FIR filter coefficient identification method and device under noise interference

Abstract

The present invention provides a method and device for identifying coefficients of an FIR filter under noise interference. By acquiring the input signal and output signal of the FIR filter, an augmented gradient iteration E-EGI algorithm based on an exponential criterion function is proposed on the basis of negative gradient search, and an augmented Newton iteration E-ENI algorithm based on an exponential criterion function is proposed using Newton search. The two algorithms are used to estimate the parameters of the FIR filter to achieve the purpose of coefficient identification. The augmented gradient iteration E-EGI algorithm and augmented Newton iteration E-ENI algorithm of the present invention have higher accuracy in parameter estimation and can effectively achieve the purpose of accurate filtering of the FIR filter.

Description

Technical Field

[0001] The invention belongs to the technical field of signal processing, and in particular relates to a method and a device for identifying FIR filter coefficients under noise interference. Background Art

[0002] Finite impulse response (FIR) filter is a common digital filter in practical engineering. It can be designed by computer synthesis coefficients, software simulation, and hardware debugging. FIR filter is more stable than infinite impulse response (IIR) filter, and its structure is simpler to implement. At the same time, with the rapid development of computer hardware, FIR filter is also constantly overcoming the situation that it is worse than IIR filter at the same order. Therefore, FIR filter is gradually becoming an important part of practical engineering projects. The accuracy of parameter estimation of FIR filter determines whether it has a higher effect in practical engineering applications.

[0003] Most of the existing algorithms for estimating FIR filter parameters are obtained by optimizing the quadratic criterion function and combining different search methods. However, among the many parameter estimation algorithms, there are criterion functions composed of the absolute value sum of errors, the fourth power of errors, and the exponential sum of squared errors. The calculation and optimization of these types of criterion functions are relatively cumbersome, and the parameter estimation accuracy is low. Summary of the invention

[0004] In order to solve the above problems existing in the prior art, the present invention provides a method and device for identifying FIR filter coefficients under noise interference. The technical problem to be solved by the present invention is achieved by the following technical solutions:

[0005] The present invention provides a method for identifying FIR filter coefficients under noise interference, comprising:

[0006] S100, obtaining an input signal and an output signal of the FIR filter, and establishing a differential equation describing the relationship between the input and the output according to the input signal and the output signal;

[0007] S200, constructing a parameter vector and an information vector according to an input signal and an output signal;

[0008] S300, transforming the difference equation using the parameter vector and the information vector to obtain an identification model of the FIR filter with sliding average and colored noise;

[0009] Among them, the parameter vector contains all the parameters to be identified of the FIR filter;

[0010] S400, using an augmented gradient iteration E-EGI algorithm based on an exponential criterion function or an augmented Newton iteration E-ENI algorithm based on an exponential criterion function to estimate a parameter vector in the identification model to obtain an estimation vector;

[0011] S500, obtaining determined values ​​of all parameters to be identified of the FIR filter from the estimated vector.

[0012] The invention provides a device for identifying coefficients of an FIR filter under noise interference, comprising a processing device for implementing a method for identifying coefficients of an FIR filter under noise interference through processing.

[0013] The present invention provides a method and device for identifying coefficients of an FIR filter under noise interference. By acquiring the input signal and output signal of the FIR filter, an augmented gradient iteration E-EGI algorithm based on an exponential criterion function is proposed on the basis of negative gradient search, and an augmented Newton iteration E-ENI algorithm based on an exponential criterion function is proposed using Newton search. These two algorithms are used to estimate the parameters of the FIR filter to achieve the purpose of coefficient identification. The augmented gradient iteration E-EGI algorithm and augmented Newton iteration E-ENI algorithm of the present invention have higher accuracy in parameter estimation and can effectively achieve the purpose of accurate filtering of the FIR filter.

[0014] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 It is a flow chart of a method for identifying FIR filter coefficients under noise interference provided by the present invention;

[0016] Figure 2a It is a calculation flow chart of the E-EGI algorithm provided by the present invention;

[0017] Figure 2b It is a calculation flow chart of the E-ENI algorithm provided by the present invention;

[0018] Figure 3 It is a curve diagram of the estimated parameter error δ of the three algorithms provided by the present invention changing with k;

[0019] Figure 4 is a curve diagram showing the variation of the estimation error δ of the E-EGI algorithm provided by the present invention with respect to k;

[0020] Figure 5 It is a curve diagram of the variation of the estimation error δ of the E-ENI algorithm provided by the present invention with respect to k. DETAILED DESCRIPTION

[0021] The present invention is further described in detail below with reference to specific embodiments, but the embodiments of the present invention are not limited thereto.

