MEMS triaxial accelerometer calibration method based on simulated annealing particle swarm optimization algorithm

Abstract

The invention discloses an MEMS triaxial accelerometer calibration method based on a simulated annealing particle swarm optimization algorithm, and the method comprises the steps: employing a centrifugal machine to calibrate an MEMS triaxial accelerometer, and enabling the angular velocity generated by the centrifugal machine to serve as the specific force input of the MEMS triaxial accelerometer; applying a particle swarm optimization algorithm based on simulated annealing to a nonlinear model for solving to-be-calibrated parameters of the MEMS triaxial accelerometer, and identifying the corresponding parameters; in the calibration process, firstly, a scale factor and a zero offset value of the triaxial accelerometer are determined through a six-position tumbling method, a particle swarm iteration initial value is determined, and the convergence speed and the stability of the algorithm are improved. The slave shaft provided with the accelerometer is rotated by 180 degrees, so that the influence of system errors of the centrifugal machine on parameter identification is reduced. According to the method, the high-order coefficient of the MEMS triaxial accelerometer is effectively excited, the uncertainty of unknown parameters of the MEMS triaxial accelerometer is remarkably reduced, and the calibration precision is greatly improved.

Description

Technical Field

[0001] The invention belongs to the technical field of MEMS inertial device parameter calibration, and mainly relates to a MEMS three-axis accelerometer calibration method based on a simulated annealing particle swarm optimization algorithm. Background Art

[0002] The development of microelectromechanical systems (MEMS) technology has led to a trend toward miniaturized, high-performance, and affordable sensors. This development has led to the development of MEMS triaxial accelerometers, which are now widely used in inertial navigation, drones, military weaponry, and other fields. MEMS-based accelerometers are inexpensive, low-power, and compact. Their signal variations are also smaller than those of traditional accelerometers, making their accuracy highly susceptible to both their own systematic errors and external random errors.

[0003] MEMS triaxial accelerometers inherently exhibit a number of non-negligible systematic errors, including their own scale factor, axis-to-axis coupling (i.e., non-orthogonality error), bias error, and mounting errors between the package and the sensor. These errors can significantly deviate from the measured data, affecting final accuracy. Therefore, calibration of MEMS triaxial accelerometers is an important research area in micro-inertial sensors.

[0004] While there's no unified method for calibrating MEMS triaxial accelerometers, methods generally fall into two categories. One involves simultaneous calibration of all three axes within the acceleration vector domain using a three-axis rate turntable. Based on the modular calibration principle proposed by Lotters, the sum of the three-axis acceleration vectors is always equal to the local gravity vector, regardless of the accelerometer's orientation within a gravitational field. Multi-position calibration methods, such as six-, twelve-, and twenty-four-position calibration methods, are designed to statically measure the triaxial acceleration output at these orientations, thereby calculating the triaxial accelerometer's zero bias, scale factor, and first-order coupling coefficient. The other type involves automated on-site calibration, which requires no sophisticated equipment or a controlled environment. Using a simple handheld accelerometer measurement platform or motion capture system rigidly connected to the accelerometer to be calibrated, the angular position of the MEMS triaxial accelerometer is captured by varying its orientation. Calibration is then performed by iteratively solving nonlinear equations. However, with the maturity of MEMS three-axis accelerometer technology and the expansion of application scenarios, the accuracy and performance of MEMS three-axis accelerometer signals need to be further improved. Summary of the Invention

[0005] The present invention addresses the need to further improve the accuracy and performance of MEMS triaxial accelerometer signals in the prior art. It provides a MEMS triaxial accelerometer calibration method based on a simulated annealing particle swarm optimization algorithm. The method uses a centrifuge to calibrate the MEMS triaxial accelerometer, using the angular velocity generated by the centrifuge as the specific force input for the MEMS triaxial accelerometer. The simulated annealing particle swarm optimization algorithm is applied to a nonlinear model for solving the parameters to be calibrated for the MEMS triaxial accelerometer, identifying the corresponding parameters. During the calibration process, the accelerometer zero bias and scale factor credible intervals are determined using a six-position tumbling method. Centrifuge error is reduced by rotating the slave axis on which the accelerometer is mounted 180 degrees. This method effectively excites the high-order coefficients of the MEMS triaxial accelerometer, significantly reducing the uncertainty of the unknown parameters and greatly improving calibration accuracy.

