A motion error compensation method and model for a rotating accelerometer gravity gradiometer

Abstract

This application belongs to the field of precision measurement technology and specifically discloses a method and model for compensating for the motion error of a rotating accelerometer and gravity gradiometer. The method includes: obtaining the motion error of the system to be compensated, constructing a motion error compensation matrix based on an established multi-parameter compensation model and the motion error; determining a parameter estimation method based on the combined output of the gravity gradiometer, and using the parameter estimation method to determine the target error transfer coefficient of the system to be compensated; inputting the target error transfer coefficient into the motion error compensation matrix to obtain an error compensation result, thereby performing error compensation on the system to be compensated. Through this application, measurement errors can be reduced, thereby improving the motion compensation effect and compensation accuracy.

Description

Technical Field

[0001] The present application belongs to the field of precision measurement technology, and more specifically, relates to a method and model for compensating motion errors of a rotating accelerometer gravity gradiometer. Background Art

[0002] The rotating accelerometer gravity gradiometer is an important gravity gradient measuring instrument at present. It has a very broad application prospect in geodetic surveying, mineral exploration and other aspects. The rotating accelerometer gravity gradiometer is a gravity gradiometer used in an aviation dynamic environment. Therefore, the post-motion error compensation technology is one of the core technologies of the rotating accelerometer gravity gradiometer.

[0003] The current motion compensation model comprehensively considers various factors of motion error transmission, and forward deduces an analytical model. An external monitoring system composed of a gyroscope and an accelerometer measures motion information. Finally, based on the analytical model and the motion information measured by the monitoring system, the error transfer coefficient is calibrated and substituted into the deduction of the motion error.

[0004] However, the current motion compensation model does not take into account the measurement errors of multiple sensors. That is to say, this method needs to monitor the linear and angular motion of three axes and requires the use of six sensor devices. The more sensors used in the compensation process, the more measurement errors there will be. For example, the time asynchrony problem between multiple sensors will introduce systematic errors, affecting the final motion error compensation effect.

[0005] Therefore, how to reduce multi-sensor measurement errors and thus improve motion compensation effects is a technical problem that needs to be solved urgently. Summary of the Invention

[0006] In view of the defects of the prior art, the purpose of this application is to provide a method and model for compensating the motion error of a rotating accelerometer gravity gradiometer, aiming to solve the problem of poor motion error compensation caused by errors in sensor measurement.

[0007] In a first aspect, the present application provides a method for compensating motion errors of a rotational accelerometer gravity gradiometer, comprising:

[0008] Acquire the motion error of the system to be compensated, and construct a motion error compensation matrix according to the established multi-parameter compensation model and the motion error;

[0009] determining a parameter estimation method based on the combined output of the gravity gradiometer, and determining a target error transfer coefficient of the system to be compensated using the parameter estimation method;

[0010] Inputting the target error transfer coefficient into the motion error compensation matrix to obtain an error compensation result, so as to perform error compensation on the system to be compensated;

[0011] Among them, the multi-parameter compensation model is based on dimensional consistency, constructed based on the error transfer coefficient and the multi-parameter compensation vector. The multi-parameter compensation vector is determined based on the linear acceleration, angular velocity and angular acceleration to determine the motion error vector, and is determined based on the motion error vector and the rotation modulation vector; the linear acceleration is obtained by performing a two-way subtraction combination to extract the horizontal linear motion based on the four-way combined accelerometer of the gravity gradiometer.

[0012] This application utilizes the four-way combined accelerometer of the gravity gradiometer to perform a two-way subtraction combination to extract the linear acceleration data of the horizontal linear motion. Compared with the existing technology, it reduces two acceleration sensors measuring the horizontal direction, that is, it reduces the measurement error of the acceleration sensor, and thus can reduce the impact of the sensor measurement error on the system accuracy. The data processing method of this application can more accurately capture the horizontal movement than the traditional method to improve the accuracy of the system measurement, thereby improving the motion compensation effect and compensation accuracy.

[0013] Optionally, the linear acceleration includes the x-axis acceleration a x , y-axis acceleration a y and z-axis acceleration a z ;

[0014] The x-axis acceleration a x and the y-axis acceleration a y It is determined based on the combined output of the four orthogonally antisymmetrically placed accelerometers of the gravity gradiometer.

