CN114964219A - A Hybrid EMD Algorithm Based on Parameter Optimization - Google Patents

Abstract

A hybrid EMD algorithm based on parameter optimization. A gyro temperature drift compensation algorithm based on parameter-containing quadratic triangle B spline and EMD decomposition belongs to the field of digital signal processing. The method is characterized in that an EMD decomposition and mutual information algorithm is adopted to carry out initial denoising on a gyro temperature drift signal, then a quadratic triangle B spline basis function with parameters is adopted to carry out fine denoising and fitting on the signal after the initial denoising, and finally the final parameter value of a quadratic triangle B spline is determined by analyzing the spectrum separation degree between the noise and the fitting signal, so that the final fitting signal is obtained and compensated. Aiming at the defects that the traditional temperature drift fitting does not remove noise and can not adjust the noise removal effect, the invention can remove noise and fit the temperature drift signal more accurately by introducing the quadratic triangle B spline basis function with parameters and combining the algorithms of EMD decomposition, mutual information noise removal, spectrum separation estimation and the like, thereby improving the precision and the effect of gyro temperature compensation.

Description

A Hybrid EMD Algorithm Based on Parameter Optimization

technical field

The invention relates to a gyroscope temperature drift compensation algorithm based on B-spline, EMD and mutual information, and belongs to the field of digital signal processing.

Background technique

The temperature drift of the gyroscope is an important factor affecting the accuracy and reliability of the gyroscope. Therefore, temperature compensation is a common method to overcome the influence of temperature. Common methods of gyro temperature compensation include support vector machine method, genetic algorithm, particle algorithm, various regression algorithms, etc. Usually, these methods directly compensate the signal output by the gyro, which means that when calculating the fitting, the noise is at the same time. It is also processed as part of the useful signal, which will inevitably introduce noise and inevitably reduce the accuracy of fitting and compensation.

EMD is a signal processing method developed in recent years. It is decomposed based on the signal time scale and is suitable for nonlinear and non-stationary signal processing. Since it does not need to determine the subjective experience parameter settings such as basis functions and decomposition layers, in some cases, it has better decomposition than wavelet transform. Effect. At the same time, EMD can not only be used for signal decomposition, but is also used more and more in the field of signal filtering. B-spline is a curve and surface fitting algorithm, which is widely used in CAGD, signal processing and many other fields. In the field of signal fitting, especially in the field of discrete data fitting, B-spline curves have been paid more and more attention by researchers due to their simplicity, continuity and derivability. Trigonometric splines and trigonometric polynomials are of great significance in both theory and practical applications. B-splines also have certain limitations. For known B-splines, since their basis functions are given, there is no flexibility in curve fitting and denoising, and the obtained results are unique, which is suitable for practical applications. inconvenience. In order to solve this problem, it is necessary to introduce a spline function with parameters, and adjust the shape and curvature of the curve according to the needs, so as to achieve more accurate denoising and fitting effects. Mutual information is a very useful information measurement method in information theory. It is used to measure the amount of information contained in a random variable about another random variable. In engineering practice, by calculating the mutual information value of two variables, the correlation between the two variables and the size of the common information can be known.

SUMMARY OF THE INVENTION

In order to solve the above problems, the present invention provides denoising for EMD noise IMF and useful IMF, the basis function of quadratic triangular B-spline with parameters and its properties, the use of the above basis function for fine denoising and gyro temperature Compensate for innovation in these four areas. First, use EMD decomposition and mutual information algorithm to initially de-noise the gyro temperature drift signal f, and initially filter the signal f _EM and the noise signal f _noise . Then use the quadratic triangular B-spline basis function (3a) with parameters to finely denoise and fit the initial denoised signal f _EM , and finally determine the quadratic triangular by analyzing the degree of spectral separation between the noise and the fitted signal. The final parameter value of the B-spline is obtained to obtain the final fitting signal f' _EM , and finally (4a) is used for final compensation. The method first performs EMD decomposition on the temperature drift data of the gyroscope. Furthermore, by performing mutual information calculation on the signal decomposed by EMD, a useful signal can be obtained to achieve the purpose of initial filtering. Finally, in view of the problem that traditional fitting cannot be finely filtered, a quadratic B-spline basis function with parameters is introduced to remove residual noise while fitting the data. By comparing the spectral separation degree of the final signal and noise, the quadratic Parameters for triangular B-splines.