[0006] In order to achieve the above object, the technical solution adopted by the present invention is: a MEMS three-axis accelerometer calibration method based on simulated annealing particle swarm optimization algorithm, comprising at least the following steps:

[0007] S1: Determine the sources of systematic errors of the MEMS triaxial accelerometer and establish an input-output model of the MEMS triaxial accelerometer based on all errors; the systematic errors include at least zero bias error, scale factor error, cross-coupling error, and installation error. The input-output model is specifically:

[0008]

[0009] Among them, [A x A y A z ] is the output measurement signal, pa x a y a z ] is the acceleration input, S ij (i≠j=x,y,z) is the cross-coupling term, S i (i=x,y,z) is the scale factor term, S ii (i=x,y,z) is the second-order error term, [θ x θ y θ z ] is the installation error angle, [b x0 b y0 b z0 ] is the zero bias error term, [e x e y e z ] is a random error;

[0010] S2: Using the six-position tumbling method, place the MEMS triaxial accelerometer at ±1g positions along the x-axis, ±1g along the y-axis, and ±1g along the z-axis. After the accelerometer stabilizes, collect data and process the data to obtain the scale factors and initial bias intervals along the three axes.

[0011] S3: Install the MEMS triaxial accelerometer on the centrifuge. The MEMS triaxial accelerometer is fixed on the slave axis workbench. The centrifuge table rotates at a given angular velocity. When the centrifuge is stable, the triaxial signals of the MEMS triaxial accelerometer are collected. After the collection is completed, the slave axis workbench is rotated 180 degrees around the centrifuge slave axis. The centrifuge table still rotates at the given angular velocity. When the centrifuge is stable, the triaxial signals of the MEMS triaxial accelerometer are collected again.

[0012] S4: Based on simulated annealing, the particle swarm optimization algorithm is applied to the nonlinear model of the MEMS triaxial accelerometer to be calibrated. The parameters to be identified are mapped to particle dimensions. The number of experimental samples represents the total number of particles. The particle swarm algorithm is used to update the velocity and position of the particles. The simulated annealing mechanism is introduced to probabilistically accept the position of the inferior solution of the particle. When the particle falls into the local optimal area, the particle moves out of the local extreme area and continues to search for a better solution in the entire space. The iterative search continues until the particle finally converges to the global optimal solution. At this time, the optimal solution position of the particle is the optimal value of the parameter to be calibrated of the MEMS triaxial accelerometer.

[0013] As an improvement of the present invention, after the acquisition in step S2, the triaxial scale factor and zero bias initial value of the MEMS triaxial accelerometer are specifically:

[0014]

[0015] Among them, K i (i=X,Y,Z) represents the initial value of the scale factor of each axis, b i (i=X,Y,Z) represents the initial value of zero bias of each axis, [A 1gi A -1gi ](i=X,Y,Z) represents the collected value of each axis at the ±1g position.

[0016] As an improvement of the present invention, after the two acquisitions in step S3, the three-axis signal output of the MEMS three-axis accelerometer is specifically:

[0017] The results of the two acquisitions on the x-axis are processed as follows:

[0018]

[0019] The results of the two acquisitions on the y-axis are processed as follows:

[0020]

[0021] The results of the two z-axis experiments were processed as follows:

[0022]

[0023] in, (i=X,Y,Z) is the processed measurement data of each axis, [a x 'a' y a z ′] is the first measurement data of each axis, [a x ″a′ y 'a z ″] is the second measurement data of each axis.

[0024] As another improvement of the present invention, step S4 specifically includes the following steps:

[0025] S41: For the identification error model: A a =K a U a +b a +e,K a is the total transformation matrix, A a is the measured value, U a is the ideal input value, b a is zero bias, e is random noise; parameter set (K a ,b a ), the error model parameter set includes at least a scale factor, a zero offset, and a cross-coupling coefficient; and constructing an objective function according to the principle of model calibration: Where N is the number of locations where experimental observations were collected;

[0026] S42: Initialize the parameters of the simulated annealing particle swarm optimization algorithm, where the scale factor and zero bias terms in the particle position are initialized to K in step S2. i (i=X,Y,Z) and b i (i=X,Y,Z), the particle velocity is initialized to 10%-20% of the parameter range, and the inertia weight ω is adaptively changed:

[0027]

[0028] Where ω m is the maximum value of inertia weight, t m is the set maximum iteration value, α is the weight change speed coefficient;

