional gyroscope in the flight control system 10-1 Tactical missile inertial guidance system 1-0.1 Marine gyro compass, strapdown heading attitude system artillery lateral position, ground vehicle inertial navigation system 0.1-0.01 Inertial navigation systems for aircraft and ships 0.01-0.001 Strategic missile, cruise missile inertial guidance system 0.01-0.0005 Table 3 Requirements for random drift rate of gyro in various applications   Comparison of three navigation-grade MEMS gyroscopes Micro-Magic Inc’s MG series is a navigation-grade MEMS gyroscope with a high level of accuracy to meet the needs of various fields. The following table compares range, bias instability, angular random walk, bias stability, scale factor, bandwidth, and noise. 　 MG-101 MG-401 MG-501 Dynamic Range (deg/s) ±100 ±400 ±500 Bias instability(deg/hr) 0.1 0.5 2 Angular Random Walk(°/√h) 0.005 0.025~0.05 0.125-0.1 Bias stability(1σ 10s)(deg/hr) 0.1 0.5 2~5 Table 4 Parameter comparison table of three navigation-grade MEMS gyroscopes I hope that through this article, you can understand the technical indicators of navigation-grade MEMS gyroscope and the comparative relationship between them. If you are interested in more knowledge about MEMS gyro, please discuss with us.   MG502 MEMS Gyroscope MG502    

Key Points Product: MEMS Gyroscope Borehole North Finding System Key Features: Components: Employs MEMS gyroscopes for north-seeking, featuring compact size, low cost, and high shock resistance. Function: Uses an improved two-position method (90° and 270°) and real-time attitude correction for precise north determination. Applications: Optimized for downhole drilling systems in complex underground environments. Data Fusion: Combines gyroscope data with local magnetic declination corrections for true north calculation, ensuring accurate navigation during drilling. Conclusion: Delivers precise, reliable, and independent north-finding capabilities, ideal for borehole and similar applications. The new MEMS gyroscope is a kind of inertial gyro with simple structure, which has the advantages of low cost, small size and resistance to high shock vibration. The inertial north seeking gyroscope can complete the independent north seeking all weather without external restrictions, and can achieve fast, high efficiency, high precision and continuous work. Based on the advantages of MEMS gyro, MEMS gyro is very suitable for downhole north finding system. This paper describes the segmented fusion research of MEMS gyro borehole north finding system. The following will introduce the improved two-position north finding, the scheme of MEMS gyro borehole fusion north finding and the determination of north finding value. Improved two-position north finding The static two-position north seeking scheme generally selects 0° and 180° as the initial and end positions of north seeking. After repeated experiments, the gyro output angular velocity is collected, and the final north seeking Angle is obtained by combining the local latitude. The experiment adopted the two-position method every 10°, collected 360° of the turntable, and a total of 36 sets of data were collected. After averaging each set of data, the measured solution values were shown in Figure 1 below. Figure 1 Fitting curve of gyroscope output from 0 to 360° As can be seen from Figure 1, the output fitting curve is a cosine curve, but the experimental data and angles are still small, and the experimental results lack accuracy. Repeated experiments were conducted, and the Angle of acquisition was extended to 0~660°, and the two-position method was conducted every 10° from 0°, and the data results were shown in Figure 2. The trend of the image is cosine curve, and there are obvious differences in data distribution. At the crest and trough of the cosine curve, the distribution of data points is scattered and the degree of fit to the curve is low, while at the place with the highest slope of the curve, the fit of data points to the curve is more obvious. Figure 2 Fitting curve of gyroscope output at two positions 0~660° Combined with the relationship between azimuth and gyro output amplitude in Figure 3, it can be concluded that the data fit is better when the two-position north finding is adopted at 90° and 270°, indicating that it is easier and more accurate to detect the north Angle in the east-west direction. Therefore, 90°, 270°, instead of 0° and 180°, are used in this paper as the two-position north seeking gyro output acquisition positions. Figure 3 Relation between azimuth and gyro output amplitude MEMS gyroscope borehole fusion northfinding When MEMS gyro is used in borehole north finding system, it is faced with complex environment, and there will be variable attitude Angle with drill bit drilling, so the solution of north Angle becomes much more complicated. In this section, based on the improvement of the two-position north finding scheme in the previous section, a method is proposed to obtain the attitude Angle by controlling rotation according to the output data information, and the included Angle with the north is obtained. The specific flow chart is shown in Figure 4. The MEMS gyroscope is transmitted to the upper computer through RS232 data interface. As shown in Figure 4, after the initial north Angle is obtained by searching north at the two positions, the next step of drilling while drilling is carried out. After receiving the north seeking instruction, the drilling work stops. The attitude Angle output by MEMS gyro is collected and transmitted to the upper computer. The rotation of the borehole north seeking system is controlled by the attitude Angle information, and the roll Angle and pitch Angle are adjusted