Improved IMU calibration method based on filtering optimization

Abstract

The invention discloses an improved IMU (Inertial Measurement Unit) calibration method based on filtering optimization, which comprises the following steps of: S1, respectively placing MEMS IMUs at three predefined positions, and acquiring acceleration data in a static state at each position; s2, identifying the random error of the MEMS IMU through Allan variance, and performing wavelet threshold filtering and denoising on the output signal of the MEMS IMU at each position by referring to the identification result to obtain a denoised signal; s3, discrete Kalman filtering processing is carried out on a result obtained after wavelet denoising; and S4, based on a Kalman filtering result, representing an output value model of the MEMS IMU accelerometer in a static state as a linear model, and based on three-position method calibration and least square modeling, solving a calibration result. According to the method, the noise characteristics are determined through Allan variance analysis, the original data output by the IMU are filtered by using a wavelet denoising technology and Kalman filtering, and the calibration precision and stability of the IMU in a static environment can be remarkably improved by combining with the three-position method for calibration.

Description

TECHNICAL FIELD

[0001] The present application relates to inertial measurement unit (IMU) calibration, in particular to an improved IMU calibration method based on filter optimization. BACKGROUND

[0002] Inertial measurement unit (IMU) is a device used for measuring and reporting the direction, acceleration and angular velocity of an object, widely used in navigation, robotics, aerospace, automotive electronics and other fields. IMU calibration is a key step to ensure its measurement accuracy, which can correct the errors of the sensor and improve the accuracy and reliability of the measurement data. However, the existing traditional multi-position calibration method has some deficiencies and defects.

[0003] During the static calibration process, the output signal of the IMU is often disturbed by various noises, which will directly affect the accuracy of the calibration result, resulting in large measurement errors of the calibrated IMU in actual use. The traditional multi-position calibration method directly processes the original data, lacks effective noise processing mechanism, and cannot effectively remove noise, thereby affecting the calibration accuracy. In addition, the traditional method needs to collect data at multiple positions, and the more positions of data collection not only increases the operation difficulty, but also may cause cumulative error, further affecting the accuracy of the calibration result. SUMMARY

[0004] The purpose of the present application is to overcome the deficiencies of the prior art, provide an improved IMU calibration method based on filter optimization, determine the noise characteristics by Allan variance analysis, use wavelet denoising technology to filter the original data output by the IMU, and combine with three-position calibration, which can significantly improve the calibration accuracy and stability of the IMU in static environment.

[0005] The purpose of the present application is achieved by the following technical solution: an improved IMU calibration method based on filter optimization, comprising the following steps:

[0006] S1. Install the MEMS IMU on a two-axis rate turntable, and level it, set the output frequency of the MEMS IMU, and start preheating, then place the MEMS IMU at three predefined positions respectively, and at each position, collect acceleration data in static state, select one position to collect for a longer time to analyze the Allan variance performance of the device MEMS IMU; during calibration, use data with the same length of time at each position.

[0007] S2. Identify the random error of the MEMS IMU by Allan variance, and based on the identification result, perform wavelet threshold filtering and denoising on the output signal of the MEMS IMU at each position to obtain the denoised signal;

[0008] S3. Perform discrete Kalman filtering on the wavelet denoising result;

[0009] S4. Based on the Kalman filter results, the output value model of the MEMS IMU accelerometer in the static state is expressed as a linear model, and the calibration result is solved based on the three-position method and least squares modeling.

[0010] The beneficial effects of the present invention are: (1) improving calibration accuracy: through Allan variance analysis and wavelet denoising technology, the present invention can effectively identify and remove noise that affects the IMU measurement accuracy, thereby improving the accuracy of the calibration results.

[0011] (2) Enhanced data stability: Kalman filter optimization processing is introduced to further smooth the denoised data, reduce data drift, and enhance the stability and reliability of the calibration data.

[0012] (3) Simplifying the operational complexity of using the calibration turntable: Compared with the traditional multi-position method, the present invention takes into account the main error factors of MEMSIMU and adopts a three-position method to reduce the operational complexity.

