Self-adaptive filtering method and system for electrochemical measurement and analysis

Abstract

The invention discloses a self-adaptive filtering method and system for electrochemical measurement analysis, and the method comprises the steps: obtaining an input signal sample of an electrochemical workstation, inputting the input signal sample into a transverse filter, and carrying out the filtering processing, thereby obtaining an output signal sample of the transverse filter; obtaining a difference between an output signal sample of the transverse filter and a preset expected response to obtain an estimation error; according to the estimation error, iterative updating is carried out on the tap weight vector through a minimum mean square error criterion, and an updated transverse filter is obtained; and performing electrochemical measurement adaptive filtering based on the updated transverse filter to obtain a filtered electrochemical measurement result. According to the embodiment of the invention, the filter coefficient can be adjusted in real time, the output error can be minimized, complex and changeable actual scenes can be dealt with, and continuous tracking and filtering effect optimization can be realized. The method can be widely applied to the technical field of electrochemical analysis.

Description

Technical Field

[0001] This application relates to the field of electrochemistry analysis technology, and particularly to an adaptive filtering method and system for electrochemical measurement and analysis. Background Art

[0002] An electrochemical workstation is a measuring instrument developed based on electrochemical test and analysis technology, and is widely used in fields such as new materials, new energy, biosensing, and corrosion protection. It generally consists of digital logic, analog signal hardware circuits, and an embedded system. By autonomously generating two response signals and receiving the signals after passing through the measured sample, the electrochemical workstation can analyze the properties of the measured sample and the degree of chemical reaction.

[0003] In electrochemical measurement, the detection of weak current and voltage signals is usually involved. These signals are easily affected by noise interference, thus affecting the accuracy of experimental results. Therefore, it is very important to adopt a suitable filtering method. In related technologies, for example, an electrochemical workstation control circuit and an electrochemical workstation, which only use a low-pass filter circuit composed of resistors and capacitors in the filtering part. Although it has advantages such as simple structure, low cost, and easy implementation, it also has problems such as limited frequency selectivity, limited dynamic range, and introduced noise. For a device and method for automatic range measurement of an electrochemical workstation, its low-pass filter selects an 8th-order elliptic low-pass filter chip, which can obtain a steeper cut-off frequency band, but also has problems such as limited flexibility, high dependence on external components, and frequency range limitation.

[0004] In summary, the technical problems existing in related technologies need to be improved. Summary of the Invention

[0005] The main purpose of the embodiments of this application is to propose an adaptive filtering method and system for electrochemical measurement and analysis, which can adjust the filter coefficients in real time and minimize the output error, cope with complex and changeable actual scenarios, and achieve continuous tracking and optimization of the filtering effect.

[0006] To achieve the above object, on the one hand, an embodiment of this application proposes an adaptive filtering method for electrochemical measurement and analysis, and the method includes:

[0007] Obtain an input signal sample of an electrochemical workstation and input it into a transversal filter for filtering processing to obtain an output signal sample of the transversal filter;

[0008] Obtain the difference between the output signal sample of the transversal filter and a preset desired response to obtain an estimated error;

[0009] According to the estimated error, iteratively update the tap weight vector through the least mean square error criterion to obtain an updated transversal filter;

[0010] Perform adaptive filtering on the electrochemistry measurement based on the updated transversal filter to obtain the filtered electrochemistry measurement result.

[0011] In some embodiments, the obtaining of the input signal sample of the electrochemistry workstation and inputting it into the transversal filter for filtering processing to obtain the output signal sample of the transversal filter includes:

[0012] Obtain the input signal sample of the electrochemistry workstation and perform conversion processing to obtain the tap input vector of the transversal filter;

[0013] Determine the tap weight vector of the transversal filter according to the number of delay units of the transversal filter and the time delay;

[0014] Input the tap input vector into the transversal filter for delay processing to obtain the delayed signal sample;

[0015] Multiply the delayed signal sample by the tap weight vector to obtain the weighted signal sample;

[0016] Add the delayed signal sample and the weighted signal sample to obtain the output signal sample of the transversal filter.

