Temperature compensation method and device of complementary integrated LMD, medium and equipment

Abstract

The invention belongs to the technical field of inertial sensing and gyroscopes, and particularly relates to a complementary integrated LMD temperature compensation method and device, a medium and equipment. The method comprises the following steps: executing a static temperature cycle test on the inertial measurement unit to obtain a temperature training signal and a rate training signal of one or more dimensions; performing multi-order complementary integration LMD decomposition on the rate training signal of each dimension, and taking a to-be-trained signal output by decomposition as a temperature drift signal; training a GRU model by adopting the temperature training signal and the temperature drift signal of each dimension to obtain a GRU temperature drift prediction model of each dimension; utilizing the GRU temperature drift prediction model of each dimension to predict a temperature actual measurement signal of the inertial measurement unit to obtain a predicted temperature drift signal, and adopting the predicted temperature drift signal to carry out temperature compensation on a rate actual measurement signal of the inertial measurement unit. According to the invention, the temperature compensation of the IMU unit can be accurately realized in real time.

Description

Technical Field

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

[0002] An inertial measurement unit (IMU) usually includes a gyroscope, an accelerometer, and a dedicated interface circuit. It is an inertial sensor used to measure the angular velocity and acceleration of a carrier. Since inertia is a basic characteristic of a mass body, the IMU can complete the measurement without any external information and without radiating any energy to the outside world. Due to its high concealment, interference-free, and complete autonomy, the IMU is regarded as an absolutely confidential navigation system and has been widely used in the fields of national economy and military systems.

[0003] With the advancement of micro-electromechanical system (MEMS) technology, the accuracy of low-cost MEMS inertial devices is getting higher and higher. MEMS IMU has also been gradually promoted to many fields such as inertial navigation, consumer electronics, automatic control, etc. due to its small size, light weight, low power consumption, easy integration, and low cost, and has been relatively maturely applied.

[0004] Due to the limitations of materials and manufacturing packaging processes, IMU is easily affected by environmental factors. Among them, the interference caused by temperature is persistent and difficult to avoid, which seriously limits the long-term accuracy and further application of IMU. Therefore, analyzing the temperature drift of IMU and performing effective calibration compensation are of great significance to improving the measurement accuracy of IMU. There are two main compensation schemes for IMU temperature drift: one is to perform ambient temperature compensation from the hardware to make the IMU work at a constant temperature; the other is to perform algorithm compensation from the software, that is, to establish a temperature compensation model in which the zero offset of IMU changes with temperature. Compared with hardware environment compensation, software algorithm compensation does not require the construction of a complex working environment. It only needs to collect enough raw data to establish a temperature compensation model for temperature compensation. Therefore, software algorithm compensation is the development trend and mainstream technology of IMU temperature compensation.

[0005] The temperature drift of IMU is not completely corresponding to the change of ambient temperature. When the ambient temperature changes, the change of temperature drift shows obvious hysteresis due to the delay of heat exchange and indication process of temperature measuring elements. When implementing software algorithm compensation, the traditional polynomial modeling temperature compensation method performs well in fitting linear sequences. However, the characteristics of the internal components of IMU will change with the ambient temperature, the variables and order of the temperature drift model are difficult to determine, and the output signal of IMU is usually non-stationary and nonlinear. Therefore, the fitting accuracy of the traditional temperature compensation model is greatly limited, and it performs poorly in the face of hysteresis errors.

[0006] In view of the above problems existing in the prior art, it is urgent to propose a temperature compensation method of an inertial measurement unit (IMU) that can suppress temperature drift and reduce full-temperature zero bias and zero bias stability. Summary of the invention

[0007] The object of the present invention is to provide a temperature compensation method, device, medium and equipment for a complementary integrated LMD, so as to suppress the temperature drift of an inertial measurement unit and reduce the temperature offset.