[0015] Alternatively, the x-axis acceleration a can be obtained by the following formula: x and the y-axis acceleration a y ;

[0016] [A1-A2]=2(a x sinΩt-a y cosΩt)

[0017] [A3-A4]=2(a x cosΩt+a y sinΩt)

[0018]

[0019] Wherein, A1, A2, A3, and A4 are the signal outputs of the four accelerometers of the gravity gradiometer, Ω is the rotation speed of the turntable of the gravity gradiometer, and t represents the measurement time.

[0020] Optionally, the method for determining the motion error vector includes:

[0021] Determining a first parameter corresponding to the linear acceleration, a second parameter corresponding to the angular velocity, and a third parameter corresponding to the angular acceleration; wherein the first parameter includes the number of linear responses, linear response item parameters, the number of nonlinear responses, and the nonlinear response item parameters of the acceleration; the second parameter includes the number of linear responses, linear response item parameters, the number of nonlinear responses, and the nonlinear response item parameters of the angular velocity; and the third parameter includes the number of linear responses, linear response item parameters, the number of nonlinear responses, and the nonlinear response item parameters of the angular acceleration;

[0022] determining a first coupling parameter of the linear acceleration and the angular acceleration, a second coupling parameter of the linear acceleration and the angular velocity, and a third coupling parameter of the angular velocity and the angular acceleration;

[0023] The motion error vector is determined based on the first parameter, the second parameter, the third parameter, the first coupling parameter, the second coupling parameter, and the third coupling parameter.

[0024] Optionally, the motion error vector is transferred to the gravity gradiometer via an accelerometer output model and installation error.

[0025] Optionally, the installation error includes an accelerometer installation position error and an accelerometer sensitive axis direction error;

[0026] The accelerometer installation position error includes: radial installation error, initial phase installation error and axial installation error;

[0027] The accelerometer sensitive axis direction error includes: misalignment angle error, pitch angle error and rotation error around the sensitive axis.

[0028] Optionally, the error transfer coefficient is composed of the radial installation error, initial phase installation error, axial installation error, misalignment angle error, pitch angle error and rotation error around the sensitive axis combined with the accelerometer linear response coefficient and the accelerometer nonlinear response coefficient.

[0029] The multi-parameter compensation model of this application is constructed based on dimensional consistency, taking into account parameters such as linear acceleration, angular velocity and angular acceleration, and comprehensively considering different types of motion error sources. The multi-parameter compensation model basically includes all motion error terms of the gradiometer and can effectively eliminate the impact of misalignment angle error, thereby making error compensation more comprehensive and accurate, further improving the motion compensation effect and compensation accuracy.

[0030] In the second aspect, the present application also provides a rotational accelerometer gravity gradiometer motion error compensation model, wherein the multi-parameter compensation model is based on dimensional consistency, and is constructed based on the error transfer coefficient and the multi-parameter compensation vector. The multi-parameter compensation vector is determined based on the linear acceleration, angular velocity and angular acceleration to determine the motion error vector, and is determined based on the motion error vector and the rotation modulation vector; the linear acceleration is obtained by extracting the horizontal linear motion through a two-way subtraction combination of the four-way combined accelerometer of the gravity gradiometer.

[0031] In a third aspect, the present application provides an electronic device comprising: at least one memory for storing programs; and at least one processor for executing the programs stored in the memory. When the program stored in the memory is executed, the processor is used to execute the method described in the first aspect or any possible implementation of the first aspect.

[0032] In a fourth aspect, the present application provides a computer-readable storage medium, which stores a computer program. When the computer program runs on a processor, the processor executes the method described in the first aspect or any possible implementation of the first aspect.

[0033] In a fifth aspect, the present application provides a computer program product, which, when executed on a processor, enables the processor to execute the method described in the first aspect or any possible implementation of the first aspect.

[0034] It can be understood that the beneficial effects of the second to fifth aspects mentioned above can be found in the relevant description of the first aspect mentioned above, and will not be repeated here.

[0035] In general, the above technical solutions conceived by this application have the following beneficial effects compared with the existing technologies:

[0036] (1) The present application utilizes the four-way combined accelerometer of the gravity gradiometer to perform a two-way subtraction combination to extract the linear acceleration data of the horizontal linear motion. Compared with the prior art, the present application reduces two acceleration sensors for measuring the horizontal direction, that is, reduces the measurement error of the acceleration sensor, and thus can reduce the impact of the sensor measurement error on the system accuracy. The data processing method of the present application can more accurately capture the horizontal motion than the traditional method to improve the accuracy of the system measurement, thereby improving the motion compensation effect and compensation accuracy.