[0017] In some embodiments, the iteratively updating the tap weight vector according to the estimation error by the least mean square error criterion to obtain the updated transversal filter includes:

[0018] Determine the correction amount according to the inner product of the estimation error and the tap input vector;

[0019] Determine the transient estimate of the gradient vector according to the correlation matrix of the tap input vector and the cross-correlation vector between the tap input vector and the preset desired response;

[0020] Combine the correction amount and the transient estimate of the gradient vector, and iteratively update the tap weight vector by the least mean square error criterion to obtain the updated transversal filter.

[0021] In some embodiments, the determining of the transient estimate of the gradient vector according to the correlation matrix of the tap input vector and the cross-correlation vector between the tap input vector and the preset desired response includes:

[0022] Determine the gradient vector according to the correlation matrix of the tap input vector and the cross-correlation vector between the tap input vector and the preset desired response;

[0023] Based on the gradient vector, select the transient estimate of the correlation matrix and the transient estimate of the cross-correlation vector to determine the transient estimate of the gradient vector.

[0024] In some embodiments, the expression of the gradient vector is specifically as follows:

[0025]

[0026] In the above formula, J(n) represents the gradient vector, p represents the cross-correlation vector, w(n) represents the tap weight vector, R represents the correlation matrix, n represents the time, represents the variance of the desired response, w H (n) represents the conjugate transpose of the tap weight vector, p H represents the conjugate transpose of the cross-correlation vector.

[0027] In some embodiments, the expression of the transient estimate of the gradient vector is specifically as follows:

[0028]

[0029] In the above formula, represents the transient estimate of the gradient vector, u(n) represents the tap input vector, d * (n) represents the preset desired response, n represents the time, u H (n) represents the conjugate transpose of the tap input vector, represents a random vector dependent on the tap input vector u(n).

[0030] In some embodiments, the expressions of the transient estimate of the correlation matrix and the transient estimate of the cross-correlation vector are specifically as follows:

[0031]

[0032] In the above formula, represents the transient estimate of the correlation matrix, represents the transient estimate of the cross-correlation vector, u(n) represents the tap input vector, d * (n) represents the preset desired response, u H (n) represents the conjugate transpose of the tap input vector.

[0033] In some embodiments, the expression of the least mean square error criterion is specifically as follows:

[0034] J(n) → J(∞)

[0035] In the above formula, J(n) represents the mean square error generated by the adaptive filter at time n, and J(∞) represents a constant.

[0036] In some embodiments, the expression for iteratively updating the tap weight vector is specifically as follows:

[0037]

[0038] In the above formula, represents the updated tap weight vector, represents the tap weight vector before update, μ represents the step size parameter, u(n) represents the tap input vector, and e * (n) represents the estimation error.

[0039] To achieve the above object, on the other hand, an embodiment of the present application proposes an adaptive filtering system for electrochemical measurement and analysis, and the system includes:

[0040] A first module, configured to obtain an input signal sample of an electrochemical workstation and input it to a transversal filter for filtering processing to obtain an output signal sample of the transversal filter;

[0041] A second module, configured to obtain the difference between the output signal sample of the transversal filter and a preset desired response to obtain an estimation error;

[0042] A third module, configured to iteratively update the tap weight vector according to the estimation error by the least mean square error criterion to obtain an updated transversal filter;

[0043] A fourth module, configured to perform electrochemical measurement adaptive filtering based on the updated transversal filter to obtain a filtered electrochemical measurement result.

[0044] The embodiments of the present application at least include the following beneficial effects: The present application provides an adaptive filtering method and system for electrochemical measurement and analysis. This solution filters the input signal sample of the electrochemical workstation by inputting it to a transversal filter, further obtains the difference between the output signal sample of the transversal filter and the preset desired response, and iteratively updates the tap weight vector according to the estimation error by the least mean square error criterion. Only the input signal and the desired response are required, and there is no need to know the precise statistical characteristics of the signal or noise in advance. Finally, electrochemical measurement adaptive filtering is performed based on the updated transversal filter, which can minimize the output error by adjusting the filter coefficients in real time, dynamically adapt to changes in the signal or noise characteristics, can handle complex and changeable actual scenarios, and can continuously track and optimize the filtering effect. Description of the Drawings

[0045] Figure 1 is a flowchart of an adaptive filtering method for electrochemical measurement and analysis provided by an embodiment of the present application;

[0046] Figure 2It is a schematic structural diagram of an adaptive filtering system for electrochemical measurement and analysis provided by an embodiment of the present application;