[0008] To achieve the above object, the present invention provides the following technical solutions:

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

[0010] The signal to be decomposed is used as an initial residual signal, and multi-order LMD processing is performed on the initial residual signal to obtain a residual signal and a product function of each order, and the highest order residual signal plus the cumulative sum of product functions of all orders are selected as the signal to be trained; each order LMD processing in the multi-order LMD processing includes the following steps:

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

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

[0013] Performing single-order LMD decomposition on the 2m corrected previous-order residual signals respectively to obtain 2m sub-product functions of the corrected previous-order residual signals; performing mean processing on the 2m sub-product functions to obtain a current-order product function;

[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; wherein m is a positive integer greater than or equal to 2.

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

[0016] The method of performing mean processing on the 2m sub-product functions to obtain the product function of the current order includes: taking the average value of the 2m sub-product functions, and using the average value as the product function of the current order; or taking the square average value of the 2m sub-product functions, and using the square average value as the product function of the current order.

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

[0018] A static temperature cycle test is performed on an inertial measurement unit to obtain a temperature training signal and a rate training signal of one or more dimensions; a multi-order complementary integrated LMD decomposition is performed on the rate training signal of each dimension, and the decomposition output signal to be trained is used as a temperature drift signal; a GRU model is trained using the temperature training signal and the temperature drift signal of each dimension to obtain a GRU temperature drift prediction model of each dimension; the temperature measured signal of the inertial measurement unit is predicted using the GRU temperature drift prediction model of each dimension to obtain a predicted temperature drift signal; and the predicted temperature drift signal is used to perform temperature compensation on the rate measured signal of the inertial measurement unit.

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

[0020] The method of training the GRU model using the temperature training signal and the temperature drift signal of each dimension to obtain the GRU temperature drift prediction model of each dimension includes the following steps:

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

[0022] Reconstructing the temperature training signal and the temperature drift signal to generate a training data set;

[0023] Resample the training data set into N training subsets, and input the N training subsets into the GRU model for training respectively, to obtain N trained GRU sub-models;

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

[0025] The reconstructing temperature training signal and temperature drift signal to generate a training data set includes: using the temperature training signal and the temperature drift signal to reconstruct the training data set according to different dimensions; or, using the temperature training signal, the temperature difference training signal, and the temperature drift signal to reconstruct the training data set according to different dimensions; the temperature difference training signal is obtained by differential processing based on the temperature training signal; or, using the temperature training signal, the rate training signal after Kartzmann filtering, and the temperature drift signal to reconstruct the training data set according to different dimensions.

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

[0027] A training data acquisition unit is configured to perform a static temperature cycle test on the inertial measurement unit to obtain a temperature training signal and a rate training signal of one or more dimensions;

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

[0029] A GRU model training unit is configured to train the GRU model using the temperature training signal and the temperature drift signal of each dimension to obtain a GRU temperature drift prediction model of each dimension;

[0030] A measured data acquisition unit is configured to acquire a temperature measured signal and a speed measured signal from an inertial measurement unit;

[0031] The GRU model unit is configured to predict the temperature measured signal of the inertial measurement unit using the GRU temperature drift prediction model of each dimension to obtain a predicted temperature drift signal;

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

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

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

[0035] Beneficial effects:

[0036] The temperature compensation method, device, medium and equipment of a complementary integrated LMD proposed in the present invention have the following beneficial effects compared with the prior art:

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

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

[0039] 3. Compared with the traditional polynomial modeling temperature compensation method, the temperature compensation method is more suitable for processing 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 can effectively suppress the temperature drift of the IMU output rate signal and significantly reduce its full-temperature zero bias and zero bias stability. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] The drawings described herein are used to provide a further understanding of the present invention and constitute a part of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings:

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

[0043] Figure 2 is a flow chart of the complementary integrated LMD method;

[0044] Figure 3 It is a flow chart of temperature compensation based on complementary integrated LMD method;

[0045] Figure 4 This is the flowchart for training the GRU model;

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

[0047] Figure 6 It is a flowchart of adaptive noise-added complementary integrated local mean decomposition;

[0048] Figure 7 It is a schematic diagram of the process of n-order LMD;

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

[0050] Fig. 9 This is the flow chart of training the integrated GRU model;