[0029] S43: Perform iterative optimization steps, dynamically adjust the inertia weight ω according to the number of iterations, learn factors c1 and c2, update the particle speed and position according to the particle swarm, and calculate the fitness value of the new position:

[0030]

[0031] Perform annealing operation:

[0032]

[0033] In the formula represents the fitness value of the particle’s new position, Represents the global optimal fitness value;

[0034] When the fitness value is lower than the global fitness value, the new solution is better and is accepted; when the fitness value is higher than the global fitness value, the new solution is worse and is rejected with a certain probability. Accepting new interpretations does not mean discarding them outright;

[0035] S44: After the particle update is completed, the global optimal value is updated based on the latest particle group position and posture. The temperature T is calculated according to T t+1 =μT t Attenuation, set the fitness function target accuracy range and the number of iterations as the convergence criterion. When the convergence criterion is met, the algorithm is terminated and the output parameters are the MEMS triaxial accelerometer parameters to be identified (K a ,b a ).

[0036] As another improvement of the present invention, in the parameter initialization of the simulated annealing particle swarm optimization algorithm, the number of particles N is given according to the experimental data, and the initial temperature T is set to T0 = 100E initial (K), the annealing coefficient μ is set to 0.9-0.99, and the learning factors c1 and c2 are adaptively adjusted according to the number of iterations. In the early stage of the algorithm, c1>c2, focusing on individual search, and in the later stage of the algorithm, c1<c2, focusing on group collaboration:

[0037]

[0038] Where c 1,max and c 2,max is the maximum value of the learning factor, c 1,min and c 2,min is the minimum value of the learning factor, t m The maximum number of iterations is set.

[0039] As a further improvement of the present invention, in the iterative optimization of step S43, the particle swarm formula is specifically:

[0040]

[0041] Among them, at the tth iteration, the velocity and position of the i-th particle are and During the iteration process, the best position searched by the i-th particle is is the average of the optimal values ​​of all individual particles, and the best position searched by the group during the iteration process is the global optimal.

[0042] Compared with the prior art, the present invention has the following beneficial effects:

[0043] (1) Based on the characteristic that the centrifuge experimental platform can excite high-order parameters, the present invention constructs a high-order input-output model, and taking into account the system error of the centrifuge, designs a scheme that can significantly reduce the system error, overcomes the influence of the static working radius error and installation misalignment angle error of the centrifuge on the experimental data; at the same time, the initial values ​​of some parameters are determined by the six-position tumbling method, ensuring the accuracy of parameter identification while narrowing the search space, improving the convergence speed, and enhancing the stability of the particle swarm optimization algorithm based on simulated annealing.

[0044] (2) The particle swarm optimization algorithm based on simulated annealing proposed in this paper improves its ability to find the global optimal solution while ensuring convergence speed and iteration accuracy, overcoming the problem of premature convergence of traditional particle swarm optimization algorithms. It also improves the calibration accuracy of MEMS triaxial accelerometers. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 A flowchart of the calibration method of the present invention;

[0046] Figure 2 Schematic diagram of the directions of the input axes of the three-axis experiment of the present invention;

[0047] Figure 3 This is a block diagram of a particle swarm algorithm based on simulated annealing in step S4 of the method of the present invention;

[0048] Figure 4 It is a convergence curve diagram without initial value based on simulated annealing particle swarm optimization algorithm of the present invention;

[0049] Figure 5 This is a convergence curve diagram with initial values ​​based on the simulated annealing particle swarm optimization algorithm of the present invention. DETAILED DESCRIPTION

[0050] The present invention will be further described below with reference to the accompanying drawings and specific embodiments. It should be understood that the following specific embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention.

[0051] Example 1

[0052] A centrifuge calibration method for a MEMS triaxial accelerometer based on a simulated annealing particle swarm optimization algorithm was developed. Considering the systematic errors of the MEMS triaxial accelerometer and the experimental characteristics of the centrifuge, a high-order input-output nonlinear model of the MEMS triaxial accelerometer was established. Data was collected at ±1g on each axis of the MEMS triaxial accelerometer using the six-position tumbling method to determine the confidence intervals for the scale factor and zero bias of each axis. Calibration experiments were then conducted using the angular velocity generated by the centrifuge as the specific force input of the MEMS triaxial accelerometer. However, the systematic errors of the centrifuge can significantly interfere with the calibration experiment. Therefore, the present invention designed an experimental method to reduce the systematic errors of the centrifuge by rotating the slave axis on which the accelerometer is mounted 180 degrees to offset the static working radius error and misalignment angle error. To address the particle swarm algorithm's tendency to fall into local optima, an annealing algorithm was introduced, allowing the particle swarm algorithm to accept solutions with poor fitness with a certain probability, thereby converging to the global optimum with probability 1.

