Adaptive variable step-size LMS filter based on hyperbolic tangent function, filtering method thereof, and computer device

Abstract

An adaptive variable step-size LMS filter based on a hyperbolic tangent function and its filtering method and computer equipment belong to the field of filter technology, and solve the problem that the LMS algorithm improved based on a nonlinear function requires too many manual adjustments of parameters and that the convergence speed and convergence accuracy of the traditional LMS algorithm cannot be satisfied simultaneously. The method of the present invention includes: determining the filter tap length and the number of iterations; initializing the filter parameters; obtaining the filter input signal vector; determining the instantaneous expected signal of the filter; obtaining the instantaneous output signal; obtaining the instantaneous error signal of the filter and the accumulated amount of the error signal based on the instantaneous output signal; obtaining the instantaneous step size using a step-size update formula based on a hyperbolic tangent function; and continuously iterating the filter tap weight coefficient vector to construct an LMS filter using the filter tap weight coefficient vector obtained after the number of iterations. The present invention is suitable for improving the performance of the LMS filter, and the filter of the present invention can be widely used in various signal processing fields.

Description

Technical Field

[0001] The present application relates to the field of filter technology, and in particular to an adaptive variable step-size LMS filter. Background Art

[0002] The Least Mean Square (LMS) filter is an algorithm for implementing a transversal filter. Compensation and tap length are key parameters affecting LMS filter performance. A larger step size results in faster convergence, but also increases the steady-state error and excess steady-state mean square error, potentially leading to algorithm divergence. A smaller step size reduces the steady-state error and excess steady-state mean square error, but also slows convergence. Therefore, determining the appropriate step size is crucial for achieving a good balance between steady-state error and excess steady-state error and convergence speed, thereby improving the performance of the LMS adaptive filtering algorithm. This is a key issue in LMS algorithm research.

[0003] In the existing technology, literature 1: Qin Jingfan, Ouyang Jingzheng. A new variable step size LMS adaptive filtering algorithm [J]. Data Acquisition and Processing, 1997(03): 171-174. Literature 2: Zhang Hongmei, Han Wangang. Research and application of a new variable step size LMS adaptive filtering algorithm [J]. Chinese Journal of Scientific Instrument, 2015, 36(08): 1822-1830. Literature 3: Lu B, Feng C, Long G. A New Variable Step-size LMS Adaptive Algorithm Based on MarrFunction [C]. 2013 International Conference on Information Technology and Applications. IEEE, 2013: 21317. Literature 4: He D, Wang M, Han Y, et al. VariableStep Size LMS Adaptive Algorithm Based on Exponential Function [C]. 2019 IEEE2nd International Conference on Information Communication and SignalProcessing (ICICSP). IEEE, 2019: 473-477.

[0004] Reference 1 constructs a nonlinear relationship between error and step size based on a Sigmoid function. However, when the LMS algorithm stabilizes, this method updates the step size too quickly, reducing its stability. Reference 2 improves the Sigmoid function's characteristics by translating and transforming it and introducing parameters, resulting in good performance. However, this algorithm suffers from a complex model and high computational complexity, which limits its flexibility. Reference 3 constructs a relationship between step size and error based on an exponential function, but using this function to update the step size is computationally intensive. Reference 4 utilizes a variable step size to update some weight coefficients. This improves algorithm performance when noise is low, but degrades when noise is high. All of the above variable step size LMS algorithms require parameters to adjust the function's characteristics, and manual parameter adjustment reduces the algorithm's practicality. Summary of the Invention

[0005] The purpose of the present invention is to solve the problems in the prior art of the LMS algorithm improved based on nonlinear functions, that is, too many parameters need to be manually adjusted and that the traditional LMS algorithm cannot simultaneously meet the convergence speed and convergence accuracy. An adaptive variable step-size LMS filter based on a hyperbolic tangent function and a method for establishing the same and a computer device are provided.