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

[0052] Fig.11 is a schematic diagram of the original rates of the x, y, and z axes of the accelerometer and the temperature compensation signals in the embodiment;

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

[0054] Fig.13 is a schematic diagram of the original rates of the x, y, and z axes of the accelerometer and the temperature compensation signals in the embodiment;

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

[0056] Fig.15 is a schematic diagram of the original rates of the x, y, and z axes of the accelerometer and the temperature compensation signals in the embodiment;

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

[0058] Fig.17 It is a schematic diagram of the original rate and temperature compensation signal of the accelerometer x, y, and z axes;

[0059] Fig.18 It is a schematic diagram of the original rate and temperature compensation signal of the gyroscope x, y, and z axes;

[0060] Fig.19 It is a schematic diagram of the original rate of the accelerometer x, y, and z axes and the temperature compensation signal. DETAILED DESCRIPTION

[0061] In order to clearly describe the technical solutions of the embodiments of the present invention, in the embodiments of the present invention, words such as "first" and "second" are used to distinguish the same items or similar items with basically the same functions and effects. For example, the first threshold and the second threshold are only used to distinguish different thresholds, and their order is not limited. Those skilled in the art can understand that words such as "first" and "second" do not limit the quantity and execution order, and words such as "first" and "second" do not necessarily limit them to be different.

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

[0063] Local Mean Decomposition (LMD) is an adaptive time-frequency analysis method used to decompose complex multi-component AM / FM signals. Compared with empirical mode decomposition, LMD has advantages in solving problems such as endpoint effects and false components. It decomposes the signal into product functions and residual components through iteration. Each product function corresponds to a single-component modulated signal, thereby obtaining instantaneous frequency and amplitude information and realizing time-frequency distribution analysis of the signal. The LMD method includes steps such as finding local extreme values, sliding average processing, demodulation and iteration, and is suitable for the analysis of non-stationary nonlinear signals.

[0064] like Figure 1 As shown in the figure, the temperature compensation technical solution of the inertial measurement unit (IMU) is mainly implemented through three parts: decomposition, modeling and compensation. In the decomposition part, the rate training signal is decomposed by using the adaptive complementary integrated 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 verified by 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 temperature measured signal of the inertial measurement unit is predicted by using the integrated GRU temperature drift prediction model to obtain the predicted temperature drift signal, and the predicted temperature drift signal is used to perform real-time temperature compensation on the rate measured signal of the inertial measurement unit to obtain a temperature compensated rate signal.

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

[0066] like Figure 2 As shown, a flowchart of LMD processing at each stage is given, and each stage of LMD processing includes the following steps:

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

[0068] Step S202: m pairs of Gaussian white noises are obtained by copying, and a positive and negative complementary correction pair is generated by using the product of the noise product function and the weight value of each pair of Gaussian white noises;

[0069] Step S203: obtaining a previous order residual signal, and correcting the previous order residual signal using the correction pair to generate 2m corrected previous order residual signals;

[0070] Among them, the previous order residual signal is corrected using the correction pair, including: adding the previous order residual signal and the product of the noise product function of each pair of Gaussian white noise and the weight value; subtracting the previous order residual signal and the product of the noise product function of each pair of Gaussian white noise and the weight value.

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

[0072] Step S205: performing mean integration processing on the 2m sub-product functions to obtain the product function of the current order; performing mean integration processing to obtain the product function of the current order includes: performing integration 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 integration 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: obtaining a current-order residual signal by summing the previous-order residual signal and the product function of the current order.

[0074] like Figure 3 As shown, a flow chart of a temperature compensation method based on the 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 a temperature training signal and a rate training signal of one or more dimensions; wherein the one or more dimensions include any one of the x, y, and z axes of the inertial measurement unit or a combination of multiple axes; and the inertial measurement unit includes a gyroscope and / or an accelerometer.

