High-precision Real-time Online Frequency Estimation Method Based on Improved Artificial Bee Colony Algorithm

Abstract

The present invention belongs to the field of digital signal processing technology and specifically discloses a high-precision, real-time, online frequency estimation method based on an improved artificial bee colony algorithm. The method comprises the following steps: obtaining a sinusoidal wave signal from a data source at the kth moment; inputting the sinusoidal wave signal into a notch filter for notch processing to obtain a filtered output signal; calculating the filtered output signal using the improved artificial bee colony algorithm to obtain an optimal normalized frequency; and converting the optimal normalized frequency into an estimated frequency of the sinusoidal wave signal to complete high-precision, real-time, online frequency estimation. The present invention solves the problem that existing frequency estimation methods cannot achieve both high precision and high real-time performance in frequency estimation, and can achieve high-precision, real-time, online frequency estimation of different sinusoidal wave signals.

Description

Technical Field

[0001] The present invention belongs to the technical field of digital signal processing, and in particular relates to a high-precision real-time online frequency estimation method based on an improved artificial bee colony algorithm. Background Art

[0002] In the field of digital signal processing, frequency is a basic parameter of a sinusoidal signal, and its estimated accuracy and real-time performance directly affect the performance of the system. For example, in radar detection, the frequency estimation accuracy of the echo determines the radial velocity and distance measurement accuracy of the measured object. Its real-time online estimation facilitates the carrier to quickly obtain target information and make corresponding decisions. In communication systems, the frequency estimation accuracy of the carrier frequency determines the quality and reliability of signal transmission. Its real-time online estimation can ensure real-time demodulation and synchronization of the signal, avoiding communication interruptions caused by processing delays. In active vibration isolation systems, vibration suppression of specific frequencies is achieved by accurately estimating the frequency of external disturbances. Its real-time online estimation can ensure that the vibration isolator adapts to changes in external disturbances in a timely manner, thereby improving vibration isolation performance.

[0003] Currently, various methods exist for frequency estimation, but they still have limitations in achieving both high accuracy and real-time performance. Direct spectral estimation using the Fourier transform and its discrete Fourier transform has gained widespread application due to its clear physical meaning, fast computational speed, and high real-time performance. However, the Fourier transform suffers from energy leakage and picket fence effects, and its accuracy depends on the length of the sampled data, limiting the accuracy of frequency estimation. The maximum likelihood algorithm is suitable for high-precision frequency estimation of sinusoidal signals, but its high computational complexity limits its application in real-time processing. The Music algorithm accurately estimates the frequency of sinusoidal signals by decomposing the signal and noise subspaces. However, its computational complexity is similarly high, involving eigenvalue decomposition and spectral peak searching, resulting in slow processing and unsuitable for real-time applications. The autoregressive model algorithm is suitable for frequency estimation of periodic or quasi-periodic sinusoidal signals. While it can guarantee good estimation performance if the model parameters are accurately estimated, its parameter estimation is constrained by sample length, resulting in a high computational load and similarly insufficient for real-time processing. Applications such as radar detection, communications, and active vibration isolation often require frequency estimation of the sensor input signal. In existing frequency estimation methods, it is difficult to achieve both high frequency estimation accuracy and high real-time performance, which can easily cause performance loss of the above-mentioned real-time system. Summary of the Invention

[0004] The purpose of the present invention is to solve the problem that existing frequency estimation methods cannot take into account both high precision and high real-time performance of frequency estimation. A high-precision real-time online frequency estimation method based on an improved artificial bee colony algorithm is proposed.

[0005] The technical solution of the present invention is: a high-precision real-time online frequency estimation method based on an improved artificial bee colony algorithm, comprising the following steps:

[0006] Get the sine wave signal of the data source at the kth moment;

[0007] The sine wave signal is input into the notch filter for notch processing to obtain a filtered output signal;

[0008] The improved artificial bee colony algorithm is used to calculate the filtered output signal to obtain the optimal normalized frequency;

[0009] The optimal normalized frequency is converted into the estimated frequency of the sine wave signal to complete high-precision real-time online frequency estimation.

