A temperature compensation method, device, medium and equipment for complementary integrated LMD

Abstract

The application belongs to the technical field of inertial sensing and gyroscopes, and particularly relates to a temperature compensation method and device for a complementary integrated LMD, a medium and equipment. The method comprises: performing a static temperature cycle test on an inertial measurement unit to obtain temperature training signals and rate training signals in one or more dimensions; performing multi-order complementary integrated LMD decomposition on the rate training signals in each dimension, taking the decomposed output to-be-trained signals as temperature drift signals; training a GRU model using the temperature training signals and the temperature drift signals in each dimension to obtain a GRU temperature drift prediction model in each dimension; predicting a temperature actually measured by the inertial measurement unit using the GRU temperature drift prediction model in each dimension to obtain a predicted temperature drift signal, and using the predicted temperature drift signal to perform temperature compensation on a rate actually measured by the inertial measurement unit. The application can realize real-time and accurate temperature compensation for the IMU unit.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of inertial sensing, and in particular to a temperature compensation method and device for complementary integrated LMD, a medium and equipment. BACKGROUND

[0002] An inertial measurement unit (IMU) generally includes a gyroscope, an accelerometer, and a special interface circuit, and is an inertial sensor for measuring angular velocity and acceleration of a carrier. Since inertia is a basic characteristic of a mass body, the IMU can complete measurement without any external information and without radiating any energy to the outside world. The IMU is regarded as an absolutely secret navigation system due to its high concealment, non-interference, and complete autonomy, and has been widely applied in the fields of national economy and military systems.

[0003] With the progress of micro-electro-mechanical system (MEMS) technology, low-cost micro-electro-mechanical inertial devices have higher and higher precision. The micro-electro-mechanical IMU has gradually been popularized to many fields such as inertial navigation, consumer electronics, automatic control, and the like, due to its small size, light weight, low power consumption, easy integration, and low cost, and has been applied relatively maturely.

[0004] Due to the limitations of materials and manufacturing and packaging processes, the IMU is susceptible to environmental factors, among which the interference caused by temperature is persistent and difficult to avoid, which seriously limits the long-term precision and further application of the IMU. Therefore, it is of great significance to analyze the temperature drift of the IMU and to effectively calibrate and compensate the temperature drift. There are mainly two compensation schemes for the temperature drift of the IMU: one is to compensate the environment temperature from the hardware to make the IMU work at a constant temperature; and the other is to compensate the algorithm from the software, that is, to establish a temperature compensation model of the zero offset of the IMU changing with temperature. Compared with the hardware environment compensation, the software algorithm compensation does not need to build a complex working environment, but only needs to collect enough original data to establish a temperature compensation model for temperature compensation. Therefore, the software algorithm compensation is the development trend and mainstream technology of the IMU temperature compensation.

[0005] The temperature drift of the IMU and the change of the environmental temperature are not a complete corresponding relationship. When the environmental temperature changes, due to the heat exchange of the temperature measuring element and the delay of the indication process, the change of the temperature drift shows a clear hysteresis phenomenon. In the implementation of the software algorithm compensation, the traditional polynomial modeling temperature compensation method performs better in the fitting of a linear sequence. However, the characteristics of the internal elements of the IMU change with the environmental temperature, the variables and the order of the temperature drift model are difficult to determine, and the output signal of the IMU is usually non-stationary and nonlinear, so the fitting precision of the traditional temperature compensation model is greatly limited, and the hysteresis error is poor.

[0006] In view of the above-mentioned problems in the existing technology, there is an urgent need to propose a temperature compensation method for inertial measurement units (IMUs) that can suppress temperature drift and reduce full-temperature zero bias and zero bias stability. Summary of the Invention

[0007] The purpose of this invention is to provide a temperature compensation method, apparatus, medium and device for complementary integrated LMDs, so as to suppress temperature drift of inertial measurement units and reduce temperature deviation.

[0008] To achieve the above objectives, the present invention provides the following technical solution:

[0009] According to one aspect of the present invention, a complementary integrated LMD method is provided, comprising:

[0010] The signal to be decomposed is used as the initial residual signal. Multi-order LMD processing is performed on the initial residual signal to obtain the residual signal and product function for each order. The highest-order residual signal, plus the sum of the product functions of all orders, is selected as the signal to be trained. Each order of LMD processing includes the following steps:

[0011] Obtain m Gaussian white noises, perform LMD operation on each Gaussian white noise to obtain the corresponding noise product function and weight value; use the product of the noise product function and the weight value of each Gaussian white noise to generate a positive and negative complementary correction pair;

[0012] Obtain the previous residual signal, and correct the previous residual signal using the correction pair to generate 2m corrected previous residual signals;

[0013] The 2m corrected previous-order residual signals are subjected to single-order LMD decomposition to obtain the sub-product functions of the 2m corrected previous-order residual signals; the mean of the 2m sub-product functions is then processed to obtain the product function of the current order.

[0014] The residual signal of the current order is obtained by subtracting the product function of the previous order residual signal and the current order residual signal; where m is a positive integer greater than or equal to 2.

[0015] The step of correcting the previous residual signal using the correction pair includes: adding the previous residual signal to the product of the noise product function and the weight value of each Gaussian white noise; and subtracting the previous residual signal from the product of the noise product function and the weight value of each Gaussian white noise.

[0016] The step of averaging the 2m sub-product functions to obtain the product function of the current order includes: taking the average of the 2m sub-product functions, and using the average as the product function of the current order; or, taking the squared average of the 2m sub-product functions, and using the squared average as the product function of the current order.

