A Hybrid EMD Algorithm Based on Parameter Optimization

Abstract

A hybrid EMD algorithm based on parameter optimization is presented. This algorithm, belonging to the field of digital signal processing, is a gyroscope temperature drift compensation algorithm based on parametric quadratic B-splines and EMD decomposition. Its key feature is the use of EMD decomposition and mutual information algorithms for initial denoising of the gyroscope temperature drift signal. Then, parametric quadratic B-spline basis functions are used to perform fine denoising and fitting on the initially denoised signal. Finally, the final parameter values ​​of the quadratic B-splines are determined by analyzing the spectral separation between the noise and the fitted signal, thus obtaining the final fitted signal and performing compensation. Addressing the shortcomings of traditional temperature drift fitting methods that lack denoising and cannot adjust the denoising effect, this invention introduces parametric quadratic B-spline basis functions, combined with EMD decomposition, mutual information denoising, and spectral separation estimation algorithms, to more accurately denoise and fit the temperature drift signal, thereby improving the accuracy and effectiveness of gyroscope temperature compensation.

Description

Technical Field

[0001] This invention relates to a hybrid EMD algorithm based on parameter optimization, belonging to the field of digital signal processing. Background Technology

[0002] Temperature drift in gyroscopes is a significant factor affecting their accuracy and reliability during use. Therefore, temperature compensation is a common method to overcome the effects of temperature. Common methods for gyroscope temperature compensation include support vector machines, genetic algorithms, particle algorithms, and various regression algorithms. These methods typically compensate directly for the gyroscope's output signal. This means that noise is treated as part of the useful signal during the fitting calculation, inevitably introducing noise and reducing the accuracy of fitting and compensation.

[0003] EMD (Extended Modulation) is a signal processing method developed in recent years. It decomposes signals based on their time scale and is suitable for nonlinear and non-stationary signal processing. Because it does not require determining subjective empirical parameters such as basis functions and the number of decomposition levels, it can achieve better decomposition results than wavelet transform in some cases. Furthermore, EMD is increasingly used not only for signal decomposition but also in signal filtering. B-splines are a curve and surface fitting algorithm widely used in CAGD (Continuous Acyclic Graph) and signal processing. In signal fitting, especially discrete data fitting, B-spline curves are increasingly valued by researchers due to their simplicity, continuity, and differentiability. Triangular splines and triangular polynomials are significant in both theoretical and practical applications. However, B-splines also have limitations. For known B-splines, the basis functions are given, leading to a lack of flexibility in curve fitting and denoising, resulting in a unique outcome and causing inconvenience in practical applications. To address this, parameterized spline functions are introduced to adjust the shape and curvature of the curve as needed, thereby achieving more accurate denoising and fitting results. Mutual information is a highly practical information metric in information theory. It is used to measure the amount of information contained in one random variable about another. In engineering applications, by calculating the mutual information value of two variables, we can determine their correlation and the extent of shared information. Summary of the Invention

[0004] To address the aforementioned problems, this invention offers innovations in four aspects: denoising the EMD noise IMF and useful IMF boundaries; the basis functions of parameterized quadratic B-splines and their properties; fine denoising using these basis functions; and gyroscope temperature compensation. First, EMD decomposition and mutual information algorithms are used to initially denoise the gyroscope temperature drift signal f, filtering the signal fE and the noise signal fnoise. Then, parameterized quadratic B-spline basis functions (3a) are used to finely denoise and fit the initially denoised signal f:. Finally, the final parameter values ​​of the quadratic B-spline are determined by analyzing the spectral separation between the noise and the fitted signal, resulting in the final fitted signal f'Ev. Finally, (4a) is used for final compensation. This method first performs EMD decomposition on the gyroscope's temperature drift data. Furthermore, mutual information calculation is performed on the EMD-decomposed signal to obtain the useful signal, achieving the purpose of initial filtering. Finally, to address the issue that traditional fitting methods cannot provide precise filtering, a parameterized quadratic B-spline basis function is introduced to remove residual noise while fitting the data. By comparing the degree of separation between the final signal and noise spectra, the parameters of the quadratic triangular B-spline are determined.

