An accelerometer calibration method and system based on ADMM algorithm

Abstract

The application relates to an accelerometer calibration method and system based on an ADMM algorithm, which comprises the following steps: constructing an error mathematical model according to zero offset errors, scale factor errors and non-orthogonal errors, and determining respective model parameters corresponding to the error mathematical model; obtaining a target function corresponding to an optimization parameter identification model; performing error optimization on the respective model parameters by using the target function corresponding to the optimization parameter identification model according to the respective model parameters, a first output value and a compensation output value, to obtain target parameters corresponding to the respective model parameters; and updating the error mathematical model according to the respective target parameters to obtain a target error mathematical model, so that the accelerometer calibrates a to-be-measured object according to the target error mathematical model. The application solves the problem of how to compensate the calibration of the accelerometer based on the ADMM algorithm, thereby improving the precision.

Description

A method and system for accelerometer calibration based on ADMM algorithm Technical Field

[0001] This invention relates to the field of accelerometer technology, and in particular to an accelerometer calibration method and system based on the ADMM algorithm. Background Technology

[0002] With the continuous development of micro-nano fabrication technology and the advancement of integrated circuit technology, microelectromechanical systems (MEMS) inertial devices have attracted increasing attention and importance. Their small size, simple fabrication, and cost-effectiveness have led them to gradually enter the consumer market, gaining attention from both consumers and engineers. However, the measurement accuracy of MEMS devices does not meet the requirements of engineering practice, and their noise levels are significantly insufficient. These shortcomings hinder the development of MEMS devices, making optimization and improvement necessary.

[0003] To improve the accuracy of MEMS accelerometers in measuring the linear velocity of a carrier, three main methods exist: optimizing the accelerometer's structural design, rigorously controlling the sensor's manufacturing precision, and performing computational compensation on the triaxial accelerometer. In practice, the manufacturing and packaging precision of MEMS devices is limited by processing equipment and conditions, making significant improvements difficult in the short term. Furthermore, structural and process improvements would increase the complexity of the triaxial accelerometer, posing new challenges to production, assembly, and debugging. Therefore, current research focuses on calibration compensation for MEMS accelerometers, primarily investigating modifications to accelerometer calibration methods. Summary of the Invention

[0004] To overcome the problem of how to compensate for accelerometer calibration and thus improve accuracy, this invention provides an accelerometer calibration method and system based on the ADMM algorithm.

[0005] In a first aspect, to solve the above-mentioned technical problems, the present invention provides an accelerometer calibration method based on the ADMM algorithm, comprising the following steps:

[0006] The zero bias error, scale factor error, non-orthogonal error, first output value, and corresponding compensation output value of the accelerometer are obtained. Based on the zero bias error, scale factor error, and non-orthogonal error, an error mathematical model is constructed, and the parameters of each model corresponding to the error mathematical model are determined. The compensation output value is the value obtained after error correction of the first output value. The zero bias error represents the offset of the measured value in the orthogonal coordinate system from the zero value when the accelerometer is stationary. The scale factor error represents the error of the accelerometer scale on the x-axis, y-axis, and z-axis, respectively. The non-orthogonal error represents the installation error of the accelerometer on the x-axis, y-axis, and z-axis, respectively.

[0007] Obtain the objective function corresponding to the preset optimization parameter identification model. The optimization parameter identification model is used to optimize each model parameter. The objective function represents the difference between the optimized model parameters and the unoptimized model parameters.

[0008] Based on each model parameter, the first output value, and the compensation output value, the objective function corresponding to the model is identified by optimizing the parameters, and error optimization is performed on each model parameter to obtain the target parameters corresponding to each model parameter.

[0009] The error mathematical model is updated based on each target parameter to obtain the target error mathematical model, so that the accelerometer can be calibrated based on the target error mathematical model.

[0010] The beneficial effects of the accelerometer calibration method based on the ADMM algorithm provided by this invention are as follows: An error mathematical model is constructed based on the zero bias error, scale factor error, and non-orthogonal error, thereby obtaining the corresponding model parameters. Then, an objective function corresponding to the optimized parameter identification model is constructed. By optimizing the parameter identification model and the objective function, the errors of each model parameter are optimized to minimize their respective errors, thus obtaining the target parameters. This leads to the construction of a target error mathematical model. At this point, the target error mathematical model compensates for the accelerometer calibration error, thereby improving the accelerometer's accuracy.

[0011] Based on the above technical solution, the accelerometer calibration method based on the ADMM algorithm of the present invention can be further improved as follows.

[0012] Furthermore, based on each model parameter, the first output value, and the compensation output value, the objective function corresponding to the model is identified through parameter optimization, and each model parameter is optimized to obtain the target parameters corresponding to each model parameter, including:

[0013] Based on each model parameter, the first output value, and the compensation output value, the objective function is split into multiple sub-functions corresponding to the model parameters;

[0014] Based on the sub-function, a pre-defined Lagrange function is introduced into the sub-function, and the sub-function with the introduced Lagrange function is augmented to determine the Lagrange transformation function. The Lagrange transformation function is then solved using the dual ascent method to determine the iterative formula for updating the parameters of each model.

[0015] Based on the iterative formula, the model parameters are iteratively updated to reduce the error, and the target parameters corresponding to each model parameter are obtained.