[0076] Step S302: performing multi-order complementary integrated LMD decomposition on the rate training signal of each dimension, and using the decomposition output signal to be trained as a temperature drift signal;

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

[0078] Step S304: using the GRU temperature drift prediction model of each dimension to predict the temperature measured signal of the inertial measurement unit to obtain a predicted temperature drift signal;

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

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

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

[0082] Step S402: reconstructing the temperature training signal and the temperature drift signal to generate a training data set; including: using the temperature training signal and the temperature drift signal to reconstruct the training data set according to different dimensions; or, using the temperature training signal, the temperature difference training signal, and the temperature drift signal to reconstruct the training data set according to different dimensions; or, using the temperature training signal, the rate training signal after the Kartzmann filter, and the temperature drift signal to reconstruct the training data set according to different dimensions.

[0083] Step S403: resampling the training data set into N training subsets, and inputting the N training subsets into the GRU model for training respectively, to obtain N trained GRU sub-models;

[0084] Step S404: N trained GRU sub-models are weightedly integrated by training weights to obtain an integrated GRU model.

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

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

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

[0088] A GRU model training unit 503 is configured to train a GRU model using a temperature training signal and a temperature drift signal of each dimension to obtain a GRU temperature drift prediction model of each dimension;

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

[0090] The GRU model unit 505 is configured to predict the temperature measured signal of the inertial measurement unit using the GRU temperature drift prediction model of each dimension to obtain a predicted temperature drift signal;

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

[0092] Perform static temperature cycle test on the inertial measurement unit (IMU) to obtain temperature training signals and rate training signals in one or more dimensions. The experimental hardware equipment for static temperature cycle test includes: temperature control turntable, micro-electromechanical (MEMS) IMU, evaluation circuit, computer and power supply. An oven is configured on the temperature control turntable. The MEMS IMU is installed in the oven of the temperature control turntable through a fixture. The MEMS IMU is connected to the computer through the evaluation circuit. The temperature change rate of the temperature control turntable oven is set to 0.5℃ / min, and the temperature cycle experiment is carried out in the range of -40℃~80℃.

[0093] Keep the turntable speed at 0, collect the static temperature cycle output of the micro-electromechanical system IMU at a sampling frequency of 2Hz, and record it as training data, including the data of the x, y, and z axes of the inertial measurement unit. The inertial measurement unit is 3 dimensions, 6 dimensions, or 9 dimensions. Taking 6 dimensions as an example, obtain the temperature training signals and rate training signals of the gyroscope and accelerometer on the x, y, and z axes. In other words, 6-dimensional temperature training signals and 6-dimensional rate training signals are obtained.

[0094] Next, the rate training signal of each dimension is subjected to multi-order local mean decomposition, and a complementary weighted Gaussian white noise product function of the same order is added in each order decomposition process. After the decomposition is completed, the highest order residual signal is extracted as the temperature drift signal.

[0095] like Figure 6 As shown, a flow chart of adaptive noise-added complementary integrated local mean decomposition is given.

[0096] The adaptive noisy complementary integrated local mean decomposition ICELMDAN, referred to as the "complementary integrated LMD method", is used 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 order of decomposition operation to correct the residual noise and overcome the shortcomings of local mean decomposition (LMD) such as modal aliasing and poor decomposition completeness.

[0097] The adaptive complementary integrated local mean decomposition with noise (ICELMDAN) needs to perform n-order decomposition. After the decomposition is completed, the highest order (i.e., n-th order) residual signal r is extracted. n(t) is the temperature drift signal, that is, the residual signal plus the decomposed n-th order product function PF i (t) and.

[0098] Taking the n-order complementary integrated LMD as an example, the following steps are included:

[0099] Step 601: the initialized 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 added to the noise product function i，j :

[0102]

[0103] Among them, β i，j represents 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) is the i-1th order residual signal, 1≤i≤n; std[] represents the standard deviation.

[0105] Step 603: Substitute the i-1th order residual signal r i--1 (t) Copy m pairs, insert a pair of complementary weighted i-th order noise product functions L into each pair i [w j (t)], that is, add β to each pair 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 the 2m new signals generated, and decompose 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 2m sub-product functions PF i，k The mean of (t) obtains the i-th order product function PF i (t):

[0108]

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

[0110] Step 606: Use the i-1th order residual signal r i--1 (t) minus the i-th order product function PF i (t) Get 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, r1(t)=r0(t)-PF1 is obtained.