[0053] The present invention applies the simulated annealing particle swarm optimization algorithm to solve the nonlinear model of the MEMS three-axis accelerometer to be calibrated parameters and identifies the corresponding parameters. Figure 1 As shown, the specific steps include:

[0054] Step S1: The systematic error of the MEMS triaxial capacitive accelerometer is expressed by a mathematical model, the error model of the MEMS triaxial accelerometer is established, the unknown parameters that need to be calibrated and solved are determined, and finally the complete high-order input and output model of the MEMS triaxial accelerometer is confirmed.

[0055] The mathematical model of input and output includes the scale factor S i (i=x,y,z), zero offset [b x0 b y0 b z0 ], cross-coupling coefficient S ij (i≠j=x,y,z), installation error coefficient [θ x θ y θ z ], second-order nonlinear coefficient S ii (i=x,y,z), random error [e x e y e z ].

[0056] Combined with the subsequent centrifuge calibration experimental platform, it is determined that the input of the acceleration signal is a second-order signal, and the input-output model is expressed as:

[0057]

[0058] Among the above model parameters, [A x A y Az ] is the output measurement signal, [a x a y a z ] is the acceleration input, S ij (i≠j=x,y,z) is the cross-coupling term, S i (i=x,y,z) is the scale factor term, S ii (i=x,y,z) is the second-order error term, [θ x θ y θ z ] is the installation error angle, [b x0 b y0 b z0 ] is the zero bias error term, [e x e y e z ] is a random error, and the error model is expressed as a matrix:

[0059] A a =K a U a +b a +e

[0060] Where K a is the total transformation matrix, A a is the measured value, U a is the ideal input value, b a is zero bias, and e is random noise.

[0061] Step S2: Place the MEMS triaxial accelerometer at the x-axis, y-axis, and z-axis positions, respectively, at ±1g. According to the ideal model with no coupling between the axes:

[0062]

[0063] The data collected at ±1g on each axis is:

[0064] and

[0065] Among them, K i (i=X,Y,Z) represents the initial value of the scale factor of each axis, b i (i=X,Y,Z) represents the initial value of zero bias of each axis, a i (i=X,Y,Z) represents the ideal acceleration input value, A i (i=X,Y,Z) represents the actual data collection value. 1gi A -1gi](i=X,Y,Z) represents the collected value of each axis at ±1g position. When the accelerometer is stable, the collected data is processed as follows:

[0066]

[0067] The scale factors and zero bias initial value intervals of the three axes are obtained through processing.

[0068] Step S3: Install the MEMS triaxial accelerometer on the centrifuge slave axis workbench, generate centripetal acceleration input by setting the angular velocity, and rotate the accelerometer 180° around the slave axis for a second experiment after a single centrifugal experiment. After collecting the two experimental data, eliminate the centrifuge static working radius error and installation misalignment angle error.

[0069] The centrifuge's own systematic errors, which cannot be ignored, come from the static working radius and the installation misalignment angle of the three axes, which will cause great interference to the calibration experiment.

[0070] Let the static working radius be R, the static radius error be ΔR, and the misalignment angle errors of the three axes of the fixture installation be [θ I θ O θ P ], the angular velocity of the centrifuge is ω, and taking the x-axis as the centripetal acceleration input as an example, the ideal acceleration input of the three axes at this time is:

[0071]

[0072] Taking the error into account, the actual working input is:

[0073]

[0074] It can be seen that the specific force input of each axis is mixed with some errors. Although the magnitude is small, under high g input, the small magnitude errors will also stimulate non-negligible interference input terms. Consider rotating the MEMS triaxial accelerometer around the slave axis workbench to the back. That is, after a single centrifugal experiment is completed, the accelerometer's posture is rotated 180° around the axis of the slave axis workbench. The centrifuge's operating angular velocity remains ω. At this time, the static operating radius changes from R + ΔR to R - ΔR. The working input is now:

[0075]

[0076] Process the three-axis acceleration ratio force input before and after attitude rotation:

[0077]

[0078] The simplified MEMS three-axis accelerometer input is:

[0079]

[0080] Considering θ i and ΔR are both small, cosθ i ≈1, sinθ i ≈θ i , the product of small quantities is a higher order small quantity and is ignored, that is, ΔR·sinθ P ≈0,ΔR·sinθ O ≈0,sinθ I sinθ P ≈0, then

[0081]

[0082] At this time, the single-axis acceleration input to each axis can be regarded as eliminating the static working radius error and misalignment angle error of the centrifuge.