The present invention adopts following technical scheme for solving its technical problem:

1. For the gyro temperature drift signal f, first use EMD to decompose to obtain each decomposed component: IMF ₁ -IMF _N , a total of N components.

2. The above decomposed IMFs are summed in pairs according to the sequence of decomposition (the sequence of component frequencies from high to low) to obtain a new set of signal components NF _i , as shown in (1) below. Perform mutual information calculation between NF _i to obtain a set of mutual information values I _i (NF _i ,NF _i+1 ), as shown in (2), where H(.) is the Shannon entropy algorithm. Calculate the discrete differential of I _i (NF _i ,NF _i+1 ), as shown in (3), when the differential reaches the maximum value, it is the boundary point of noise and useful signal. If the maximum value is Δ _i at this time, it is the maximum value, Then IMF _i+2 is the boundary between noise and useful signal, that is, when k ≥ i+2, IMF _k is a useful signal, as shown in (4), so as to obtain the preliminary filtered signal f _EM and noise signal f _noise , such as (5 ) shown.

NF _i =IMF _i +IMF _i+1 ,i=1,...,N-1 (1)

I _i (NF _i ,NF _i+1 )=H(NF _i )+H(NF _i+1 )-H(NF _i ,NF _i+1 ) (2)

Δ _i =I _i+1 (NF _i+1 ,NF _i+2 )-I _i (NF _i ,NF _i+1 ),i=1,...,N-2 (3)

3. Perform fine filtering on the f _EM in the previous step. A set of quadratic triangular B-spline function bases with parameters is introduced, as shown in (6), where the value range of parameters b ₁ , b ₂ is -1≤b ₁ , b ₂ ≤1, and when b ₁ , When b ₂ is -1, the fitting curve is the closest to the original signal, and the denoising effect is the smallest; when b ₁ and b ₂ are 1, the fitting curve is the farthest from the original signal, which is a straight line at the midpoint of the original signal. Connected, the denoising effect is the greatest. The above-mentioned parametric quadratic triangular B-spline function base needs to meet the conditions of (7), where P ₀ (b ₁ ,t) and P ₂ (b ₂ ,t) are monotonic within the value range of parameters b ₁ , b ₂ increases; P ₁ (b ₁ , b ₂ , t) decreases monotonically. At the same time, this basis function also guarantees C ¹ continuity. Take different values of parameters b ₁ , b ₂ to fit f _EM . Assuming that three consecutive points on f _EM are M ₁ , M ₂ and M ₃ respectively, the fitting curve signal of this section can be obtained as f _E ' _M , as shown in (8). Due to the modal aliasing of EMD decomposition, it is necessary to compare the spectra of f _EM and f _E ′ _M , and adjust the values of parameters b ₁ and b ₂ at the same time until the two spectra no longer overlap.

f' _EM = M ₁ ·P ₀ (b ₁ ,t)+M ₂ ·P ₁ (b ₁ ,b ₂ ,t)+M ₃ ·P ₂ (b ₂ ,t) (8)

4. Compensate the temperature drift signal of the gyroscope. Perform uniform compensation on the obtained finely denoised fitting signal f′ _EM and noise f _noise , and obtain the compensated signal as f _comp , as shown in (9).

f _comp = ff _noise - f' _EM (9)

Description of drawings

Fig. 1 is a schematic diagram of EMD judging noise, useful IMF and preliminary filtering method.

FIG. 2 is a schematic diagram of a method for fine filtering and fitting with a quadratic triangular B-spline with parameters.

FIG. 3 is a flow chart of temperature compensation of the gyro using the above method.

Detailed ways

The invention will be described in further detail below in conjunction with the accompanying drawings.

Figure 1 is a schematic diagram of EMD judgment noise, useful IMFs and preliminary filtering. First, the temperature drift signal of the gyro is decomposed by EMD to obtain each IMF component. The IMF components are summed in pairs in the order of high frequency to low frequency, and a new set of signal components is required. The mutual information is obtained sequentially among the new signal components, and the position with the largest differential (ie, difference) is found, so as to determine the boundary between the noise IMF and the useful IMF, and achieve the purpose of preliminary filtering.