[0006] The present invention is achieved through the following technical solutions. On the one hand, the present invention provides an adaptive variable step-size LMS filtering method based on a hyperbolic tangent function, the method comprising:

[0007] Determine the filter tap length and number of iterations;

[0008] Initializing filter parameters, the filter parameters including a filter output signal vector, a filter error signal, and a filter tap weight coefficient vector;

[0009] Get the filter input signal vector ;

[0010] Determine the instantaneous expected signal of the filter ;

[0011] According to the instantaneous expected signal of the nth iteration And the filter tap weight coefficient vector W(n), obtain the instantaneous output signal of the nth iteration ;

[0012] According to the instantaneous output signal , get the filter instantaneous error signal , and the accumulated amount of the error signal ;

[0013] Using the step size update formula based on the hyperbolic tangent function, with the goal of minimizing the error signal, the instantaneous step size is obtained ;

[0014] The filter tap weight coefficient vector is continuously iterated using the filter input signal vector, instantaneous step size, filter instantaneous error signal and error accumulation to construct an LMS filter with the filter tap weight coefficient vector obtained after reaching the number of iterations.

[0015] Furthermore, the instantaneous output signal The method to obtain is to use the formula

[0016]

[0017] Where N is the total length of the input signal vector,

[0018] Get the instantaneous output signal .

[0019] Furthermore, the filter instantaneous error signal The method to obtain is to use the formula

[0020]

[0021] Get the instantaneous error signal of the filter .

[0022] Furthermore, the accumulated amount of the error signal The method to obtain is to use the formula

[0023]

[0024] Get the accumulated amount of the error signal .

[0025] Furthermore, the instantaneous step length The method for obtaining is to use the step size update formula based on the hyperbolic tangent function

[0026]

[0027] in, is the accumulated amount of error signal The average value of

[0028] Get the instantaneous step length .

[0029] Furthermore, the iterative method of the filter tap weight coefficient vector is to use the formula

[0030]

[0031] The filter tap weight coefficient vector is iterated.

[0032] In a second aspect, the present invention provides an adaptive variable step-size LMS filter based on a hyperbolic tangent function, the filter being designed according to the method described above.

[0033] In a third aspect, the present invention provides a computer device comprising a memory and a processor, wherein the memory stores a computer program, and when the processor runs the computer program stored in the memory, an adaptive variable step-size LMS filtering method based on a hyperbolic tangent function as described above is executed.

[0034] In a fourth aspect, the present invention provides a computer-readable storage medium, in which a plurality of computer instructions are stored, and the plurality of computer instructions are used to enable a computer to execute an adaptive variable-step-size LMS filtering method based on a hyperbolic tangent function as described above.

[0035] In a fifth aspect, the present invention provides a computer program product, which, when executed by a processor, implements the adaptive variable-step-size LMS filtering method based on the hyperbolic tangent function as described above.

[0036] Beneficial effects of the present invention:

[0037] First, the core content of the variable step-size LMS algorithm is to use a larger step size when the error is large and a smaller step size when the error is small. Therefore, it is feasible to use the error and step size to construct a nonlinear function or a new cost function to update the LMS filter. The present invention adopts an adaptive variable step-size LMS filter based on the hyperbolic tangent function, which achieves a better balance between error and convergence speed, and can meet both convergence speed and convergence accuracy.

[0038] Secondly, in the prior art, when using a nonlinear function to construct a nonlinear relationship between step size and error, it is necessary to use some constant parameters to transform the nonlinear function in terms of function shape. The method and system of the present invention do not require manual adjustment of these parameters, thereby improving the practicality of filtering.

[0039] The present invention proposes a variable step-size adaptive filtering algorithm that does not require manual parameter adjustment and has good filtering performance, which is more convenient in engineering applications.

[0040] The present invention is suitable for improving the performance of an LMS filter, and the filter of the present invention can be widely used in various signal processing fields. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] In order to more clearly illustrate the technical solution of the present application, the following is a brief introduction to the drawings required for use in the embodiments. Obviously, for ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0042] Figure 1 A schematic flow chart of a filter establishment method of the present invention;

[0043] Figure 2 The mean square error comparison chart of the filtering methods when the input signal is white noise (SNR=20dB);

[0044] Figure 3 This is a comparison chart of the EMSE filtering methods when the input signal is white noise (SNR=20dB);

[0045] Figure 4 The mean square error comparison chart of the filtering methods when the input signal is white noise generated by the first-order AR(1) model (SNR=20dB);

[0046] Figure 5 This is the EMSE comparison chart of the filtering methods when the input signal is white noise generated by the first-order AR(1) model (SNR=20dB);

[0047] Figure 6 This is a comparison chart of the mean square error of the filtering methods when SNR=20dB;

[0048] Figure 7 This is the EMSE comparison chart of the filtering methods under the condition of SNR=20dB;

[0049] Figure 8 This is the learning curve of the method of the present invention under different signal-noise conditions. DETAILED DESCRIPTION

[0050] The embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present invention, but are not to be construed as limiting the present invention.