[0017] According to another aspect of the present invention, a temperature compensation method based on the complementary integrated LMD method is provided, comprising the following steps:

[0018] A static temperature cycling test is performed on the inertial measurement unit (IMU) to obtain temperature training signals and rate training signals in one or more dimensions. Multi-order complementary integrated LMD decomposition is performed on the rate training signal in each dimension, and the decomposition output signal is used as the temperature drift signal. A GRU model is trained using the temperature training signal and temperature drift signal in each dimension to obtain a GRU temperature drift prediction model for each dimension. The measured temperature signal of the IMU is predicted using the GRU temperature drift prediction model for each dimension to obtain a predicted temperature drift signal. The predicted temperature drift signal is then used to perform temperature compensation on the measured rate signal of the IMU.

[0019] The one or more dimensions include any one or a combination of the x, y, and z axes of the inertial measurement unit; the inertial measurement unit includes a gyroscope and / or an accelerometer.

[0020] The process of training a GRU model using temperature training signals and temperature drift signals for each dimension to obtain a GRU temperature drift prediction model for each dimension includes the following steps:

[0021] Build a GRU model and initialize the nodes and weights of the GRU model;

[0022] Reconstruct the temperature training signal and temperature drift signal to generate a training dataset;

[0023] The training dataset is resampled into N training subsets, and each of the N training subsets is input into the GRU model for training, resulting in N trained GRU sub-models.

[0024] The N trained GRU sub-models are weighted and integrated using training weights, and the resulting GRU model is used as the GRU temperature drift prediction model.

[0025] The method of reconstructing the temperature training signal and temperature drift signal to generate a training dataset includes: reconstructing the temperature training signal and temperature drift signal according to different dimensions to generate a training dataset; or, reconstructing the temperature training signal, temperature difference training signal, and temperature drift signal according to different dimensions to generate a training dataset; wherein the temperature difference training signal is obtained by performing difference processing on the temperature training signal; or, reconstructing the temperature training signal, the rate training signal after Karl von Schönbrunn filtering, and the temperature drift signal according to different dimensions to generate a training dataset.

[0026] According to another aspect of the present invention, a temperature compensation device based on the complementary integrated LMD method is provided, comprising:

[0027] The training data acquisition unit is configured to perform a static temperature cycle test on the inertial measurement unit to obtain temperature training signals and rate training signals in one or more dimensions.

[0028] The LMD unit is configured to perform multi-order complementary integrated LMD decomposition on the rate training signal for each dimension, and use the decomposition output training signal as a temperature drift signal.

[0029] The GRU model training unit is configured to train the GRU model using temperature training signals and temperature drift signals for each dimension, thereby obtaining the GRU temperature drift prediction model for each dimension.

[0030] The measured data acquisition unit is configured to acquire measured temperature and measured velocity signals from the inertial measurement unit;

[0031] The GRU model unit is configured to use the GRU temperature drift prediction model for each dimension to predict the measured temperature signal of the inertial measurement unit and obtain the predicted temperature drift signal.

[0032] The temperature compensation unit is configured to perform temperature compensation on the measured rate signal of the inertial measurement unit using the predicted temperature drift signal.

[0033] According to another aspect of the present invention, a computer storage medium is provided, wherein instructions are stored therein, which, when executed, implement the complementary integrated LMD method and the temperature compensation method.

[0034] According to another aspect of the present invention, a computing device is provided, including a processor and a communication interface coupled to the processor; the processor is configured to run computer programs or instructions to implement the complementary integrated LMD method and the temperature compensation method.

[0035] Beneficial effects:

[0036] The temperature compensation method, apparatus, medium, and device of the complementary integrated LMD proposed in this invention have the following advantages compared with the prior art:

[0037] 1. The temperature compensation method described above adds complementary weighted Gaussian white noise product functions of the same order to each decomposition of ICELMDAN, which overcomes the shortcomings of LMD mode aliasing and poor decomposition completeness, and can better filter random noise and abnormal noise mixed in the original IMU rate signal.

[0038] 2. The temperature compensation method described above achieves higher prediction accuracy and better generalization performance than a single GRU model through resampling ensemble learning.

[0039] 3. Compared with the traditional polynomial modeling temperature compensation method, the temperature compensation method described above is more suitable for handling non-stationary and nonlinear IMU temperature drift signals, performs better in the face of hysteresis errors, and has higher fitting accuracy of the compensation model.

[0040] 4. The temperature compensation method described above can effectively suppress the temperature drift of the IMU output rate signal and significantly reduce its full-temperature zero bias and zero bias stability. Attached Figure Description

[0041] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this invention, illustrate exemplary embodiments of the invention and are used to explain the invention, but do not constitute an undue limitation of the invention. In the drawings:

[0042] Figure 1 This is a schematic diagram illustrating the principle of temperature compensation based on the complementary integrated LMD method.

[0043] Figure 2 This is a flowchart of the complementary integration LMD method;

[0044] Figure 3 This is a flowchart of temperature compensation based on the complementary integrated LMD method.

[0045] Figure 4 This is a flowchart of training a GRU model;

[0046] Figure 5 This is a schematic diagram of a temperature compensation device based on the complementary integrated LMD method.

[0047] Figure 6 This is a flowchart illustrating the adaptive noise-adding complementary integrated local mean decomposition process.

[0048] Figure 7 This is a flowchart illustrating an n-order LMD.

[0049] Figure 8 This is a schematic diagram of a single-layer GRU model;

[0050] Figure 9 This is a flowchart of the process of training and obtaining the ensemble GRU model;

[0051] Figure 10 This is a schematic diagram of the original rates of the gyroscope along the x, y, and z axes and the temperature compensation signals in the embodiment.

[0052] Figure 11 This is a schematic diagram of the original velocities and temperature compensation signals of the accelerometer along the x, y, and z axes in the embodiment.

[0053] Figure 12 This is a schematic diagram of the original rates of the gyroscope along the x, y, and z axes and the temperature compensation signals in the embodiment.

[0054] Figure 13 This is a schematic diagram of the original velocities and temperature compensation signals of the accelerometer along the x, y, and z axes in the embodiment.