[0083] Therefore, a MEMS triaxial accelerometer was mounted on the centrifuge's slave table. The x-axis signal was first used as the centripetal acceleration specific force input. The centrifuge motor was then operated at a given angular velocity ω (the centripetal acceleration input must be at least greater than g). Once the centrifuge stabilized, data acquisition of the triaxial output signals began. After data acquisition was complete, the slave table was rotated 180° around the centrifuge's slave axis. The negative x-axis signal was used as the centripetal acceleration specific force input. The centrifuge motor was then operated at the given angular velocity ω. Data acquisition resumed after stabilization. This process was repeated for the y- and z-axis centrifugal acceleration signals to obtain the corresponding experimental data. Figure 2 Schematic diagram of the orientation of the input shaft and other axes in this embodiment, from left to right, the x, y, and z axes are the positive installation orientations of the input shaft.

[0084] For the two experiments on the x-axis, the experimental results are processed as follows:

[0085]

[0086] For the two experiments on the y-axis, the experimental results are processed as follows:

[0087]

[0088] For the two experiments on the z-axis, the experimental results are processed as follows:

[0089]

[0090] Any acceleration input processing of each axis has a corresponding acceleration output processing.

[0091] Step S4: Globally optimize the experimental data based on the simulated annealing particle swarm optimization algorithm (SAPSO), and solve the error model parameters by dynamically adjusting the inertia weight, learning factor, and annealing temperature. Specifically, the following steps are performed: mapping the parameters to be identified into the particle dimension vector in the particle swarm; mapping the number of samples into the total number of particles; constructing a fitness function as the optimization objective to minimize the residual sum of squares between the measured value and the model prediction value; combining the velocity update formula of the particle swarm algorithm and the probability acceptance mechanism of simulated annealing to iteratively update the particle position until the convergence criterion is met; and outputting the global optimal solution as the calibration parameter of the MEMS triaxial accelerometer.

[0092] The particle swarm optimization (PSO) is a swarm-based stochastic optimization algorithm. It treats each individual as a massless and volumeless particle in the search space, assigning each particle a certain velocity. It then adjusts its state based on the current optimal position and the optimal position of the entire swarm, gradually moving toward the optimal region. Its main steps include initializing the swarm, updating the individual and global optimal positions, updating particle velocities and positions, determining convergence conditions, and returning to iteration. However, it suffers from the disadvantages of being prone to getting stuck in local minima, premature convergence, and insufficient optimization accuracy. The simulated annealing (SA) algorithm, derived from the thermodynamic process of solid cooling, is the process by which the energy of an object reaches its minimum value as the temperature decreases. Based on the Metropolis criterion, it accepts not only the optimal solution but also less favorable solutions with the probability of temperature variation during the temperature drop. This facilitates the search for the global optimal solution and prevents getting stuck in local optimal solutions. However, excessive data volumes and high initial temperatures can lead to slow convergence.

[0093] Combining the advantages of the above two types of algorithms: the particle swarm algorithm has a fast iteration speed, a relatively simple structure and easy parameter adjustment; the simulated annealing algorithm has a higher search accuracy and is easier to converge to the global optimal solution. The present invention adopts a method for solving the optimal solution of nonlinear equations based on the simulated annealing particle swarm (SA-PSO) algorithm, mapping the parameters to be identified into the particle dimensions in space, and the number of experimental samples represents the total number of particles. The particle swarm algorithm is then used to update the velocity and position of the particles, and a simulated annealing mechanism is introduced. The position of the inferior solution of the particle is probabilistically accepted. When the particle falls into the local optimal area, the particle is adjusted out of the local extreme value area and can continue to search for a better solution in the entire space. As the number of iterations increases, the particle finally converges to the global optimal solution. The optimal solution position of the particle is the optimal value of the parameter to be calibrated of the MEMS three-axis accelerometer.