[0022] like Figure 1 As shown, the present invention provides a method for identifying FIR filter coefficients under noise interference, comprising:

[0023] S100, obtaining an input signal and an output signal of the FIR filter, and establishing a differential equation describing the relationship between the input and the output according to the input signal and the output signal;

[0024] A filter is a system that filters the signal to be processed to achieve the desired effect. In actual control systems, there are often various noise interferences. The identification of noise models is conducive to the control and prediction of filter systems. Among the colored noise models, the moving average (MA) model is a more commonly used description of colored noise.

[0025] Considering the FIR filter with sliding average colored noise, the differential equation representing the relationship between input and output in S100 is:

[0026] y(t)=B(z)u(t)+D(z)v(t) (1);

[0027] in, and are the input signal and output signal of the FIR filter respectively, is zero mean with variance σ 2 The random white noise sequence is represented by t, which represents the discrete time variable, that is, the variable takes a value at time tT, where T is the sampling period; z -1 is the unit shift operator, z -1 y(t)=y(t-1), B(z) and D(z) are time-invariant polynomials with constant terms of the unit shift operator z-1, represents the coefficients of the FIR filter, represents the coefficient of the noise term, n b Indicates the order of the coefficients of the FIR filter, n d represents the order of the coefficients of the noise term, represents the field of real numbers, and := means defining the symbol on the left side of the equal sign as the expression on the right side.

[0028] S200, constructing a parameter vector and an information vector according to an input signal and an output signal;

[0029] Assuming the order n b and n d Given, let n be: =n b +n d , define the parameter vector and information vector in S200 as:

[0030]

[0031]

[0032] Among them, θ is the parameter vector containing all the parameters to be identified, is the information vector.

[0033] S300, transforming the difference equation using the parameter vector and the information vector to obtain an identification model of the FIR filter with sliding average and colored noise;

[0034] According to the above definition, system (1) can be converted into the identification model in S300, which is specifically expressed as:

[0035]

[0036] The above formula is the identification model of the FIR filter with colored noise and sliding average. The parameter vector θ contains all the parameters to be identified of the FIR filter. The goal of the present invention is to estimate the coefficients of the filter through sampling values.

[0037] S400, using an augmented gradient iteration E-EGI algorithm based on an exponential criterion function or an augmented Newton iteration E-ENI algorithm based on an exponential criterion function to estimate a parameter vector in the identification model to obtain an estimation vector;

[0038] The following introduces the specific sources and solution process of the augmented gradient iteration E-EGI algorithm based on the exponential criterion function and the augmented Newton iteration E-ENI algorithm:

[0039] S410, defining a criterion function according to the identification model, and calculating a gradient vector and a Hessian matrix of the exponential criterion function;

[0040] S411, obtaining a first estimated expression of the parameter vector according to the gradient vector minimization criterion function, and obtaining a second estimated expression of the parameter vector using the Newton search minimization criterion function;

[0041] S412, obtaining an expression of the information vector using the estimated value of the white noise and the step size;

[0042] S413, obtaining a calculation formula of the E-EGI algorithm based on the first estimated expression of the parameter vector and the estimated expression of the information vector, and obtaining a calculation formula of the E-ENI algorithm based on the second estimated expression of the parameter vector and the estimated expression of the information vector.

[0043] Considering the sampling data from t = 1 to t = L, the exponential criterion function is defined according to the identification model as:

[0044]

[0045] Let k = 1, 2, 3, ... be the iteration variable, represents the estimate of the parameter vector θ obtained in the kth iteration. Find the criterion function J 1 (θ) is the first-order partial derivative of the parameter vector, the criterion function J 1 The gradient vector of (θ) is:

[0046]

[0047]

[0048]

[0049] Use negative gradient search to minimize the criterion function J 1 (θ) The first estimated expression is:

[0050]

[0051] Among them, in order to ensure the convergence of the parameter vector, the matrix The eigenvalues ​​of are all within the unit circle, and there are no repeated eigenvalues ​​on the unit circle. The step size μ k Must meet:

[0052]

[0053] According to the above derivation process, we can get the exponential criterion function-based extended gradient iterative algorithm (E-EGI algorithm) for identifying the parameter vector θ of the FIR-MA system:

[0054] The calculation formula of the E-EGI algorithm in S440 is:

[0055]

[0056]

[0057]

[0058]

[0059]

[0060]

[0061] in, Superscripts indicate estimates.

