An Improved Wavelet Thresholding Denoising Method

Abstract

This invention claims protection for an improved wavelet thresholding denoising method. The method decomposes a noisy signal through several layers of wavelet decomposition, obtaining the corresponding high-frequency wavelet coefficients for each layer. The amplitude of the corresponding wavelet coefficients is analyzed; those for useful signals are lower, while those for noise are higher. An improved threshold function is applied to process the wavelet coefficients at each layer, retaining coefficients below the threshold and discarding those above. These wavelet coefficients are then reconstructed using inverse wavelet transform, outputting the denoised signal. This invention constructs a new threshold function to address the shortcomings of traditional wavelet denoising algorithms in noise reduction. Experimental data processing results show that the new threshold function effectively suppresses the influence of random errors in the inertial measurement unit. Compared to the original compromise threshold algorithm, the signal-to-noise ratio is improved, the root mean square error is reduced, and the scheme of this invention achieves better signal smoothness and excellent denoising effect compared to traditional denoising schemes.

Description

Technical Field

[0001] This invention belongs to the field of inertial measurement unit technology and relates to an improved wavelet threshold-based denoising method. Background Technology

[0002] Compared to traditional gyroscopes, microelectromechanical systems (MEMS) inertial devices offer advantages such as lower production costs, smaller size, and lower overall power consumption, leading to their wide range of applications, including positioning, aerospace, and automotive. However, due to imperfect construction and inadequate compensation methods, they suffer from significant random drift errors, reducing navigation and positioning accuracy and hindering long-term navigation. Therefore, to significantly improve gyroscope navigation accuracy and enhance its practical value, the key lies in reducing the errors of MEMS gyroscopes.

[0003] At the hardware platform level, factors contributing to noise in the output of an inertial measurement unit include drift errors inherent in the device itself, interference between components (such as electromagnetic interactions), and errors in the receiving equipment's signal output. Among these errors, the most critical to address is the noise generated by the device itself.

[0004] Due to the uncertainty of the application environment, MEMS gyroscope signals exhibit non-stationary characteristics, making it difficult to obtain accurate error models. There are two main methods to improve the output performance of MEMS gyroscopes: one is to improve output performance through industrial and process technologies, such as improving vacuum packaging technology for sensitive structures, temperature compensation technology, integration level, and micromachining technology. However, limited by current process technologies, for every order of magnitude increase in MEMS accuracy, the cost increases by tens or even hundreds of times, making MEMS gyroscopes far less competitive than fiber optic gyroscopes or mechanical gyroscopes in high-precision fields. The second method relies on mathematical methods to correct the output by modeling the system. Considering that MEMS gyroscopes are generally not used alone but are fused with other sensors to jointly complete navigation tasks, Kalman filtering algorithms are often used. However, the performance of MEMS gyroscopes is easily affected by the external environment, and the random drift of the gyroscope has nonlinear, non-stationary, and slowly time-varying characteristics, affecting the accuracy of its statistical characteristics, which in turn leads to inaccurate system model establishment, thereby reducing the system filtering accuracy and even causing filter divergence.

[0005] For the output of the inertial measurement unit (IMU), noise reduction methods include classic finite-length impulse response (FIR) filtering, Wiener filtering, and adaptive filtering. These methods have certain drawbacks, namely, spectral overlap between the useful signal and noise. Meanwhile, wavelet transform excels in time-frequency local characterization, reducing high-frequency noise in the output by mitigating the difference between the wavelet coefficients of the desired output signal and the noise in the wavelet domain. It transforms the data by adding a window function to the original data and does not require a precise error model when processing non-stationary signals.

[0006] In the existing technology, Yao Zhijuan and Gu Jiajia proposed a signal denoising algorithm based on an improved wavelet threshold function, and its threshold processing formula is as follows: In this approach, the threshold is divided into three segments. While this solution addresses some issues related to soft and hard thresholds, the algorithm itself is complex and difficult to implement. Furthermore, a wavelet denoising method based on an improved threshold function, proposed by Xing Hongyan, Wu Yeli, and Li Jin, involves two adjustable parameters. However, the results of this method are not readily apparent or direct when adjusting these parameters.

[0007] Therefore, in the wavelet thresholding denoising method, this invention proposes an improved wavelet threshold function based on the compromise method. At the same time, by applying this function and using the wavelet denoising method to process the MEMS gyroscope output, the signal-to-noise ratio is significantly reduced, and the accuracy of the output signal is improved. Summary of the Invention

[0008] This invention aims to solve the problems of the prior art. An improved method based on wavelet threshold denoising is proposed, which significantly reduces the signal-to-noise ratio of the obtained MEMS gyroscope output signal and improves the accuracy of the output signal.