[0013] (4) Enhanced robustness: By optimizing the data processing process, the method of the present invention can maintain high calibration accuracy even in a noisy environment, thereby enhancing the robustness of the method. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 Flow chart of the method of the present invention. DETAILED DESCRIPTION

[0015] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings, but the protection scope of the present invention is not limited to the following.

[0016] like Figure 1 As shown, an improved IMU calibration method based on filtering optimization includes the following steps:

[0017] S1. Install the MEMS IMU on a dual-axis rate turntable, level it, set the output frequency of the MEMS IMU, and start it for warm-up. Then, place the MEMS IMU in three predefined positions and collect static acceleration data at each position.

[0018] 1) Install the MEMS imu on the 2TS-450 dual-axis rate turntable and level it. Set the imu output frequency to 100 Hz and start preheating for 5 minutes.

[0019] 2) Place the IMU in three predefined positions: X-axis downward, Y-axis downward, and Z-axis downward. Collect static accelerometer data at each position, with a collection time of 3 minutes for two positions and 2 hours for the other.

[0020] S2. For locations with a 2-hour acquisition time, identify the random error of the MEMS IMU using the Allan variance of the output signal. Based on the identification results, perform wavelet threshold filtering to denoise the MEMS IMU output signal at each location to obtain the denoised signal.

[0021] The random error of IMU is identified with the help of Allan variance:

[0022] Allan variance is a statistical tool used to assess the stability of time series data, and is particularly important in frequency stability assessment. MEMS-IMUs can be affected by factors such as manufacturing processes and structural defects, which can affect sensor performance, causing the MEMS IMU's output signal to exhibit non-stationary characteristics, thereby affecting the accuracy of the INS. For certain non-stationary random processes, when their classical variance diverges, their Allan variance persists, which is an advantage of the Allan variance analysis method. The following relationship exists between the MEMS IMU random error and the power spectral density:

[0023]

[0024] Where τ is the correlation time and f is the frequency. σ2(τ) is the Allan variance value, which represents the variance under the correlation time τ. w (f) Power spectral density function, which represents the energy distribution of noise in the frequency domain. The transfer function converts the frequency domain power spectral density to the time domain Allan variance. When the measurement information passes through the filter, it is adjusted to detect different noise sources. The standard Allan variance has five terms, which are related to the acquisition time and the device itself. The Allan variance can be expressed as the sum of the squares of the five random errors:

[0025]

[0026] in, is the quantization noise, is the angle random walk, Zero bias instability, is the rate random walk, Identification of noise sources such as rate ramps.

[0027] The five noise sources included in the standard Allan variance are:

[0028]

[0029] Allan variance directly reads according to different slopes, and the slope of the corresponding item does not mean that there is no error or the error is small and can be ignored;

[0030] Wavelet denoising is mainly based on the characteristics of wavelet transform, which removes noise and retains key information of the signal by decomposing the signal, threshold processing and reconstructing the signal. The wavelet transform of a continuous function can be expressed as

[0031]

[0032] In the formula, ψ(t) is obtained by scaling and shifting the mother wavelet ψ(t) a represents the scale factor, and b represents the time-varying factor. If the values of a and b are taken as discrete forms, the discrete wavelet transform can be obtained.

[0033] Wavelet threshold denoising mainly includes the following three steps:

[0034] 1) Wavelet decomposition: select the wavelet basis and decomposition level according to the Allan variance analysis data, decompose the noisy signal, and obtain the approximation coefficient and detail coefficient.

[0035] The Allan variance curve is plotted on the logarithmic coordinate, and different types of noise have different performances on the curve: for high-frequency noise, a wavelet basis function with good high-frequency suppression capability can be selected, such as Daubechies (db) series or Symlet (sym) series, and a smaller number of decomposition levels (such as 2-3 layers) can be used to avoid excessive decomposition and increase the complexity of calculation; for low-frequency and very low-frequency noise, a wavelet basis function with good low-frequency suppression capability can be selected, such as Coiflet (coif) series or Biorthogonal

[0036] (bior) series, and a larger number of decomposition levels (such as 4-5 layers) can be used to better separate noise and signal. For example, if the IMU data is mainly affected by high-frequency noise, the db4 wavelet basis function can be selected, and the decomposition level is 3; if it is mainly affected by low-frequency noise, the coif3 wavelet basis function can be selected, and the decomposition level is 4.