[0051] Implementation method 1: Figure 1 As shown, an adaptive variable step-size LMS filtering method based on a hyperbolic tangent function, the method comprising:

[0052] Determine the filter tap length and number of iterations;

[0053] Initializing filter parameters, the filter parameters including a filter output signal vector, a filter error signal, and a filter tap weight coefficient vector;

[0054] Get the filter input signal vector , ;

[0055] Determine the instantaneous expected signal of the filter ;

[0056] According to the instantaneous expected signal of the nth iteration And the filter tap weight coefficient vector W(n), obtain the instantaneous output signal of the nth iteration ;

[0057] According to the instantaneous output signal , get the filter instantaneous error signal , and the accumulated amount of the error signal ;

[0058] Using the step size update formula based on the hyperbolic tangent function, with the goal of minimizing the error signal, the instantaneous step size is obtained ;

[0059] The filter tap weight coefficient vector is continuously iterated using the filter input signal vector, instantaneous step size, filter instantaneous error signal and error accumulation to construct an LMS filter with the filter tap weight coefficient vector obtained after reaching the number of iterations.

[0060] First, this embodiment adopts an adaptive variable step-size LMS filter based on the hyperbolic tangent function, which achieves a better balance between error and convergence speed, and both convergence speed and convergence accuracy can be met simultaneously;

[0061] Secondly, this embodiment does not require manual adjustment of these parameters, thereby improving the practicality of filtering.

[0062] It should be noted that the method of this embodiment is iteratively operated after updating the filter tap weight coefficient vector, specifically: Figure 1 As shown, it is determined whether the current number of iterations is equal to the maximum number of iterations set at the beginning. If it is equal, the current filter tap weight coefficient vector is determined as the filter weight coefficient vector. If it is less than, continue to update the iteration and return to the step of obtaining the filter input signal vector.

[0063] Implementation method 2: This implementation method further limits the adaptive variable step size LMS filtering method based on the hyperbolic tangent function described in implementation method 1. In this implementation method, the instantaneous output signal The acquisition method is further limited, including:

[0064] The instantaneous output signal The method to obtain is to use the formula

[0065]

[0066] Where N is the total length of the input signal vector, is an element in W(n), x(nk-1) is The elements in

[0067] Get the instantaneous output signal .

[0068] This embodiment gives an instantaneous output signal The acquisition method can satisfy both convergence speed and convergence accuracy.

[0069] Implementation method three, this implementation method is a further limitation of the adaptive variable step size LMS filtering method based on the hyperbolic tangent function described in implementation method one. In this implementation method, the instantaneous error signal of the filter is The acquisition method is further limited, including:

[0070] The filter instantaneous error signal The method to obtain is to use the formula

[0071]

[0072] Get the instantaneous error signal of the filter .

[0073] This embodiment gives the filter instantaneous error signal The acquisition method can satisfy both convergence speed and convergence accuracy.

[0074] Implementation method 4: This implementation method further limits the adaptive variable step size LMS filtering method based on the hyperbolic tangent function described in implementation method 1. In this implementation method, the cumulative amount of the error signal is The acquisition method is further limited, including:

[0075] The accumulated amount of the error signal The method to obtain is to use the formula

[0076]

[0077] Get the accumulated amount of the error signal .

[0078] This embodiment gives the cumulative amount of the error signal The acquisition method can satisfy both convergence speed and convergence accuracy.

[0079] Implementation method 5: This implementation method further limits the adaptive variable step size LMS filtering method based on the hyperbolic tangent function described in implementation method 1. In this implementation method, the instantaneous step size is The acquisition method is further limited, including:

[0080] The instantaneous step length The method for obtaining is to use the step size update formula based on the hyperbolic tangent function

[0081]

[0082] in, is the accumulated amount of error signal The average value of

[0083] Get the instantaneous step length .