[0047] Figure 3 It is a schematic flow diagram of data processing of an electrochemical workstation provided by an embodiment of the present application;

[0048] Figure 4 It is a schematic structural framework diagram of an adaptive transversal filter provided by an embodiment of the present application;

[0049] Figure 5 It is a schematic flow diagram of an adaptive filtering method provided by an embodiment of the present application;

[0050] Figure 6 It is a schematic framework diagram of the structure of a transversal filter provided by an embodiment of the present application;

[0051] Figure 7 It is a schematic model diagram of a weight adaptive control algorithm provided by an embodiment of the present application;

[0052] Figure 8 It is a schematic signal flow diagram of the least mean square algorithm provided by an embodiment of the present application;

[0053] Figure 9 It is a schematic framework diagram of an adaptive noise canceller provided by an embodiment of the present application;

[0054] Figure 10 It is a schematic framework diagram of adaptive noise cancellation provided by an embodiment of the present application;

[0055] Figure 11 It is a schematic framework diagram of an adaptive spectral enhancer provided by an embodiment of the present application;

[0056] Figure 12 It is a schematic flow diagram of adaptive spectral enhancement provided by an embodiment of the present application. Detailed implementation manners

[0057] In order to make the objectives, technical solutions and advantages of the present application more clear and understandable, the present application will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application. When the following description refers to the accompanying drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the embodiments of the present application. They are only examples of systems and methods consistent with some aspects of the embodiments of the present application as detailed in the appended claims.

[0058] It can be understood that the terms "first", "second", etc. used in this application may be used herein to describe various concepts, but unless otherwise specified, these concepts are not limited by these terms. These terms are only used to distinguish one concept from another. For example, without departing from the scope of the embodiments of this application, the first information may also be referred to as the second information, and similarly, the second information may also be referred to as the first information. Depending on the context, the words "if", "when" as used herein may be interpreted as "when...", "while...", or "in response to determining".

[0059] The terms "at least one", "a plurality of", "each", "any one", etc. used in this application, at least one includes one, two or more than two, a plurality includes two or more than two, each refers to each one of the corresponding plurality, and any one refers to any one of the plurality.

[0060] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by those of ordinary skill in the technical field to which this application belongs. The terms used herein are only for the purpose of describing the embodiments of this application and are not intended to limit this application.

[0061] Refer to Figure 1 , Figure 1 is a flowchart of an adaptive filtering method for electrochemical measurement and analysis provided for the embodiments of the present invention. Refer to Figure 1 , and the method includes the following steps:

[0062] S100. Obtain an input signal sample of the electrochemical workstation and input it into a transversal filter for filtering processing to obtain an output signal sample of the transversal filter;

[0063] It should be noted that in some embodiments, step S100 may include:

[0064] S110. Obtain an input signal sample of the electrochemical workstation and perform conversion processing to obtain a tap input vector of the transversal filter;

[0065] In this embodiment, as Figure 3 shown, the digital circuit part of the electrochemical workstation generates excitation signals such as triangular waves and sine waves and obtains corresponding analog excitation signals through a digital-to-analog conversion chip. The analog excitation signals pass through the measured sample and a standard resistor, and two output signals are obtained under the control of a potentiostat. The function of the potentiostat is to keep the electrode at a constant target potential, so that the potential difference at the electrode / solution interface can be accurately controlled artificially, thereby accurately controlling the driving force of the electrochemical reaction. The two output signals are then effectively preprocessed through a dynamic bias adjustment circuit and a gain adjustment circuit, so as to reduce signal distortion in the link before the signal enters the acquisition module.

[0066] In the acquisition module, the electrochemical workstation converts the signal from analog to digital to obtain a digital signal, and then filters it through an adaptive filtering algorithm. This linear adaptive filtering algorithm consists of two basic processes. One is the filtering process, which includes calculating the response of the linear filter output to the input signal and generating an estimation error by comparing the output result with the desired response. The other is the adaptive process, which automatically adjusts the filter parameters according to the estimation error.

[0067] These two processes work together to form a feedback loop, as Figure 4 shown. The overall process is as Figure 5 shown. First, we have a transversal filter, whose function is to complete the filtering process. Second, we have an algorithm for adaptively controlling the tap weights of the transversal filter, which is as follows:

[0068] S120. Determine the tap weight vector of the transversal filter according to the number of delay units of the transversal filter and the time delay; S130. Input the tap input vector into the transversal filter for delay processing to obtain the delayed signal samples; S140. Multiply the delayed signal samples by the tap weight vector to obtain the weighted signal samples; S150. Add the delayed signal samples and the weighted signal samples to obtain the output signal samples of the transversal filter.

