Method for dynamic calibration of sensitivity of linear-angular vibration sensor based on multi-frequency sinusoidal excitation

Abstract

The application discloses a kind of line angular vibration sensor sensitivity dynamic calibration method based on multi-frequency sine excitation.It includes constructing line angular vibration sensor sensitivity dynamic calibration device based on multi-frequency sine excitation;Providing multi-frequency sine line angular excitation;Collecting motion sequence image and output signal;Solving the line angular excitation displacement of the line angular vibration sensor to be calibrated;Calculating the sensitivity of the line angular vibration sensor to be calibrated and the like steps.The method is efficient, accurate and simplifies the calibration process;Using monocular vision-based method to measure the vibration displacement of line angular vibration sensor under different frequencies, only a simple monocular vision measurement system is needed;The multi-frequency sine line angular excitation output by line and angular vibration generating device can be controlled, and the influence of other additional excitation on the sensor can also be effectively avoided;It is suitable for different types of sensors, and the multi-frequency sine excitation method has a wide range of applications, which can be used to calibrate different types of line angular vibration sensors, such as gyroscopes and accelerometers.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of image processing and sensor calibration, and particularly relates to a line and angular vibration sensor sensitivity dynamic calibration method based on multi-frequency sinusoidal excitation. BACKGROUND

[0002] The line and angular vibration sensor as a basic dynamic parameter measurement unit has been widely applied in the fields of precision manufacturing, navigation guidance, building structure health monitoring, etc. The line and angular vibration sensor with accurate sensitivity can improve the reliability of monitoring and measurement, help to respond to the dynamic changes of the system in time and accurately, thereby improving the system performance, safety, reducing the risk of failure, and providing more reliable data support. Generally, the sensitivity of the line and angular vibration sensor is considered to be known in precision in actual engineering application, and the precision is crucial to ensure the high performance and reliability of the measurement system. However, the existing calibration method often cannot accurately calibrate the sensitivity of the line and angular vibration sensor in a short time, and has problems such as low efficiency, poor flexibility and large error caused by point-by-point operation, so there is an urgent need for an accurate and efficient calibration method to ensure the calibration precision and efficiency of the line and angular vibration sensor. SUMMARY

[0003] In order to solve the above problems, the purpose of the present application is to provide an efficient, flexible and accurate line and angular vibration sensor sensitivity dynamic calibration method, which can significantly improve the efficiency of vibration calibration.

[0004] In order to achieve the above purpose, the line and angular vibration sensor sensitivity dynamic calibration method based on multi-frequency sinusoidal excitation provided by the present application comprises the following steps in sequence:

[0005] 1) Constructing a line and angular vibration sensor sensitivity dynamic calibration device based on multi-frequency sinusoidal excitation;

[0006] 2) Fastening the high-contrast target and the calibrated line and angular vibration sensor in the line and angular vibration sensor sensitivity dynamic calibration device based on multi-frequency sinusoidal excitation to the workbench surface of the line and angular vibration generating device at the same time, then generating a multi-frequency sinusoidal excitation signal with no mutual interference in frequency spectrum by using a signal generator, so that the high-contrast target, the calibrated line and angular vibration sensor and the workbench surface of the line and angular vibration generating device have consistent motion characteristics, and the motion control of the line and angular vibration generating device is realized based on the excitation signal, and the multi-frequency sinusoidal line and angular excitation is provided for the calibrated line and angular vibration sensor;

[0007] 3) Using a camera to collect the motion sequence images of the high-contrast target, using a data acquisition card to collect the output signals of the calibrated line and angular vibration sensor, and transmitting the motion sequence images and the output signals to an image and signal processing and display unit;

[0008] 4) The ROI of the motion sequence image is determined by the image and signal processing and display unit using the template matching method to eliminate the interference of background noise and similar edges, and the motion feature edges in the ROI are accurately extracted by the LSD method, and the line angle excitation displacement of the calibrated line angle vibration sensor is calculated according to the extracted motion feature edges;

[0009] 5) The SAM is used to fit the calculated line angle excitation displacement and the output signal of the calibrated line angle vibration sensor, and the excitation displacement and the output signal amplitude of the calibrated line angle vibration sensor corresponding to each frequency are obtained by solving the sparse matrix composed of the overdetermined equation set, and finally the sensitivity of the calibrated line angle vibration sensor is calculated by using the excitation displacement and the output signal amplitude.