[0010] Preferably, when the sinusoidal wave signal is input into the notch filter for notch processing, the optimal normalized frequency obtained by the improved artificial bee colony algorithm at the current moment is fed back to the notch filter as the optimal normalized frequency in the notch filter parameter setting when notch processing is performed at the next moment, and the initial normalized frequency in the notch filter parameter setting is randomly set.

[0011] Preferably, the calculation formula of the filtered output signal is:

[0012]

[0013] in, Indicates the k The filtered output signal at time Indicates the k The sine wave signal at time Represents a notch filter, represents the polar radius of the notch filter used to control the notch width, represents the optimal normalized frequency, Represents a complex frequency-domain variable in a discrete system.

[0014] Preferably, the step of calculating the filtered output signal using the improved artificial bee colony algorithm to obtain the optimal normalized frequency specifically includes the following steps:

[0015] S01. Randomly generate initial nectar sources and assign them to the leader bees; each nectar source represents a possible normalized frequency;

[0016] S02. Generate new nectar sources by following bees and searching locally in the nectar source neighborhood of the leading bee. ;

[0017] S03. Calculate the initial nectar source and all new nectar sources based on the filtered output signal of the notch filter The fitness value of the first greedy selection is performed according to the fitness value to obtain the optimal nectar source ; If the nectar source of the leading bee is replaced, the loop counter is reset; if the nectar source of the leading bee is not replaced, the loop counter is increased by 1;

[0018] S04. Use the memory table to store the optimal nectar source obtained by the first greedy selection at the current moment and the previous L-1 moments , and select the optimal nectar source value in the memory table Get new nectar source ; Wherein, L represents the storage length of the memory table;

[0019] S05. New nectar source obtained based on memory table The optimal nectar source obtained by the first greedy choice Perform a second greedy selection to obtain the new optimal nectar source If the optimal nectar source The new best nectar source Replace, then reset the cycle counter; if the optimal nectar source The best nectar source that has not been discovered Replace, then the loop counter increases by 1;

[0020] S06. When the cycle counter reaches the set value, the scout bee is activated and the three-level chaotic mapping strategy is used to make the scout bee find the optimal nectar source value in the memory table. Search within the neighborhood of the , and update the new optimal nectar source ;

[0021] S07. Using leading bees to find the best nectar source and the new optimal nectar source Update the good solution;

[0022] S08. Determine whether the iteration termination condition is met. If so, the iteration is terminated and the optimal solution of the honey source, that is, the optimal normalized frequency, is output; if not, return to step S02; wherein, the iteration termination condition is that the filtering accuracy of the notch filter meets the frequency estimation requirements, and the value of the optimal normalized frequency obtained by iteration no longer changes.

[0023] As a preference, in step S01, the initial The nectar source is allocated to the corresponding There are a number of leading bees, and the generation formula of the initial nectar source is:

[0024]

[0025] in, Indicates the The location of the nectar source corresponding to the leading bee at the initial moment is , Indicates the minimum value of nectar source, represents a random number between [0, 1], Indicates the maximum value of the nectar source.

[0026] As an option, in step S02, the new nectar source The calculation formula is:

[0027]

[0028] in, Indicates the The nectar source corresponding to the leader bee is The location at the moment, Represents a random number in the range [-1, 1], Indicates the randomly selected The nectar source corresponding to the leader bee is t The location at the moment, and .

[0029] Preferably, the calculation formula of the fitness value in step S03 is:

[0030]

[0031] in, Indicates the The fitness value corresponding to each nectar source is represents the objective function value of the notch filter filtering optimization problem, represents the absolute value operation, represents the control parameter, Indicates the filter output value of the notch filter Converted to the time domain value, express The differential scaling factor is , Indicates the filter output value of the notch filter The derivative with respect to time.

[0032] Preferably, the formula of the three-level chaotic mapping strategy in step S06 is:

[0033]

[0034] in, Indicates the updated optimal nectar source, 、 and represents the chaotic map at each level, 、 and Represents the judgment threshold parameter, 、 and represents the search step size corresponding to each level of chaotic mapping, Indicates the filter output value of the notch filter Convert the value to the time domain.