[0069] In some specific embodiments, the transversal filter is as Figure 6 shown. The tap inputs u(n), u(n - 1), ···, u(n - M + 1) are the elements of the M×1 tap input vector u(n), where M - 1 is the number of delay units; these inputs span a multi-dimensional space (defined by μ n ). Correspondingly, the tap weights are the elements of the M×1 tap weight vector . The value obtained by calculating this vector through the adaptive filtering algorithm represents an estimation, and when the number of iterations approaches infinity, the expected value of this estimation may approach the Wiener solution w o (for a wide-sense stationary process).

[0070] In the filtering process, the desired response d(n) participates in the processing together with the tap input vector u(n). In this case, given an input, the transversal filter generates an output as an estimation of the desired response d(n). Therefore, we can define the estimation error e(n) as the difference between the desired response and the actual filter output. The estimation error e(n) and the tap input vector u(n) are both added to the adaptive control part, so the feedback loop around the tap weights is a closed loop.

[0071] S200. Obtain the difference between the output signal sample of the transversal filter and the preset desired response to obtain an estimation error;

[0072] S300. According to the estimation error, iteratively update the tap weight vector by the least mean square criterion to obtain an updated transversal filter;

[0073] It should be noted that in some embodiments, step S300 may include:

[0074] S310. Determine a correction amount according to the inner product of the estimation error and the tap input vector;

[0075] Specifically, as Figure 7 shown, first, for k = 0, 1, ···, M - 2, M - 1, find the inner product of the estimation error e(n) and the tap input u(n - k). The obtained result defines the correction amount which will be applied to the in the (n + 1)-th iteration. The scaling factor used in the calculation is represented by a positive number μ, which is called the step-size parameter.

[0076] S320. Determine a transient estimate of the gradient vector according to the correlation matrix of the tap input vector and the cross-correlation vector between the tap input vector and the preset desired response;

[0077] In some embodiments, step S320 may include: S321. Determine the gradient vector according to the correlation matrix of the tap input vector and the cross-correlation vector between the tap input vector and the preset desired response; S322. Based on the gradient vector, select the transient estimate of the correlation matrix and the transient estimate of the cross-correlation vector to determine the transient estimate of the gradient vector.

[0078] In this embodiment, the adaptive filter includes feedback during its operation, which causes stability problems. In this case, a meaningful criterion, namely the stability criterion, is required, and its expression is:

[0079] J(n) → J(∞) when n → ∞

[0080] where J(n) is the mean square error generated by the adaptive filter at time n, and its final value J(∞) is a constant. An algorithm that satisfies this requirement is stable in the mean square sense. To make the adaptive algorithm meet this requirement, the step-size parameter μ must satisfy certain conditions related to the spectral content of the input signal.

[0081] The difference between the final value J(∞) and the J obtained by the Wiener solution min is called the excess mean square error, denoted as J ex (∞). This difference represents the cost of replacing the deterministic method in the steepest descent algorithm with the method of controlling the tap weights in the adaptive filter by an adaptive (random) mechanism. Jex (∞) and J min The ratio of (∞) to J is called the misadjustment, which is a measure of the difference between the steady-state solution obtained by the adaptive filtering algorithm and the Wiener solution. However, it should be recognized that the misadjustment is under the control of the designer. In particular, the feedback loop acting on the tap weights is very much like a low-pass filter, and its "average" time constant is inversely proportional to the step-size parameter μ. Therefore, by setting a smaller μ, the adaptive process can proceed more slowly, and the influence of gradient noise on the tap weights can be largely filtered out. This can also greatly reduce the influence of the misadjustment.

[0082] If the gradient vector at each iteration n can be measured precisely and if the step-size parameter μ is appropriately selected, the tap weight vector obtained by the steepest descent algorithm will converge to the Wiener solution. However, in fact, precise measurement of the gradient vector is impossible because it requires prior knowledge of the correlation matrix R of the tap inputs and the cross-correlation vector p between the tap inputs and the desired response. Therefore, when the algorithm operates in an unknown environment, the gradient vector must be estimated based on the available data.