[0037] (2) The multi-parameter compensation model of this application is constructed based on dimensional consistency, taking into account parameters such as linear acceleration, angular velocity and angular acceleration, and comprehensively considering different types of motion error sources. The multi-parameter compensation model basically includes all motion error terms of the gradiometer and can effectively eliminate the impact of misalignment angle error, thereby making the error compensation more comprehensive and accurate, and further improving the motion compensation effect and compensation accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 This is one of the flow charts of the method for compensating the motion error of the rotation accelerometer gravity gradiometer provided in the embodiment of the present application;

[0039] Figure 2 Schematic diagram of the structure of the rotational accelerometer gravity gradiometer and its corresponding motion error monitoring system provided in an embodiment of the present application;

[0040] Figure 3 This is a second flow chart of a method for compensating for motion errors of a rotational accelerometer gravity gradiometer provided in an embodiment of the present application;

[0041] Figure 4 It is a structural diagram of an electronic device provided in an embodiment of the present application. DETAILED DESCRIPTION

[0042] In order to make the purpose, technical solutions and advantages of this application more clear, the following further describes this application in detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain this application and are not intended to limit this application.

[0043] The term "and / or" as used herein describes an association between related objects, indicating that three possible relationships exist. For example, "A and / or B" can represent: A exists alone, A and B exist simultaneously, or B exists alone. The symbol " / " as used herein indicates that the related objects are in an "or" relationship, for example, A / B means either A or B.

[0044] The terms "first" and "second" in this specification and claims are used to distinguish different objects rather than to describe a specific order of objects. For example, "first response message" and "second response message" are used to distinguish different response messages rather than to describe a specific order of response messages.

[0045] In the embodiments of this application, words such as "exemplary" or "for example" are used to indicate examples, illustrations, or descriptions. Any embodiment or design described as "exemplary" or "for example" in the embodiments of this application should not be interpreted as being preferred or advantageous over other embodiments or designs. Rather, the use of words such as "exemplary" or "for example" is intended to present the relevant concepts in a concrete manner.

[0046] In the description of the embodiments of the present application, unless otherwise specified, "multiple" means two or more, for example, multiple processing units means two or more processing units, etc.; multiple elements means two or more elements, etc.

[0047] Next, the technical solutions provided in the embodiments of this application are introduced.

[0048] Reference Figure 1 The present application provides a method for compensating motion errors of a rotational accelerometer gravity gradiometer, comprising:

[0049] S101. Obtaining the motion error of the system to be compensated, and constructing a motion error compensation matrix based on the established multi-parameter compensation model and the motion error;

[0050] S102. Determine a parameter estimation method based on the combined output of the gravity gradiometer, and use the parameter estimation method to determine the target error transfer coefficient of the system to be compensated;

[0051] S103. Inputting the target error transfer coefficient into the motion error compensation matrix to obtain an error compensation result to perform error compensation on the system to be compensated;

[0052] Among them, the multi-parameter compensation model is based on dimensional consistency, constructed based on the error transfer coefficient and the multi-parameter compensation vector. The multi-parameter compensation vector is determined based on the linear acceleration, angular velocity and angular acceleration to determine the motion error vector, and is determined based on the motion error vector and the rotation modulation vector; the linear acceleration is obtained by performing a two-way subtraction combination to extract the horizontal linear motion based on the four-way combined accelerometer of the gravity gradiometer.

[0053] Specifically, step S101 is a process of motion error monitoring and compensation matrix construction, which is as follows:

[0054] The system uses gravity gradiometer measurements to obtain the output data of a multi-channel accelerometer. By combining two of the four accelerometers using a two-way subtraction method, linear acceleration data for horizontal linear motion can be extracted. Based on the principle of dimensional consistency, a multi-parameter compensation model was established. This model considers multiple parameters, including linear acceleration, angular velocity, and angular acceleration, to describe various potential error sources during the system's motion.

[0055] Furthermore, a motion error compensation matrix is ​​constructed based on the established multi-parameter compensation model and the motion error data obtained from the gravity gradiometer. Effective real-time compensation can be performed based on the actual monitored motion error to improve the measurement accuracy and stability of the system.