[0010] In step 1), the line angle vibration sensor sensitivity dynamic calibration device based on multi-frequency sinusoidal excitation includes a signal generator, a line and angle vibration generating device, a high-contrast target, an illumination device, a camera, a data acquisition card and an image and signal processing and display unit; wherein the high-contrast target and the calibrated line angle vibration sensor are fastened to the workbench surface of the line and angle vibration generating device; the lens of the camera faces the high-contrast target; the illumination device is arranged on the side of the camera to provide illumination for the camera to ensure the quality of the obtained image; the image and signal processing and display unit is electrically connected with the signal generator, the camera and the data acquisition card respectively; the signal generator and the data acquisition card are also electrically connected with the line and angle vibration generating device and the calibrated line angle vibration sensor respectively; the signal generator generates a multi-frequency sinusoidal signal to control the line and angle vibration generating device to output a multi-frequency sinusoidal line angle excitation on the workbench surface;

[0011] In step 2), the multiple frequencies f k in the spectrum non-interference multi-frequency sinusoidal excitation signal x(t) need to meet:

[0012]

[0013] Wherein, f0 and p0 are the base frequency and the base prime number respectively, p i is a prime number greater than the base prime number p0, f k is the base frequency f0 and the subsequent frequency of the base frequency f0 within the ten octave range of the base frequency f0, ω k and x k are the angular frequency and amplitude corresponding to the frequency f k respectively, (-1) k is used to reduce the overshoot caused by the summation symbol, and t is time.

[0014] In step 4), the ROI of the motion sequence image is determined by the image and signal processing and display unit using template matching method to eliminate the interference of background noise and similar edges, and the motion feature edges in the ROI are accurately extracted by LSD method, and the method for calculating the linear angular excitation displacement of the linear angular vibration sensor according to the extracted motion feature edges is:

[0015] 4.1) The image and signal processing and display unit reads the motion sequence image of the high-contrast target photographed by the camera{F j (x,y)}; the distortion coefficient of the camera 7 is adjusted by continuously iterating using a nonlinear optimization algorithm based on the least square method principle to minimize the difference between the actual image and the theoretical image;

[0016] 4.2) The Harris corner point detection algorithm is used to preliminarily locate the feature points in the image, and then the sub-pixel interpolation fitting method is used to obtain the relative coordinates of each feature point;

[0017] 4.3) The relationship between the feature points on the high-contrast target in the known world coordinate system and their pixel projection points in the photographed image is collected to establish a coordinate conversion linear equation set, and then the relative coordinates of each feature point are converted into absolute coordinates in the world coordinate system using the above coordinate conversion linear equation set;

[0018] 4.4) Based on the template matching method, the circular region of the motion sequence image{F j (x,y)} is determined according to the absolute coordinates of the feature points;

[0019] 4.5) The position of the center of the circular region is further determined and the ROI is determined;

[0020] 4.6) The straight line edges in the ROI are extracted based on the LSD method, the translation change and direction vector change of the straight line edges are estimated by combining the feature point matching between adjacent frame images, and the linear angular excitation displacement{s(t j ) of the calibrated linear angular vibration sensor is calculated.

[0021] In step 5), the SAM method is used to fit the calculated linear angular excitation displacement and the output signal of the calibrated linear angular vibration sensor, and the excitation displacement and the output signal amplitude of the calibrated linear angular vibration sensor corresponding to each frequency are obtained by solving the sparse matrix composed of the overdetermined equation set, and finally the sensitivity of the calibrated linear angular vibration sensor is calculated using the excitation displacement and the output signal amplitude. The method is: the linear angular excitation displacement{s(t j ) obtained from the motion sequence image{F k (x,y)} is the displacement amplitude of each frequency f j , and the following SAM method is used for fitting:

[0022] s(t j )=Acos(ω k t j )-Bsin(ω k t j )+C (2)

[0023] The equation in matrix form is:

[0024]

[0025] Where t j is the sampling time of the corresponding jth image, A and B are the corresponding sinusoidal components, C is the offset component, and D is the corresponding matrix, the excitation displacement at different frequencies f k and the output signal amplitude V(t) of the calibrated angular vibration sensor are obtained by solving the overdetermined equation set composed of m equations (3); finally, the sensitivity of the calibrated angular vibration sensor at different frequencies is calculated using the above excitation displacement and output signal amplitude V(t).