[0062] The steps of the E-EGI algorithm to calculate the filter parameter estimation vector are as follows. The flowchart of calculating the parameter estimation vector is shown in Figure 2. The specific process is as follows:

[0063] S420, initialize so that the initial values ​​of all variables are zero when t≤0, set the iteration variable k=1, give the offline data length L, and set the parameter estimation accuracy ε; and set the estimation vector Noise term Take p 0 =10 6 ;

[0064] S421, using E-EGI algorithm (13) to obtain the estimated information vector

[0065] S422, using E-EGI algorithm (14) and (15) to obtain the intermediate vector and the intermediate matrix And use formula (11) to determine the fixed step size μ k ;

[0066] S423, update the parameter estimation vector by formula (10) And use equation (16) to calculate the estimate of the noise term

[0067] S424, Comparison and if The k value is increased by 1 and jumps to S421; otherwise, the parameter estimation vector of the output filter is Terminate the iterative calculation process.

[0068] In the optimization method, compared with the negative gradient search, the Newton search has a faster descent rate. In order to further improve the parameter estimation accuracy of the identification method, the present invention can also use the Newton search method for derivation.

[0069] By finding the criterion function J 1 The second-order partial derivative of (θ) with respect to the parameter vector gives the Hessian matrix:

[0070]

[0071] Using Newton search, minimize the criterion function J 1 (θ) The second estimated expression is:

[0072]

[0073] because and The unknown noise term v(ti) is included, and equation (4) cannot be calculated directly. Here, the k-1th estimated value of v(ti) is used to define Estimates:

[0074]

[0075] Similarly, the same problem exists as in the E-EGI algorithm. The right side of equation (12) contains an unmeasurable information vector Therefore, the parameter estimates cannot be calculated. Using the definition of equation (13), the unmeasurable vector Use it to estimate Instead, we can get and Estimates and Based on the above derivation process, we can get the exponential criterion function-based extended Newtoniterative algorithm (E-ENI algorithm) for identifying the parameter vector of the FIR-MA system. The calculation formula of the E-ENI algorithm is:

[0076]

[0077]

[0078]

[0079]

[0080]

[0081]

[0082]

[0083] in, Superscripts indicate estimates.

[0084] The steps of calculating the parameter estimation vector by the E-ENI algorithm are as follows: Figure 3 As shown, the specific process is as follows:

[0085] S430, initialization makes all variables zero when t≤0, sets iteration variable k=1, gives offline data length L, and sets parameter estimation accuracy ε; and sets estimation vector Noise term Take p 0 =10 6 ;

[0086] S431, using E-EGI algorithm (13) to obtain the estimated information vector

[0087] S432, using E-EGI algorithm, equations (9), (14) and (15) to obtain the matrix Middle vector and the intermediate matrix And use formula (11) to determine the fixed step size μ k ;

[0088] S433, update the parameter estimation vector using equation (12) And use equation (16) to calculate the estimate of the noise term

[0089] S434, Comparison and if The k value is increased by 1 and jumps to S431; otherwise, the parameter estimation vector of the output filter is Terminate the iterative calculation process.

[0090] S500, obtaining determined values ​​of all parameters to be identified of the FIR filter from the estimated vector.

[0091] The invention provides a FIR filter coefficient identification device under noise interference, which is used to implement a FIR filter coefficient identification method under noise interference.

[0092] The coefficient recognition effect of the present invention is illustrated by simulation experiments below.

[0093] Generally speaking, for a system identification algorithm, its identification performance is related to the information used. In other words, the richer the information used by the algorithm, the better the identification effect. 1 Therefore, under the same conditions, the performance of the E-ENI algorithm is relatively higher than that of the E-EGI algorithm.

[0094] In order to show the advantages of the E-EGI and E-ENI algorithms proposed in this paper based on the exponential criterion function, the present invention refers to the extended gradient-based iterative algorithm (EGI algorithm) based on the quadratic criterion function and compares it with the above two algorithms in the simulation part.