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

[0114] It needs to be further explained 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 decomposition and processing time, but too few orders will lead to modal aliasing, and too few noises will reduce the completeness of decomposition and make it difficult to filter out residual noise. Therefore, as for the specific decomposition order n and the specific amount of Gaussian white noise m, a suitable empirical value should be selected based on the actual signal processing results. For example, 3≤n≤100, 5≤m≤100.

[0115] As an example, it is assumed that the decomposition order n=6, the number of Gaussian white noises m=10, and the signal-to-noise ratio ε=5.

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

[0117] like Figure 7 As shown, a schematic diagram of the process of n-order LMD is given, including the following steps:

[0118] Step 701: input a 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) to be decomposed signal x(t);

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

[0121] Step 704: According to the local extreme point n k Calculate the local mean point m k and the 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 the local envelope point a k Perform sliding average respectively to obtain the local mean m i，j (t) and the local envelope a i，j (t);

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

[0126]

[0127] Step 707: Determine the demodulated signal s i,j (t) Is it a pure FM signal: If s i,j (t) is a pure FM signal, jump to step 708; otherwise, update the cyclic signal x′(t) to the demodulated signal s i，j (t), then increase the cyclic order j by 1, and jump to step 703 to recalculate the local extreme point n of the cyclic signal x′(t) k ;

[0128] As an example, the demodulated signal s is determined in the following manner: i，j (t) Is it a pure FM signal: Calculate the demodulated signal s i，j The local envelope of (t) i，j+1 (t), if a i，j+1 (t)≡1, then the demodulated signal s i，j (t) is a pure FM signal.

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

[0130] The demodulated signal s i，j (t) is iteratively multiplied with the j local envelopes of the i-th order to obtain 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 Get the updated residual signal r(t): 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 so, jump to step 710; otherwise, update the signal to be decomposed x(t) to the residual signal r(t), then add 1 to the decomposition order i, and jump to step 702;

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

[0135]

[0136] Combination Figure 6 and Figure 7 From the LMD decomposition process shown in the figure, it can be seen that the adaptive noise complementary integrated local mean decomposition (ICELMDAN) needs to perform n-order decomposition. After the decomposition is completed, the highest order residual signal r is extracted. n (t) is the temperature drift signal, which is the rate training signal minus the decomposed n-th order product function PF i (t) Sum:

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

[0138]

[0139] like Figure 8 As shown in the figure, a structural diagram of a single-layer GRU model is given.

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

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

[0144] Among them, x t ,y t 、h t 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 (·) are the input weight, loop weight, bias, and activation function of the reset gate R respectively;

[0146] U z , W z 、b z 、f z (·) are the input weight, loop weight, bias, and activation function of update gate Z respectively;

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

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

[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 (·) are the input weight, loop weight, 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 Expressed as: y t =f y (Vh t +c)

[0152] Among them, V, c, f y (·) are the output weight, bias and activation function, respectively, and f y (·) is generally the Purelin transfer function.

[0153] After the GRU model is trained, each network parameter is a constant, including the input weight (U r , U z , U h ), cycle weight (W r , W z , W h ), output weight (V), and bias (b r , b z , b h , c), then the current state h t and the output vector y t It can be simplified as:

[0154]

[0155] in, Represents the state update function of the simplified GRU model; Represents the nonlinear transfer function obtained by the GRU model, that is, from the input vector x t To the output vector y t Dynamic mapping.

[0156] like Fig. 9 As shown, a flowchart of training the integrated GRU model is given.