[0016] The beneficial effects of adopting the above-mentioned further scheme are as follows: by splitting the objective function into multiple sub-functions corresponding to model parameters, the global problem is decomposed into smaller and easier-to-solve local sub-problems. Then, by introducing the Lagrange function into the sub-functions and augmenting the sub-functions with the Lagrange function, the Lagrange transformation function is determined. Finally, the solution to the global problem is obtained by solving the Lagrange transformation function, thereby obtaining the iterative formula. The model parameters are then iteratively updated to reduce the error using the iterative formula to obtain the objective parameters.

[0017] Furthermore, based on the zero bias error, scale factor error, and non-orthogonal error, the above-mentioned error mathematical model is constructed, including:

[0018] Based on the zero bias error, scale factor error, non-orthogonality error, first output value, and first gravitational acceleration, an error mathematical model is constructed using the first formula, which is:

[0019] E(W) = ||(K+T)a+b||-g;

[0020] Where E(W) represents the error mathematical model, b represents the zero bias error, K represents the scale factor error, T represents the non-orthogonal error, a represents the output value, and g represents the first gravitational acceleration.

[0021] The beneficial effect of adopting the above-mentioned further scheme is that an error mathematical model is constructed through the first formula, thereby obtaining the various model parameters through the error mathematical model.

[0022] Furthermore, the method also includes:

[0023] Obtain the N second output values ​​corresponding to the accelerometer;

[0024] Obtain the objective function corresponding to the preset optimized parameters identification model, including:

[0025] Based on the zero bias error, scale factor error, non-orthogonality error, second gravitational acceleration, and N second output values, the optimized parameter identification model is determined using the second formula, which is:

[0026]

[0027] Where W represents the optimized parameter identification model, N represents the number of output values, b represents the zero bias error, K represents the scale factor error, T represents the non-orthogonal error, a represents the second output value, g represents the second gravitational acceleration, and i represents the i-th second output value.

[0028] Based on the optimized parameter identification model and N second output values, the objective function is determined using the third formula, which is:

[0029]

[0030] Where, minf N (W) represents the objective function, N represents the number of output values, and i represents the i-th output value. i (W) represents the i-th output value, E i (W) T This represents the result of transposing the i-th output value, and W represents the optimized parameter identification model.

[0031] The beneficial effect of adopting the above-mentioned further scheme is that by constructing an optimized parameter identification model through the second formula and then constructing an objective function through the third formula, the model parameters can be optimized for error through the optimized parameter identification model and the objective function.

[0032] Furthermore, based on the various model parameters, the first output value, and the compensation output value, the objective function is broken down into multiple sub-functions corresponding to the model parameters, including:

[0033] Based on the first output value, the compensated output value, and each model parameter, the objective function is broken down into multiple sub-functions corresponding to the model parameters using the fourth formula, which is:

[0034] staq+b=A;

[0035] in, Let represent a sub-function, a represent the first output value, A represent the compensation output value, and q and b represent the model parameters, respectively.

[0036] The beneficial effect of adopting the above-mentioned further scheme is that, through the fourth formula, a sub-function is constructed, thereby breaking down the global problem corresponding to the objective function into smaller, easier-to-solve local sub-problems.

[0037] Furthermore, based on the sub-function, a preset Lagrange function is introduced into the sub-function, and the sub-function with the introduced Lagrange function is augmented to determine the Lagrange transform function, including:

[0038] Based on the subfunction and the Lagrange function, the Lagrange transform function is determined by augmenting the subfunction that incorporates the Lagrange function using the fifth formula. The fifth formula is:

[0039]

[0040] Among them, L ρ (q,b,λ) denotes the Lagrange transform function, f(q)+g(b)+λ T(aq+bA) represents a sub-function that incorporates the Lagrange function, where a represents the first output value, A represents the compensated output value, q and b represent the model parameters, λ is the Lagrange multiplier vector, and ρ is the quadratic penalty function factor.

[0041] By solving the Lagrange transform function using the dual ascent method, the iterative formulas for updating the parameters of each model are determined, including:

[0042] Using the dual ascent method, the Lagrange transform function is solved through the sixth formula to determine the iterative formula, where the sixth formula is:

[0043]

[0044] Where, q (k) b (k) Let q and b represent the results obtained by iterating the model parameters q and b k times respectively, where q and b represent the model parameters, and λ is the Lagrange multiplier vector. (k) Let λ represent the result obtained by iterating k times. (k-1) Let λ represent the result obtained after k-1 iterations, where a represents the first output value and A represents the compensation output value.

[0045] The beneficial effect of adopting the above-mentioned further scheme is that: by using the fifth formula, the Lagrange transformation function is constructed, and then by using the sixth formula, the Lagrange transformation function is solved. Thus, by solving the local subproblems (Lagrange transformation function), the solution to the global problem (objective function) is obtained.

[0046] Furthermore, the method also includes:

[0047] The Lagrange transform function is standardized using the ADMM algorithm, and then the standardized function is further processed using the seventh formula to obtain the enhanced Lagrange function. The seventh formula is as follows:

[0048]

[0049] Among them, L ρ (q,b,w) represents the enhancement Lagrangian function, w represents the ratio of λ to ρ, a represents the first output value, A represents the compensation output value, q and b represent the model parameters, λ is the Lagrange multiplier vector, and ρ is the quadratic penalty function factor.