[0037] 2) Threshold processing: select the threshold according to the noise characteristics, process the detail coefficient, and remove the noise coefficient.

[0038] 3) Signal reconstruction: use the processed coefficient to perform wavelet inverse transform to obtain the denoised signal.

[0039] S3. Perform discrete Kalman filter processing on the wavelet denoised result;

[0040] The present application considers that low-frequency noise can be further processed by Kalman filtering, which can effectively reduce the drift phenomenon of data and provide more accurate accelerometer estimation. The Kalman filter model of the accelerometer is established as follows:

[0041] 1. State equation

[0042] x k =x k-1 +b k-1 +w k

[0043] b k =b k-1 +u k

[0044] where x k : true acceleration value, b k : time-varying zero offset (low-frequency drift), w k , u k : process noise (Gaussian white noise)

[0045] w k ~ N (0, Q): acceleration change noise (variance Q reflects dynamic uncertainty)

[0046] u k ~ N (0, U): zero offset drift noise (variance U controls the drift rate)

[0047] v k ~ N (0, R): measurement noise (variance R is determined by sensor performance and wavelet denoising effect)

[0048] 2. Measurement equation

[0049] The measurement equation maps the state vector to the measurement space. For the accelerometer, the measurement equation can be expressed as:

[0050] z k =x k +v k

[0051] where z k is the accelerometer measurement value at time k, v k is the measurement noise, which is assumed to be Gaussian white noise with variance

[0052] The state equation is brought into the five formulas of Kalman filter,

[0053]

[0054] P k =I-Kk H k -P k / k-1

[0055] S4. Based on the Kalman filter result, the output value model of the MEMS IMU accelerometer in the static state is represented as a linear model, and the calibration result is solved based on the three-position method calibration and least square modeling.

[0056] 1) Error model

[0057] Taking the acceleration error model as an example, since the nonlinear error caused by the cross interference term and the nonlinear term of the MEMS device itself is far lower than the linear error, the output value model of the MEMS accelerometer in the static state can be represented as a linear model:

[0058]

[0059] Where, A x ,A y ,A z accelerometer output; k xx ,k yy ,k zz : scale factor (proportionality coefficient); b x ,b y ,b z : zero offset; f x ,f y ,f z : gravity component in the carrier coordinate system.

[0060] 2) Three-position calibration experiment

[0061] Select three independent positions to cover three axes with gravity excitation: position 1 (Z axis downward): [f x ,f y ,f z ] = [0, 0, g]; position 2 (X axis downward): [f x ,f y ,f z ] = [g, 0, 0]; position 3 (Y axis downward): [f x ,f y ,f z ] = [0, g, 0];

[0062] Collect the output [A x,k ,A y,k ,A z,k ] (k = 1, 2, 3) at each position (collect 2 hours of data for Allan variance analysis, then based on the analysis result, collect three minutes of data at each position, and take the average value after wavelet denoising and Kalman filtering as the collected output at each position)

[0063] 3) Least square modeling (three-axis joint solution)

[0064] Combine the equations of all positions as:

[0065]

[0066] Briefly: Y = HX

[0067] 4) Least square solution

[0068] The parameter solution is:

[0069] X = (H T H) -1 H T Y

[0070] Solve:

[0071] X = [k xx ,k yy ,k zz ,b x ,b y ,b z ] T

[0072] The present application significantly improves the accuracy and stability of IMU calibration through the following key technical means:

[0073] (1) Allan variance analysis: determine the noise characteristics of IMU through Allan variance analysis. Allan variance is a statistical tool for evaluating the stability of time series data, especially important in frequency stability evaluation. Through Allan variance analysis of IMU output data, the noise characteristics can be evaluated in detail. These information is crucial for selecting the appropriate wavelet basis function and determining the number of wavelet decomposition layers, thus providing a scientific basis for subsequent wavelet denoising, such as: the Allan variance curve is plotted in logarithmic coordinates, different types of noise have different performances on the curve. For high-frequency noise, a wavelet basis function with good high-frequency suppression capability can be selected, such as the Daubechies (db) series or Symlet (sym) series, and a smaller number of decomposition layers (such as 2-3 layers) can be used to avoid excessive decomposition and increase computational complexity; for low-frequency noise, a wavelet basis function with good low-frequency suppression capability can be selected, such as the Coiflet (coif) series or Biorthogonal (bior) series, and a larger number of decomposition layers (such as 4-5 layers) can be used to better separate noise and signal.