[0035] As a preference, in step S07, if the new optimal nectar source Equal to the maximum value of nectar source or minimum value , then update the optimal nectar source , otherwise update the new optimal nectar source , the specific formula is:

[0036]

[0037] in, Indicates guiding bees to the best nectar source and the new optimal nectar source Update the obtained good solution.

[0038] Preferably, when converting the optimal normalized frequency into the estimated frequency of the sinusoidal wave signal, the relationship between the optimal normalized frequency and the estimated frequency of the sinusoidal wave signal is:

[0039]

[0040] in, express The optimal normalized frequency at the moment, represents the cosine function, Represents the estimated frequency of the sine wave signal at the kth moment.

[0041] The beneficial effects of the present invention are:

[0042] 1. The present invention takes into account both the accuracy and real-time performance of frequency estimation, and can achieve high-precision real-time online estimation of the frequency of a sine wave signal.

[0043] 2. The present invention is not affected by the initial value of the frequency during the optimization convergence process, has high reliability, simple operating logic, and is easy to implement in hardware.

[0044] 3. The present invention can effectively avoid the non-convergence caused by the minimum point or zero point in the frequency estimation process by adding a memory table and two greedy selections.

[0045] 4. This invention employs a three-level chaotic mapping strategy to determine convergence conditions. The first level further enhances convergence speed, preventing scout bees from updating nectar sources that stray from optimal solutions. The second level balances convergence and convergence accuracy. The third level is a refined judgment, improving convergence accuracy. Through this three-level execution strategy, scout bees continuously transmit nectar sources with high nectar content to leader bees, which in turn update optimal solutions.

[0046] 5. By introducing a differential term into the fitness function, the present invention can avoid the problem that the fitness function takes a maximum value when the perturbation function is 0, thereby causing an erroneous judgment in the greedy selection process. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 The figure shows a flow chart of a high-precision real-time online frequency estimation method based on an improved artificial bee colony algorithm provided in Example 1 of the present invention.

[0048] Figure 2 The flowchart shows the specific steps of calculating the filtered output signal using the improved artificial bee colony algorithm to obtain the optimal normalized frequency provided in Example 1 of the present invention.

[0049] Figure 3 The figure shows a curve diagram of the frequency to be estimated provided in embodiment 2 of the present invention.

[0050] Figure 4 Shown is a curve diagram of the output signal of the notch filter provided in Example 2 of the present invention. DETAILED DESCRIPTION

[0051] The exemplary embodiments of the present invention will now be described in detail with reference to the accompanying drawings. It should be understood that the embodiments shown and described in the accompanying drawings are merely exemplary and are intended to illustrate the principles and spirit of the present invention, rather than to limit the scope of the present invention.

[0052] Example 1:

[0053] like Figure 1 As shown, a high-precision real-time online frequency estimation method based on an improved artificial bee colony algorithm includes the following steps:

[0054] S1. Get the sine wave signal of the data source at the kth moment;

[0055] S2. Input the sine wave signal into the notch filter for notch processing to obtain a filtered output signal;

[0056] S3. Calculate the filtered output signal using an improved artificial bee colony algorithm to obtain an optimal normalized frequency;

[0057] S4. Convert the optimal normalized frequency into the estimated frequency of the sine wave signal to complete high-precision real-time online frequency estimation.

[0058] In this embodiment, when the sinusoidal wave signal is input into the notch filter for notch processing, the optimal normalized frequency obtained by the improved artificial bee colony algorithm at the current moment is fed back to the notch filter as the optimal normalized frequency in the notch filter parameter setting when notch processing is performed at the next moment. The initial normalized frequency in the notch filter parameter setting is randomly set. Since the proposed improved ABC algorithm has global convergence, it can eventually converge to the frequency that minimizes the notch filter energy output within the preset frequency band, that is, the optimal normalized frequency.

[0059] In this embodiment, the calculation formula of the filtered output signal is:

[0060]

[0061] in, Indicates the k The filtered output signal at time Indicates the k The sine wave signal at time Represents a notch filter, The polar radius of the notch filter used to control the notch width is represented by , represents the optimal normalized frequency, Represents a complex frequency-domain variable in a discrete system.