[0157] The establishment of 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: reconstructing the temperature training signal and the temperature drift signal into an enhanced data set, and dividing the enhanced data set 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 the output vector y i The dimensions do not need to correspond, and the training data sets X and Y can be reconstructed in different dimensions according to the input signal. For example:

[0161] (1) Input temperature signal T t , predict the temperature drift signal d t , reconstruct and generate training data sets 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 , predict the temperature drift signal d t , reconstruct and generate training data sets 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 , predict the temperature drift signal d t , reconstruct and generate training data sets X and Y:

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

[0169] Among them, x t is the input vector of the GRU model at time t, y t is the output target corresponding to the GRU model at time t; T t ,d t are the temperature training signal and temperature drift signal at time t respectively;

[0170] l is the memory step length, corresponding to the number of input layer nodes n of the GRU model i = l, and the number of output layer nodes is n o =1, indicating that in the GRU temperature drift prediction model, the temperature signal sequence (T 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 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 the state update function and nonlinear transfer function express.

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

[0173] Step 904: N trained GRU sub-models (GRU 1 to GRU N) are trained by adjusting the training weights a k 、b k Weighted integration to obtain the integrated GRU model:

[0174]

[0175] in, and Represents the state update function and nonlinear transfer function of the integrated GRU model; a k 、b k is the integrated weight of the integrated GRU model; and Represents the state update function and nonlinear transfer function of the kth GRU sub-model.

[0176] Step 905: Input the training set into the integrated GRU model to train the integrated weight a k 、b k , get the trained integrated GRU model;

[0177] Step 906: Input the validation set into the trained integrated GRU model to obtain the prediction root mean square error (RMSE) on the validation set, use the prediction RMSE to evaluate the generalization performance of the integrated GRU model, and use this to optimize the number of nodes in the GRU model; specifically, continuously adjust the number of input layer nodes n of the GRU modeli and the number of hidden layer nodes n h , and repeat the training and validation of the integrated GRU model until the prediction RMSE of the integrated GRU model on the validation set is minimized.

[0178] Step 907: After training and verification are completed, the temperature drift prediction model obtained by integrating the GRU model can be expressed as a state update function and nonlinear transfer function

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

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

[0181]

[0182] The temperature training signal and temperature drift signal of each dimension are used to train the GRU model to obtain the GRU temperature drift prediction model of each dimension; the temperature measured signal of the inertial measurement unit is predicted using the GRU temperature drift prediction model of one or more dimensions to obtain a predicted temperature drift signal, and the predicted temperature drift signal is used to perform temperature compensation on the rate measured signal of the inertial measurement unit.

[0183] For the above-mentioned temperature compensation method, the temperature compensation method of the inertial measurement unit is verified through specific experiments, which proves the effectiveness of the temperature compensation method of the inertial measurement unit and its superiority over the existing technology. In the experimental verification, the experimental hardware equipment includes: a temperature control turntable, a micro-electromechanical (MEMS) IMU, an evaluation circuit, a computer and a power supply. An oven is configured on the temperature control turntable, and the micro-electromechanical IMU is installed in the oven of the temperature control turntable through a fixture, and the micro-electromechanical IMU is connected to the computer through the evaluation circuit.

[0184] The temperature change rate of the temperature-controlled turntable oven was set to 0.5°C / min, and the temperature cycle experiment was carried out in the range of -40°C to 80°C. The turntable speed was kept at 0, and the static temperature cycle output of the micro-electromechanical IMU was collected at a sampling frequency of 2Hz and recorded as training data, including the temperature data of the gyroscope x, y, and z axes, respectively. Fig.10 As shown in 10A, 10B, and 10C, the temperature data of the accelerometer x, y, and z axes are respectively as follows Fig.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 x, y, and z axes are as follows: Fig.12 As shown in 12A, 12B, and 12C, the angular velocity data of the accelerometer x, y, and z axes are respectively as follows Fig.13 As shown in 13A, 13B, and 13C, a total of 6-axis rate training signals are obtained.

[0186] After performing 6th-order ICELMDAN decomposition on the rate training signal, the n=6th-order residual signal is taken as the temperature drift signal. Fig.14 As shown in 14A, 14B, and 14C, the rate training signals and temperature drift signals of the gyroscope x, y, and z axes are respectively given. Fig.15 As shown in 15A, 15B, and 15C in FIG. 1 , the rate training signals and temperature drift signals of the accelerometer x, y, and z axes are respectively given. In the above drawings related to the accelerometer, the accelerometer is simply labeled 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 the temperature drift signal are reconstructed according to the aforementioned format and divided into 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, 10 GRU sub-models are trained with the 10 training subsets, and the 10 trained GRU sub-models are weighted integrated to obtain an integrated GRU model.