[0074] (2) Wavelet denoising: Based on the results of Allan variance analysis, select the appropriate wavelet basis function and decomposition level, and perform wavelet denoising on the original data output by the IMU. Wavelet denoising can effectively remove high-frequency noise while preserving the key information of the signal. The wavelet denoising method mainly includes three steps of wavelet decomposition, threshold processing and signal reconstruction. By setting the threshold to filter the signal coefficients, denoising is achieved. The introduction of wavelet denoising significantly improves the purity of the data, providing a higher quality data basis for the subsequent calibration process.

[0075] (3) Kalman filter optimization: Perform Kalman filter optimization on the wavelet denoised data. Kalman filter is an optimal estimation method based on linear systems, which can optimally estimate the system state under the condition of known system model and noise statistical characteristics. Through Kalman filter, the drift phenomenon of the data can be further reduced, and more accurate accelerometer and gyroscope estimates can be provided. The introduction of Kalman filter further optimizes the data processing process, improves the stability and reliability of the calibration results.

[0076] (4) Improved discrete calibration: The non-linear error caused by the cross-interference term and non-linear term of the MEMS IMU device itself is much lower than the linear error, so we can represent the output value model of the MEMS accelerometer in a static state as a linear model, and only consider the proportional factor and zero bias error of each axis during calibration. Traditional multi-position calibration methods, such as the 6-position method and the 12-position method, although provide more independent equations to estimate error parameters, these methods have the problems of complex operation, large cumulative error in multiple position conversion, and being affected by environmental changes. In contrast, the three-position method can obtain high-precision calibration results even with less position data through an optimized data processing process. Each axis has 2 unknowns, a total of 6 unknowns (3 axes x 2 unknowns / axis), and each position provides 3 independent equations, so 3 positions can provide 9 independent equations to meet the needs of estimating all unknowns. Through effective noise processing (such as wavelet denoising), the purity and reliability of the data can be significantly improved, so that the data of the three positions is sufficient to provide enough independent equations to estimate all unknowns without the need for additional positions. This not only reduces the complexity of operation, but also reduces the cumulative error caused by position switching and data acquisition process, further improving the accuracy of the calibration results.

[0077] By comprehensive application of the above key technical means, the present application not only solves the deficiency of the traditional multi-position calibration method in noise processing, but also optimizes the calibration process, and significantly improves the calibration stability of the MEMS-IMU in a static environment. Specifically, the present application determines the noise characteristics of the MEMS-IMU through Allan variance analysis, selects appropriate wavelet basis functions and decomposition layers according to the analysis results, and performs wavelet denoising processing on the original data output by the MEMS-IMU, effectively removing noise and retaining key information of the signal. Subsequently, the data after wavelet denoising is further optimized by Kalman filtering, reducing the drift phenomenon of the data and providing more accurate accelerometer and gyroscope estimation values. Finally, combined with the improved three-position calibration algorithm, even with fewer measurement times and reduced operation complexity, a higher precision calibration result can be obtained.

[0078] In summary, the IMU calibration method based on filtering optimization proposed by the present application has strict logical feasibility in principle. First, Allan variance analysis can accurately quantify the energy distribution of the noise in each frequency band of the IMU output signal, providing a theoretical basis for subsequent targeted denoising. Through the multi-resolution analysis characteristic of wavelet transform, the high-frequency noise can be effectively filtered out, and the signal-to-noise ratio (SNR) of the signal is significantly improved. This process essentially separates the noise energy from the signal through threshold processing. Kalman filtering dynamically compensates for low-frequency drift by establishing a state space model containing time-varying zero bias and using optimal estimation theory.