[0083] To derive an estimation method for the gradient vector the most obvious strategy is to substitute the estimates of the correlation matrix R and the cross-correlation vector between the tap inputs and the desired response, and their expressions are:

[0084]

[0085] For convenience, it is rewritten in the following form:

[0086]

[0087] The simplest choice of the estimator is to use the transient estimates of R and p based on the tap input vector and the desired response, which are defined respectively as:

[0088]

[0089] Therefore, the transient estimate of the gradient vector is:

[0090]

[0091] In the above formula, denotes the transient estimate of the gradient vector, u(n) denotes the tap input vector, d * (n) denotes the preset desired response, n denotes the time instant, u H (n) denotes the conjugate transpose of the tap input vector, denotes a random vector dependent on the tap input vector u(n).

[0092] S330. Combine the correction amount with the transient estimate of the gradient vector, and iteratively update the tap weight vector according to the least mean square error criterion to obtain an updated transversal filter.

[0093] In some specific embodiments, substituting the estimated gradient vector into the steepest descent algorithm, a new recursive relation for updating the tap vector can be obtained, and its expression is:

[0094]

[0095] Here, we use a hat symbol to represent the tap weight vector to distinguish it from the result obtained by the steepest descent algorithm. Equivalently, the result can be written in three basic relation forms as follows:

[0096] First is the filtered output, and its expression is:

[0097]

[0098] Furthermore, estimate the error or error signal, and its expression is:

[0099] e(n) = d(n) - y(n)

[0100] Finally, perform the adaptation of the tap weight vector, and its expression is:

[0101]

[0102] The algorithm described above is the complex form of the adaptive filtering algorithm. In each iteration or time update, this algorithm requires the knowledge of u(n), d(n) and the most recent values. Figure 8 The signal flow graph representation of the adaptive filtering algorithm in the form of a feedback model is given. This signal flow graph clearly illustrates the simplicity of the adaptive filtering algorithm. In particular, it can be found from the figure that the adaptive filtering algorithm only requires 2M + 1 complex multiplications and 2M complex additions in one iteration, where M is the number of tap weights in the adaptive transversal filter. The adaptive filtering algorithm is iterative in nature, and the algorithm itself can average these estimates during the adaptation process.

[0103] S400. Perform adaptive filtering on the electrochemical measurement based on the updated transversal filter to obtain the filtered electrochemical measurement result.

[0104] Furthermore, the embodiments of the present invention will be specifically described with reference to the accompanying drawings:

[0105] As Figure 9 shown, the adaptive filtering algorithm can suppress the sinusoidal interference that damages the signal carrying the excitation generated waveform in the electrochemical workstation. The process is asFigure 10 As shown, the basic input consists of an excitation-generated waveform signal and uncorrelated sinusoidal interferences, while the reference input is a sinusoidal interference in a correlated form. For the adaptive filter, a transversal filter with tap weight adaptation based on the least mean square algorithm is adopted. This filter uses the reference input to estimate the sinusoidal signal contained in the basic input terminal. Therefore, by subtracting the output of the adaptive filter from the basic input, the influence of the sinusoidal noise can be eliminated. There are two characteristics of using this adaptive noise canceller in an electrochemical workstation. One is that the canceller works like an adaptive notch filter, and its zero point is determined by the angular frequency ω0 of the sinusoidal interference. Therefore, the canceller is adjustable, and its tuning frequency varies with ω0. The other is that by choosing a sufficiently small μ, the notch of the frequency response of the canceller can be made very steep at the sinusoidal interference. Therefore, different from ordinary notch filters, we can control the frequency response of the adaptive noise canceller.

[0106] As Figure 11 shown, this filtering method can be used as an adaptive line enhancer for a system to detect sinusoidal signals submerged in a broadband noise environment. The process is as Figure 12 shown. The line enhancer is actually a degenerate form of the adaptive noise canceller. In this degenerate form, the reference signal consists of a delay of the basic signal. The delay denoted by Δ is called the prediction depth or decorrelation time delay of the adaptive line enhancer, and it is measured in units of the sampling period. The reference signal u(n - Δ) is processed by the transversal filter to generate an error signal e(n), which is defined as the difference between the actual input u(n) and the output y(n) = u(n) of the adaptive line enhancer. The error signal e(n) is used in turn to excite the least mean square algorithm to adjust the M tap weights of the filter.