[0009] To achieve the above objectives, the technical solution adopted by the present invention is: an improved wavelet threshold denoising method, comprising the following steps:

[0010] 1) The noisy signal from the MEMS gyroscope is decomposed into several layers of wavelet decomposition to obtain the corresponding coefficients of the high-frequency wavelet at each layer;

[0011] 2) Using an improved threshold function, process the wavelet coefficients of each layer, keeping coefficients below the threshold and discarding those above it;

[0012] 3) Use inverse wavelet transform to reconstruct the wavelet coefficients obtained in step 2), and output the filtered MEMS gyroscope signal.

[0013] The present invention also provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the above-described improved wavelet thresholding denoising method.

[0014] Finally, the present invention provides an electronic device including a MEMS gyroscope, a memory, a processor, and a computer program stored in the memory and running on the processor, wherein the processor executes the computer program to implement the steps of the improved wavelet thresholding denoising method described above.

[0015] The innovation of this invention lies in the improvement of the threshold function in the traditional wavelet threshold denoising algorithm, which has the advantages of facilitating the calculation of the denoised signal and avoiding signal distortion and inaccuracy.

[0016] This invention addresses the problems of discontinuity in hard thresholding functions, which can cause oscillations in the denoised signal, and the discrepancy between wavelet coefficients estimated by soft thresholding functions and wavelet coefficients of the original signal, which can lead to distortion after signal reconstruction.

[0017] This invention can provide a solution by changing the parameters in the threshold function. This allows the function to switch between soft and hard threshold functions, broadening its application range. Attached Figure Description

[0018] Figure 1 This is an overall flowchart of the present invention;

[0019] Figure 2 The MEMS gyroscope was placed on a horizontal surface under a constant temperature of 25°C, and static signals were acquired at a sampling frequency of 50 Hz. The results were obtained by processing the gyroscope signals using a soft thresholding function in a wavelet denoising algorithm.

[0020] Figure 3 Under the above conditions, the result is obtained by applying the hard threshold function to the wavelet denoising algorithm to process the gyroscope signal;

[0021] Figure 4 The result is obtained by applying a compromise threshold function to the wavelet denoising algorithm to process the gyroscope signal under the above conditions.

[0022] Figure 5 The result is obtained by applying the improved threshold function of the present invention to the wavelet denoising algorithm to process the gyroscope signal under the above conditions. Detailed Implementation

[0023] The technical solutions of the embodiments of the present invention will be clearly and thoroughly described below with reference to the accompanying drawings. The described embodiments are merely some embodiments of the present invention.

[0024] An improved wavelet thresholding denoising method is proposed. The noisy MEMS gyroscope signal is decomposed into several layers of wavelet decomposition to obtain the corresponding coefficients of the high-frequency wavelets at each layer. The amplitude of the corresponding wavelet coefficients is analyzed, and an improved threshold function is used to process the wavelet coefficients at each layer, retaining coefficients below the threshold and discarding those above. These wavelet coefficients are then reconstructed using inverse wavelet transform, outputting the denoised signal. This denoised signal exhibits very few glitches, more closely approximates the ideal signal, retains more complete information, and shows a significant improvement in denoising performance. The overall structure is as follows: Figure 1 As shown.

[0025] The improved wavelet thresholding denoising method includes the following steps:

[0026] 1) Wavelet transform is applied to process the original noisy input MEMS gyroscope signal, thereby determining the wavelet basis functions and the number of decomposition levels. After several layers of wavelet decomposition, the corresponding high-frequency wavelet coefficients for each layer can be obtained. The amplitude of the corresponding wavelet coefficients is analyzed; the amplitude is lower for useful signals and higher for noise.

[0027] In selecting wavelet basis functions, those more suitable for MEMS signal denoising are chosen. The primary aspects to address are support and the order of the vanishing moments. Excessive support increases the time-domain resolution, leading to increased computational complexity. The order of the vanishing moments primarily reflects the singularity of the signal. The choice depends on the specific characteristics of the signal. Due to its good symmetry, the sym wavelet is selected as the wavelet basis function in this invention.