[0005] To solve its technical problem, the present invention adopts the following technical solution:

[0006] 1. The gyroscope temperature drift signal f is first decomposed using EMD to obtain the decomposed components: IMF1-IMF N There are N components in total;

[0007] 2. The decomposed IMFs are summed pairwise according to the decomposition order to obtain a new set of signal components NF. i The decomposition order is from high to low component frequencies, as shown in (2a) below, for NF i Mutual information is calculated between them to obtain a set of mutual information values ​​I. i (NF i ,NF i+1 As shown in (2b), where H(.) is the Shannon entropy algorithm, for I i (NF i ,NF i+1 Find the discrete derivative, as shown in (2c). When the derivative reaches its maximum value, it is the boundary between noise and useful signal. If the maximum value at this time is Δ... i Then IMF i+2 The boundary between noise and useful signal, i.e., when k≥i+2, is defined by the IMF. k The useful signal is shown in (2d), thus obtaining the preliminary filtered signal f. EM and noise signal f noise As shown in (2e);

[0008] NFi =IMF i +IMF i+1 ,i=1,…,N-1(2a)

[0009] I i (NF i ,NF i+1 )=H(NF i )+H(NF i+1 )-H(NF i ,NF i+1 (2b)

[0010] Δ i =I i+1 (NF i+1 ,NF i+2 )-I i (NF i ,NF i+1 ), i=1,…,N-2 (2c)

[0011]

[0012] 3. Regarding f in the previous step EM To perform fine filtering, a set of parametric quadratic B-spline function bases is introduced, as shown in (3a). The range of parameters b1 and b2 is -1 ≤ b1, b2 ≤ 1. When b1 and b2 are -1, the fitted curve is closest to the original signal, and the denoising effect is minimal. When b1 and b2 are 1, the fitted curve is furthest from the original signal. The straight line connecting the midpoint of the fitted curve and the original signal is then drawn. The parametric quadratic B-spline function bases must satisfy the condition in (3b), where P0(b1,t) and P2(b 2, t) is monotonically increasing within the range of parameters b1, b2; P1(b1, b2, t) is monotonically decreasing. Meanwhile, this basis function also guarantees C 1 Continuous, taking different values ​​of parameters b1 and b2 for f EM To perform fitting, assume f EM If the three consecutive points are M1, M2, and M3, then the fitted curve signal for this segment can be obtained as f′. EM As shown in (3c), due to the modal aliasing of EMD decomposition, it is necessary to compare f EM and f′ EM The spectrum,

[0013] Simultaneously adjust the values ​​of parameters b1 and b2 until their spectra no longer overlap;

[0014]

[0015] f′EM=M1·P0(b1,t)+M2·P1(b1,b2,t)+M3·P2(b2,t) (3c)

[0016] (4) Compensate for the gyroscope temperature drift signal and refine the above-obtained denoised fitting signal f′. EM It is a real drift signal, noise f noise After uniform compensation, the compensated signal is f. comp As shown in (4a);

[0017] f comp =ff noise -f′ EM (4a) Attached Figure Description

[0018] Figure 1 A schematic diagram illustrating noise assessment, useful IMF, and preliminary filtering methods for EMD;

[0019] Figure 2 A schematic diagram of a fine filtering and fitting method for parametric quadratic B-splines;

[0020] Figure 3 This is a flowchart for performing gyroscope temperature compensation using the above method. Detailed Implementation

[0021] The invention will now be described in further detail with reference to the accompanying drawings.

[0022] Figure 1 The diagram illustrates the EMD (Electronic Dynamics Decomposition) process for identifying noise, useful IMFs, and preliminary filtering. First, the gyroscope temperature drift signal is decomposed using EMD to obtain individual IMF components. The IMF components are then summed pairwise in order from high to low frequency, resulting in a new set of signal components. The mutual information between these new signal components is then calculated sequentially, and the location of the largest differential (i.e., difference) is identified. This determines the boundary between the noisy IMF and the useful IMF, achieving the purpose of preliminary filtering.