[0062] In this embodiment, the improved artificial bee colony algorithm includes three basic elements: leader bees, follower bees, and scout bees. The leader bees' role is to initially randomly search for nectar sources within the domain of definition and memorize all food-related information to maintain a good solution. Follower bees, based on the information shared by the leader bees, complete a local search for nectar sources near the leader bees. The leader and follower bees then perform greedy selection based on the fitness function of the corresponding nectar source. The improved artificial bee colony algorithm is used to calculate the filtered output signal to obtain the optimal normalized frequency, as shown in Figure 1. Figure 2 As shown, the specific steps include:

[0063] S01. Randomly generate initial nectar sources and assign them to the leader bees; each nectar source represents a possible normalized frequency;

[0064] S02. Generate new nectar sources by following bees and searching locally in the nectar source neighborhood of the leading bee. ;

[0065] S03. Calculate the initial nectar source and all new nectar sources based on the filtered output signal of the notch filter The fitness value of the first greedy selection is performed according to the fitness value to obtain the optimal nectar source ; If the nectar source of the leading bee is replaced, the loop counter is reset; if the nectar source of the leading bee is not replaced, the loop counter is increased by 1;

[0066] S04. Use the memory table to store the optimal nectar source obtained by the first greedy selection at the current moment and the previous L-1 moments , and select the optimal nectar source value in the memory table Get new nectar source ; Wherein, L represents the storage length of the memory table;

[0067] S05. New nectar source obtained based on memory table The optimal nectar source obtained by the first greedy choice Perform a second greedy selection to obtain the new optimal nectar source If the optimal nectar source The new best nectar source Replace, then reset the cycle counter; if the optimal nectar source The best nectar source that has not been discovered Replace, then the loop counter increases by 1;

[0068] S06. When the cycle counter reaches the set value, the scout bee is activated and the three-level chaotic mapping strategy is used to make the scout bee find the optimal nectar source value in the memory table. Search within the neighborhood of the , and update the new optimal nectar source ;

[0069] S07. Using leading bees to find the best nectar source and the new optimal nectar source Update the good solution;

[0070] S08. Determine whether the iteration termination condition is met. If so, the iteration is terminated and the optimal solution of the honey source, that is, the optimal normalized frequency, is output. At this time, the frequency output value in the frequency output module remains constant; if not, return to step S02; wherein, the iteration termination condition is that the filtering accuracy of the notch filter meets the frequency estimation requirements, and the value of the optimal normalized frequency obtained by iteration no longer changes.

[0071] In this embodiment, in step S01, the initial The nectar source is allocated to the corresponding There are a number of leading bees, and the generation formula of the initial nectar source is:

[0072]

[0073] in, Indicates the The location of the nectar source corresponding to the leading bee at the initial moment is , Indicates the minimum value of nectar source, represents a random number between [0, 1], Indicates the maximum value of the nectar source.

[0074] In this embodiment, in step S02, the new nectar source The calculation formula is:

[0075]

[0076] in, Indicates the The nectar source corresponding to the leader bee is The location at the moment, Represents a random number in the range [-1, 1], Indicates the randomly selected The nectar source corresponding to the leader bee is t The location at the moment, and .

[0077] In this embodiment, the calculation formula of the fitness value in step S03 is:

[0078]

[0079] in, Indicates the The fitness value corresponding to each nectar source is represents the objective function value of the notch filter filtering optimization problem, represents the absolute value operation, represents the control parameters, Indicates the filter output value of the notch filter Converted to the time domain value, express The differential scaling factor is , Indicates the filter output value of the notch filter The derivative with respect to time.

[0080] In this embodiment, the formula of the three-level chaotic mapping strategy in step S06 is:

[0081]

[0082] in, Indicates the updated optimal nectar source, 、 and represents the chaotic map at each level, 、 and Represents the judgment threshold parameter, 、 and represents the search step size corresponding to each level of chaotic mapping, Indicates the filter output value of the notch filter Convert to the time domain value; in order to make the scout bee get the optimal nectar source value in the memory table The embodiment of the present invention adopts a chaotic mapping with high probability of center aggregation and low probability of dispersion at both ends. , whose expression is:

[0083]

[0084] Can be completed with is the center value and the radius is Random number The generation of To set the threshold, is a random number between (0, 1), Represents the series of chaotic maps.