[0055] Figure 14 This is a schematic diagram of the original rates of the gyroscope along the x, y, and z axes and the temperature compensation signals in the embodiment.

[0056] Figure 15 This is a schematic diagram of the original velocities and temperature compensation signals of the accelerometer along the x, y, and z axes in the embodiment.

[0057] Figure 16 This is a schematic diagram of the original rates of the gyroscope along the x, y, and z axes and the temperature compensation signals in the embodiment.

[0058] Figure 17 This is a schematic diagram of the original velocities and temperature compensation signals along the x, y, and z axes of the accelerometer.

[0059] Figure 18 This is a schematic diagram of the original speeds and temperature compensation signals of the gyroscope's x, y, and z axes;

[0060] Figure 19 This is a schematic diagram of the original velocities and temperature compensation signals along the x, y, and z axes of the accelerometer. Detailed Implementation

[0061] To facilitate a clear description of the technical solutions in the embodiments of the present invention, the terms "first" and "second" are used to distinguish identical or similar items with essentially the same function and effect. For example, the first threshold and the second threshold are merely used to distinguish different thresholds and do not limit their order. Those skilled in the art will understand that the terms "first" and "second" do not limit the quantity or execution order, and that the terms "first" and "second" are not necessarily different.

[0062] For ease of understanding, the temperature compensation method for the inertial measurement unit provided by this invention is illustrated below with specific examples. It should be understood that the following examples are for explanation only and are not intended to be limiting.

[0063] Local Mean Decomposition (LMD) is an adaptive time-frequency analysis method used to decompose complex multi-component amplitude-frequency modulated (AM / FM) signals. Compared to Empirical Mode Decomposition (EMD), LMD has advantages in addressing end-point effects and spurious components. It iteratively decomposes the signal into product functions and residual components, with each product function corresponding to a single-component modulated signal, thereby obtaining instantaneous frequency and amplitude information and enabling time-frequency distribution analysis of the signal. The LMD method includes steps such as finding local extrema, moving average processing, demodulation, and iteration, and is suitable for the analysis of non-stationary and nonlinear signals.

[0064] like Figure 1 As shown, the temperature compensation technology for the inertial measurement unit (IMU) is implemented through three parts: decomposition, modeling, and compensation. In the decomposition part, the rate training signal is decomposed using adaptive complementary local mean decomposition with noise (ICELMDAN), and the temperature drift signal is extracted after decomposition. In the modeling part, the GRU model is trained and validated using the temperature training signal and the temperature drift signal, and an integrated GRU temperature drift prediction model is established. In the compensation part, the integrated GRU temperature drift prediction model is used to predict the measured temperature signal of the inertial measurement unit to obtain the predicted temperature drift signal. The predicted temperature drift signal is then used to perform real-time temperature compensation on the measured rate signal of the inertial measurement unit to obtain the temperature-compensated rate signal.

[0065] In the decomposition part, the complementary ensemble LMD method is adopted, including: taking the signal to be decomposed as the initial residual signal, performing multi-order LMD processing on the initial residual signal to obtain the residual signal of each order; and selecting one of the multiple residual signals as the training signal.

[0066] like Figure 2 The diagram shows the LMD processing flowchart at each stage. Each stage of LMD processing includes the following steps:

[0067] Step S201: Obtain m Gaussian white noises, perform LMD analysis on each Gaussian white noise to obtain the corresponding noise product function, and obtain the weight value corresponding to each Gaussian white noise, where m is a positive integer;

[0068] Step S202: Duplicate m pairs of Gaussian white noise, and generate positive and negative complementary correction pairs by using the product of the noise product function and the weight value of each pair of Gaussian white noise;

[0069] Step S203: Obtain the previous residual signal, and correct the previous residual signal using the correction pair to generate 2m corrected previous residual signals;

[0070] The correction of the previous residual signal using the correction pair includes: adding the previous residual signal to the product of the noise product function and the weight value of each pair of Gaussian white noise; and subtracting the previous residual signal from the product of the noise product function and the weight value of each pair of Gaussian white noise.

[0071] Step S204: Perform single-order LMD decomposition on the 2m corrected first-order residual signals respectively to obtain the sub-product function of each corrected first-order residual signal;

[0072] Step S205: Perform mean ensemble processing on the 2m sub-product functions to obtain the product function of the current order; performing mean ensemble processing to obtain the product function of the current order includes: performing ensemble processing on the 2m sub-product functions by taking the average value, and using the average value as the product function of the current order; or, performing ensemble processing on the 2m sub-product functions by taking the square average value, and using the square average value as the product function of the current order.

[0073] Step S206: Summing the product function of the previous order residual signal and the current order residual signal yields the current order residual signal.

[0074] like Figure 3 As shown, a flowchart of the temperature compensation method based on the above complementary integrated LMD method is given, including the following steps:

[0075] Step S301: Perform a static temperature cycle test on the inertial measurement unit to obtain temperature training signals and rate training signals in one or more dimensions; wherein, the one or more dimensions include any one or a combination of multiple axes of the inertial measurement unit, namely the x, y, and z axes; the inertial measurement unit includes a gyroscope and / or an accelerometer.

[0076] Step S302: Perform multi-order complementary integrated LMD decomposition on the rate training signal of each dimension, and use the decomposition output training signal as the temperature drift signal.

[0077] Step S303: Train the GRU model using the temperature training signal and temperature drift signal for each dimension to obtain the GRU temperature drift prediction model for each dimension;

[0078] Step S304: Use the GRU temperature drift prediction model for each dimension to predict the measured temperature signal of the inertial measurement unit and obtain the predicted temperature drift signal.

[0079] Step S305: Use the predicted temperature drift signal to perform temperature compensation on the measured rate signal of the inertial measurement unit.