[0056] Step S102 is the process of parameter estimation and target error propagation coefficient determination. First, a suitable parameter estimation method is determined based on the combined output data of the gravity gradiometer. The parameter estimation method is typically the least squares method. Then, based on the selected parameter estimation method, target error propagation coefficients are determined. These coefficients reflect how errors in the system propagate and affect the system's measurement capabilities over time and with changing motion states.

[0057] Step S103 is a process of implementing error compensation, in which the determined target error transfer coefficient is embedded into the previously constructed motion error compensation matrix to adjust and compensate for the motion error in the system measurement.

[0058] The embodiment of the present application utilizes the four-way combined accelerometer of the gravity gradiometer to perform a two-way subtraction combination to extract the linear acceleration data of the horizontal linear motion, which can reduce the impact of the sensor measurement error on the system accuracy. The data processing method of the present application can more accurately capture the horizontal motion than the traditional method to improve the accuracy of the system measurement, thereby improving the motion compensation effect and compensation accuracy, and realizing accurate compensation and control of motion errors.

[0059] Optionally, the linear acceleration includes the x-axis acceleration a x , y-axis acceleration a y and z-axis acceleration a z ;

[0060] The x-axis acceleration a x and the y-axis acceleration a y It is determined based on the combined output of the four orthogonally antisymmetrically placed accelerometers of the gravity gradiometer.

[0061] Reference Figure 2 , when there is an angular error between the monitoring system coordinate system and the actual coordinate system of the gravity gradiometer, taking linear acceleration as an example, the actual monitored linear acceleration is:

[0062] A x =h x a x +k1a v +k2a z

[0063] A y =h y a y +k3a x +k4a z

[0064] A z =h z a z +k5a x +k6a v

[0065] A x A y =(h x a x +k1a y +k2a z )·(h y a y + k3a x + k4a z )

[0066] =k1h y a x a y +k1k3a x a x +h1k4a x a z +

[0067] k1h y a y a y +k1k3a y a x +h1k4a y a z +

[0068] k2h y a z a y +k2k3a z a x +h2k4a z a z

[0069] Among them, h x 、h y 、h z They are the monitoring error angles of the three degrees of freedom, k1 is the first-order term coefficient, and k2-k8 are the second-order term coefficients.

[0070] The linear acceleration detected by the monitoring system includes the linear acceleration information of the other two axes due to the presence of the misalignment angle. However, all error terms (, k, k) generated by the misalignment angle are angular errors. Angle is a dimensionless quantity and is therefore also included in the motion error transfer coefficient in the multi-parameter compensation model. It can be assumed that the motion error transfer coefficient obtained by parameter estimation and solving the multi-parameter compensation model includes the misalignment angle error between the coordinate systems. In summary, the multi-parameter compensation model can effectively eliminate the impact of the misalignment angle error between coordinate systems.

[0071] The combined output of the rotating accelerometer and gravity gradiometer is to suppress the linear acceleration by two-way addition combination and suppress the angular acceleration by four-way subtraction combination, thereby converting the gravity gradient signal (Γ xx -Γ yy ) and Γ xy Modulate to around twice the speed:

[0072] E out =A1+A2-A3-A4

[0073] 2R(Γ xx -Γ yy )sin 2Ωt-4RΓ xy cos 2Ωt

[0074] Where R is the radius of the turntable and Ω is the rotation speed of the turntable.

[0075] Reference Figure 3 , Figure 3 This is a flowchart of a post-compensation method for gravity gradiometer motion errors based on a multi-parameter compensation model. First, a motion error compensation matrix is ​​calculated based on the multi-parameter compensation model and the motion errors measured by the monitoring system. Then, an appropriate parameter estimation method (such as the least squares method) is selected based on the combined output of the gravity gradiometer to solve for the error transfer coefficient. Finally, the error transfer coefficient is substituted into the motion error compensation matrix calculated in the first step to achieve final error compensation. The multi-parameter compensation model is the core component of the compensation algorithm; an accurate model is crucial for achieving high-precision error compensation.

[0076] Furthermore, in this embodiment, the rotating accelerometer gravity gradiometer suppresses linear acceleration through a two-way addition combination, and suppresses angular acceleration through a four-way subtraction combination to retain the gravity gradient. Conversely, the two-way subtraction combination can deduct the angular acceleration and gravity gradient and retain the XY axis acceleration. This method can simplify the monitoring system and reduce the number of acceleration sensors for monitoring the two horizontal axes.