[0188] The integrated GRU model was trained and verified using the training set and validation set. After multiple adjustments and evaluations, the number of nodes in the input layer, hidden layer, and output layer of the GRU model was determined to be n respectively. i =1,n h =10,n o =1, and the state update function of the integrated GRU temperature drift prediction model is obtained. and nonlinear transfer function

[0189] Using the training data output by the IMU static temperature cycle, a total of 6 integrated GRU temperature drift prediction models for 6 axes, including the gyro x, y, z axis and the accelerometer x, y, z axis, were established. Using these 6 models and the IMU training data, simulated temperature compensation was performed on the computer. The compensation results are shown in Figure 2. Fig.16 As shown in 16A, 16B, and 16C, the original rate signals and temperature compensation signals of the gyroscope x, y, and z axes are given respectively. Fig.17 As shown in 17A, 17B, and 17C, the original rate signals and temperature compensation signals of the accelerometer x, y, and z axes are given respectively.

[0190] In order to verify the effectiveness of the proposed temperature compensation method, these six models are programmed according to the compensation method of equations (8)-(10) and written into the IMU prototype to achieve real-time temperature compensation of the IMU rate signal. The same static temperature cycle experiment is performed on the IMU prototype written with the proposed temperature compensation algorithm, and the measured temperature compensation signal output by the IMU prototype is collected, as shown in Figure 2. Fig.18 As shown in 18A, 18B, and 18C, the original rate signals and temperature compensation signals of the gyroscope x, y, and z axes are respectively given. Fig.19 As shown in 19A, 19B, and 19C, the original rate signals and temperature compensation signals of the accelerometer x, y, and z axes are given respectively. It can be seen that the proposed temperature compensation method effectively suppresses the temperature drift of the IMU rate signal.

[0191] In order to further verify the effectiveness and adaptability of the proposed temperature compensation method, the proposed temperature compensation method and the traditional polynomial temperature compensation method are simultaneously applied to three IMU prototypes, and the same static temperature cycle experiment is performed on the three IMUs respectively, and the temperature compensation signals of the two methods are collected and compared with the original rate signals. Tables 1, 2 and 3 compare the original rate signals, the compensation signals of the traditional method and the compensation signals of the proposed method output by the three IMU prototypes in the static temperature cycle experiment respectively. It can be seen that the various indicators of the proposed method in the measured temperature compensation experiment of the three IMU prototypes are better than those of the traditional method, and compared with the original rate signal, the full-temperature zero bias and zero bias stability of the compensation signal of the proposed method are significantly reduced.

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

[0193]

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

[0195]

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

[0197]

[0198]

[0199] Compared with the prior art, the IMU temperature compensation method based on ICELMDAN and integrated GRU provided by the present invention adds a complementary weighted Gaussian white noise product function of the same order to each order decomposition of ICELMDAN, which overcomes the shortcomings of LMD modal aliasing and poor decomposition completeness, and can better filter the mixed random noise and abnormal noise in the IMU original rate signal; and the integrated GRU temperature compensation model obtains higher prediction accuracy and better generalization performance than the single GRU model through the resampling ensemble learning method; in addition, compared with the traditional polynomial modeling temperature compensation method, the proposed integrated GRU temperature compensation method is more suitable for processing 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.

[0200] The IMU prototype was tested and verified that the temperature compensation method of the integrated GRU can effectively suppress the temperature drift of the IMU output rate signal and significantly reduce its full-temperature zero bias and zero bias stability. Moreover, on the same IMU prototype, the temperature compensation effect of the temperature compensation method is significantly better than the traditional polynomial modeling temperature compensation method.