to 0. The heading Angle at this moment is the Angle between the sensitive axis and the magnetic north direction. In this scheme, the Angle between MEMS gyroscope and true north direction can be obtained in real time by collecting attitude Angle information. Figure 4 Fusion north finding flow chart The north seeking value is determined In the fusion north finding scheme, the improved two-position north finding was performed on the MEMS gyroscope. After the north finding was completed, the initial north position was obtained, the heading Angle θ was recorded, and the initial attitude state was (0,0,θ), as shown in Figure 5(a). When the bit is drilling, the attitude Angle of the gyroscope changes, and the roll Angle and pitch Angle are regulated by the rotary table, as shown in Figure 5(b). As shown in Figure 5(b), when drilling the bit, the system receives the attitude Angle information of the attitude instrument, and needs to judge the sizes of roll Angle γ ‘and pitch Angle β’, and rotate them through the rotation control system to make them turn to 0. At this time, the output heading Angle data is the Angle between the sensitive axis and the magnetic north direction. The Angle between the sensitive axis and the true north direction should be obtained according to the relationship between the magnetic north and the true north direction, and the true north Angle should be obtained by combining the local magnetic declination Angle. The solution is as follows: θ’=Φ-∆φ In the above formula, θ ‘drill bit and the true north direction Angle, ∆φ is the local magnetic declination Angle, Φ is the drill bit and magnetic north Angle. Figure 5 Change of initial and drilling attitude Angle The north seeking value is determined In this chapter, the north finding scheme of MEMS gyroscope underground north finding system is studied. Based on the two-position north finding scheme, an improved two-position north finding scheme with 90° and 270° as starting positions is proposed. With the continuous progress of MEMS gyroscope, MEMS north-seeking gyroscope can achieve independent north finding, such as MG2-101, its dynamic measurement range is 100°/s, can work in the environment of -40 ° C ~+85 ° C, its bias instability is 0.1°/hr, and the angular velocity random walk is 0.005°/√hr. I hope you can understand the north finding scheme of MEMS gyroscope through this article, and look forward to discussing professional issues with you.   MG502 MEMS Gyroscope MG502    

Key Points Product: Pure Inertial Navigation System (INS) Based on IMU Key Features: Components: Uses MEMS accelerometers and gyroscopes for real-time measurement of acceleration and angular velocity. Function: Integrates initial position and attitude data with IMU measurements to calculate real-time position and attitude. Applications: Ideal for indoor navigation, aerospace, autonomous systems, and robotics. Challenges: Addresses sensor errors, cumulative drift, and dynamic environment impacts with calibration and filtering methods. Conclusion: Provides precise positioning in challenging environments, with robust performance when combined with auxiliary positioning systems like GPS.   The law of instrument constant drift with temperature of a gyro theodolite is a complex phenomenon, which involves the interaction of multiple components and systems within the instrument. Instrument constant refers to the measurement reference value of the gyro-theodolite under specific conditions. It is crucial to ensure measurement accuracy and stability. Temperature changes will cause the drift of instrument constants, mainly because the differences in thermal expansion coefficients of materials cause changes in the instrument structure, and the performance of electronic components changes with temperature changes. This drift pattern is often nonlinear because different materials and components respond differently to temperature. In order to study the drift of the instrument constants of a gyro theodolite with temperature, a series of experiments and data analysis are usually required. This includes calibrating and measuring the instrument at different temperatures, recording changes in instrument constants, and analyzing the relationship between temperature and instrument constants. Through the analysis of experimental data, the trend of instrument constants changing with temperature can be found, and an attempt can be made to establish a mathematical model to describe this relationship. Such models can be based on linear regression, polynomial fitting, or other statistical methods and are used to predict and compensate for drift in instrument constants at different temperatures. Understanding the drift of the instrument constants of a gyro theodolite with temperature is very important to improve measurement accuracy and stability. By taking corresponding compensation measures, such as temperature control, calibration and data processing, the impact of temperature on instrument constants can be reduced, thereby improving the measurement performance of the gyro theodolite. It should be noted that the specific drift rules and compensation methods may vary depending on different gyro theodolite models and application scenarios. Therefore, in practical applications, corresponding measures need to be studied and implemented according to specific situations. The study of the drift pattern of instrument constants of gyro theodolite with temperature usually involves monitoring and analyzing the performance of the instrument under different temperature conditions. The purpose of such research is to understand how changes in temperature affect the instrument constants of a gyro theodolite and possibly find a way to