[0107] Consider an input signal γ(n) consisting of a sinusoidal component submerged in broadband noise u(n) under the test conditions of electrochemical impedance spectroscopy, that is, where

[0108] In the above formula, is a random phase shift, and γ(n) is noise with zero mean and variance of . The adaptive line enhancer acts as a signal detector based on the following two functions:

[0109] One is that the prediction depth Δ is assumed to be large enough to eliminate the autocorrelation between the noise γ(n) in the original input signal and the noise γ(n - Δ) in the reference signal, and a phase shift ω0Δ is introduced between these two input sinusoidal components.

[0110] The other is that the tap weights of the transversal filter are adjusted using the least mean square algorithm to minimize the mean square error of the error signal, thereby compensating for the unknown phase shift ω0Δ.

[0111] The final result of these two effects is to produce an output signal y(n) composed of a sine wave contained in zero-mean noise. In particular, when ω0 is a multiple of π / M other than 0 or π, the output signal can be expressed as:

[0112]

[0113] In the above formula is the phase shift, and γ out (n) represents the noise output.

[0114] The scale factor is defined as:

[0115]

[0116] where M is the length of the transversal filter.

[0117] Furthermore, the expression for the signal-to-noise ratio SNR is:

[0118]

[0119] In the above formula, SNR represents the signal-to-noise ratio at the input of the adaptive line enhancer.

[0120] According to the output signal formula, it acts as a self-tuning filter, and its frequency response has a peak at the angular frequency ω0 of the input sine wave, thus acting as a line enhancer. When the SNR at the input of the line enhancer is appropriate, the output of the line enhancer will be approximately equal to the input sine component on average, so that a simple adaptive system can detect the sine signal in broadband noise.

[0121] In summary, the embodiments of the present invention have the following improvement points compared with the prior art:

[0122] 1) Compared with other filtering methods such as using an RC low-pass filter, a Sallen-Key filter, or an IIR filter for filtering, the adaptive filtering method of this design can minimize the output error by adjusting the filter coefficients in real time and dynamically adapt to changes in the signal or noise characteristics, and can continuously track and optimize the filtering effect.

[0123] 2) The adaptive filtering algorithm only requires the input signal and the desired response, and does not need to know the precise statistical characteristics of the signal or noise in advance, such as frequency and power spectrum.

[0124] 3) The adaptive filtering algorithm can be configured into various structures, supporting single-object or multi-object optimization. While Sallen-Key is usually used in analog circuits to achieve specific frequency responses, such as low-pass filtering, although IIR can achieve efficient filtering in the digital domain, its function is single and it cannot be dynamically adjusted. Through continuous learning and adjustment, adaptive filtering can handle complex and changing actual scenarios, while traditional filters are more efficient in simple and static scenarios.

[0125] Please refer to Figure 2 , the embodiment of the present application also provides an adaptive filtering system for electrochemical measurement and analysis, which can implement the above-mentioned adaptive filtering method for electrochemical measurement and analysis. The system includes:

[0126] The first module 201 is used to obtain the input signal sample of the electrochemical workstation and input it to the transversal filter for filtering processing to obtain the output signal sample of the transversal filter;

[0127] The second module 202 is used to obtain the difference between the output signal sample of the transversal filter and the preset desired response to obtain the estimation error;

[0128] The third module 203 is used to iteratively update the tap weight vector according to the estimation error by the least mean square error criterion to obtain the updated transversal filter;

[0129] The fourth module 204 is used to perform adaptive filtering on electrochemical measurement based on the updated transversal filter to obtain the filtered electrochemical measurement result.

[0130] It can be understood that the content in the above method embodiments is applicable to the system embodiments of the present application. The functions specifically implemented by the system embodiments of the present application are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those of the above method embodiments.

[0131] The preferred embodiments of the embodiments of the present application have been described above with reference to the drawings, and thus do not limit the scope of rights of the embodiments of the present application. Any modifications, equivalent replacements, and improvements made by those skilled in the art without departing from the scope and essence of the embodiments of the present application shall be within the scope of rights of the embodiments of the present application.