[0050] By solving the Lagrange transform function using the dual ascent method, the iterative formulas for updating the parameters of each model are determined, including:

[0051] The enhanced Lagrangian function is solved by the dual ascent method, and the iterative formula for updating the parameters of each model is determined.

[0052] The beneficial effect of adopting the above-mentioned further scheme is that the Lagrange transform function is standardized by the ADMM algorithm to obtain the enhanced Lagrange function, thereby reducing the amount of computation when updating the various model parameters to reduce errors in iterative updates.

[0053] Furthermore, by solving the enhanced Lagrangian function using the dual ascent method, the iterative formulas for updating the parameters of each model are determined, including:

[0054] Based on the dual ascent method, the enhanced Lagrangian function is solved using the eighth formula, and the iterative formula is determined. The eighth formula is:

[0055]

[0056] Where, q (k) b (k) Let q and b represent the results obtained by iterating model parameters q and b k times respectively, where q and b represent the model parameters, a represents the first output value, A represents the compensated output value, and w represents the ratio of λ to ρ. (k) This represents the result obtained by iterating w k times. (k-1) This represents the result obtained by iterating w for k-1 times.

[0057] The beneficial effect of adopting the above-mentioned further scheme is that by solving the enhanced Lagrangian function through the eighth formula, the iterative formula is determined, and then the various model parameters are iteratively updated to reduce the error through the iterative formula.

[0058] Secondly, the present invention provides an accelerometer calibration system based on the ADMM algorithm, comprising:

[0059] The model parameter acquisition module is used to acquire the zero bias error, scale factor error, non-orthogonal error, first output value, and compensation output value corresponding to the accelerometer. Based on the zero bias error, scale factor error, and non-orthogonal error, it constructs an error mathematical model and determines the various model parameters corresponding to the error mathematical model. The compensation output value is the value obtained after error correction of the first output value. The zero bias error represents the offset of the measured value in the orthogonal coordinate system relative to the zero value when the accelerometer is stationary. The scale factor error represents the error of the accelerometer scale on the x-axis, y-axis, and z-axis, respectively. The non-orthogonal error represents the installation error of the accelerometer on the x-axis, y-axis, and z-axis, respectively.

[0060] The objective function module is used to obtain the objective function corresponding to the preset optimization parameter identification model. The optimization parameter identification model is used to optimize each model parameter. The objective function represents the difference between the optimized model parameters and the unoptimized model parameters.

[0061] The target parameter module is used to identify the objective function corresponding to the model by optimizing the parameters based on each model parameter, the first output value and the compensation output value, and to perform error optimization on each model parameter to obtain the target parameters corresponding to each model parameter.

[0062] The calibration module is used to update the error mathematical model according to each target parameter to obtain the target error mathematical model, so that the accelerometer can be calibrated according to the target error mathematical model.

[0063] Thirdly, the present invention also provides an electronic device, including a memory, a processor, and a program stored in the memory and running on the processor, wherein the processor executes the program to implement the steps of the above-described method for accelerometer calibration based on the ADMM algorithm.

[0064] Fourthly, the present invention also provides a computer-readable storage medium storing instructions that, when executed on a terminal device, cause the terminal device to perform the steps of a method for accelerometer calibration based on the ADMM algorithm. Attached Figure Description

[0065] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0066] Figure 1 is a flowchart illustrating an accelerometer calibration method based on the ADMM algorithm according to an embodiment of the present invention;

[0067] Figure 2 is a schematic diagram of an accelerometer calibration system based on the ADMM algorithm according to an embodiment of the present invention. Detailed Implementation

[0068] The following embodiments are further explanations and supplements to the present invention and do not constitute any limitation on the present invention.

[0069] The following describes, with reference to the accompanying drawings, a method and system for accelerometer calibration based on the ADMM algorithm according to an embodiment of the present invention.

[0070] This invention discloses an accelerometer calibration method based on the ADMM algorithm. The method is applied to a terminal device. In this application, the terminal device is used as the execution subject to describe the solution. The terminal device can be a computer, server, etc., used to execute the steps of an accelerometer calibration method based on the ADMM algorithm.

[0071] Optionally, as shown in Figure 1, the present invention provides a method for accelerometer calibration based on the ADMM algorithm, comprising the following steps:

[0072] Step S1: Obtain the zero bias error, scale factor error, non-orthogonal error, first output value, and compensation output value corresponding to the accelerometer. Based on the zero bias error, scale factor error, and non-orthogonal error, construct an error mathematical model and determine the model parameters corresponding to the error mathematical model. The compensation output value is the value obtained after error correction of the first output value. The zero bias error represents the offset of the measured value relative to the zero value in the orthogonal coordinate system when the accelerometer is stationary. The scale factor error represents the error of the accelerometer scale on the x-axis, y-axis, and z-axis, respectively. The non-orthogonal error represents the installation error of the accelerometer on the x-axis, y-axis, and z-axis, respectively.

[0073] The first output value refers to the measurement value obtained by the accelerometer during the measurement process. The error mathematical model represents the relationship between the zero bias error, scale factor error, non-orthogonal error, and various model parameters. Different zero bias errors, scale factor errors, and non-orthogonal errors can correspond to different error mathematical models. The specific implementation method of constructing the error mathematical model based on the zero bias error, scale factor error, and non-orthogonal error will be described below and will not be repeated here.