[0084] In this embodiment, when a nonlinear function is used to construct a nonlinear relationship between the step size and the error, there is no need to use some constant parameters to transform the nonlinear function in terms of function shape, and there is no need to manually adjust these parameters, which improves the practicality of the filtering and can also meet the convergence speed and convergence accuracy at the same time.

[0085] It should be noted that, in this embodiment, the pseudo code of the parameter-free variable step-size LMS algorithm based on the hyperbolic tangent function is:

[0086]

[0087]

[0088]

[0089]

[0090] Implementation method 6: This implementation method further limits the adaptive variable step size LMS filtering method based on the hyperbolic tangent function described in implementation method 1. In this implementation method, the iterative method of the filter tap weight coefficient vector is further limited, specifically including:

[0091] The iterative method of the filter tap weight coefficient vector is to use the formula

[0092]

[0093] The filter tap weight coefficient vector is iterated.

[0094] This embodiment provides an iterative method for the filter tap weight coefficient vector, which can simultaneously meet the convergence speed and convergence accuracy.

[0095] The related technical effects of the present invention are given below:

[0096] It should be noted that the relevant references in this section include: Reference 5: Benesty J, Rey H, Vega LR, et al. A Nonparametric Vss NLMS Algorithm [J]. IEEE Signal Processing Letters, 2006, 13(10): 581-584.

[0097] Document 6: Huang HC, Lee J. A New Variable Step-size NLMS Algorithm and Its Performance Analysis[J]. IEEE Transactions on Signal Processing, 2012, 60(4):2055-2060.

[0098] Reference 7: Zhang Jianwu, Yu Hao, Zhang Qianhua. Improved variable step-size LMS algorithm for hyperbolic tangent function[J]. Journal of Communications, 2020, v.41;No.403(11):120-127.

[0099] Document 8: Zhao S, Man Z, Suiyang K. A Fast Variable Step-size LMSAlgorithm with System Identification[C]. IEEE Conference on Industrial Electronics&Applications. IEEE, 2007.

[0100] Document 9: Shi K, Ma X. A Variable-step-size NLMS Algorithm UsingStatistics of Channel Response[J]. Signal Processing, 2010, 90(6):2107-2111

[0101] The numerical simulation analysis of the variable step-size LMS algorithm based on the hyperbolic tangent function of the present invention is carried out, and its performance indicators in system identification are compared with those of the NPVSS-LMS algorithm in document 5, the VSS-NLMS algorithm in document 6, the IVSS-LMS algorithm in document 7, and the MRVSS-LMS algorithm in document 8.

[0102] The algorithm iterations are 80,000 times, and each learning curve is the statistical average of 200 independent simulations. The initialization settings of the simulation analysis are consistent with those in Reference 9: the unknown system is a finite impulse response filter, and its weight coefficients are given by Produced, among which , To conform to the Gaussian distribution with a mean of 0 and a variance of 0.09, the order of the system and the order of the filter are both .

[0103] The convergence performance of different variable step-size LMS algorithms is analyzed. The comparison algorithm parameters used in the numerical simulation are from the original literature 5-7, see Table 1.

[0104] Table 1 Comparison of algorithm parameter selection

[0105] Table1 Comparison algorithm parameter selection

[0106]

[0107] 1. Technical effects of steady-state mean square error and excess mean square error:

[0108] Case 1: The input signal is: white noise;

[0109] The unknown system to be simulated is a time-invariant system, and its order Filter input signal is a Gaussian signal with a mean of 0 and a variance of 1. System noise Also select a Gaussian signal with a mean of 0 and a signal-to-noise ratio (SNR) of 20dB.

[0110] In case 1, the comparison of mean square error and EMSE value of the algorithm of the present invention and other algorithms is shown in the figure below. Figure 2 、 3 shown.

[0111] Depend on Figure 2 、 3 It can be seen that in the early stage of algorithm convergence, the convergence speed of the algorithm of the present invention is similar to that of the VSS-NLMS algorithm and the IVSS-LMS algorithm, and is superior to the convergence speed of the NPVSS-LMS algorithm and the MRVSS-LMS algorithm. When the algorithm tends to a steady state, the steady-state EMSE of the algorithm proposed by the present invention reaches -45dB, among which the steady-state EMSE values ​​of the VSS-NLMS algorithm and the IVSS-LMS algorithm are -20dB and -22dB, respectively, which are much larger than the algorithm proposed by the present invention. There is also a certain gap between the steady-state EMSE of NPVSS-LMS and MRVSS-LMS and the algorithm proposed by the present invention, and the convergence speed is slower than that of the algorithm proposed by the present invention.