Claims

1. An adaptive filtering method for electrochemical measurement and analysis, characterized in that, The method includes the following steps: Obtain an input signal sample of an electrochemical workstation and input it into a transversal filter for filtering processing to obtain an output signal sample of the transversal filter; Obtain the difference between the output signal sample of the transversal filter and a preset desired response to obtain an estimation error; According to the estimation error, iteratively update the tap weight vector by the least mean square error criterion to obtain an updated transversal filter; Based on the updated transversal filter, perform adaptive filtering on electrochemical measurements to obtain a filtered electrochemical measurement result.

2. The method according to claim 1, wherein The obtaining an input signal sample of an electrochemical workstation and inputting it into a transversal filter for filtering processing to obtain an output signal sample of the transversal filter includes: Obtain the input signal sample of the electrochemical workstation and perform conversion processing to obtain a tap input vector of the transversal filter; According to the number of delay units of the transversal filter and the time delay, determine the tap weight vector of the transversal filter; Input the tap input vector into the transversal filter for delay processing to obtain a delayed signal sample; Multiply the delayed signal sample by the tap weight vector to obtain a weighted signal sample; Add the delayed signal sample and the weighted signal sample to obtain the output signal sample of the transversal filter.

3. The method according to claim 2, wherein The according to the estimation error, iteratively update the tap weight vector by the least mean square error criterion to obtain an updated transversal filter includes: Determine a correction amount according to the inner product of the estimation error and the tap input vector; According to the correlation matrix of the tap input vector and the cross-correlation vector between the tap input vector and the preset desired response, determine a transient estimate of the gradient vector; Combine the correction amount and the transient estimate of the gradient vector, and iteratively update the tap weight vector by the least mean square error criterion to obtain the updated transversal filter.

4. The method according to claim 3, wherein The according to the correlation matrix of the tap input vector and the cross-correlation vector between the tap input vector and the preset desired response, determine a transient estimate of the gradient vector includes: According to the correlation matrix of the tap input vector and the cross-correlation vector between the tap input vector and the preset desired response, determine the gradient vector; Based on the gradient vector, select a transient estimate of the correlation matrix and a transient estimate of the cross-correlation vector to determine the transient estimate of the gradient vector.

5. The method according to claim 4, wherein The expression of the gradient vector is specifically as follows: In the above formula, J(n) represents the gradient vector, p represents the cross-correlation vector, w(n) represents the tap weight vector, R represents the correlation matrix, n represents the time instant, represents the variance of the desired response, w H (n) represents the conjugate transpose of the tap weight vector, p H represents the conjugate transpose of the cross-correlation vector.

6. The method according to claim 4, wherein The expression of the transient estimate of the gradient vector is specifically as follows: In the above formula, represents the transient estimate of the gradient vector, u(n) represents the tap input vector, and d * (n) represents the preset desired response, n represents the time, and u H (n) represents the conjugate transpose of the tap input vector, represents a random vector that depends on the tap input vector u(n).

7. The method according to claim 4, wherein The expressions of the transient estimate of the correlation matrix and the transient estimate of the cross-correlation vector are specifically as follows: In the above formula, represents the transient estimate of the correlation matrix, represents the transient estimate of the cross-correlation vector, u(n) represents the tap input vector, and d * (n) represents the preset desired response, and u H (n) represents the conjugate transpose of the tap input vector.

8. The method according to claim 1, characterized in that The expression of the least mean square error criterion is specifically as follows: J(n) → J(∞) In the above formula, J(n) represents the mean square error generated by the adaptive filter at time n, and J(∞) represents a constant.

9. The method according to claim 3, wherein The expression for iteratively updating the tap weight vector is specifically as follows: In the above formula, represents the updated tap weight vector, represents the tap weight vector before update, μ represents the step size parameter, u(n) represents the tap input vector, and e * (n) represents the estimation error.

10. An adaptive filtering system for electrochemical measurement and analysis, characterized in that, The system includes: The first module is used to obtain an input signal sample of an electrochemical workstation and input it into a transversal filter for filtering processing to obtain an output signal sample of the transversal filter; The second module is used to obtain the difference between the output signal sample of the transversal filter and a preset desired response to obtain an estimation error; The third module is used to iteratively update the tap weight vector according to the estimation error by the least mean square error criterion to obtain an updated transversal filter; The fourth module is used to perform adaptive filtering of electrochemical measurements based on the updated transversal filter to obtain a filtered electrochemical measurement result.

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