[0074] Step S2: Obtain the objective function corresponding to the preset optimization parameter identification model. The optimization parameter identification model is used to optimize the error of each model parameter. The objective function represents the difference between the optimized model parameters and the unoptimized model parameters.

[0075] Among them, optimizing the error values ​​of each model parameter involves performing error optimization on each model parameter. Specifically, the error of this model parameter refers to the error between the accelerometer measurement value and the true value caused by zero bias error, scale factor error, and non-orthogonality error.

[0076] Step S3: Based on each model parameter, the first output value, and the compensation output value, identify the objective function corresponding to the model by optimizing the parameters, perform error optimization on each model parameter, and obtain the target parameters corresponding to each model parameter;

[0077] Specifically, performing error optimization on each model parameter to obtain the target parameter corresponding to each model parameter means performing error optimization on each model parameter to obtain the target parameter corresponding to that model parameter. The target parameter is the model parameter after error optimization.

[0078] Step S4: Update the error mathematical model according to each target parameter to obtain the target error mathematical model, so that the accelerometer can be calibrated according to the target error mathematical model.

[0079] The specific implementation method of calibrating the test object based on the target error mathematical model of the accelerometer can be achieved based on existing technology, and will not be elaborated here.

[0080] Optionally, in practical use, the accelerometer calibration mathematical model is A = (K + T)a + b, where a = (a x a y a z ) T This indicates the output value of the accelerometer before error compensation (a). x a y a z These represent the output values ​​of the accelerometer on the x, y, and z axes before error compensation, respectively (T represents the transpose matrix symbol), A = (A x A y A z ) T This indicates the output value of the accelerometer after error compensation (A). x A y A z These represent the error-compensated output values ​​of the accelerometer on the x, y, and z axes, respectively, where T represents the transpose matrix symbol, b = (b x b y b z ) T This represents the offset of the measured value relative to zero in an orthogonal coordinate system when the accelerometer is at rest. This indicates that the accelerometer scale is on the x-axis (k... x ), y-axis (k y ) and z-axis (k z The corresponding error on ) This indicates the installation error (β) of the accelerometer along the x, y, and z axes, respectively. xy This represents the unit input on the y-axis, the x-axis output of the accelerometer due to installation errors, and so on, with the remaining β... xz β yx β yz β zx β zy (Parameters not elaborated), because under ideal conditions, the ideal orthogonal coordinate system S B With accelerometer coordinate system S S The relation is: S B =TS S When the origins of the ideal coordinate system and the accelerometer coordinate system coincide, and their z-axis also coincide, then the angle β... yx β zx β zy Zero, non-orthogonal error Accelerometer calibration requires estimation of the following unknown parameters Under static conditions, the square root of the ideal measurement value of the accelerometer is equal to the gravitational acceleration g. Therefore, the mathematical function of the accelerometer error is E(W) = ||(K+T)a+b||-g. The objective function of the parameter identification and optimization model for the accelerometer is... (It should be noted that the objective function corresponding to the third formula below is derived by summing the above objective function N times.)

[0081] Optionally, based on the above, in step S1, an error mathematical model is constructed according to the zero bias error, scale factor error, and non-orthogonal error, including:

[0082] Based on the zero bias error, scale factor error, non-orthogonality error, first output value, and first gravitational acceleration, an error mathematical model is constructed using the first formula, which is:

[0083] E(W) = ||(K+T)a+b||-g;

[0084] Where E(W) represents the error mathematical model, b represents the zero bias error, K represents the scale factor error, T represents the non-orthogonal error, a represents the output value, and g represents the first gravitational acceleration.

[0085] Optionally, the method further includes:

[0086] Obtain the N second output values ​​corresponding to the accelerometer;

[0087] Obtain the objective function corresponding to the preset optimized parameters identification model, including:

[0088] Based on the zero bias error, scale factor error, non-orthogonality error, second gravitational acceleration, and N second output values, the optimized parameter identification model is determined using the second formula, which is:

[0089]

[0090] Where W represents the optimized parameter identification model, N represents the number of output values, b represents the zero bias error, K represents the scale factor error, T represents the non-orthogonal error, a represents the second output value, g represents the second gravitational acceleration, and i represents the i-th second output value.

[0091] Based on the optimized parameter identification model and N second output values, the objective function is determined using the third formula, which is:

[0092]

[0093] Where, minf N(W) represents the objective function, N represents the number of output values, and i represents the i-th output value. i (W) represents the i-th output value, E i (W) T This represents the result of transposing the i-th output value, and W represents the optimized parameter identification model.

[0094] Alternatively, directly solving the objective function is quite difficult. Therefore, this application proposes to use the Alternating Direction Multiplier Method (ADMM) to solve the objective function. The ADMM algorithm decomposes the large global problem into multiple smaller, easier-to-solve local subproblems through a decomposition and coordination process, and obtains the solution to the large global problem by coordinating the solutions of the subproblems.