[0112] Case 2, the input signal is: white noise generated by a first-order AR(1) model;

[0113] The initial conditions of the unknown system are the same as those in Case 1. The filter input signal The white noise with mean 0 and variance 1 is generated by AR(1) model. AR(1) model consists of the first-order system Generates system noise signal A Gaussian signal with a mean of 0 is still used, and the signal-to-noise ratio SNR=20dB.

[0114] In case 2, the comparison of mean square error and EMSE of the algorithm of the present invention and other algorithms is shown in the figure below. Figure 4 、 5 shown.

[0115] Depend on Figure 4 、 5 It can be seen that when SNR=20dB, all algorithms can converge. In the early stage of algorithm convergence, the convergence speed of the algorithm proposed in the present invention is similar to that of the VSS-NLMS algorithm and the IVSS-LMS algorithm, and both are better than the convergence speed of the NPVSS-LMS algorithm and the MRVSS-LMS algorithm. When the algorithm tends to steady state, the steady-state EMSE of the algorithm proposed in the present invention reaches -37dB, and the steady-state EMSE values ​​of the VSS-NLMS algorithm and the IVSS-LMS algorithm are -23dB and -20dB respectively, which are much larger than the algorithm proposed in the present invention. The steady-state EMSE of the MRVSS-LMS algorithm is better than that of the VSS-NLMS algorithm and the IVSS-LMS algorithm, but the convergence speed is slower than that of the algorithm proposed in the present invention and the final steady-state EMSE value is greater than that of the algorithm proposed in the present invention. The NPVSS-LMS algorithm is inferior to the MRVSS-LMS algorithm and the algorithm proposed in the present invention in terms of both convergence speed and convergence accuracy. After simulation of the two cases, it can be seen that the performance of the algorithm proposed in the present invention is worse than that of other algorithms.

[0116] 2. Technical Effects of Algorithm Tracking:

[0117] Unknown system initial conditions, filter input signal The parameters are consistent with those in the algorithm mean square error comparison. Filter input signal is a white noise with a mean of 0 and a variance of 1 generated by the AR(1) model. When the number of iterations is 40,000, the unknown system weight coefficient Medium parameters The variance of is changed from 0.09 to 0.05, and the simulation is performed under the signal-to-noise ratio SNR=20dB.

[0118] When SNR=20dB, the tracking performance of the algorithm proposed in this invention and other comparison algorithms is as follows: Figure 6 、 7 shown.

[0119] Figure 6 、 7 The results show that all algorithms converge again after changing the unknown system, and the reconvergence speed and steady-state EMSE value remain largely unchanged with system changes. Because the algorithm of the present invention uses the average error value instead of the instantaneous error value, its convergence speed is slightly slower than the initial convergence when the system changes, which is basically the same as the MRVSS-LMS algorithm. However, the steady-state EMSE value of the present algorithm is superior to that of other algorithms.

[0120] 3. Related technical effects of convergence of different signal-to-noise ratio algorithms:

[0121] Unknown system initial conditions, filter input signal The parameters are consistent with those in the algorithm mean square error comparison. System noise is a Gaussian signal with a mean of 0. The signal-to-noise ratio (SNR) is 20 dB. When the number of iterations is 40,000, the unknown system weight coefficients are Medium parameters The variance of α changes from 0.09 to 0.05.

[0122] The performance of the algorithm under various signal-to-noise ratios is as follows Figure 8 shown.

[0123] Depend on Figure 8 It can be seen that the proposed algorithm has good convergence performance in various situations. In the case of low signal-to-noise ratio, the proposed algorithm can still maintain good tracking performance.

[0124] In order to solve the problems that the LMS algorithm improved based on nonlinear functions requires too many manual adjustments of parameters and that the traditional LMS algorithm cannot simultaneously meet the convergence speed and convergence accuracy, the present invention designs a variable step-size adaptive filtering algorithm that does not require manual adjustment of parameters and has good filtering performance, which is more convenient in engineering applications.