[0080] like Figure 4 As shown, in step S303 above, the GRU model is trained using the temperature training signal and temperature drift signal for each dimension to obtain the GRU temperature drift prediction model for each dimension, including the following steps:

[0081] Step S401: Construct the GRU model and initialize the nodes and weights of the GRU model;

[0082] Step S402: Reconstruct the temperature training signal and temperature drift signal to generate a training dataset; including: reconstructing the temperature training signal and temperature drift signal according to different dimensions to generate a training dataset; or, reconstructing the temperature training signal, temperature difference training signal, and temperature drift signal according to different dimensions to generate a training dataset; or, reconstructing the temperature training signal, the rate training signal after Karl von Schönbrunn filtering, and the temperature drift signal according to different dimensions to generate a training dataset.

[0083] Step S403: Resample the training dataset into N training subsets, and input the N training subsets into the GRU model for training to obtain N trained GRU sub-models;

[0084] Step S404: Integrate the N trained GRU sub-models by weighting the training weights to obtain the integrated GRU model.

[0085] like Figure 5 As shown, a schematic diagram of a temperature compensation device based on the above-described complementary integrated LMD method is presented, including:

[0086] The training data acquisition unit 501 is configured to perform a static temperature cycle test on the inertial measurement unit to obtain temperature training signals and rate training signals in one or more dimensions.

[0087] LMD decomposition unit 502 is configured to perform multi-order complementary integrated LMD decomposition on the rate training signal for each dimension, and use the decomposition output training signal as a temperature drift signal.

[0088] GRU model training unit 503 is configured to train the GRU model using temperature training signals and temperature drift signals for each dimension, so as to obtain the GRU temperature drift prediction model for each dimension.

[0089] The measured data acquisition unit 504 is configured to acquire measured temperature signals and measured velocity signals from the inertial measurement unit;

[0090] GRU model unit 505 is configured to use the GRU temperature drift prediction model for each dimension to predict the measured temperature signal of the inertial measurement unit and obtain the predicted temperature drift signal.

[0091] Temperature compensation unit 506 is configured to use the predicted temperature drift signal to perform temperature compensation on the measured rate signal of the inertial measurement unit.

[0092] A static temperature cycling test was performed on the inertial measurement unit (IMU) to obtain temperature and rate training signals in one or more dimensions. The experimental hardware for the static temperature cycling test included a temperature-controlled turntable, a microelectromechanical system (MEMS) IMU, evaluation circuitry, a computer, and a power supply. An oven was mounted on the temperature-controlled turntable, and the MEMS IMU was installed inside the oven via a fixture. The MEMS IMU was connected to the computer through the evaluation circuitry. The temperature rate of the oven was set to 0.5℃ / min, and the temperature cycling experiment was conducted within the range of -40℃ to 80℃.

[0093] The turntable speed is kept at 0, and the static temperature cycle output of the microelectromechanical unit (IMU) is acquired at a sampling frequency of 2Hz and recorded as training data. This data includes data from the inertial measurement unit (IMU) along the x, y, and z axes. The IMU can have 3, 6, or 9 dimensions. Taking 6 dimensions as an example, temperature training signals and velocity training signals are acquired along the gyroscope and accelerometer axes (x, y, z). In other words, 6-dimensional temperature training signals and 6-dimensional velocity training signals are obtained.

[0094] Next, multi-order local mean decomposition is performed on the rate training signal for each dimension. In each decomposition process, complementary weighted Gaussian white noise products of the same order are added. After the decomposition is completed, the highest-order residual signal is extracted as the temperature drift signal.

[0095] like Figure 6 As shown, a flowchart of adaptive noise-adding complementary ensemble local mean decomposition is presented.

[0096] An adaptive noise-added complementary ensemble local mean decomposition method (ICELMDAN, or "complementary ensemble LMD method") is adopted to perform local mean decomposition (LMD). ICELMDAN is an improved LMD algorithm that adds a complementary weighted Gaussian white noise product function of the same order to each decomposition operation to correct residual noise and overcome the shortcomings of local mean decomposition (LMD) such as mode mixing and poor decomposition completeness.

[0097] The Adaptive Noise-Complementary Integrated Local Means Decomposition (ICELMDAN) requires n-order decomposition. After decomposition, the highest-order (i.e., the nth-order) residual signal r is extracted. n(t) is the temperature drift signal, i.e., the residual signal plus the decomposed nth-order product function PF. i The sum of (t).

[0098] Taking n-order complementary ensemble LMD as an example, the steps include:

[0099] Step 601: The initial residual signal r0(t) is the input signal to be decomposed x(t), r0(t) = x(t);

[0100] For m Gaussian white noise w j (t) Perform i-th order LMD decomposition to obtain their i-th order noise product function L i [w j (t)];

[0101] Step 602: Calculate the weight β of the noise product function. i，j :

[0102]

[0103] Where, β i，j Let represent the weight of the i-th order noise product function of the i-th Gaussian white noise in the i-th order ICELMDAN decomposition;

[0104] ε is the set signal-to-noise ratio; L i [w j [(t)] is the i-th order noise product function of the j-th Gaussian white noise; r i-1 (t) represents the (i-1)th order residual signal, 1≤i≤n; std[] represents the standard deviation.

[0105] Step 603: Convert the (i-1)th order residual signal r i--1 (t) Duplicate m pairs, and insert a pair of complementary weighted i-th order noise product functions L into each pair. i [w j [(t)], that is, β is added to each pair respectively. i，j L i [w j [(t)] and -β i，j L i [w j (t)]; For example, when i = 1, we get r0(t) + β 1，j L1[w j (t)] and r0(t)-β 1，j L1[w j [(t)], 1≤j≤m.

[0106] Step 604: Perform single-order LMD decomposition on each of the 2m newly generated signals, resulting in 2m sub-product functions PF. i，k(t); for example, when i=1, we get PF. 1,k , 1≤k≤2m.