[0095] Optionally, based on the ADMM algorithm described above, and according to each model parameter, the first output value, and the compensation output value, the objective function corresponding to the model is identified by optimizing the parameters, and each model parameter is optimized to obtain the target parameters corresponding to each model parameter, including:

[0096] Based on each model parameter, the first output value, and the compensation output value, the objective function is split into multiple sub-functions corresponding to the model parameters;

[0097] Based on the sub-function, a pre-defined Lagrange function is introduced into the sub-function, and the sub-function with the introduced Lagrange function is augmented to determine the Lagrange transformation function. The Lagrange transformation function is then solved using the dual ascent method to determine the iterative formula for updating the parameters of each model.

[0098] Based on the iterative formula, the model parameters are iteratively updated to reduce the error, and the target parameters corresponding to each model parameter are obtained.

[0099] Optionally, based on each model parameter, the first output value, and the compensation output value, the objective function is split into multiple sub-functions corresponding to the model parameters, including:

[0100] Based on the first output value, the compensated output value, and each model parameter, the objective function is broken down into multiple sub-functions corresponding to the model parameters using the fourth formula, which is:

[0101] staq+b=A;

[0102] in, Let represent a sub-function, a represent the first output value, A represent the compensation output value, and q and b represent the model parameters, respectively.

[0103] Optionally, the above involves introducing a preset Lagrange function into the sub-function and augmenting the sub-function with the introduced Lagrange function to determine the Lagrange transform function, including:

[0104] Based on the subfunction and the Lagrange function, the Lagrange transform function is determined by augmenting the subfunction that incorporates the Lagrange function using the fifth formula. The fifth formula is:

[0105]

[0106] Among them, L ρ (q,b,λ) denotes the Lagrange transform function, f(q)+g(b)+λ T (aq+bA) represents a sub-function that incorporates the Lagrange function, where a represents the first output value, A represents the compensated output value, q and b represent the model parameters, λ is the Lagrange multiplier vector, and ρ is the quadratic penalty function factor.

[0107] The above method uses the dual ascent method to solve the Lagrange transform function and determines the iterative formulas for updating the various model parameters, including:

[0108] Using the dual ascent method, the Lagrange transform function is solved through the sixth formula to determine the iterative formula, where the sixth formula is:

[0109]

[0110] Where, q (k) b (k) Let q and b represent the results obtained by iterating the model parameters q and b k times respectively, where q and b represent the model parameters, and λ is the Lagrange multiplier vector. (k) Let λ represent the result obtained by iterating k times. (k-1) Let λ represent the result obtained after k-1 iterations, where a represents the first output value and A represents the compensation output value.

[0111] Alternatively, although the global problem can be transformed into smaller, easier-to-solve local subproblems, the computational cost remains high. Therefore, a method is introduced into the Lagrange transform function to address this issue. The inverse operation of the square expansion is performed, thereby standardizing the Lagrange transform function using the ADMM algorithm. Therefore, the following is introduced: After that, it can be transformed for In subsequent iterative updates of the model parameters to reduce error, the model parameters q and b are independent. This can be ignored when updating q and b, thus reducing the computational load.

[0112] Optionally, based on the above, the method further includes:

[0113] The Lagrange transform function is standardized using the ADMM algorithm, and then the standardized function is further processed using the seventh formula to obtain the enhanced Lagrange function. The seventh formula is as follows:

[0114]

[0115] Among them, L ρ (q,b,w) represents the enhancement Lagrangian function, w represents the ratio of λ to ρ, a represents the first output value, A represents the compensation output value, q and b represent the model parameters, λ is the Lagrangian multiplier vector, and ρ is the quadratic penalty function factor;

[0116] The above method uses the dual ascent method to solve the Lagrange transform function and determines the iterative formulas for updating the various model parameters, including:

[0117] The enhanced Lagrangian function is solved by the dual ascent method, and the iterative formula for updating the parameters of each model is determined.

[0118] Optionally, the above-mentioned method of solving for the enhanced Lagrangian function using the dual ascent method determines the iterative formulas used to update the parameters of each model, including:

[0119] Based on the dual ascent method, the enhanced Lagrangian function is solved using the eighth formula, and the iterative formula is determined. The eighth formula is:

[0120]

[0121] Where, q (k) b (k) Let q and b represent the results obtained by iterating model parameters q and b k times respectively, where q and b represent the model parameters, a represents the first output value, A represents the compensated output value, and w represents the ratio of λ to ρ. (k) This represents the result obtained by iterating w k times. (k-1) This represents the result obtained by iterating w for k-1 times.

[0122] Optionally, in the eighth formula, the error reduction is first iterated and updated with q as a variable, and then the error reduction is iterated and updated with b as a variable. At this time, the information of q is already the latest. The eighth formula is iterated and updated until convergence, and the optimal solution of each model parameter, i.e. the target parameter, can be obtained.

[0123] As shown in Figure 2, this embodiment of the invention also provides an accelerometer calibration system based on the ADMM algorithm, comprising:

[0124] The model parameter acquisition module 201 is used to acquire the zero bias error, scale factor error, non-orthogonal error, first output value and compensation output value corresponding to the accelerometer, and to construct an error mathematical model based on the zero bias error, scale factor error and non-orthogonal error, and to determine the various model parameters corresponding to the error mathematical model. The compensation output value is the value obtained after error correction of the first output value. The zero bias error represents the offset of the measured value in the orthogonal coordinate system relative to the zero value when the accelerometer is stationary. The scale factor error represents the error of the accelerometer scale on the x-axis, y-axis and z-axis respectively. The non-orthogonal error represents the installation error of the accelerometer on the x-axis, y-axis and z-axis respectively.