[0026] The multi-frequency sinusoidal excitation-based angular vibration sensor sensitivity dynamic calibration method provided by the application has the following advantages:

[0027] 1. The method is efficient, accurate and simplifies the calibration process. Compared with the traditional calibration method of testing each frequency one by one, this method can calibrate the sensitivity of different frequencies in the range of fundamental frequency to ten times frequency through one operation, saving at least one order of magnitude of calibration time and avoiding the large amount of time consumption caused by repeated point-by-point operation in the traditional calibration method.

[0028] 2. The method uses a monocular vision-based method to measure the vibration displacement of the angular vibration sensor at different frequencies, only requiring a simple monocular vision measurement system.

[0029] 3. The application can control the multi-frequency sinusoidal line and angular excitation output by the line and angular vibration generating device through the design of the generated multi-frequency sinusoidal signal without mutual interference, and can effectively avoid the influence of other additional excitations on the sensor.

[0030] 4. The method is suitable for different types of sensors, and the multi-frequency sinusoidal excitation method has a wide range of applications and can be used to calibrate different types of line and angular vibration sensors, such as gyroscopes and accelerometers. BRIEF DESCRIPTION OF DRAWINGS

[0031] Figure 1 The structure diagram of the multi-frequency sinusoidal excitation-based angular vibration sensor sensitivity dynamic calibration device constructed in the application is used for line vibration sensor calibration.

[0032] Figure 2 This is a schematic diagram of the dynamic calibration device for the sensitivity of a linear angular vibration sensor based on multi-frequency sinusoidal excitation constructed in this invention, used for angular vibration sensor calibration.

[0033] Figure 3 Flowchart of the dynamic sensitivity calibration method for a linear angle vibration sensor based on multi-frequency sinusoidal excitation provided by the present invention;

[0034] Figure 4 This is a flowchart of the multi-frequency sinusoidal excitation displacement calculation based on monocular vision;

[0035] Figures 5(a) and (b) show the sensitivity calibration results and relative standard deviation data of the linear vibration sensor using the method of the present invention, compared with those using laser interferometry (LI) and the traditional monocular vision method (MV).

[0036] Figure 6 shows (a) and (b) comparisons of the sensitivity calibration results and relative standard deviation data of the angular vibration sensor using the method of the present invention, compared with those using laser interferometry (LI) and the traditional monocular vision method (MV). Detailed Implementation

[0037] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0038] like Figure 3 As shown, the dynamic calibration method for the sensitivity of a linear angle vibration sensor based on multi-frequency sinusoidal excitation provided by the present invention includes the following steps performed in sequence:

[0039] 1) Construct a dynamic calibration device for the sensitivity of a linear angle vibration sensor based on multi-frequency sinusoidal excitation;

[0040] like Figure 1 , 2 As shown, the dynamic calibration device for the sensitivity of a line-angle vibration sensor based on multi-frequency sinusoidal excitation includes a signal generator 1, a line and angle vibration generator 2, a high-contrast target 4, an illumination device 6, a camera 7, a data acquisition card 8, and an image and signal processing and display unit 9. The high-contrast target 4 and the line-angle vibration sensor 5 to be calibrated are fixed to the worktable 3 of the line and angle vibration generator 2. The lens of the camera 7 faces the high-contrast target 4. The illumination device 6 is located on one side of the camera 7 to provide illumination for the camera 7, ensuring the quality of the acquired image. The image and signal processing and display unit 9 is electrically connected to the signal generator 1, the camera 7, and the data acquisition card 8. The signal generator 1 and the data acquisition card 8 are also electrically connected to the line and angle vibration generator 2 and the line-angle vibration sensor 5 to be calibrated. The signal generator 1 generates a multi-frequency sinusoidal signal to control the line and angle vibration generator 2 to output multi-frequency sinusoidal line-angle excitation from its worktable 3.

[0041] 2) The high-contrast target 4 and the line angle vibration sensor 5 to be calibrated in the above-mentioned dynamic calibration device for line angle vibration sensor sensitivity based on multi-frequency sinusoidal excitation are simultaneously fastened to the worktable 3 of the line and angle vibration generator 2. Then, the signal generator 1 generates a multi-frequency sinusoidal excitation signal with no mutual interference in the spectrum, so that the high-contrast target 4, the line angle vibration sensor 5 to be calibrated and the worktable 3 of the line and angle vibration generator 2 have consistent motion characteristics. Based on the excitation signal, the motion control of the line and angle vibration generator 2 is realized, and multi-frequency sinusoidal line angle excitation is provided for the line angle vibration sensor 5 to be calibrated.