[0107] Step 605: Solve for the 2m sub-product functions PF i，k The mean of (t) is used to obtain the i-th order product function PF. i (t):

[0108]

[0109] For example, when i=1, we will get

[0110] Step 606: Use the (i-1)th order residual signal r i--1 (t) minus the i-th order product function PF i (t) Obtain the i-th order residual signal r i (t):

[0111] r i (t)=r i-1 (t)-PF i (t);

[0112] For example, when i=1, we get r1(t)=r0(t)-PF1.

[0113] Referring to steps 601 to 606 above, local mean decomposition based on the ICELMDAN algorithm can be achieved. When i = n, r n (t)=r n-1 (t)-PF n (t);

[0114] It needs further explanation that during the execution of the ICELMDAN algorithm, reducing the decomposition order *n* and the amount of Gaussian white noise *m* can reduce the complexity of the decomposition and the processing time. However, too low an order can lead to mode aliasing, and too little noise can reduce the completeness of the decomposition, making it difficult to filter out residual noise. Therefore, the specific decomposition order *n* and the specific amount of Gaussian white noise *m* should be selected based on an appropriate empirical value according to the actual signal processing results. For example, 3 ≤ *n* ≤ 100, 5 ≤ *m* ≤ 100.

[0115] As an example, we set the decomposition order n = 6, the amount of Gaussian white noise m = 10, and the signal-to-noise ratio ε = 5.

[0116] The LMD decomposition mentioned in steps 601 and 604 above is an adaptive decomposition method for analyzing non-stationary signals generated by nonlinear systems.

[0117] like Figure 7 The diagram shows the flowchart of an n-order LMD, including the following steps:

[0118] Step 701: Input the signal to be decomposed x(t), initialize the decomposition order i to 1, and the cycle order j to 1;

[0119] Step 702: Initialize the cyclic signal x′(t) as the signal to be decomposed x(t);

[0120] Step 703: Calculate the local extremum point n of the cyclic signal x′(t). k ;

[0121] Step 704: Based on the local extreme point n k Calculate the local mean point m k and local envelope point a k ;

[0122] As an example, the specific calculation method is as follows:

[0123]

[0124] Step 705: For the local mean point m k and local envelope point a k Perform moving averages separately to obtain the local mean m. i，j (t) and local envelope a i，j (t);

[0125] Step 706: Subtract the local mean m from the cyclic signal x′(t). i，j (t), then divided by the local envelope a i，j (t) yields the demodulated signal s i，j (t):

[0126]

[0127] Step 707: Determine the demodulated signal s i,j (t) Whether it is a pure frequency modulation signal: If s i,j If x′(t) is a pure frequency modulation signal, then proceed to step 708; otherwise, update the cyclic signal x′(t) to the demodulated signal s. i，j (t), then increment the cycle order j by 1, and jump to step 703 to recalculate the local extremum point n of the cyclic signal x′(t). k ;

[0128] As an example, the demodulated signal s is determined in the following way. i，j (t) Whether it is a pure frequency modulation signal: Calculate the demodulated signal s i，j The local envelope a of (t) i，j+1 (t), if a i，j+1 If (t)≡1, then the demodulated signal s i，j (t) is a pure frequency modulated signal.

[0129] Step 708: Calculate the i-th order product function PF i The residual signal r(t) is then updated, and the specific calculation method is as follows:

[0130] Demodulated signal s i，j Multiplying (t) by the j-th local envelope iterations of order i yields the i-th order product function PF. i :

[0131]

[0132] Subtract the i-th order product function PF from the signal to be decomposed x(t). i The updated residual signal r(t) is obtained as follows: r(t) = x(t) - PF i (t)

[0133] Step 709: Determine whether the decomposition order i is greater than or equal to the LMD order n. If yes, proceed to step 710; otherwise, update the signal to be decomposed x(t) to the residual signal r(t), increment the decomposition order i by 1, and proceed to step 702.

[0134] Step 710: End the nth-order LMD decomposition, and output the obtained residual signal r(t) and the total nth-order product function PF. i :

[0135]

[0136] Combination Figure 6 and Figure 7 As shown in the LMD decomposition process, the adaptive noise-added complementary ensemble local mean decomposition (ICELMDAN) requires n decomposition orders. After decomposition, the highest-order residual signal r is extracted. n (t) serves as the temperature drift signal, i.e., the rate training signal minus the decomposed nth-order product function PF. i The sum of (t):

[0137] r n (t)=r n-1 (t)-PF n (t)

[0138]

[0139] like Figure 8 As shown, a schematic diagram of the structure of a single-layer GRU model is presented.

[0140] The reset gate R of the single-layer GRU model is represented as:

[0141] R = f r (U r xt +W r h t-1 +b r )

[0142] The update gate Z of the single-layer GRU model is represented as:

[0143] Z = f z (U z x t +W z h t-1 +b z )

[0144] Where, x t y t h t These are the input vector, output vector, and state vector of the GRU model at time t, respectively.

[0145] U r W r b r f r (·) represents the input weights, cyclic weights, bias, and activation function of the reset gate R, respectively;

[0146] U z W z b z f z (·) represents the input weights, recurrent weights, bias, and activation function of the update gate Z, respectively;

[0147] f r (·) and fz(·) are usually Sigmoid functions.

[0148] After receiving the gating signal, the value of the candidate state H is calculated by resetting the gate R, and then selectively added to the current state h according to the update gate Z. t In order to achieve the functions of forgetting and selective memory.

[0149] H = f h [U h x t +W h (R⊙h t-1 )+b h ]; h t =Z⊙h t-1 +(1-Z)⊙H

[0150] Among them, U h W h b h f h (·) represent the input weights, recurrent weights, bias, and activation function of the candidate state H, respectively; f h(·) is usually the Tanh function; ⊙ is the Hadamard product.