[0094] The above experimental data were processed using the particle swarm optimization algorithm based on simulated annealing for parameter identification. In the D-dimensional space, the total number of particles is N. At the t-th iteration, the velocity and position of the i-th particle are and During the iteration process, the best position searched by the i-th particle is It is called individual optimality. The best position searched by the group during the iteration process It is called the global optimum. In the next iteration, the speed and position of the particle at the next moment in the search space are determined by the particle itself and the group experience and the inertia weight ω. In order to reduce the probability of particles falling into the local optimum, the average value of the individual optimal values ​​of all particles is taken as Instead of the individual optimal value of a single particle, the improved particle swarm optimization iterative update formula is:

[0095]

[0096] The specific practical steps of this step are as follows Figure 3 As shown:

[0097] First, determine the identification error model parameter set (K a ,b a ), which includes the scale factor, zero offset, first-order inter-axis coupling coefficient, second-order nonlinear coefficient, and second-order nonlinear coupling coefficient of the MEMS triaxial accelerometer. The fitness function is constructed based on the principle of modular calibration: Where N is the number of positions collected by experimental observation. When the fitness function reaches the minimum value, that is, the optimal value, the parameters obtained are the parameters to be calibrated for the accelerometer. The position vector of each particle corresponds to (K a ,b a ), and define the parameter range for each parameter according to the corresponding physical meaning.

[0098] Then, the SA-PSO algorithm parameters are initialized: the number of particles N is given according to the experimental data, and the learning factors c1 and c2 are adaptively adjusted according to the number of iterations. In the early stage of the algorithm, c1>c2 is designed to focus on individual search; in the later stage of the algorithm, c1<c2 is designed to focus on group collaboration.

[0099]

[0100] Where c 1,max and c 2,max is the maximum value of the learning factor, c 1,min and c 2,min is the minimum value of the learning factor, t m The maximum number of iterations is set.

[0101] The initial temperature T can be set according to the initial fitness, set as T0 = 100E initial (K), annealing coefficient μ is generally

[0102] Set to 0.9 to 0.99, the larger the annealing coefficient, the stronger the algorithm's global search capability, but the slower the convergence speed, and vice versa. The inertia weight determines the degree to which each particle retains its own motion state in each iteration during the velocity update, and its value is adaptively changed:

[0103]

[0104] Where ω m is the maximum value of inertia weight, t m is the maximum value of the set iteration, and α is the weight change rate coefficient. The scale factor and zero bias in the particle's initial dimension are given by the initial value interval, and subsequent iterations must not exceed this interval, otherwise the iteration will terminate immediately. The remaining identification parameters are randomized to ensure coverage of the global solution space. The particle velocity is also initialized to approximately 10%-20% of the parameter range to prevent premature convergence.

[0105] Then, the iterative optimization step is performed, and the inertia weight ω and learning factors c1 and c2 are dynamically adjusted according to the number of iterations. Then, the particle speed and position are updated according to the particle swarm formula, and the fitness value of the new position is calculated:

[0106]

[0107] Perform annealing operation:

[0108]

[0109] In the formula represents the fitness value of the particle’s new position, Represents the global optimal fitness value. When the fitness value is lower than the global fitness value, the new solution is better and is accepted. When the fitness value is higher than the global fitness value, the new solution is worse and is accepted with probability. Accept the new solution and do not discard it directly. After the particle update is completed, the global optimal value is updated based on the latest particle group position and posture. The temperature T is calculated according to T t+1 =μT t Attenuation, the algorithm termination condition is set by giving the final convergence criterion: the standard deviation of the parameter change reaches the required accuracy requirement and the set maximum number of iterations.

[0110] Figure 4 The objective function E(K) is obtained by establishing the SA-PSO algorithm with the x-axis as the input direction. t Convergence diagram, the experimental data after processing in step S3 corresponds to the particle swarm sample, the initial value is random, and the SA-PSO algorithm is iterated in step S4. The termination conditions are set as follows: the number of iterations is 200, and the standard deviation of each parameter change is less than 10 -2From the figure, we can see that although the algorithm has fallen into a local optimal solution during the iteration, the existence of the annealing mechanism makes the objective function jump out of the local optimal solution and continue to search for the global optimal solution. It can be seen that the fitness function converges to 10 after about 120 iterations. -3 . Figure 5 The objective function E(K) obtained by establishing the SA-PSO algorithm with the x-axis as the input direction is t Convergence diagram, the scale factor and zero bias initial value interval after step S2 correspond to the initial values ​​of the corresponding dimensions of the particle swarm, and the initial values ​​of the remaining dimensions are random. The experimental data after step S3 corresponds to the particle swarm sample. The SA-PSO algorithm is iterated through step S4. The termination condition is the same as Figure 4 The conditions are consistent. It can be seen that the fitness function converges to 10 when the number of iterations under the initial value condition is about 40. -3 .