[0077] The x-axis acceleration a is obtained by the following formula x and the y-axis acceleration a y ;

[0078] [A1-A2]=2(a x sinΩt-a y cosΩt)

[0079] [A3-A4]=2(a x cosΩt+a y sinΩt)

[0080]

[0081] Wherein, A1, A2, A3, and A4 are the signal outputs of the four accelerometers of the gravity gradiometer, Ω is the rotation speed of the turntable of the gravity gradiometer, and t represents the measurement time.

[0082] Optionally, the method for determining the motion error vector includes:

[0083] Determining a first parameter corresponding to the linear acceleration, a second parameter corresponding to the angular velocity, and a third parameter corresponding to the angular acceleration; wherein the first parameter includes the number of linear responses, linear response item parameters, the number of nonlinear responses, and the nonlinear response item parameters of the acceleration; the second parameter includes the number of linear responses, linear response item parameters, the number of nonlinear responses, and the nonlinear response item parameters of the angular velocity; and the third parameter includes the number of linear responses, linear response item parameters, the number of nonlinear responses, and the nonlinear response item parameters of the angular acceleration;

[0084] determining a first coupling parameter of the linear acceleration and the angular acceleration, a second coupling parameter of the linear acceleration and the angular velocity, and a third coupling parameter of the angular velocity and the angular acceleration;

[0085] The motion error vector is determined based on the first parameter, the second parameter, the third parameter, the first coupling parameter, the second coupling parameter, and the third coupling parameter.

[0086] It should be noted that the motion error vector is transmitted to the gravity gradiometer via the accelerometer output model and installation error.

[0087] Furthermore, the installation error includes an accelerometer installation position error and an accelerometer sensitive axis direction error;

[0088] The accelerometer installation position error includes: radial installation error, initial phase installation error and axial installation error;

[0089] The accelerometer sensitive axis direction error includes: misalignment angle error, pitch angle error and rotation error around the sensitive axis.

[0090] Reference Figure 2 , A1, A2, A3, and A4 are the four accelerometers used by the rotating accelerometer gravity gradiometer to measure gradients. The dotted line in the figure is the measurement coordinate system of the gravity gradiometer, accelerometer, and gyroscope. It can be seen from the figure that there is a certain misalignment angle error between the coordinate systems. Therefore, there is an error between the motion information monitored by the sensor in the monitoring system and the motion information actually felt by the gravity gradiometer. That is, the misalignment angle error will cause the motion information measured by the monitoring system to be inaccurate, affecting the subsequent compensation effect.

[0091]

[0092] From this formula, we can see that the response of the accelerometer can be divided into two categories: linear response and nonlinear response. The linear response coefficient is: first-order term (k1). The higher the order of the nonlinear response, the lower the coefficient. Therefore, only the second-order term is considered, that is, the nonlinear response coefficient is: second-order term (K2 K4 K5 K6 K7 K8). Therefore, the dimension of the linear response of the accelerometer is L / T 2 , the corresponding unit is m / s 2 , the dimension of the nonlinear response is L 2 / T 4 , the corresponding unit is m 2 / s 4 In summary, the transmission of motion error must satisfy the above two dimensions. In the three-dimensional coordinate system, the motion noise that satisfies the above dimensions includes: linear acceleration, angular velocity and angular acceleration, and the corresponding dimensions are: L / T 2 , 1 / T, 1 / T 2 , the units are m / s 2 , 1 / s, 1 / s 2 , where angular velocity and angular acceleration are coupled with the radius of the turntable (dimension L, unit m) and then responded by the accelerometer. Based on dimensional consistency, the following derivation and combination are carried out based on the three parameters of linear acceleration, angular velocity and angular acceleration. Among them, linear acceleration, angular velocity and angular acceleration all contain degrees of freedom in the three directions of XYZ in space: n=3. According to dimensional consistency, linear acceleration, angular velocity and angular acceleration all have linear response terms and nonlinear response terms; in addition, there is a coupling effect between the three, namely: linear acceleration and angular acceleration coupling, linear acceleration and angular velocity coupling and angular velocity and angular acceleration coupling. According to dimensional consistency, the three coupling terms only contain nonlinear response terms.