[0023] Figure 2 This paper describes a method for fine filtering and fitting using parametric quadratic B-splines. The steps are as follows: First, arbitrarily select values ​​for parameters b1 and b2 (e.g., the median value of 0), and then obtain the fitted signal of the initially filtered signal. Perform spectral analysis on the fitted signal and the noise signal. If there is superposition, increase the values ​​of parameters b1 and b2, with the step size set according to actual needs. Fit the signal again with the new parameters, repeating the above steps until the spectra of the fitted signal and the noise signal no longer overlap.

[0024] Figure 3To comprehensively utilize EMD, parametric B-splines, and mutual information for gyroscope temperature drift compensation, the main idea is to sequentially apply EMD decomposition, mutual information to determine noise and useful IMF, parametric quadratic B-splines for fine denoising and fitting, thereby achieving the purpose of denoising and fitting. Finally, the denoised fitted signal is compensated.

Claims

1. A hybrid EMD algorithm based on parameter optimization, characterized in that... Includes the following steps: (1) The gyroscope temperature drift signal f is first decomposed using EMD to obtain the decomposed components: IMF1-IMF N There are N components in total; (2) Summing the IMFs after the above decomposition in the order of decomposition yields a new set of signal components NFs. i The decomposition order is from high to low component frequencies, as shown in (2a) below, for NF i Mutual information is calculated between them to obtain a set of mutual information values ​​I. i (NF i ,NF i+1 As shown in (2b), where H(.) is the Shannon entropy algorithm, for I i (NF i ,NF i+1 Find the discrete derivative, as shown in (2c). When the derivative reaches its maximum value, it is the boundary between noise and useful signal. If the maximum value at this time is Δ... i Then IMF i+2 The boundary between noise and useful signal, i.e., when k≥i+2, is defined by the IMF. k The useful signal is shown in (2d), thus obtaining the preliminary filtered signal f. EM and noise signal f noise As shown in (2e); NF i =IMF i +IMF i+1 ,i=1,…,N-1 (2a) I i (NF i ,NF i+1 )=H(NF i )+H(NF i+1 )-H(NF i ,NF i+1 ) (2b) Δ i =I i+1 (NF i+1 ,NF i+2 )-I i (NF i ,NF i+1 ),i=1,…,N-2 (2c) (3) Regarding f in the previous step EM To perform fine filtering, a set of parametric quadratic B-spline function bases is introduced, as shown in (3a). The range of parameters b1 and b2 is -1 ≤ b1, b2 ≤ 1. When b1 and b2 are -1, the fitted curve is closest to the original signal, and the denoising effect is minimal. When b1 and b2 are 1, the fitted curve is furthest from the original signal. A straight line is drawn connecting the midpoint of the fitted curve and the original signal. The parametric quadratic B-spline function bases must satisfy the condition in (3b), where P0(b1,t) and P2(b2,t) are monotonically increasing within the range of parameters b1 and b2, while P1(b1,b2,t) is monotonically decreasing. At the same time, this basis function also guarantees C 1 Continuous, taking different values ​​of parameters b1 and b2 for f EM To perform fitting, assume f EM If the three consecutive points are M1, M2, and M3, then the fitted curve signal for this segment can be obtained as f′. EM As shown in (3c), due to the modal aliasing of EMD decomposition, it is necessary to compare f EM and f′ EM The spectrum, Simultaneously adjust the values ​​of parameters b1 and b2 until their spectra no longer overlap; f′EM=M1·P0(b1,t)+M2·P1(b1,b2,t)+M3·P2(b2,t) (3c) (4) Compensate for the gyroscope temperature drift signal and refine the above-obtained denoised fitting signal f′. EM It is a real drift signal, noise f noise After uniform compensation, the compensated signal is f. comp As shown in (4a); f comp =f-f noise -f′ EM (4a) In summary, using EMD as the initial denoising algorithm for gyroscope temperature drift signals can remove most of the noise. At the same time, by introducing parameterized quadratic B-spline basis functions and adjusting the parameter values, further fine denoising and fitting can be performed, thereby improving the accuracy of gyroscope temperature drift compensation.

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