compensate or correct for this temperature effect. Instrumental constants generally refer to the inherent properties of an instrument under specific conditions, such as standard temperature. For gyro theodolite, instrument constants may be related to its measurement accuracy, stability, etc. When the ambient temperature changes, the material properties, mechanical structure, etc. inside the instrument may change, thus affecting the instrument constants. To study this drift pattern, the following steps are usually required: Select a range of different temperature points to cover the operating environments a gyroscopic theodolite may encounter.Take multiple directional measurements at each temperature point to obtain sufficient data samples.Analyze the data and observe the trend of instrument constants as a function of temperature.Try to build a mathematical model to describe this relationship, such as linear regression, polynomial fitting, etc.Use this model to predict instrument constants at different temperatures and possibly develop methods to compensate for temperature effects. A mathematical model might look like this: K(T) = a + b × T + c × T^2 + … Among them, K(T) is the instrument constant at temperature T, and a, b, c, etc. are the coefficients to be fitted. This kind of research is of great significance for improving the performance of gyro theodolite under different environmental conditions. It should be noted that specific research methods and mathematical models may vary depending on specific instrument models and application scenarios. Summarize The law of instrument constant drift with temperature of a gyro theodolite is a complex phenomenon, which involves the interaction of multiple components and systems within the instrument. Instrument constant refers to the measurement reference value of the gyro-theodolite under specific conditions. It is crucial to ensure measurement accuracy and stability. Temperature changes will cause the drift of instrument constants, mainly because the differences in thermal expansion coefficients of materials cause changes in the instrument structure, and the performance of electronic components changes with temperature changes. This drift pattern is often nonlinear because different materials and components respond differently to temperature. In order to study the drift of the instrument constants of a gyro theodolite with temperature, a series of experiments and data analysis are usually required. This includes calibrating and measuring the instrument at different temperatures, recording changes in instrument constants, and analyzing the relationship between temperature and instrument constants. Through the analysis of experimental data, the trend of instrument constants changing with temperature can be found, and an attempt can be made to establish a mathematical model to describe this relationship. Such models can be based on linear regression, polynomial fitting, or other statistical methods and are used to predict and compensate for drift in instrument constants at different temperatures. Understanding the drift of the instrument constants of a gyro theodolite with temperature is very important to improve measurement accuracy and stability. By taking corresponding compensation measures, such as temperature control, calibration and data processing, the impact of temperature on instrument constants can be reduced, thereby improving the measurement performance of the gyro theodolite. It should be noted that the specific drift rules and compensation methods may vary depending on different gyro theodolite models and application scenarios. Therefore, in practical applications, corresponding measures need to be studied and implemented according to specific situations. The study of the drift pattern of instrument constants of gyro theodolite with temperature usually involves monitoring and analyzing the performance of the instrument under different temperature conditions. The purpose of such research is to understand how changes in temperature affect the instrument constants of a gyro theodolite and possibly find a way to compensate or correct for this temperature effect. Instrumental constants generally refer to the inherent properties of an instrument under specific conditions, such as standard temperature. For gyro theodolite, instrument constants may be related to its measurement accuracy, stability, etc. When the ambient temperature changes, the material properties, mechanical structure, etc. inside the instrument may change, thus affecting the instrument constants. To study this drift pattern, the following steps are usually required: Select a range of different temperature points to cover the operating environments a gyroscopic theodolite may encounter.Take multiple directional measurements at each temperature point to obtain sufficient data samples.Analyze the data and observe the trend of instrument constants as a function of temperature.Try to build a mathematical model to describe this relationship, such as linear regression, polynomial fitting, etc.Use this model to predict instrument constants at different temperatures and possibly develop methods to compensate for temperature effects. A mathematical model might look like this: K(T) = a + b × T + c × T^2 + … Among them, K(T) is the instrument constant at temperature T, and a, b, c, etc. are the coefficients to be fitted. This kind of research is of great significance for improving the performance of gyro theodolite under different environmental conditions. It should be noted that specific research methods and mathematical models may vary depending on specific instrument models and application scenarios.   MG502 MEMS Gyroscope MG502