[0125] The objective function module 202 is used to obtain the objective function corresponding to the preset optimization parameter identification model. The optimization parameter identification model is used to optimize each model parameter. The objective function represents the difference between the optimized model parameters and the unoptimized model parameters.

[0126] The target parameter module 203 is used to identify the target function corresponding to the model by optimizing the parameters based on each model parameter, the first output value and the compensation output value, and to perform error optimization on each model parameter to obtain the target parameters corresponding to each model parameter.

[0127] The calibration module 204 is used to update the error mathematical model according to each target parameter to obtain the target error mathematical model, so that the accelerometer can be calibrated according to the target error mathematical model.

[0128] Optionally, the target parameter module 203 mentioned above also includes:

[0129] The sub-function module is used to split the objective function into multiple sub-functions corresponding to the model parameters based on each model parameter, the first output value, and the compensation output value.

[0130] The iterative formula module is used to introduce a preset Lagrangian function into the sub-function based on the sub-function, augment the sub-function with the introduced Lagrangian function, determine the Lagrangian transformation function, and solve the Lagrangian transformation function through the dual ascent method to determine the iterative formula used to update the parameters of each model.

[0131] The iterative update module is used to iteratively update each model parameter according to the iterative formula to reduce the error, and obtain the target parameter corresponding to each model parameter.

[0132] Optionally, the above-mentioned model parameter acquisition module 201 is specifically used for:

[0133] Based on the zero bias error, scale factor error, and non-orthogonal error, an error mathematical model is constructed, including:

[0134] Based on the zero bias error, scale factor error, non-orthogonality error, first output value, and first gravitational acceleration, an error mathematical model is constructed using the first formula, which is:

[0135] E(W) = ||(K+T)a+b||-g;

[0136] Where E(W) represents the error mathematical model, b represents the zero bias error, K represents the scale factor error, T represents the non-orthogonal error, a represents the output value, and g represents the first gravitational acceleration.

[0137] Optionally, the system may also include:

[0138] The second output value acquisition module is used to acquire N second output values ​​corresponding to the accelerometer.

[0139] The objective function module 202 described above is specifically used for:

[0140] Based on the zero bias error, scale factor error, non-orthogonality error, second gravitational acceleration, and N second output values, the optimized parameter identification model is determined using the second formula, which is:

[0141]

[0142] Where W represents the optimized parameter identification model, N represents the number of output values, b represents the zero bias error, K represents the scale factor error, T represents the non-orthogonal error, a represents the second output value, g represents the second gravitational acceleration, and i represents the i-th second output value.

[0143] Based on the optimized parameter identification model and N second output values, the objective function is determined using the third formula, which is:

[0144]

[0145] Where, minf N (W) represents the objective function, N represents the number of output values, and i represents the i-th output value. i (W) represents the i-th output value, E i (W) T This represents the result of transposing the i-th output value, and W represents the optimized parameter identification model.

[0146] Optionally, the above sub-function module is specifically used for:

[0147] Based on the first output value, the compensated output value, and each model parameter, the objective function is broken down into multiple sub-functions corresponding to the model parameters using the fourth formula, which is:

[0148] staq+b=A;

[0149] in, Let represent a sub-function, a represent the first output value, A represent the compensation output value, and q and b represent the model parameters, respectively.

[0150] Optionally, the above iterative formula module is specifically used for:

[0151] Based on the subfunction and the Lagrange function, the Lagrange transform function is determined by augmenting the subfunction that incorporates the Lagrange function using the fifth formula. The fifth formula is:

[0152]

[0153] Among them, L ρ (q,b,λ) denotes the Lagrange transform function, f(q)+g(b)+λ T (aq+bA) denotes a subfunction that incorporates the Lagrange function, where a represents the first output value, A represents the compensated output value, q and b represent the model parameters, λ is the Lagrange multiplier vector, and ρ is the quadratic penalty function factor.

[0154] The iterative formula module described above, when determining the iterative formulas for updating various model parameters by solving the Lagrange transform function using the dual ascent method, is specifically used for:

[0155] Using the dual ascent method, the Lagrange transform function is solved through the sixth formula to determine the iterative formula, where the sixth formula is:

[0156]

[0157] Where, q (k) b (k) Let q and b represent the results obtained by iterating the model parameters q and b k times respectively, where q and b represent the model parameters, and λ is the Lagrange multiplier vector. (k) Let λ represent the result obtained by iterating k times. (k-1) Let λ represent the result obtained after k-1 iterations, where a represents the first output value and A represents the compensation output value.

[0158] Optionally, the system may also include:

[0159] The Enhanced Lagrange Function module is used to standardize the Lagrange transform function using the ADMM algorithm, and then process the standardized function using the seventh formula to obtain the enhanced Lagrange function. The seventh formula is:

[0160]

[0161] L ρ (q,b,w) represents the enhancement Lagrangian function, w represents the ratio of λ to ρ, a represents the first output value, A represents the compensation output value, q and b represent the model parameters, λ is the Lagrangian multiplier vector, and ρ is the quadratic penalty function factor;

[0162] Optionally, the above iterative formula module is also used for:

[0163] The enhanced Lagrangian function is solved by the dual ascent method, and the iterative formula for updating the parameters of each model is determined.