[0042] The multiple frequencies f in the multi-frequency sinusoidal excitation signal x(t) with no mutual interference in the spectrum k Must meet:

[0043]

[0044] Where f0 and p0 are the fundamental frequency and the number of primes, respectively, and p i f is a prime number greater than the primal number p0. k ω represents the fundamental frequency f0 and its subsequent frequencies within its tenth octave range. k and x k They are frequencies f k The corresponding angular frequency and amplitude, (-1) k Used to reduce the overshoot effect caused by the summation symbol, where t is time.

[0045] 3) Use camera 7 to acquire high-contrast motion sequence images of target 4 {F j (x,y)}, the output signal of the line angle vibration sensor 5 is acquired using data acquisition card 8, and the motion sequence image {F j (x,y)} and the output signal are transmitted to the image and signal processing and display unit 9;

[0046] 4) The image and signal processing and display unit 9 uses template matching to determine the above motion sequence image {F}. j The ROI of (x,y)} is used to eliminate the interference of background noise and similar edges. Then, the motion feature edges in the ROI are accurately extracted by the LSD method, and the line angle excitation displacement of the line angle vibration sensor 5 is calculated based on the extracted motion feature edges.

[0047] The method is:

[0048] 4.1) As Figure 4 As shown, the image and signal processing and display unit 9 reads the motion sequence images of the high-contrast target 4 captured by the camera 7 {F j(x, y)}, by using a non-linear optimization algorithm based on the principle of least squares, the distortion coefficients of camera 7 are adjusted by iteration to minimize the difference between the actual image and the theoretical image;

[0049] 4.2) The Harris corner detection algorithm is used to preliminarily locate the feature points in the image, and then the sub-pixel interpolation fitting method is used to obtain the relative coordinates of each feature point;

[0050] 4.3) The linear equation set of coordinate transformation is established by collecting the relationship between the feature points on the high-contrast target 4 in the known world coordinate system and their pixel projection points in the captured image, and then the linear equation set of coordinate transformation is used to convert the relative coordinates of each feature point into absolute coordinates in the world coordinate system;

[0051] 4.4) Based on the template matching method, the circular region of the motion sequence image {F j (x, y)} is determined according to the absolute coordinates of the feature points;

[0052] 4.5) The position of the center of the circular region is further obtained and the ROI is determined;

[0053] 4.6) The straight line edge in the ROI is extracted based on the LSD method, and the translation change and direction vector change of the straight line edge are estimated by combining the feature point matching between adjacent frame images, and then the line angle excitation displacement {s(t j )} of the calibrated line angle vibration sensor 5 is solved.

[0054] 5) The SAM is used to fit the line angle excitation displacement solved above and the output signal of the calibrated line angle vibration sensor, and by solving the sparse matrix composed of over-determined equation set, the excitation displacement and the output signal amplitude of the calibrated line angle vibration sensor corresponding to each frequency are obtained, and finally the sensitivity of the calibrated line angle vibration sensor is calculated by using the excitation displacement and the output signal amplitude.

[0055] The method is:

[0056] The line angle excitation displacement {s(t j )} obtained from the motion sequence image {F j (x, y)} is the displacement amplitude of each frequency f k , and the following SAM method is used for fitting:

[0057] s(t j ) = A cos (ω k t j ) - B sin (ω k t j ) + C (2)

[0058] The matrix equation is:

[0059]

[0060] wherein, t j is the sampling time of the corresponding jth frame image, A and B are the corresponding sinusoidal components, C is the offset component, D is the corresponding matrix, the excitation displacement at different frequencies f k and the output signal amplitude V(t) of the calibrated angular vibration sensor 5 are obtained by solving the overdetermined equation system composed of m equations of formula (3) respectively; finally, the sensitivity of the calibrated angular vibration sensor 5 at different frequencies is calculated by using the above excitation displacement and the output signal amplitude V(t).

[0061] Embodiment

[0062] The specific parameters of the line-angular vibration sensor sensitivity dynamic calibration device based on multi-frequency sinusoidal excitation in the embodiment are as follows: FSG (RIGOL DG 4202) is used as the signal generator 1 to generate multi-frequency sinusoidal signals in the range of 0.01-10 Hz, the calibrated line-angular vibration sensor 5 (MSV 3000 and BW-VG 527), the long-stroke exciter (ESZ185-400) and the turntable (NIM-001) are the line and angular vibration generating devices 2 mentioned in the application, which are used to provide multi-frequency line-angular excitation for the calibrated line-angular vibration sensor 5, the lighting device 6 is a 60W incandescent lamp, the CMOS camera 7 (OS10-V3-4K) with an effective frame rate of 200 fps and the DAQ card (NI USB6210) with an effective sampling rate of 1000 Hz are used as the data acquisition card 8 to collect the motion sequence images and the output signals of the calibrated line-angular vibration sensor 5.