[0093] The motion error vector composed of linear acceleration, angular velocity and angular acceleration is:

[0094] Linear acceleration: X a (a x ,a y ,a z );

[0095] Number of linear response terms:

[0096] Linear response term parameter: a x (t),a y (t),a z (t);

[0097] Number of nonlinear response terms:

[0098] Nonlinear response term parameters:

[0099]

[0100] in, is the symbol of the combination number. For example: in the nonlinear response term, is a parameter with only one degree of freedom, is a parameter with two degrees of freedom x a y a x a z a y a z .

[0101] Angular velocity: X ω (ω x ,ω y ,ω z );

[0102] Number of linear response terms:

[0103] Linear response term parameters:

[0104]

[0105] Number of nonlinear response terms:

[0106] Nonlinear response term parameters:

[0107]

[0108] Angular acceleration:

[0109] Number of linear response terms:

[0110] Linear response term parameters:

[0111] Number of nonlinear response terms:

[0112] Nonlinear response term parameters:

[0113]

[0114] Linear acceleration and angular acceleration coupling:

[0115] Number of nonlinear response terms:

[0116] Nonlinear response term parameters:

[0117]

[0118] Linear acceleration and angular velocity coupling: X a,ω (a x ,a y ,a z ,ω x ,ω y ,ω z );

[0119] Number of nonlinear response terms:

[0120] Nonlinear response term parameters:

[0121]

[0122] Angular velocity and angular acceleration coupling:

[0123] Number of nonlinear response terms:

[0124] Nonlinear response term parameters:

[0125]

[0126] Motion error vector:

[0127] The motion error vector composed of linear acceleration, angular velocity and angular acceleration is: There are 84 items in total. Due to the rotation modulation effect of the turntable, It will be modulated by the turntable to the components of the single frequency and double frequency of the rotation speed. The components modulated to the single frequency and double frequency are much higher than the higher frequency, so the components above the double frequency modulation can be ignored.

[0128] Turntable rotation modulation vector: R(Ω) = [sin2Ωt cos2Ωt sinΩt cosΩt 1];

[0129] From the perspective of dimensional consistency analysis: the rotation modulation vector is a dimensionless parameter, which only changes the frequency characteristics of the motion error vector and does not change the dimension. Therefore, the 84-parameter motion error vector and the 5-parameter turntable rotation modulation vector can be directly combined to form a multi-parameter compensation vector containing 420 parameters.

[0130]

[0131] It should be noted that the motion error vector is not only transmitted to the gravity gradiometer output through the linear and nonlinear response terms in the accelerometer output model, but also through installation errors. These errors include two types: accelerometer position error and accelerometer sensitive axis orientation error. Accelerometer position error includes radial, initial, and axial errors. Accelerometer sensitive axis orientation errors include misalignment angle error, pitch angle error, and rotational error around the sensitive axis.

[0132] Among them, the radial installation error is coupled with the angular velocity and angular acceleration and then responded by the accelerometer. The other five items are dimensionless angular errors, so they can be coupled with any motion error vector and finally expressed as the transfer coefficient of the motion error vector. The motion error vector is transmitted to the final output of the gravity gradiometer through the motion error transfer coefficient. The motion error transfer coefficient is composed of six installation errors, accelerometer linear response coefficient and accelerometer nonlinear response coefficient. Each motion error vector corresponds to an error transfer coefficient, so there are a total of 420 motion error transfer coefficients. The motion error transfer coefficient and the multi-parameter compensation vector together constitute a multi-parameter compensation model. The model is derived based on the theoretical basis of dimensional consistency. Therefore, all error sources that do not destroy the dimensional consistency are included in the motion error transfer coefficient, which can be obtained using the parameter estimation method without knowing the specific expression of each error transfer coefficient. The motion error (f) of the gravity gradiometer is determined by the multi-parameter compensation vector (X 420× ) and the error transfer coefficient (A 1×420 ) are jointly determined as shown in the following formula:

[0133]

[0134] Where a is the linear acceleration, ω is the angular velocity, is the angular acceleration, and Ω is the rotation speed of the turntable.

[0135] Optionally, the error transfer coefficient is composed of the radial installation error, initial phase installation error, axial installation error, misalignment angle error, pitch angle error and rotation error around the sensitive axis combined with the accelerometer linear response coefficient and the accelerometer nonlinear response coefficient.