[0151] The final output vector y of the GRU model t Represented as: y t =f y (Vh t +c)

[0152] Among them, V, c, f y (·) represent the output weights, biases, and activation functions, respectively, f y (·) is generally a Purelin transfer function.

[0153] After training, all network parameters of the GRU model are deterministic constants, including the input weights (U... r U z U h ), recurrent weights (W) r W z W h ), output weights (V) and biases (b) r b z b h c), then the current state h t and output vector y t This can be simplified as follows:

[0154]

[0155] in, This represents the state update function of the simplified GRU model; This represents the nonlinear transfer function obtained through the GRU model, i.e., from the input vector x. t To output vector y t Dynamic mapping.

[0156] like Figure 9 The flowchart shown is a process for training the ensemble GRU model.

[0157] Building a GRU temperature drift prediction model using temperature training signals and temperature drift signals includes the following steps:

[0158] Step 901: Construct a GRU model and initialize the nodes and weights of the GRU model; wherein the nodes include input layer nodes, hidden layer nodes and output layer nodes.

[0159] Step 902: Reconstruct the temperature training signal and temperature drift signal into an augmented dataset, and divide the augmented dataset into a training set and a validation set for training and validation of the integrated GRU model, respectively.

[0160] GRU model input vector x i and output vector y i The dimensions do not need to correspond; the training dataset X and Y can be reconstructed according to different dimensions based on the input signal. For example:

[0161] (1) Input temperature signal T t Predicting temperature drift signal d t Reconstruct and generate training datasets X and Y:

[0162]

[0163] Y = [y l y l+1 …y l+n ]=[d l d l+1 …d l+n ]

[0164] (2) Input temperature signal T t Temperature difference signal ΔT t Predicting temperature drift signal d t Reconstruct and generate training datasets X and Y:

[0165]

[0166] Y = [y l y l+1 …y l+n ]=[d l d l+1 …d l+n ]

[0167] (3) Input temperature signal T t The rate signal ω after Kalman filtering t Predicting temperature drift signal d t Reconstruct and generate training datasets X and Y:

[0168] Y = [y l y l+1 …y l+n ]=[d l d l+1 …d l+n ]

[0169] Where, x t Let y be the input vector of the GRU model at time t. t Let T be the output target of the GRU model at time t; t d t These are the temperature training signal and temperature drift signal at time t, respectively;

[0170] l is the memory step size, corresponding to the number of input layer nodes n in the GRU model. i =l, and the number of output layer nodes n o =1 indicates that in the GRU temperature drift prediction model, a temperature signal sequence (T) of length l is used. t-l+1 ,T t-l+2 ,…,T t-1 ,T t To predict the temperature drift signal d at the current time t. t .

[0171] Step 903: Resample the training set into N training subsets, and input each of the N training subsets into the GRU model for training, to obtain N trained GRU sub-models (GRU 1 to GRU N); the N GRU sub-models can be updated using a state update function. and nonlinear transfer function express.

[0172] As an example, the training set is resampled into N training subsets by Bootstrap sampling, which means drawing the same number of samples as the training set with replacement from the training set as a training subset.

[0173] Step 904: Combine the N trained GRU sub-models (GRU 1 to GRU N) by adjusting the training weights a. k b k Weighted ensemble yields the ensembled GRU model:

[0174]

[0175] in, and Represents the state update function and nonlinear transfer function of the ensemble GRU model; a k b k For the ensemble weights of the ensemble GRU model; and Let represent the state update function and nonlinear transfer function of the k-th GRU sub-model.

[0176] Step 905: Input the training set into the ensemble GRU model to train the ensemble weights a k b k The trained ensemble GRU model is obtained.

[0177] Step 906: Input the validation set into the trained ensemble GRU model to obtain the root mean square error (RMSE) of predictions on the validation set. Use the RMSE to evaluate the generalization performance of the ensemble GRU model and optimize the number of nodes in the GRU model accordingly. Specifically, continuously adjust the number of input layer nodes n of the GRU model. i and the number of hidden layer nodes n h The training and validation of the ensemble GRU model are repeated until the ensemble GRU model minimizes the RMSE of its predictions on the validation set.

[0178] Step 907: After training and validation, the temperature drift prediction model obtained from the ensemble GRU model can be represented as a state update function. and nonlinear transfer function

[0179] The predicted temperature drift signal is obtained by using an integrated GRU temperature drift prediction model and measured temperature signals, and real-time temperature compensation is performed on the measured rate signal. The initial temperature signal (T1, T2, ..., T...) is then used. l-2 ,T l-1 ) and the state vector h of the integrated GRU model l-1 Using nonlinear transfer functions and measured temperature signal T t Predict the temperature drift signal at the current time t (t≥l). Using state update function Update the state vector of the ensemble GRU model Where, x t =[T t-l+1 ;T t-l+2 ;…;T t-1 ;T t ] represents the input vector of the ensemble GRU model at time t (t≥l).

[0180] Using temperature drift signal d t Compensate for the measured output signal ω at the current time t (t≥l) t and output temperature compensation signal

[0181]

[0182] The GRU model is trained using temperature training signals and temperature drift signals for each dimension to obtain a GRU temperature drift prediction model for each dimension. The measured temperature signal of the inertial measurement unit is predicted using one or more GRU temperature drift prediction models to obtain a predicted temperature drift signal. The predicted temperature drift signal is then used to perform temperature compensation on the measured rate signal of the inertial measurement unit.

[0183] To verify the aforementioned temperature compensation method, specific experiments were conducted, demonstrating its effectiveness and superiority over existing technologies. The experimental hardware included a temperature-controlled turntable, a microelectromechanical system (MEMS) IMU, an evaluation circuit, a computer, and a power supply. An oven was mounted on the temperature-controlled turntable, and the MEMS IMU was installed inside the oven via a fixture. The MEMS IMU was connected to the computer through the evaluation circuit.