[0063] In order to verify the precision and speed of the sensitivity dynamic calibration method of the line and angular vibration sensor based on multi-frequency sinusoidal excitation provided by the application, the sensitivity calibration of the linear vibration sensor in the frequency range of 0.01-10 Hz and the angular vibration sensor in the frequency range of 0.01-5 Hz is realized by using the method of the application. Fig. 5 is the sensitivity calibration result of the linear vibration sensor by using the method of the application, the laser interference method (LI) and the traditional monocular vision method (MV); Fig. 6 is the sensitivity calibration result of the angular vibration sensor by using the method of the application, the laser interference method (LI) and the traditional monocular vision method (MV). As shown in the results of Fig. 5 and Fig. 6, the average values of the sensitivity of the method of the application, the LI and the MV are highly consistent, the relative absolute deviations of the calibration results of the linear vibration sensor are less than 0.30% and 0.16% respectively, the maximum relative standard deviation (RStd) of the method of the application is about 0.16%, which is less than 0.51% of the LI and slightly greater than 0.14% of the MV. In the calibration results of the angular vibration sensor, the maximum relative absolute deviations of the method of the application, the LI and the MV are 0.51% and 0.23% respectively, the RStd of the method of the application is about 0.26%, and the RStd of the LI and the MV are 0.22% and 0.20% respectively. Although they have similar precision, with the decrease of the frequency, the time cost of the calibration of the method of the application decreases sharply, and the efficiency can be improved by one order of magnitude.

[0064] The above description is a detailed introduction of the embodiments of the application, which is not used to limit the application in any form. The skilled in the art can make a series of optimization, improvement and modification on the basis of the application. Therefore, the protection scope of the application should be limited by the appended claims.

Claims

1. A method for dynamic calibration of sensitivity of a linear angular vibration sensor based on multi-frequency sinusoidal excitation, characterized by: The calibration method comprises the following steps in sequence: 1) constructing a multi-frequency sinusoidal excitation-based linear angular vibration sensor sensitivity dynamic calibration device; 2) simultaneously fastening the high-contrast target and the calibrated linear angular vibration sensor in the multi-frequency sinusoidal excitation-based linear angular vibration sensor sensitivity dynamic calibration device on the workbench of the linear and angular vibration generating device, then generating a multi-frequency sinusoidal excitation signal with no mutual interference in frequency spectrum by using a signal generator, so that the high-contrast target, the calibrated linear angular vibration sensor and the workbench of the linear and angular vibration generating device have consistent motion characteristics, and motion control of the linear and angular vibration generating device is realized based on the excitation signal to provide multi-frequency sinusoidal linear angular excitation for the calibrated linear angular vibration sensor; 3) using a camera to collect motion sequence images of the high-contrast target, using a data acquisition card to collect output signals of the calibrated linear angular vibration sensor, and transmitting the motion sequence images and the output signals to an image and signal processing and display unit; 4) using a template matching method to determine the ROI of the motion sequence images by the image and signal processing and display unit to eliminate the interference of background noise and similar edges, accurately extracting the motion characteristic edges in the ROI by an LSD method, and calculating the linear angular excitation displacement of the calibrated linear angular vibration sensor according to the extracted motion characteristic edges; 5) using SAM to fit the calculated linear angular excitation displacement and the corresponding output signals of the calibrated linear angular vibration sensor, obtaining the excitation displacement and the output signal amplitude of the calibrated linear angular vibration sensor corresponding to each frequency by solving the sparse matrix composed of over-determined equations, and finally calculating the sensitivity of the calibrated linear angular vibration sensor by using the excitation displacement and the output signal amplitude.