[0125] The technical solution of the present invention to solve the above technical problems is to use a parameter-free variable step-size LMS algorithm based on a hyperbolic tangent function to initialize the filter parameters, determine the filter tap length and the number of iterations; obtain the filter input signal vector, determine the filter instantaneous expected signal; according to the first The instantaneous expected signal and filter tap weight coefficient vector are iterated to obtain the The instantaneous output signal of the iteration is used to determine the instantaneous error signal of the filter and the accumulated amount of the error signal , with the goal of minimizing the error signal, the proposed step size update formula is used to calculate the instantaneous step size ; Using the filter input vector, instantaneous step size, instantaneous error signal, and error accumulation, the filter tap coefficient vector is continuously iterated to construct the LMS filter by obtaining the weight coefficient vector after reaching the number of iterations.

[0126] The algorithm flow chart is as follows Figure 1 Shown, including:

[0127] The tap length and number of iterations of the proposed variable step-size LMS filter are determined according to the filter input signal. First, the tap length of the proposed variable step-size LMS filter is initially determined. and the number of iterations , the tap coefficient vector and the number of iterations of the proposed variable step-size LMS filter are adjusted through iterative updating;

[0128] Initialize the filter output signal, filter error signal, and filter tap weight coefficient vector;

[0129] Get filter input signal vector block , that is, the input signal vector block of the filter with respect to the tap length, ;

[0130] Determine the expected signal ;

[0131] Calculate the output signal , ;

[0132] Calculate error value , The cumulative error is ;

[0133] Calculate instantaneous step size ;

[0134] Update weight coefficient vector .

Claims

1. An adaptive variable step-size LMS filtering method based on hyperbolic tangent function, characterized in that: The method comprises: Determine the filter tap length and number of iterations; Initializing filter parameters, the filter parameters including a filter output signal vector, a filter error signal, and a filter tap weight coefficient vector; Get the filter input signal vector ; Determine the instantaneous expected signal of the filter ; According to the instantaneous expected signal of the nth iteration And the filter tap weight coefficient vector W(n), obtain the instantaneous output signal of the nth iteration ; According to the instantaneous output signal , get the filter instantaneous error signal , and the accumulated amount of the error signal ; Using the step size update formula based on the hyperbolic tangent function, with the goal of minimizing the error signal, the instantaneous step size is obtained , the instantaneous step length The method for obtaining is to use the step size update formula based on the hyperbolic tangent function in, is the accumulated amount of error signal The average value of Get the instantaneous step length ; The filter tap weight coefficient vector is continuously iterated using the filter input signal vector, instantaneous step size, filter instantaneous error signal and error accumulation to construct an LMS filter with the filter tap weight coefficient vector obtained after reaching the number of iterations.

2. The adaptive variable step-size LMS filtering method based on the hyperbolic tangent function according to claim 1 is characterized in that: The instantaneous output signal The method to obtain is to use the formula Where N is the total length of the input signal vector, Get the instantaneous output signal .

3. The adaptive variable step-size LMS filtering method based on the hyperbolic tangent function according to claim 1 is characterized in that: The filter instantaneous error signal The method to obtain is to use the formula Get the instantaneous error signal of the filter .

4. The adaptive variable step-size LMS filtering method based on the hyperbolic tangent function according to claim 1 is characterized in that: The accumulated amount of the error signal The method to obtain is to use the formula Obtain the cumulative amount of the error signal .

5. The adaptive variable step-size LMS filtering method based on hyperbolic tangent function according to claim 1 is characterized in that: The iterative method of the filter tap weight coefficient vector is to use the formula The filter tap weight coefficient vector is iterated.

6. An adaptive variable step-size LMS filter based on a hyperbolic tangent function, characterized in that: A filter designed according to the method of any one of claims 1-5.

7. A computer device comprising a memory and a processor, wherein a computer program is stored in the memory, wherein: When the processor runs the computer program stored in the memory, the steps of the method according to any one of claims 1 to 5 are performed.

8. A computer-readable storage medium, characterized in that The computer-readable storage medium stores a plurality of computer instructions, and the plurality of computer instructions are used to enable a computer to execute the method according to any one of claims 1 to 5.

9. A computer program product, characterized in that When the computer program is executed by a processor, the method according to any one of claims 1 to 5 is implemented.

Images