[0095] Achieve Results

[0096] Consider the following FIR filter model for colored noise with sliding average:

[0097] y(t)=B(z)u(t)+D(z)v(t),

[0098] B(z)=b 1 z -1 +b 2 z -2 =1.28z -1 -1.88z -2 ,

[0099] D(z)=1+d 1 z -1 +d 2 z -2 =1-1.55z -1 +0.68z -2 .

[0100] θ=[b 1 , b 2 , d 1 , d 2 ] = [1.28, -1.88, -1.55, 0.68] T .

[0101] The system input {u(t)} uses an uncorrelated continuous excitation signal sequence with zero mean and unit variance, and {v(t)} uses a sequence with zero mean and variance σ 2 =0.30 2 The simulated measurement data length L=3000 is set, and the parameters of the above system are estimated using EGI, E-EGI and E-ENI algorithms. Parameter estimation values ​​and their estimation errors The results of the changes with the number of iterations k are as follows Figure 3 And as shown in Table 1.

[0102] In order to test the impact of interference on the performance of the proposed method, the E-EGI algorithm and the E-ENI algorithm are used to update the system parameters under different noise levels, namely, σ 2 =[0.10 2 , 0.30 2 , 0.50 2 ]. Estimated error see Figure 4 , Figure 5 .

[0103] Table 1 Parameter estimates and estimation errors

[0104]

[0105] According to the simulation results, we can know that:

[0106] (1) As the iteration variable k increases, the parameter estimates of the three algorithms are getting closer and closer to the true values, which shows that the E-EGI algorithm and E-ENI algorithm proposed in this paper are effective for identifying FIR-MA systems.

[0107] (2) Under the same simulation conditions, compared with the EGI algorithm, the parameter estimation accuracy of the E-EGI algorithm and the E-ENI algorithm proposed in this paper is higher, and among the three algorithms, the parameter estimation accuracy of E-ENI is the best.

[0108] (3) For the FIR-MA system, when the noise level is very low, it is not conducive to identifying the parameters of the noise model D(z). Therefore, when the noise variance gradually becomes smaller, the parameter estimation accuracy of the E-EGI algorithm and the E-ENI algorithm will decrease.

[0109] The present invention provides a coefficient identification method for an FIR filter with colored noise and sliding average. By defining an exponential criterion function, using gradient search and Newton search, an E-EGI algorithm and an E-ENI algorithm are obtained. Numerical examples show that the two derived algorithms have better parameter estimation accuracy than the EGI algorithm. This shows that the method proposed by the present invention is more effective than the existing method and can effectively identify the coefficients of the FIR filter.

[0110] In addition, the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" and "second" may explicitly or implicitly include one or more of the features. In the description of the present invention, the meaning of "plurality" is two or more, unless otherwise clearly and specifically defined.

[0111] Although the present application is described herein in conjunction with various embodiments, in the process of implementing the claimed application, those skilled in the art may understand and implement other variations of the disclosed embodiments by reviewing the drawings, the disclosure, and the appended claims. In the claims, the word "comprising" does not exclude other components or steps, and "a" or "an" does not exclude a plurality of components or steps.

[0112] The above contents are further detailed descriptions of the present invention in combination with specific preferred embodiments, and it cannot be determined that the specific implementation of the present invention is limited to these descriptions. For ordinary technicians in the technical field to which the present invention belongs, several simple deductions or substitutions can be made without departing from the concept of the present invention, which should be regarded as falling within the protection scope of the present invention.

Claims

1. A method for identifying FIR filter coefficients under noise interference, It is characterized in that include: S100, obtaining an input signal and an output signal of the FIR filter, and establishing a differential equation describing the relationship between the input and the output according to the input signal and the output signal; S200, constructing a parameter vector and an information vector according to an input signal and an output signal; S300, transforming the difference equation using the parameter vector and the information vector to obtain an identification model of the FIR filter with sliding average and colored noise; Among them, the parameter vector contains all the parameters to be identified of the FIR filter; S400, using an augmented gradient iteration E-EGI algorithm based on an exponential criterion function or an augmented Newton iteration E-ENI algorithm based on an exponential criterion function to estimate a parameter vector in the identification model to obtain an estimation vector; S500, obtaining determined values ​​of all parameters to be identified of the FIR filter from the estimated vector.