[0136] The embodiment of the present application performs motion compensation by constructing a multi-parameter compensation model for the motion error of the rotating accelerometer gravity gradiometer. The multi-parameter compensation model basically includes all the motion error terms of the gradiometer and can effectively eliminate the impact of the misalignment angle error.

[0137] In the second aspect, the present application also provides a rotational accelerometer gravity gradiometer motion error compensation model, wherein the multi-parameter compensation model is based on dimensional consistency, and is constructed based on the error transfer coefficient and the multi-parameter compensation vector. The multi-parameter compensation vector is determined based on the linear acceleration, angular velocity and angular acceleration to determine the motion error vector, and is determined based on the motion error vector and the rotation modulation vector; the linear acceleration is obtained by extracting the horizontal linear motion through a two-way subtraction combination of the four-way combined accelerometer of the gravity gradiometer.

[0138] Reference Figure 4 Based on the methods in the above embodiments, an embodiment of the present application provides an electronic device, which may include: a processor 410, a communications interface 420, a memory 430, and a communication bus 440, wherein the processor 410, the communications interface 420, and the memory 430 communicate with each other via the communication bus 440. The processor 410 may call logic instructions in the memory 430 to execute the methods in the above embodiments.

[0139] In addition, the logic instructions in the above-mentioned memory 430 can be implemented in the form of a software functional unit and can be stored in a computer-readable storage medium when sold or used as an independent product. Based on this understanding, the technical solution of the present application, or the part that contributes to the prior art, or the part of the technical solution can be embodied in the form of a software product, which is stored in a storage medium and includes a number of instructions for enabling a computer device (which can be a personal computer, server, or network device, etc.) to execute all or part of the steps of the method described in each embodiment of the present application.

[0140] Based on the method in the above embodiment, an embodiment of the present application provides a computer-readable storage medium, which stores a computer program. When the computer program runs on a processor, the processor executes the method in the above embodiment.

[0141] Based on the method in the above embodiment, an embodiment of the present application provides a computer program product. When the computer program product runs on a processor, the processor executes the method in the above embodiment.

[0142] It is understood that the processor in the embodiments of the present application may be a central processing unit (CPU), or may be other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field programmable gate arrays (FPGA), or other programmable logic devices, transistor logic devices, hardware components, or any combination thereof. The general-purpose processor may be a microprocessor or any conventional processor.

[0143] The method steps in the embodiments of the present application can be implemented by hardware or by a processor executing software instructions. The software instructions can be composed of corresponding software modules, which can be stored in random access memory (RAM), flash memory, read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), registers, hard disks, mobile hard disks, CD-ROMs or any other form of storage medium known in the art. An exemplary storage medium is coupled to the processor so that the processor can read information from the storage medium and write information to the storage medium. Of course, the storage medium can also be a component of the processor. The processor and the storage medium can be located in an ASIC.

[0144] In the above embodiments, it can be implemented in whole or in part by software, hardware, firmware or any combination thereof. When implemented using software, it can be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, the process or function described in the embodiment of the present application is generated in whole or in part. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted via the computer-readable storage medium. The computer instructions can be transmitted from one website, computer, server or data center to another website, computer, server or data center via a wired (e.g., coaxial cable, optical fiber, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) method. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that includes one or more available media integrated. The available medium can be a magnetic medium (e.g., a floppy disk, a hard disk, a tape), an optical medium (e.g., a DVD), or a semiconductor medium (e.g., a solid state drive (SSD)).

[0145] It will be understood that the various numerical numbers involved in the embodiments of the present application are merely distinctions for the convenience of description and are not intended to limit the scope of the embodiments of the present application.

[0146] It is easy for those skilled in the art to understand that the above is only a preferred embodiment of the present application and is not intended to limit the present application. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present application should be included in the scope of protection of the present application.