[0184] The temperature change rate of the temperature-controlled turntable oven was set to 0.5℃ / min, and a temperature cycling experiment was conducted within the range of -40℃ to 80℃. The turntable speed was kept at 0, and the static temperature cycle output of the microelectromechanical unit (MEMS) was acquired at a sampling frequency of 2Hz and recorded as training data, including the temperature data of the gyroscope's x, y, and z axes, as shown below. Figure 10 As shown in Figures 10A, 10B, and 10C, the temperature data of the accelerometer along the x, y, and z axes are as follows: Figure 11 As shown in 11A, 11B, and 11C, a total of 6-axis temperature training signals are obtained.

[0185] The angular velocity data of the gyroscope along the x, y, and z axes are as follows: Figure 12 As shown in Figures 12A, 12B, and 12C, the angular velocity data of the accelerometer along the x, y, and z axes are respectively as follows: Figure 13 As shown in 13A, 13B, and 13C, a total of 6-axis rate training signals are obtained.

[0186] After performing a 6th-order ICELMDAN decomposition on the rate training signal, the n=6th-order residual signal is taken as the temperature drift signal. For example... Figure 14 Figures 14A, 14B, and 14C show the rate training signals and temperature drift signals for the x, y, and z axes of the gyroscope, respectively. Figure 15 Figures 15A, 15B, and 15C show the rate training signals and temperature drift signals for the accelerometer along the x, y, and z axes, respectively. In the above figures involving the accelerometer, the accelerometer is simplified as "accelerometer".

[0187] Furthermore, a GRU model can be constructed, and the number of nodes, weights, and biases of the GRU model can be initialized. The temperature training signal and temperature drift signal are reconstructed according to the aforementioned format and divided into two parts: a training set and a validation set (n...). 训练集 :n 验证集 =3:1). The training set is resampled into 10 training subsets, and 10 GRU sub-models are trained using the 10 training subsets. The 10 trained GRU sub-models are then weighted and ensembled to obtain the ensemble GRU model.

[0188] The ensemble GRU model was trained and validated using training and validation sets. After multiple adjustments and evaluations, the number of nodes in the input, hidden, and output layers of the GRU model was determined to be n. i =1, n h =10, n o =1, thus obtaining the state update function of the integrated GRU temperature drift prediction model. and nonlinear transfer function

[0189] Using training data from the IMU's static temperature cycle output, six integrated GRU temperature drift prediction models were established, comprising six axes: gyroscope (x, y, z axes) and accelerometer (x, y, z axes). Temperature compensation simulations were then performed on a computer using these six models and the IMU's training data. The compensation results are shown below. Figure 16 Figures 16A, 16B, and 16C show the original rate signals and temperature-compensated signals for the x, y, and z axes of the gyroscope, respectively. Figure 17 Figures 17A, 17B, and 17C show the original velocity signals and temperature-compensated signals for the x, y, and z axes of the accelerometer, respectively.

[0190] To verify the effectiveness of the proposed temperature compensation method, these six models were programmed and written into the IMU prototype according to the compensation methods of equations (8)-(10) to achieve real-time temperature compensation of the IMU rate signal. The same static temperature cycling experiment was then performed again on the IMU prototype with the proposed temperature compensation algorithm, and the measured temperature compensation signal output by the IMU prototype was collected, such as... Figure 18 Figures 18A, 18B, and 18C show the original rate signals and temperature-compensated signals for the x, y, and z axes of the gyroscope, respectively. Figure 19 Figures 19A, 19B, and 19C show the original velocity signals and temperature-compensated signals for the x, y, and z axes of the accelerometer, respectively. It can be seen that the proposed temperature compensation method effectively suppresses the temperature drift of the IMU velocity signal.

[0191] To further verify the effectiveness and adaptability of the proposed temperature compensation method, the proposed method and the traditional polynomial temperature compensation method were simultaneously applied to three IMU prototypes. The same static temperature cycling experiment was conducted on each of the three IMUs, and the temperature compensation signals from both methods were collected and compared with the original rate signals. Tables 1, 2, and 3 compare the original rate signals, the traditionally compensated signals, and the proposedly compensated signals from the three IMU prototypes during the static temperature cycling experiment. It can be seen that the proposed method outperforms the traditional method in all aspects of the measured temperature compensation experiments on the three IMU prototypes. Furthermore, compared with the original rate signal, the proposed method significantly reduces the full-temperature zero bias and zero bias stability of the compensated signal.

[0192] Table 1: Comparison of temperature compensation results using the present invention and conventional methods on IMU prototype No. 1

[0193]

[0194] Table 2: Comparison of temperature compensation results using the present invention and conventional methods on IMU prototype No. 2

[0195]

[0196] Table 3: Comparison of temperature compensation results using the present invention and the conventional method on IMU prototype No. 3

[0197]

[0198]

[0199] Compared with existing technologies, the IMU temperature compensation method based on ICELMDAN and integrated GRU provided in this invention adds complementary weighted Gaussian white noise product functions of the same order to each decomposition of ICELMDAN, overcoming the shortcomings of LMD mode aliasing and poor decomposition completeness, and can better filter random noise and anomalous noise mixed in the original IMU rate signal. In addition, the integrated GRU temperature compensation model achieves higher prediction accuracy and better generalization performance than the single GRU model through resampling ensemble learning. Furthermore, compared with the traditional polynomial modeling temperature compensation method, the proposed integrated GRU temperature compensation method is more suitable for handling non-stationary and nonlinear IMU temperature drift signals, performs better in the face of hysteresis error, and has higher fitting accuracy of the compensation model.

[0200] Verified in actual testing on an IMU prototype, the temperature compensation method of the integrated GRU effectively suppresses the temperature drift of the IMU output rate signal and significantly reduces its full-temperature zero bias and zero bias stability. Furthermore, on the same IMU prototype, the temperature compensation effect of the proposed method is significantly better than that of the traditional polynomial modeling temperature compensation method.