2. The method for dynamic calibration of sensitivity of a multi-frequency sinusoidal excitation based linear angular vibration sensor according to claim 1, wherein: In step 1), the multi-frequency sinusoidal excitation-based linear angular vibration sensor sensitivity dynamic calibration device comprises a signal generator (1), a linear and angular vibration generating device (2), a high-contrast target (4), an illumination device (6), a camera (7), a data acquisition card (8) and an image and signal processing and display unit (9); wherein the high-contrast target (4) and the calibrated linear angular vibration sensor (5) are fastened on the workbench (3) of the linear and angular vibration generating device (2); the lens of the camera (7) faces the high-contrast target (4); the illumination device (6) is arranged on one side of the camera (7) to provide illumination for the camera (7) to ensure the quality of the acquired images; the image and signal processing and display unit (9) is electrically connected with the signal generator (1), the camera (7) and the data acquisition card (8) respectively; the signal generator (1) and the data acquisition card (8) are also electrically connected with the linear and angular vibration generating device (2) and the calibrated linear angular vibration sensor (5) respectively; the signal generator (1) generates a multi-frequency sinusoidal signal to control the linear and angular vibration generating device (2) to output multi-frequency sinusoidal linear angular excitation.

3. The method for dynamic calibration of sensitivity of a multi-frequency sinusoidal excitation based linear angular vibration sensor as claimed in claim 1, wherein: In step 2) the plurality of frequencies f in the spectrum of the mutually interference-free multi-frequency sinusoidal excitation signal x(t) k must be fulfilled: Where f0 and p0 are the fundamental frequency and the number of primes, respectively, and p i f is a prime number greater than the primal number p0. k ω represents the fundamental frequency f0 and its subsequent frequencies within its tenth octave range. k and x k They are frequencies f k The corresponding angular frequency and amplitude, (-1) k Used to reduce the overshoot effect caused by the summation symbol, where t is time.

4. The method for dynamic sensitivity calibration of a multi-frequency sinusoidal excitation based linear angular vibration sensor according to claim 2, wherein: In step 4), the ROI of the motion sequence image is determined by the image, signal processing and display unit using template matching method to eliminate the interference of background noise and similar edges, and the motion feature edges in the ROI are accurately extracted by LSD method, and the method for calculating the line angle excitation displacement of the line angle vibration sensor according to the extracted motion feature edges is: 4.1) The signal processing and display unit (9) reads the sequence of images of the high-contrast target (4) filmed by the camera (7) {F j (x,y)}, using a non-linear optimization algorithm based on the least square method, the distortion coefficients of the camera (7) are adjusted by iteration to minimize the difference between the actual and theoretical images. 4.2) The feature points in the image are preliminarily located by using Harris corner point detection algorithm, and then the relative coordinates of the feature points are obtained by using sub-pixel interpolation fitting method; 4.3) The relationship between the feature points on the high-contrast target (4) in the known world coordinate system and the pixel projection points in the photographed image is collected to establish a coordinate conversion linear equation set, and then the relative coordinates of the feature points are converted into absolute coordinates in the world coordinate system by using the coordinate conversion linear equation set; 4.4) Based on the absolute coordinates of the feature points above, the motion sequence image {F j (x,y)} is determined based on the template matching method; 4.5) The position of the center of the circular region is further calculated and the ROI is determined; 4.6) Extract the straight line edge in ROI based on LSD method, estimate the translation change and its direction vector change of the straight line edge combined with the feature point matching between adjacent frame images, and then solve the line angle excitation displacement {s(t j )} of the line angle vibration sensor (5).

5. The method for dynamic calibration of sensitivity of a multi-frequency sinusoidal excitation based linear angular vibration sensor as claimed in claim 4, wherein: In step 5), the calculated line angle excitation displacement and the output signal of the calibrated line angle vibration sensor are fitted by using SAM, the excitation displacement and the output signal amplitude of the calibrated line angle vibration sensor corresponding to each frequency are obtained by solving the sparse matrix composed of over-determined equation set, and finally the sensitivity of the calibrated line angle vibration sensor is calculated by using the excitation displacement and the output signal amplitude. The line angular excitation displacement {s(t j )} obtained from the motion sequence images {F j (x,y)} is the displacement amplitude for each frequency f k , which is fitted using the following SAM method: s(t j ) = A cos(ω k t j ) - B sin(ω k t j ) + C (2) The equation in matrix form is: where t j is the sampling time of the corresponding jth image, A and B are the corresponding sinusoidal components, C is the offset component, D is the corresponding matrix, the excitation displacement at different frequencies f k and the output signal amplitude V(t) of the calibrated angular vibration sensor (5) are obtained by solving the overdetermined equation set composed of m equations of (3); finally, the sensitivity of the calibrated angular vibration sensor (5) at different frequencies is calculated using the above excitation displacement and output signal amplitude V(t).

Images