[0111] Figure 4 and Figure 5 By comparison, we can see that although the final objective function converges to roughly the same value, Figure 5 The convergence speed and stability under the conditions are significantly better than Figure 4 , improve the speed of the algorithm and avoid wasting resources in searching in unreasonable solution spaces. All parameters have converged to the target optimal value, and the algorithm model can be considered to be stable and the identification results are reliable. Stop the operation and output the parameters obtained, which are the parameters of the MEMS triaxial accelerometer to be identified (K a ,b a ), the generalization ability of the model can be verified by using test data that has not participated in the training, and the effect of parameter identification can be determined by calculating the residual RMS value.

[0112] It should be noted that the above content merely illustrates the technical idea of ​​the present invention and cannot be used to limit the scope of protection of the present invention. For ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention. These improvements and modifications all fall within the scope of protection of the claims of the present invention.

Claims

1. A MEMS triaxial accelerometer calibration method based on simulated annealing particle swarm optimization algorithm is characterized by: A MEMS triaxial accelerometer is calibrated using a centrifuge. The angular velocity generated by the centrifuge is used as the specific force input of the MEMS triaxial accelerometer. A simulated annealing particle swarm optimization algorithm is applied to solve a nonlinear model of the MEMS triaxial accelerometer parameters to be calibrated, and the corresponding parameters are identified. During the calibration process, the accelerometer zero bias and scale factor credible intervals are determined using a six-position tumbling method. The centrifuge error is reduced by rotating the slave axis on which the accelerometer is mounted 180 degrees.

2. The MEMS triaxial accelerometer calibration method based on simulated annealing particle swarm optimization algorithm according to claim 1, characterized in that: At least the following steps are included: S1: Determine the sources of systematic errors of the MEMS triaxial accelerometer and establish an input-output model of the MEMS triaxial accelerometer based on all errors; the systematic errors include at least zero bias error, scale factor error, cross-coupling error, and installation error. The input-output model is specifically: Among them, [A x A y A z ] is the output measurement signal, [a x a y a z ] is the acceleration input, S ij (i≠j=x,y,z) is the cross-coupling term, S i (i=x,y,z) is the scale factor term, S ii (i=x,y,z) is the second-order error term, [θ x θ y θ z ] is the installation error angle, [b x0 b y0 b z0 ] is the zero bias error term, [e x e y e z ] is a random error; S2: Using the six-position tumbling method, place the MEMS triaxial accelerometer at ±1g positions along the x-axis, ±1g along the y-axis, and ±1g along the z-axis. After the accelerometer stabilizes, collect data to obtain the scale factors and initial bias intervals along the three axes. S3: Install the MEMS triaxial accelerometer on the centrifuge. The MEMS triaxial accelerometer is fixed on the slave axis workbench. The centrifuge table rotates at a given angular velocity. When the centrifuge is stable, the triaxial signals of the MEMS triaxial accelerometer are collected. After the collection is completed, the slave axis workbench is rotated 180 degrees around the centrifuge slave axis. The centrifuge table still rotates at the given angular velocity. When the centrifuge is stable, the triaxial signals of the MEMS triaxial accelerometer are collected again. S4: Based on simulated annealing, the particle swarm optimization algorithm is applied to the nonlinear model of the MEMS triaxial accelerometer to be calibrated. The parameters to be identified are mapped to particle dimensions. The number of experimental samples represents the total number of particles. The particle swarm algorithm is used to update the velocity and position of the particles. The simulated annealing mechanism is introduced to probabilistically accept the position of the inferior solution of the particle. When the particle falls into the local optimal area, the particle jumps out of the local extreme area and continues to search for a better solution in the entire space. The iterative search continues until the particle finally converges to the global optimal solution. At this time, the optimal solution position of the particle is the optimal value of the parameter to be calibrated of the MEMS triaxial accelerometer.