2. The FIR filter coefficient identification method under noise interference according to claim 1, It is characterized in that The differential equation representing the relationship between input and output in S100 is: y(t)=B(z)u(t)+D(z)v(t) (1); in, and are the input signal and output signal of the FIR filter respectively, is zero mean with variance σ 2 The random white noise sequence is represented by t, which represents the discrete time variable, that is, the variable takes a value at time tT, where T is the sampling period; z -1 is the unit shift operator, z -1 y(t)=y(t-1), B(z) and D(z) are unit shift operators z -1 The constant term of the time-invariant polynomial is represents the coefficients of the FIR filter, represents the coefficient of the noise term, n b Indicates the order of the coefficients of the FIR filter, n d represents the order of the coefficients of the noise term, represents the field of real numbers, and := means defining the symbol on the left side of the equal sign as the expression on the right side.

3. The FIR filter coefficient identification method under noise interference according to claim 2, It is characterized in that The parameter vector and information vector in S200 are: Among them, θ is the parameter vector containing all the parameters to be identified, is the information vector.

4. The FIR filter coefficient identification method under noise interference according to claim 3, It is characterized in that The identification model in S300 is:

5. The FIR filter coefficient identification method under noise interference according to claim 4, It is characterized in that Before S400, the FIR filter coefficient identification method under noise interference also includes: S410, defining a criterion function according to the identification model, and calculating a gradient vector and a Hessian matrix of the exponential criterion function; Among them, the exponential criterion function is: Criterion function J 1 The gradient vector of (θ) is: The Hessian matrix is: S411, obtaining a first estimated expression of the parameter vector according to the gradient vector minimization criterion function, and obtaining a second estimated expression of the parameter vector using the Newton search minimization criterion function; The first estimated expression is: Among them, the step size μ k must satisfy The second estimated expression is: S412, obtaining an expression of the information vector using the estimated value of the white noise and the step size; Among them, the expression of the information vector is: S413, obtaining a calculation formula of the E-EGI algorithm based on the first estimated expression of the parameter vector and the estimated expression of the information vector, and obtaining a calculation formula of the E-ENI algorithm based on the second estimated expression of the parameter vector and the estimated expression of the information vector.

6. The FIR filter coefficient identification method under noise interference according to claim 5, It is characterized in that The calculation formula of the E-EGI algorithm in S440 is: in, Superscripts indicate estimates.

7. The FIR filter coefficient identification method under noise interference according to claim 6, It is characterized in that In S400, the parameter vector in the identification model is estimated by using the augmented gradient iteration E-EGI algorithm based on the exponential criterion function to obtain an estimated vector including: S420, initialize so that the initial values ​​of all variables are zero when t≤0, set the iteration variable k=1, give the offline data length L, and set the parameter estimation accuracy ε; and set the estimation vector Noise term Take p 0 =10 6 ; S421, using E-EGI algorithm (13) to obtain the estimated information vector S422, using E-EGI algorithm (14) and (15) to obtain the intermediate vector and the intermediate matrix And use formula (11) to determine the fixed step size μ k ; S423, update the parameter estimation vector by formula (10) And use equation (16) to calculate the estimate of the noise term S424, Comparison and if The k value is increased by 1 and jumps to S421; otherwise, the parameter estimation vector of the output filter is Terminate the iterative calculation process.

8. The method for identifying FIR filter coefficients under noise interference according to claim 5, It is characterized in that The calculation formula of the E-ENI algorithm in S440 is: in, Superscripts indicate estimates.

9. The FIR filter coefficient identification method under noise interference according to claim 8, It is characterized in that In S400, the parameter vector in the identification model is estimated by using the augmented Newton iteration E-ENI algorithm based on the exponential criterion function to obtain the estimated vector including: S430, initialization makes all variables zero when t≤0, sets iteration variable k=1, gives offline data length L, and sets parameter estimation accuracy ε; and sets estimation vector Noise term Take p 0 =10 6 ; S431, using E-EGI algorithm (13) to obtain the estimated information vector S432, using E-EGI algorithm, equations (9), (14) and (15) to obtain the matrix Middle vector and the intermediate matrix And use formula (11) to determine the fixed step size μ k ; S433, update the parameter estimation vector using equation (12) And use equation (16) to calculate the estimate of the noise term S434, Comparison and if The k value is increased by 1 and jumps to S431; otherwise, the parameter estimation vector of the output filter is Terminate the iterative calculation process.

10. A device for identifying FIR filter coefficients under noise interference, It is characterized in that It comprises a processing device for implementing the FIR filter coefficient identification method under noise interference as described in any one of claims 1 to 9 through processing.

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