[0201] Although the invention has been described in conjunction with specific features and embodiments, it is obvious that various modifications and combinations can be made therein without departing from the spirit and scope of the invention. Accordingly, this specification and drawings are merely illustrative of the invention and are considered to cover any and all modifications, variations, combinations, or equivalents within the scope of the invention. Clearly, those skilled in the art can make various alterations and modifications to the invention without departing from its spirit and scope. Thus, if such modifications and modifications fall within the scope of the invention and its equivalents, the invention is also intended to include such modifications and modifications.

Claims

1. A temperature compensation method for complementary integrated LMDs, characterized in that, include: Obtain temperature training signals and rate training signals in one or more dimensions; The rate training signal for each dimension is subjected to multi-order complementary integrated LMD decomposition, and the decomposition output training signal is used as the temperature drift signal. The GRU model is trained using the temperature training signal and temperature drift signal for each dimension to obtain the GRU temperature drift prediction model for each dimension. The measured temperature signal of the inertial measurement unit is predicted by using the GRU temperature drift prediction model for each dimension, and the predicted temperature drift signal is obtained. The predicted temperature drift signal is used to perform temperature compensation on the measured rate signal of the inertial measurement unit. The complementary integrated LMD decomposition includes: The signal to be decomposed is used as the initial residual signal. Multi-order LMD processing is performed on the initial residual signal to obtain the residual signal and product function for each order. The highest-order residual signal, plus the sum of the product functions of all orders, is selected as the signal to be trained. Each order of LMD processing includes the following steps: Obtain m Gaussian white noises, perform LMD operation on each Gaussian white noise to obtain the corresponding noise product function and weight value; use the product of the noise product function and the weight value of each Gaussian white noise to generate a positive and negative complementary correction pair; Obtain the previous residual signal, and correct the previous residual signal using the correction pair to generate 2m corrected previous residual signals; The 2m corrected first-order residual signals are subjected to single-order LMD decomposition to obtain the sub-product functions of the 2m corrected first-order residual signals. The product function of the current order is obtained by averaging the 2m sub-product functions; The residual signal of the current order is obtained by subtracting the product function of the previous order residual signal and the current order residual signal. Where m is a positive integer greater than or equal to 2.

2. The temperature compensation method according to claim 1, characterized in that, The correction of the previous residual signal using the correction pair includes: The product of the previous residual signal and the noise product function of each Gaussian white noise and the weight value is added together. The product of the previous residual signal and the product of the noise product function and the weight value of each Gaussian white noise is subtracted.

3. The temperature compensation method according to claim 1, characterized in that, The step of averaging the 2m sub-integral functions to obtain the current-order integral function includes: Take the average of the 2m sub-product functions, and use the average as the product function of the current order; or, take the squared average of the 2m sub-product functions, and use the squared average as the product function of the current order.

4. The temperature compensation method according to claim 1, characterized in that, The temperature training signals and rate training signals of one or more dimensions are obtained by performing static temperature cycling tests on the inertial measurement unit.

5. The temperature compensation method according to claim 4, characterized in that, The one or more dimensions include inertial measurement units. , , The inertial measurement unit includes any one or a combination of axes; the inertial measurement unit includes a gyroscope and / or an accelerometer.

6. The temperature compensation method according to claim 4, characterized in that, The process of training a GRU model using temperature training signals and temperature drift signals for each dimension to obtain a GRU temperature drift prediction model for each dimension includes the following steps: Build a GRU model and initialize the nodes and weights of the GRU model; Reconstruct the temperature training signal and temperature drift signal to generate a training dataset; The training dataset is resampled into N training subsets, and each of the N training subsets is input into the GRU model for training, resulting in N trained GRU sub-models. The N trained GRU sub-models are weighted and integrated using training weights, and the resulting GRU model is used as the GRU temperature drift prediction model.

7. The temperature compensation method according to claim 6, characterized in that, The reconstructed temperature training signal and temperature drift signal generate a training dataset, including: A training dataset is generated by reconstructing temperature training signals and temperature drift signals according to different dimensions. Alternatively, a training dataset can be generated by reconstructing the temperature training signal, temperature difference training signal, and temperature drift signal according to different dimensions; the temperature difference training signal is obtained by performing differential processing on the temperature training signal. Alternatively, a training dataset can be generated by reconstructing the temperature training signal, the rate training signal after Karlzmann filtering, and the temperature drift signal according to different dimensions.

8. A temperature compensation device based on the temperature compensation method of claim 1, characterized in that, include: The training data acquisition unit is configured to perform a static temperature cycle test on the inertial measurement unit to obtain temperature training signals and rate training signals in one or more dimensions. The LMD unit is configured to perform multi-order complementary integrated LMD decomposition on the rate training signal for each dimension, and use the decomposition output training signal as a temperature drift signal. The GRU model training unit is configured to train the GRU model using temperature training signals and temperature drift signals for each dimension, thereby obtaining the GRU temperature drift prediction model for each dimension. The measured data acquisition unit is configured to acquire measured temperature and measured velocity signals from the inertial measurement unit; The GRU model unit is configured to use the GRU temperature drift prediction model for each dimension to predict the measured temperature signal of the inertial measurement unit and obtain the predicted temperature drift signal. The temperature compensation unit is configured to perform temperature compensation on the measured rate signal of the inertial measurement unit using the predicted temperature drift signal.

9. A computer storage medium, characterized in that, The computer storage medium stores instructions that, when executed, implement the temperature compensation method according to any one of claims 1 to 7.

10. A computing device, characterized in that, It includes a processor and a communication interface coupled to the processor; the processor is used to run computer programs or instructions to implement the temperature compensation method according to any one of claims 1 to 7.

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