[0164] Optionally, the above iterative formula module is specifically used for:

[0165] Based on the dual ascent method, the enhanced Lagrangian function is solved using the eighth formula, and the iterative formula is determined. The eighth formula is:

[0166]

[0167] Where, q (k) b (k) Let q and b represent the results obtained by iterating model parameters q and b k times respectively, where q and b represent the model parameters, a represents the first output value, A represents the compensated output value, and w represents the ratio of λ to ρ. (k) This represents the result obtained by iterating w k times. (k-1) This represents the result obtained by iterating w for k-1 times.

[0168] An electronic device according to an embodiment of the present invention includes a memory, a processor, and a program stored in the memory and running on the processor. When the processor executes the program, it implements some or all of the steps of the above-described method for accelerometer calibration based on the ADMM algorithm.

[0169] The electronic device can be a computer, and the corresponding program is computer software. The parameters and steps of the electronic device of the present invention can be referred to the parameters and steps in the embodiment of the accelerometer calibration method based on ADMM algorithm in the above text, and will not be repeated here.

[0170] Those skilled in the art will recognize that this invention can be implemented as a system, method, or computer program product. Therefore, this disclosure can be embodied in the following forms: it can be entirely hardware, entirely software (including firmware, resident software, microcode, etc.), or a combination of hardware and software, generally referred to herein as a "circuit," "module," or "system." Furthermore, in some embodiments, the invention can also be implemented as a computer program product contained in one or more computer-readable media, which contains computer-readable program code. Computer-readable storage media can be, for example, but not limited to—electrical, magnetic, optical, electromagnetic, infrared, or semiconductor systems, apparatuses, or devices, or any combination thereof.

[0171] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0172] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention.

Claims

1. A method for accelerometer calibration based on the ADMM algorithm, characterized in that, The steps include: obtaining the zero bias error, scale factor error, non-orthogonal error, first output value, and corresponding compensated output value of the accelerometer; constructing an error mathematical model based on the zero bias error, scale factor error, and non-orthogonal error; determining the various model parameters corresponding to the error mathematical model; the compensated output value being the first output value after error correction; the zero bias error representing the offset of the measured value relative to zero in an orthogonal coordinate system when the accelerometer is stationary; and the scale factor error representing the offset of the accelerometer scale on the x, y, and z axes, respectively. The corresponding errors, the non-orthogonal errors representing the installation errors of the accelerometer along the x, y, and z axes respectively; obtaining the objective function corresponding to the preset optimization parameter identification model, the optimization parameter identification model being used to optimize each model parameter, the objective function representing the difference between the optimized model parameters and the unoptimized model parameters; based on each model parameter, the first output value, and the compensation output value, error optimization is performed on each model parameter using the objective function corresponding to the optimization parameter identification model to obtain the target parameters corresponding to each model parameter; further optimization is performed based on each target parameter. The new error mathematical model yields a target error mathematical model, enabling the accelerometer to calibrate the test object based on the target error mathematical model. The step of identifying the target function corresponding to the model through the optimization parameters based on each model parameter, the first output value, and the compensation output value, and optimizing each model parameter to obtain the target parameters corresponding to each model parameter, includes: decomposing the target function into multiple sub-functions corresponding to multiple model parameters based on each model parameter, the first output value, and the compensation output value; introducing a preset Lagrange function into the sub-functions based on the sub-functions, and augmenting the sub-functions with the introduced Lagrange function to determine the Lagrange transform function; solving the Lagrange transform function using the dual ascent method to determine the iterative formula for updating each model parameter; iteratively updating each model parameter to reduce error based on the iterative formula to obtain the target parameter corresponding to each model parameter; further includes: standardizing the Lagrange transform function using the ADMM algorithm, and processing the standardized function using a seventh formula to obtain an enhanced Lagrange function, wherein the seventh formula is: ;in, This represents the enhanced Lagrange function. express and The ratio, Indicates the first output value. Indicates the compensation output value. and These represent the model parameters, Let Lagrange multiplier vectors be used. The factor is a quadratic penalty function; the step of solving the Lagrange transform function by the dual ascent method to determine the iterative formula for updating each of the model parameters includes: solving the enhanced Lagrange function by the dual ascent method to determine the iterative formula for updating each of the model parameters.

2. The method according to claim 1, characterized in that, The step of constructing an error mathematical model based on the zero bias error, scale factor error, and non-orthogonal error includes: constructing an error mathematical model using a first formula based on the zero bias error, scale factor error, non-orthogonal error, first output value, and first gravitational acceleration, wherein the first formula is: ;in, Represents the mathematical model of error. Indicates zero bias error. Indicates scale factor error, Indicates non-orthogonal error. Indicates the output value. This represents the first gravitational acceleration.

3. The method according to claim 2, characterized in that, Also includes: Obtain the corresponding accelerometer A second output value; The process of obtaining the objective function corresponding to the preset optimized parameter identification model includes: based on the zero bias error, scale factor error, non-orthogonality error, second gravitational acceleration, and... The second output value is used to determine the optimized parameter identification model through the second formula, whereby the second formula is: ;in, This represents the optimized parameter identification model. Indicates the number of output values. Indicates zero bias error. Indicates scale factor error, Indicates non-orthogonal error. This represents the second output value. This represents the second gravitational acceleration. Indicates the first A second output value; based on the optimization parameters, the model is identified and The second output value is used to determine the objective function using a third formula, wherein the third formula is: ;in, Describe the objective function. Indicates the number of output values. Indicates the first One output value, Indicates the first One output value, Indicates the first The result of transposing each output value. This represents the optimized parameter identification model.