Claims

1. A method for compensating motion errors of a rotating accelerometer gravity gradiometer, characterized in that: include: Acquire the motion error of the system to be compensated, and construct a motion error compensation matrix according to the established multi-parameter compensation model and the motion error; determining a parameter estimation method based on the combined output of the gravity gradiometer, and determining a target error transfer coefficient of the system to be compensated using the parameter estimation method; Inputting the target error transfer coefficient into the motion error compensation matrix to obtain an error compensation result, so as to perform error compensation on the system to be compensated; Among them, the multi-parameter compensation model is based on dimensional consistency, constructed based on error transfer coefficient and multi-parameter compensation vector, the multi-parameter compensation vector is based on linear acceleration, angular velocity and angular acceleration to determine the motion error vector, and is determined based on the motion error vector and the rotation modulation vector; the linear acceleration is obtained by extracting the horizontal linear motion by combining two-way subtraction of the four-way combined accelerometer of the gravity gradiometer; the linear acceleration includes the x-axis acceleration , y-axis acceleration and z-axis acceleration ; The x-axis acceleration and y-axis acceleration It is determined based on two-way subtraction combination output of four orthogonally and antisymmetrically placed accelerometers of the gravity gradiometer; x-axis acceleration and y-axis acceleration Obtained by the following formula; in, 、 are the signal outputs of the four accelerometers of the gravity gradiometer, is the rotation speed of the turntable of the gravity gradiometer, Indicates the measurement time.

2. The method for compensating the motion error of a rotational accelerometer gravity gradiometer according to claim 1, wherein: The method for determining the motion error vector includes: Determining a first parameter corresponding to the linear acceleration, a second parameter corresponding to the angular velocity, and a third parameter corresponding to the angular acceleration; wherein the first parameter includes the number of linear responses, linear response item parameters, the number of nonlinear responses, and the nonlinear response item parameters of the acceleration; the second parameter includes the number of linear responses, linear response item parameters, the number of nonlinear responses, and the nonlinear response item parameters of the angular velocity; and the third parameter includes the number of linear responses, linear response item parameters, the number of nonlinear responses, and the nonlinear response item parameters of the angular acceleration; determining a first coupling parameter of the linear acceleration and the angular acceleration, a second coupling parameter of the linear acceleration and the angular velocity, and a third coupling parameter of the angular velocity and the angular acceleration; The motion error vector is determined based on the first parameter, the second parameter, the third parameter, the first coupling parameter, the second coupling parameter, and the third coupling parameter.

3. The method for compensating the motion error of a rotational accelerometer gravity gradiometer according to claim 1, wherein: The motion error vector is transferred to the gravity gradiometer via the accelerometer output model and installation error.

4. The method for compensating the motion error of a rotational accelerometer gravity gradiometer according to claim 3, wherein: The installation error includes the accelerometer installation position error and the accelerometer sensitive axis direction error; The accelerometer installation position error includes: radial installation error, initial phase installation error and axial installation error; The accelerometer sensitive axis direction error includes: misalignment angle error, pitch angle error and rotation error around the sensitive axis.

5. The method for compensating the motion error of a rotational accelerometer gravity gradiometer according to claim 4, wherein: The error transfer coefficient is composed of the radial installation error, initial phase installation error, axial installation error, misalignment angle error, pitch angle error and rotation error around the sensitive axis combined with the accelerometer linear response coefficient and the accelerometer nonlinear response coefficient.

6. A method for establishing a motion error compensation model for a rotating accelerometer gravity gradiometer, characterized in that: The multi-parameter compensation model is based on dimensional consistency and is constructed based on an error transfer coefficient and a multi-parameter compensation vector. The multi-parameter compensation vector is determined based on linear acceleration, angular velocity, and a motion error vector determined by angular acceleration, and is determined based on the motion error vector and a rotation modulation vector. The linear acceleration is obtained by extracting horizontal linear motion by performing a two-way subtraction combination based on the four-way combined accelerometer of the gravity gradiometer. The linear acceleration includes the x-axis acceleration , y-axis acceleration and z-axis acceleration ; The x-axis acceleration and y-axis acceleration It is determined based on two-way subtraction combination output of four orthogonally and antisymmetrically placed accelerometers of the gravity gradiometer; x-axis acceleration and y-axis acceleration Obtained by the following formula; in, 、 are the signal outputs of the four accelerometers of the gravity gradiometer, is the rotation speed of the turntable of the gravity gradiometer, Indicates the measurement time.

7. An electronic device, characterized in that: include: at least one memory for storing a computer program; At least one processor is used to execute the program stored in the memory. When the program stored in the memory is executed, the processor is used to execute the method according to any one of claims 1 to 5.

8. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed on a processor, the processor is caused to execute the method according to any one of claims 1 to 5.

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