[0085] In this embodiment, in step S07, if the new optimal nectar source Equal to the maximum value of nectar source or minimum value , then update the optimal nectar source , otherwise update the new optimal nectar source , the specific formula is:

[0086]

[0087] in, Indicates guiding bees to the best nectar source and the new optimal nectar source Update the obtained good solution.

[0088] In this embodiment, when the optimal normalized frequency is converted into the estimated frequency of the sinusoidal wave signal, the relationship between the optimal normalized frequency and the estimated frequency of the sinusoidal wave signal is:

[0089]

[0090] in, express The optimal normalized frequency at the moment, represents the cosine function, Represents the estimated frequency of the sine wave signal at the kth moment.

[0091] Example 2:

[0092] On the basis of Example 1, the embodiment of the present invention performs a numerical simulation test based on Matlab to verify the performance of the high-precision real-time online frequency estimation method based on the improved artificial bee colony algorithm proposed in the present invention.

[0093] Assume that the sampling rate is 10K Hz, the input sine signal amplitude is 1, the frequency is 250Hz, and the signal-to-noise ratio of the white noise added to the input signal is 20dB. , , , , , , , , , , The frequency interval to be estimated is (0, 500), so , .in, and is the control parameter of frequency estimation, which is used to adapt to different types of input signals. The final simulation results are as follows: Figure 3 and Figure 4 shown.

[0094] Figure 3 The change curve of the estimated frequency shows that after the simulation starts, the optimal estimated frequency is found after 1.1s and no longer changes. The corresponding frequency is 249.975Hz, which has a relative error of 0.01% compared with the theoretical value of 250Hz. Figure 4 The output signal curve of the notch filter shows that the output of the notch filter has a step-by-step convergence process. After 1.1s, the output amplitude of the notch filter is the same as the white noise. The notch filter completely filters the 250Hz signal component, thereby achieving high-precision real-time online identification of the input signal.

[0095] In summary, the high-precision, real-time, online frequency estimation method based on an improved artificial bee colony algorithm proposed in the present invention can quickly find the optimal solution within a wide search range and optimize it to the best through local search, thereby improving the accuracy and real-time performance of frequency estimation. The initial frequency of the method is randomly generated and is not affected by the preset initial frequency, which is highly reliable. Its operating logic is simple and easy to implement in hardware. It has application potential in the field of digital signal processing and is beneficial for application scenarios such as radar detection, communication, and active vibration isolation that require both high-precision and high-real-time frequency estimation.

[0096] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and it should be understood that the scope of protection of the present invention is not limited to such specific descriptions and embodiments. Those skilled in the art can make various other specific variations and combinations based on the technical teachings disclosed in the present invention without departing from the essence of the present invention, and such variations and combinations are still within the scope of protection of the present invention.

Claims

1. A high-precision real-time online frequency estimation method based on an improved artificial bee colony algorithm, characterized in that: The following steps are involved: Get the sine wave signal of the data source at the kth moment; The sine wave signal is input into the notch filter for notch processing to obtain a filtered output signal; The improved artificial bee colony algorithm is used to calculate the filtered output signal to obtain the optimal normalized frequency, which specifically includes the following steps: S01. Randomly generate initial nectar sources and assign them to the leader bees; each nectar source represents a possible normalized frequency; S02. Generate new nectar sources by following bees and searching locally in the nectar source neighborhood of the leading bee. ; S03. Calculate the initial nectar source and all new nectar sources based on the filtered output signal of the notch filter The fitness value of the first greedy selection is performed according to the fitness value to obtain the optimal nectar source ; If the nectar source of the leading bee is replaced, the loop counter is reset; if the nectar source of the leading bee is not replaced, the loop counter is increased by 1; S04. Use the memory table to store the optimal nectar source obtained by the first greedy selection at the current moment and the previous L-1 moments , and select the optimal nectar source value in the memory table Get new nectar source ; Wherein, L represents the storage length of the memory table; S05. New nectar source obtained based on memory table The optimal nectar source obtained by the first greedy choice Perform a second greedy selection to obtain the new optimal nectar source If the optimal nectar source The new best nectar source Replace, then reset the cycle counter; if the optimal nectar source The best nectar source that has not been discovered Replace, then the loop counter increases by 1; S06. When the cycle counter reaches the set value, the scout bee is activated and the three-level chaotic mapping strategy is used to make the scout bee find the optimal nectar source value in the memory table. Search within the neighborhood of the , and update the new optimal nectar source ; S07. Using leading bees to find the best nectar source and the new optimal nectar source Update the good solution; S08. Determine whether the iteration termination condition is met. If so, the iteration is terminated and the optimal solution of the honey source, i.e., the optimal normalized frequency, is output; if not, return to step S02; wherein the iteration termination condition is that the filtering accuracy of the notch filter meets the frequency estimation requirement and the value of the optimal normalized frequency obtained by iteration does not change; The optimal normalized frequency is converted into the estimated frequency of the sine wave signal to complete high-precision real-time online frequency estimation.