[0201] Although the present invention has been described in conjunction with specific features and embodiments thereof, it is apparent that various modifications and combinations may be made thereto without departing from the spirit and scope of the present invention. Accordingly, this specification and the accompanying drawings are merely exemplary illustrations of the present invention and are deemed to cover any and all modifications, variations, combinations or equivalents within the scope of the present invention. Obviously, those skilled in the art may make various modifications and variations to the present invention without departing from the spirit and scope of the present invention. Thus, the present invention is intended to include such modifications and variations if they fall within the scope of the present invention and its equivalents.

Claims

1. A complementary integrated LMD method, characterized in that: include: The signal to be decomposed is used as an initial residual signal, and multi-order LMD processing is performed on the initial residual signal to obtain a residual signal and a product function of each order, and the highest order residual signal plus the cumulative sum of product functions of all orders are selected as the signal to be trained; each order LMD processing in the multi-order LMD processing includes the following steps: Obtain m Gaussian white noises, perform LMD operation on each Gaussian white noise to obtain a corresponding noise product function and a weight value; generate a positive and negative complementary correction pair using the product of the noise product function and the weight value of each Gaussian white noise; Acquire a previous order residual signal, and correct the previous order residual signal using the correction pair to generate 2m corrected previous order residual signals; Performing single-order LMD decomposition on the 2m corrected first-order residual signals respectively to obtain sub-product functions of the 2m corrected first-order residual signals; Performing mean processing on the 2m sub-product functions to obtain a product function of the current order; Difference is calculated between the previous order residual signal and the product function of the current order to obtain the current order residual signal; Here, m is a positive integer greater than or equal to 2.

2. The complementary integrated LMD method according to claim 1, characterized in that: The correcting the previous order residual signal using the correction pair comprises: The previous order residual signal and the product of the noise product function of each Gaussian white noise and the weight value are added together; The previous order residual signal and the product of the noise product function and the weight value of each Gaussian white noise are subtracted.

3. The complementary integrated LMD method according to claim 1, characterized in that: The step of performing mean processing on the 2m sub-product functions to obtain the product function of the current order includes: An average value is taken for the 2m sub-product functions, and the average value is used as the product function of the current order; or, a square average value is taken for the 2m sub-product functions, and the square average value is used as the product function of the current order.

4. A temperature compensation method based on the complementary integrated LMD method of claim 1, characterized in that: The following steps are involved: Performing a static temperature cycle test on the inertial measurement unit to obtain a temperature training signal and a rate training signal in one or more dimensions; Performing multi-order complementary integrated LMD decomposition on the rate training signal of each dimension, and using the decomposition output signal to be trained as a temperature drift signal; The GRU model is trained using the temperature training signal and temperature drift signal of each dimension to obtain the GRU temperature drift prediction model of each dimension; The GRU temperature drift prediction model of each dimension is used to predict the temperature measured signal of the inertial measurement unit to obtain a predicted temperature drift signal; The predicted temperature drift signal is used to perform temperature compensation on a rate measurement signal of an inertial measurement unit.

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

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

7. The temperature compensation method according to claim 6, characterized in that: The reconstructing the temperature training signal and the temperature drift signal to generate a training data set includes: The temperature training signal and the temperature drift signal are reconstructed in different dimensions to generate a training data set; Alternatively, a temperature training signal, a temperature difference training signal, and a temperature drift signal are used to reconstruct and generate a training data set according to different dimensions; the temperature difference training signal is obtained by performing differential processing on the temperature training signal; Alternatively, a temperature training signal, a rate training signal after Kartzman filtering, and a temperature drift signal are used to reconstruct a training data set in different dimensions.

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

9. A computer storage medium, characterized in that: The computer storage medium stores instructions, and when the instructions are executed, the complementary integrated LMD method described in any one of claims 1 to 3 and the temperature compensation method described in any one of claims 4 to 7 are implemented.

10. A computing device, characterized in that It comprises a processor and a communication interface coupled to the processor; the processor is used to run a computer program or instruction to implement the complementary integrated LMD method described in any one of claims 1 to 3, and to implement the temperature compensation method described in any one of claims 4 to 7.

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