3. The method for centrifuge calibration of a MEMS triaxial accelerometer based on simulated annealing particle swarm optimization algorithm according to claim 2, characterized in that: In step S2, the six-position tumbling method is applied to collect data after the accelerometer is stable. The three-axis signal output of the MEMS three-axis accelerometer is specifically: Among them, K i (i=X,Y,Z) represents the initial value of the scale factor of each axis, b i (i=X,Y,Z) represents the initial value of zero bias of each axis, [A 1gi A -1gi ](i=X,Y,Z) represents the collected value of each axis at the ±1g position.

4. The method for centrifuge calibration of a MEMS triaxial accelerometer based on simulated annealing particle swarm optimization algorithm according to claim 2, characterized in that: After the two acquisitions in step S3, the three-axis signal output of the MEMS three-axis accelerometer is specifically: The results of the two acquisitions on the x-axis are processed as follows: The results of the two acquisitions on the y-axis are processed as follows: The results of the two z-axis experiments were processed as follows: in, is the processed measurement data of each axis, [a x ′ a′ y a′ z ] is the first measurement data of each axis, [a″ x a″ y a″ z ] is the second measurement data of each axis.

5. The centrifuge calibration method for a MEMS triaxial accelerometer based on a simulated annealing particle swarm optimization algorithm according to claim 3, characterized in that: The step S4 specifically includes the following steps: S41: Determine a parameter set in an identification error model, wherein the identification error model is specifically: A a =K a U a +b a +e Among them, K a is the total transformation matrix, A a is the measured value, U a is the ideal input value, b a is zero bias, e is random noise; The error model parameter set includes at least a scale factor, a zero offset, a first-order cross-coupling coefficient, and a second-order cross-coupling coefficient; an objective function is constructed according to the principle of model calibration: Where N is the number of locations where experimental observations were collected; S42: Initialize the parameters of the simulated annealing particle swarm optimization algorithm, where the scale factor and zero bias terms in the particle position are initialized to K i (i=X,Y,Z) and b i (i=X,Y,Z), the particle velocity is initialized to 10%-20% of the parameter range, the learning factors c1 and c2 are adaptively adjusted according to the number of iterations; the inertia weight ω is adaptively changed: Where ω m is the maximum value of inertia weight, t m is the set maximum iteration value, α is the weight change speed coefficient; S43: Perform iterative optimization steps, dynamically adjust the inertia weight ω according to the number of iterations, learn factors c1 and c2, update the particle speed and position according to the particle swarm, and calculate the fitness value of the new position: Perform annealing operation: In the formula represents the fitness value of the particle’s new position, Represents the global optimal fitness value; When the fitness value is lower than the global fitness value, the new solution is better and is accepted; when the fitness value is higher than the global fitness value, the new solution is worse and is rejected with probability P. i t Accepting new interpretations does not mean discarding them outright; S44: After the particle update is completed, the global optimal value is updated based on the latest particle group position and posture. The temperature T is calculated according to T t+1 =μT t Attenuation, set the fitness function target accuracy range and the number of iterations as the convergence criterion. When the convergence criterion is met, the algorithm is terminated and the output parameters are the MEMS triaxial accelerometer parameters to be identified (K a ,b a ).

6. The method for calibrating a MEMS tri-axis accelerometer based on a simulated annealing particle swarm optimization algorithm according to claim 5, wherein: In the parameter initialization of the simulated annealing particle swarm optimization algorithm, the number of particles N is given according to the experimental data, and the initial temperature T is set to T0 = 100E. initial (K), the annealing coefficient μ is set to 0.9~0.99, and the learning factors c1 and c2 are adaptively adjusted according to the number of iterations. In the early stage of the algorithm, c1>c2, focusing on individual search, and in the later stage of the algorithm, c1<c2, focusing on group collaboration: Where c 1,max and c 2,max is the maximum value of the learning factor, c 1,min and c 2,min is the minimum value of the learning factor, t m The maximum number of iterations is set.

7. The method for calibrating a MEMS tri-axis accelerometer based on a simulated annealing particle swarm optimization algorithm according to claim 6, wherein: In the iterative optimization of step S43, the particle swarm formula is specifically: Among them, at the tth iteration, the velocity and position of the i-th particle are and During the iteration process, the best position searched by the i-th particle is is the average of the optimal values ​​of all individual particles, and the best position searched by the group during the iteration process is the global optimal.

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