Figure 2 describes the method for fine filtering and fitting of quadratic triangular B-splines with parameters. The steps are to first arbitrarily take the values of parameters b ₁ and b ₂ (for example, the median value 0), and then obtain the signal after preliminary filtering. the fitted signal. Perform spectrum analysis on the fitted signal and the noise signal. If there is superposition, increase the values of parameters b ₁ and b ₂ , and set the step size according to actual needs. The signal under the new parameters is fitted again, and the above steps are repeated until the spectrum between the fitted signal and the noise signal is no longer superimposed.

Figure 3 shows the method of comprehensively using EMD, B-splines with parameters and mutual information to compensate the temperature drift of the gyroscope. The main idea is to use EMD decomposition, mutual information to judge noise and useful IMF, and quadratic triangle B-splines with parameters in order Fine denoising and fitting, so as to achieve the purpose of denoising and fitting, and finally compensate the fitting signal after denoising.

Claims (1)

1. A method for gyro temperature drift signal decomposition, filtering, fitting and compensation, comprising the steps of:

(1) firstly, decomposing a gyro temperature drift signal f by using EMD to obtain each decomposition component: IMF ₁ -IMF _N And N components.

(2) The IMF after the decomposition is subjected to pairwise summation according to the decomposition sequence (the sequence of the component frequencies from high to low) to obtain a group of new signal components NF _i This is as shown in (2a) below. For NF _i Mutual information calculation is carried out to obtain a group of mutual information values I _i (NF _i ,NF _i+1 ) As shown in (2b), where H (.) is shannon entropy algorithm. To I _i (NF _i ,NF _i+1 ) The discrete differentiation is made, as shown in (2c), and when the differentiation takes a maximum value, the point is the boundary point between noise and useful signal, and when the maximum value is Δ _i At maximum, then IMF _i+2 Is a noise and useful signal boundary, i.e. when k ≧ i +2, IMF _k For the useful signal, as shown in (2d), to obtain a preliminary filtered signal f _EM And a noise signal f _noise As shown in (2 e).

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) For f in the previous step _EM Fine filtering is performed. Introducing a set of B-spline function bases with parameters of quadratic trigonometry, as shown in (3a), wherein the parameter B ₁ ,b ₂ Has a value range of-1 to b ₁ ,b ₂ 1 or less, and when b is ₁ ,b ₂ When-1 is taken, the fitting curve is closest to the original signal, and the denoising effect is minimum; when b is ₁ ,b ₂ And when 1 is taken, the fitted curve is farthest away from the original signal, and is a straight line connecting line of the middle point of the original signal, so that the denoising effect is maximum. The above-described parametric quadratic trigonometric B-spline function basis needs to satisfy the condition of (3B), wherein P ₀ (b ₁ T) and P ₂ (b ₂ T) at parameter b ₁ ,b ₂ Monotonically increases within the value range of (a); p ₁ (b ₁ ,b ₂ And t) is monotonically decreasing. At the same time, the basis function also ensures C ¹ And (4) continuous. Taking parameter b ₁ ,b ₂ Different value pairs f _EM Fitting is performed, assuming f _EM The upper three continuous points are respectively M ₁ 、M ₂ 、M ₃ Then the fitted curve signal of this segment can be found to be f' _EM As shown in (3 c). Contrast f is required due to modal aliasing of EMD decomposition _EM And f' _EM While adjusting the parameter b ₁ ,b ₂ Until there is no more overlap between the two spectra.

f′ _EM ＝M ₁ ·P ₀ (b ₁ ,t)+M ₂ ·P ₁ (b ₁ ,b ₂ ,t)+M ₃ ·P ₂ (b ₂ ,t) (3c)

(4) And compensating the gyro temperature drift signal. Fitting signal f 'obtained after fine denoising' _EM (considered as true drift signal), noise f _noise Performing unified compensation to obtain a compensated signal f _comp As shown in (4 a).

f _comp ＝f-f _noise -f′ _EM (4a)

In conclusion, the EMD is used as an initial denoising algorithm of the gyro temperature drift signal, so that most of noise can be removed, a quadratic triangle B spline basis function with parameters is introduced, and further fine denoising and fitting can be performed by adjusting the values of the parameters, so that the temperature drift compensation precision of the gyro is improved.

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