[0079] The reduction of noise level directly improves the calibration accuracy, and its mechanism mainly reflects in three aspects: first, the denoised signal is closer to the true physical quantity, making the linear assumption in the calibration model closer to the actual situation; second, the reduction of residual noise reduces the disturbance error in the least squares solving process, making the parameter estimation more stable; finally, the tracking and compensation of time-varying zero bias by Kalman filtering effectively suppresses the systematic deviation caused by zero drift in the traditional calibration method. The three-position orthogonal calibration design ensures the good condition of the calibration equation set through the linearly independent projection of the gravity vector on the basis of noise suppression, making the least squares solution have higher numerical stability. This progressive optimization from noise suppression to parameter estimation constitutes a complete precision improvement closed loop at the principle level.

[0080] The above description shows and describes one preferred embodiment of the present application, but as previously described, it should be understood that the present application is not limited to the form disclosed herein, should not be considered as excluding other embodiments, and can be used in various other combinations, modifications and environments, and can be modified by the above teachings or related art or knowledge within the scope of the inventive concept described herein. Any modification and change made by those skilled in the art without departing from the spirit and scope of the present application shall be within the protection scope of the appended claims of the present application.

Claims

1. An improved IMU calibration method based on filtering optimization, characterized by: The following steps are involved: S1. Install the MEMSIMU on a dual-axis rate turntable, level it, set the output frequency, and start preheating. Then, place the MEMSIMU in three predefined positions and collect static acceleration data at each position. S2. Identify the random error of the MEMSIMU using the Allan variance. Based on the identification results, perform wavelet threshold filtering and denoising on the output signal of the MEMSIMU at each position to obtain the denoised signal. S3. Perform discrete Kalman filtering on the wavelet denoising result; S4. Based on the Kalman filter results, the output value model of the MEMSIMU accelerometer in the static state is expressed as a linear model, and the calibration result is solved based on the three-position method calibration and least squares modeling.

2. The improved IMU calibration method based on filtering optimization according to claim 1, characterized in that: The three predefined positions include X-axis downward, Y-axis downward, and Z-axis downward.

3. The improved IMU calibration method based on filtering optimization according to claim 1, characterized in that: The step S2 comprises: S201. Identify the random error of MEMSIMU by Allan variance; S202. Select the wavelet basis and decomposition level according to the identification result of the Allan variance, decompose the noisy signal, and obtain the approximate coefficient and detail coefficient; S203. Select a threshold, process the detail coefficient, and remove the noise coefficient; S204. Perform inverse wavelet transform using the processed coefficients to obtain a denoised signal.

4. The improved IMU calibration method based on filtering optimization according to claim 1, characterized in that: In step S3, low-frequency noise is further processed by Kalman filtering to reduce data drift and provide more accurate accelerometer estimation.

5. The improved IMU calibration method based on filtering optimization according to claim 1, characterized in that: The step S4 comprises: S401. The output value model of the MEMSIMU accelerometer at rest after Kalman filtering is expressed as a linear model: Among them, A x ,A y ,A z Accelerometer output after Kalman filtering; k xx ,k yy ,k zz is the scale factor; b x ,b y ,b z is zero bias; f x ,f y ,f z is the gravity component in the carrier coordinate system; S402. Make the gravity excitation cover three axes according to the three independent positions selected in step S1: Position 1, Z axis downward: [f x ,f y ,f z ]=[0,0,g]; Position 2, X-axis downward: [f x ,f y ,f z ]=[g,0,0]; Position 3, Y axis down: [f x ,f y ,f z ]=[0,g,0]; Each position is output according to step S401, and is recorded as [A x,k ,A y,k ,A z,k ],k=1,2,3 S403. Least Squares Modeling: Combining the equations for all positions gives: In short: Y = HX; S404. Through least squares solution, the parameter solution is obtained as: X=(H T H) -1 H T Y The calibration result is: X=[k xx ,k yy ,k zz ,b x ,b y ,b z ] T 。

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