2. The high-precision real-time online frequency estimation method based on the improved artificial bee colony algorithm according to claim 1 is characterized in that: When the sinusoidal wave signal is input into the notch filter for notch processing, the optimal normalized frequency obtained by the improved artificial bee colony algorithm at the current moment is fed back to the notch filter as the optimal normalized frequency in the notch filter parameter setting when notch processing is performed at the next moment. The initial normalized frequency in the notch filter parameter setting is randomly set.

3. The high-precision real-time online frequency estimation method based on the improved artificial bee colony algorithm according to claim 2, characterized in that: The calculation formula of the filtered output signal is: in, Indicates the k The filtered output signal at time Indicates the k The sine wave signal at time Represents a notch filter, represents the polar radius of the notch filter used to control the notch width, represents the optimal normalized frequency, Represents a complex frequency-domain variable in a discrete system.

4. The high-precision real-time online frequency estimation method based on the improved artificial bee colony algorithm according to claim 1, characterized in that: In step S01, the initial The nectar source is allocated to the corresponding There are a number of leading bees, and the generation formula of the initial nectar source is: in, Indicates the The location of the nectar source corresponding to the leading bee at the initial moment is , Indicates the minimum value of nectar source, represents a random number between [0, 1], Indicates the maximum value of the nectar source.

5. The high-precision real-time online frequency estimation method based on the improved artificial bee colony algorithm according to claim 1 is characterized in that: In step S02, the new nectar source The calculation formula is: in, Indicates the The nectar source corresponding to the leader bee is The location at the moment, Represents a random number in the range [-1, 1], Indicates the randomly selected The nectar source corresponding to the leader bee is t The location at the moment, and .

6. The high-precision real-time online frequency estimation method based on the improved artificial bee colony algorithm according to claim 1, characterized in that: The calculation formula of the fitness value in step S03 is: in, Indicates the The fitness value corresponding to each nectar source is represents the objective function value of the notch filter filtering optimization problem, represents the absolute value operation, represents the control parameter, Indicates the filter output value of the notch filter Converted to the time domain value, express The differential scaling factor is , Indicates the filter output value of the notch filter The derivative with respect to time.

7. The high-precision real-time online frequency estimation method based on the improved artificial bee colony algorithm according to claim 1, characterized in that: The formula of the three-level chaotic mapping strategy in step S06 is: in, Indicates the updated optimal nectar source, 、 and represents the chaotic map at each level, 、 and Represents the judgment threshold parameter, 、 and represents the search step size corresponding to each level of chaotic mapping, Indicates the filter output value of the notch filter Convert the value to the time domain.

8. The high-precision real-time online frequency estimation method based on the improved artificial bee colony algorithm according to claim 4, characterized in that: In step S07, if the new optimal nectar source Equal to the maximum value of nectar source or minimum value , then update the optimal nectar source , otherwise update the new optimal nectar source , the specific formula is: in, Indicates guiding bees to the best nectar source and the new optimal nectar source Update the obtained good solution.

9. The high-precision real-time online frequency estimation method based on the improved artificial bee colony algorithm according to claim 1, characterized in that: When the optimal normalized frequency is converted into the estimated frequency of the sine wave signal, the relationship between the optimal normalized frequency and the estimated frequency of the sine wave signal is: in, express The optimal normalized frequency at the moment, represents the cosine function, Represents the estimated frequency of the sine wave signal at the kth moment.

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