4. The method according to claim 3, characterized in that, The step of splitting the objective function into multiple sub-functions corresponding to the model parameters based on each of the model parameters, the first output value, and the compensation output value includes: splitting the objective function into multiple sub-functions corresponding to the model parameters using a fourth formula based on the first output value, the compensation output value, and each of the model parameters, wherein the fourth formula is: ;in, Represents a subfunction. Indicates the first output value. Indicates the compensation output value. and These represent the model parameters.

5. The method according to claim 4, characterized in that, The step of introducing a preset Lagrange function into the sub-function based on the sub-function, and augmenting the sub-function with the introduced Lagrange function to determine the Lagrange transform function includes: augmenting the sub-function with the introduced Lagrange function using a fifth formula based on the sub-function and the Lagrange function to determine the Lagrange transform function, wherein the fifth formula is: ;in, Represents the Lagrange transform function. This indicates a subfunction that introduces the Lagrange function. Indicates the first output value. Indicates the compensation output value. and These represent the model parameters, Let Lagrange multiplier vectors be used. The factor is a quadratic penalty function; the step of solving the Lagrange transform function using the dual ascent method to determine the iterative formula for updating each of the model parameters includes: solving the Lagrange transform function using the sixth formula according to the dual ascent method to determine the iterative formula, wherein the sixth formula is: ;in, Representing model parameters respectively Iteration The results and model parameters obtained this time Iteration The result obtained this time and These represent the model parameters, Let Lagrange multiplier vectors be used. express Iteration The result obtained this time express Iteration The result obtained this time Indicates the first output value. This indicates the compensation output value.

6. The method according to claim 1, characterized in that, The step of solving the enhanced Lagrangian function using the dual ascent method to determine the iterative formula for updating each of the model parameters includes: solving the enhanced Lagrangian function using the eighth formula according to the dual ascent method to determine the iterative formula, wherein the eighth formula is: ;in, Representing model parameters respectively Iteration The results and model parameters obtained this time Iteration The result obtained this time and These represent the model parameters, Indicates the first output value. Indicates the compensation output value. express Iteration The result obtained this time express Iteration The result obtained this time It is a factor of the quadratic penalty function.

7. An accelerometer calibration system based on the ADMM algorithm, characterized in that, include: The model parameter acquisition module is used to acquire the zero bias error, scale factor error, non-orthogonal error, first output value, and compensation output value corresponding to the accelerometer, and to construct an error mathematical model based on the zero bias error, scale factor error, and non-orthogonal error, and to determine the various model parameters corresponding to the error mathematical model. The compensation output value is the value obtained after error correction of the first output value. The zero bias error represents the offset of the measured value relative to zero in the orthogonal coordinate system when the accelerometer is stationary. The scale factor error represents the error of the accelerometer scale on the x-axis, y-axis, and z-axis, respectively. The non-orthogonal error represents the installation error of the accelerometer on the x-axis, y-axis, and z-axis, respectively. The objective function module is used to obtain the objective function corresponding to the preset optimization parameter identification model. The optimization parameter identification model is used to optimize each model parameter, and the objective function represents the difference between the optimized model parameters and the unoptimized model parameters. The target parameter module is used to identify the target function corresponding to the model through the optimization parameters based on each of the model parameters, the first output value and the compensation output value, and to perform error optimization on each of the model parameters to obtain the target parameters corresponding to each of the model parameters. The calibration module is used to update the error mathematical model according to each of the target parameters to obtain a target error mathematical model, so that the accelerometer can be calibrated according to the target error mathematical model. The target parameter module is specifically used to: decompose the target function into multiple sub-functions corresponding to the model parameters according to each of the model parameters, the first output value, and the compensation output value; introduce a preset Lagrange function into the sub-function according to the sub-function, and augment the sub-function with the introduced Lagrange function to determine the Lagrange transform function; and solve the Lagrange transform function by the dual ascent method to determine the iterative formula for updating each of the model parameters. According to the iterative formula, each of the model parameters is iteratively updated to reduce the error, thereby obtaining the target parameter corresponding to each model parameter; it also includes: standardizing the Lagrange transform function using the ADMM algorithm, and processing the standardized function using a seventh formula to obtain the enhanced Lagrange function, wherein the seventh formula is: ;in, This represents the enhanced Lagrange function. express and The ratio, Indicates the first output value. Indicates the compensation output value. and These represent the model parameters, Let Lagrange multiplier vectors be used. The factor is a quadratic penalty function; the step of solving the Lagrange transform function by the dual ascent method to determine the iterative formula for updating each of the model parameters includes: solving the enhanced Lagrange function by the dual ascent method to determine the iterative formula for updating each of the model parameters.

8. An electronic device comprising a memory, a processor, and a program stored in the memory and running on the processor, characterized in that, When the processor executes the program, it implements the steps of an accelerometer calibration method based on the ADMM algorithm as described in any one of claims 1 to 6.

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