[0028] The number of decomposition levels is a crucial factor affecting the final output signal's noise reduction performance. Increasing the number of decomposition levels makes the distinction between the wavelet coefficients of the useful signal and the wavelet coefficients of the noise more obvious, allowing for easier separation. However, setting the number of levels too high can lead to the following consequences: the signal obtained after the inverse wavelet transform will have an increased offset from the original signal, resulting in severe signal distortion, which is detrimental to processing MEMS signals. In wavelet denoising, the number of wavelet decomposition levels is typically 3-6. This invention selects a decomposition level of 4 levels.

[0029] 2) For the input signal, a corresponding threshold function is used to resolve the high-frequency wavelet coefficients. Specifically, an improved threshold function is applied to process the wavelet coefficients of each layer, keeping coefficients below the threshold and discarding those above it.

[0030] If the threshold is set too high, some useful data will be removed; if it is too low, the denoising effect will be poor. Furthermore, the choice of threshold function affects the smoothness of the reconstructed signal. This wavelet denoising algorithm, which applies an improved threshold function, produces a smoother waveform in its output signal, and also achieves higher reconstruction accuracy, with the signal average value close to the true value.

[0031] The proposed new improved threshold function is shown in the following equation:

[0032] (1)

[0033] in , It is a regulating factor. , , , These refer to the wavelet transform coefficients before and after denoising, respectively. It is a threshold; It is represented as a symbolic function.

[0034] From analytical expression (1), we can obtain:

[0035] 1) hour,

[0036] when hour,

[0037] (2)

[0038] hour,

[0039] (3)

[0040] Equation (1) in Continuity at that point leads to equation (1) in continuous.

[0041] 2) hour,

[0042] (4)

[0043] hour,

[0044] (5)

[0045] when hour:

[0046] (6)

[0047] In summary, equation (1) is based on It is an asymptote.

[0048] The construction method of equation (1) is similar to that of a general threshold function. The main focus is on finding a way to... Partially zeroed out, only processing In terms of aspects. Equations (2) and (3) show that the function is continuous, thus avoiding issues with the output, such as severe oscillations, similar to a hard threshold function. Equations (4), (5), and (6) show that the function... For asymptotes. When the wavelet coefficients At that time, let and The distance is close to zero, thus avoiding the constant bias problem present in the soft thresholding function. This can be achieved by changing the parameters. ,when When this occurs, the function is a soft threshold function. This is a hard thresholding function. Therefore, it can be deduced that the parameters can be changed to become a soft or hard thresholding function, thus broadening its application range.

[0049] 3) Then, the wavelet coefficients retained in step 2) are used for wavelet reconstruction using inverse wavelet transform to output the desired filtered MEMS gyroscope signal.

[0050] The sym wavelet is selected, the decomposition level is set to 4, the threshold function in this invention is applied for processing, and then the wavelet is reconstructed to obtain the output signal.

[0051] Figures 2-5 For comparison with the effects of other threshold functions.

[0052] Compared to the other three threshold functions, this wavelet denoising algorithm, which uses an improved threshold function, produces a smoother waveform in its signal output. Furthermore, it has higher reconstruction accuracy and the average signal value is close to the true value.

Claims

1. An improved wavelet thresholding denoising method, characterized in that, Includes the following steps: 1) The noisy signal output by the MEMS gyroscope is decomposed into several layers of wavelet decomposition to obtain the corresponding coefficients of the high-frequency wavelet at each layer. 2) Using an improved threshold function, process the wavelet coefficients of each layer, remove wavelet coefficients whose absolute value is less than the threshold, and retain wavelet coefficients whose absolute value is greater than or equal to the threshold after correction according to the improved threshold function. The improved threshold function is shown in the following equation: in , It is a regulating factor. , , , These refer to the wavelet transform coefficients before and after denoising, respectively. It is a threshold. It is a symbolic function; 3) Use inverse wavelet transform to reconstruct the wavelet coefficients obtained in step 2), and output the filtered MEMS gyroscope signal.

2. The improved wavelet thresholding denoising method according to claim 1, characterized in that: In step 1), the sym wavelet is selected as the wavelet basis function.

3. The improved wavelet thresholding denoising method according to claim 1, characterized in that: The wavelet decomposition in step 1) has 3-6 layers.

4. The improved wavelet thresholding denoising method according to claim 3, characterized in that: The wavelet decomposition in step 1) has 4 layers.

5. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the improved wavelet thresholding denoising method according to any one of claims 1 to 4.

6. An electronic device comprising a MEMS gyroscope, a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the improved wavelet threshold denoising method according to any one of claims 1 to 4.

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