A method for underwater acoustic signal Doppler estimation based on improved firefly algorithm

Abstract

The application provides a kind of underwater acoustic signal Doppler estimation method based on improved firefly algorithm, adopts pseudo-random sequence to construct transmitting signal, improves signal in mobile underwater acoustic communication scene anti-multipath interference, broadband Doppler effect ability;At receiving end, first, through larger step size, Doppler is roughly estimated, in the narrowed Doppler factor search range, based on variable scale chaos strategy, improved firefly algorithm is used, the correlation of received signal and local reference signal carrying different Doppler factors is used to construct objective function, the fitness value is calculated, the Doppler estimation is converted into continuous optimization problem, with lower calculation complexity, the Doppler estimation precision meeting the synchronization demand of underwater acoustic communication is obtained, and the estimation stability in larger Doppler range is guaranteed by using the Doppler sensitive property of the method.

Description

Technical Field

[0001] This invention belongs to the field of Doppler estimation technology for mobile underwater acoustic communication, and particularly relates to a Doppler estimation method for underwater acoustic signals based on an improved firefly algorithm. Background Technology

[0002] For mobile underwater acoustic communication, the low speed of sound in water leads to Doppler effects that cause frequency shifts and temporal scale variations in broadband underwater acoustic communication signals. Therefore, Doppler factor estimation and Doppler compensation are necessary during receiver processing. Doppler block estimation methods use linear frequency modulated (LFM) signals as synchronization signals, leveraging their Doppler insensitivity and large time-bandwidth product to minimize the probability of false detection. However, this method only yields the average Doppler factor over the signal duration, not the instantaneous Doppler factor estimate. The fuzzy function method, based on Doppler-sensitive signals, adjusts the Doppler factor and delay time within a certain step size in both the time and frequency domains, within the possible Doppler and delay ranges. By finding the transmitted signal version most relevant to the received signal, it achieves Doppler and delay estimation of the received signal. The fuzzy function method achieves high Doppler estimation accuracy at the cost of increasing the number of local copy correlators, facing a dilemma of insufficient estimation accuracy or excessive hardware complexity. In addition, as a synchronization signal for mobile underwater acoustic communication, the construction of the signal also needs to consider the impact of severe multipath and Doppler effects in the underwater acoustic channel on the estimation accuracy, as well as the stability of the estimation results. Summary of the Invention

[0003] To address the aforementioned issues, this invention provides a Doppler estimation method for underwater acoustic signals based on an improved firefly algorithm. This method can suppress multipath interference in underwater acoustic channels, improve the stability and accuracy of Doppler estimation, and effectively improve the estimation accuracy error caused by multipath interference and temporal scale variations in broadband signals in mobile underwater acoustic communication.

[0004] A method for Doppler estimation of underwater acoustic signals based on an improved firefly algorithm includes the following steps:

[0005] S1: The broadband underwater acoustic signal constructed based on the pseudo-random sequence is modulated onto the transmission frequency band by a carrier wave to obtain the transmitted signal;

[0006] S2: After the transmitted signal passes through the underwater acoustic channel, it reaches the receiver and is correlated with local reference signals carrying different Doppler factors. The Doppler factor corresponding to the maximum correlation is used as the coarse estimate of the Doppler factor, and the Doppler fine search interval is constructed using the coarse estimate of the Doppler factor as the midpoint of the interval.

[0007] S3: Determine the initial position of each firefly in the firefly population within the Doppler fine search range, and calculate the luminous intensity of each firefly under the initial position conditions.

[0008] S4: Determine whether the maximum number of iterations has been reached. If yes, the position corresponding to the firefly with the strongest current luminous intensity is the Doppler factor precise estimation result. If no, proceed to step S5.

[0009] S5: The firefly with the strongest current luminosity randomly changes its position, and the other fireflies move closer to the firefly with the strongest current luminosity according to the set rules, completing the position update of all fireflies. Then, under the conditions of each updated position, the luminosity of each firefly is recalculated, and step S4 is repeated.

[0010] Furthermore, the correlation calculation method in step S2 is as follows:

[0011]

[0012] in, To preset the Doppler factor, Δ step To preset the search step size, and These are the preset minimum and preset maximum values, respectively. For local reference signal and Doppler factor The correlation coefficient, where N is the number of sampling points, and r(n) is the receiver's correlation coefficient at 1 / T. c T is the digital signal obtained by sampling frequency. c It is the chip duration, T s Let T be the symbol duration, c(l) be a pseudo-random sequence of length L, and l = 0, 1, ..., L-1. c f is the spread spectrum chip spacing. c Let g(t) be the center frequency of the transmitted signal carrier, and g(t) be the pulse shaping function. If g(t) is a rectangular pulse, then... |·| represents taking the absolute value;

[0013] The Doppler factor corresponding to the highest correlation is used as the rough estimate of the Doppler factor. Represented as:

[0014]

[0015] At the same time, the Doppler fine search range is denoted as

[0016] Furthermore, let the Doppler fine search range be denoted as... in, This is a rough estimate of the Doppler factor, Δ stepLet m be the number of fireflies in the firefly population, and let x be the initial position of each firefly. i The setup method is as follows:

[0017]

[0018] Where i = 1, 2, ..., m, rand i It is a random number between [0,1].

[0019] Meanwhile, the calculation method for the luminous intensity of each firefly under the initial position conditions is as follows:

[0020]

[0021] Among them, I i For the i-th firefly at the initial position x i The luminous intensity is given by N, where N is the number of sampling points, and r(n) is the luminous intensity at the receiver at a frequency of 1 / T. c T is the digital signal obtained by sampling frequency. c It is the chip duration, T s Let T be the symbol duration, c(l) be a pseudo-random sequence of length L, and l = 0, 1, ..., L-1. c f is the spread spectrum chip spacing. c Let g(t) be the center frequency of the transmitted signal carrier, and g(t) be the pulse shaping function. If g(t) is a rectangular pulse, then... |·| represents taking the absolute value.

[0022] Furthermore, the remaining fireflies, according to pre-defined rules, approach the firefly with the strongest current light intensity, specifically as follows:

[0023]

[0024] in, Let x be the updated position of the i-th firefly. j For the firefly with the strongest luminosity, j = 1, 2, ..., m, α is the set step size, β(d ij Let d be the attraction of the firefly j with the strongest luminosity to the i-th firefly. ij Let be the distance between the firefly j with the strongest current luminosity and the i-th firefly.

[0025] Furthermore, attraction β(d ij The calculation method for ) is as follows:

[0026]

[0027] Where β0 is the attractive force at the light source, and β0 is a set constant, γ is the light absorption coefficient based on the chaotic variable scaling transformation, and we have:

[0028] γ=τu k+1

[0029] u k+1 =τQ(u k )

[0030] Where τ = q / MaxGeneration, q is the current iteration number in the Firefly Algorithm, MaxGeneration is the maximum iteration number set in the Firefly Algorithm, k is the current iteration number in the chaotic variable scaling transformation, and Q(·) is the chaotic mapping operator.

[0031] Furthermore, the transmitted signal s(t) is:

[0032]

[0033] in, Let c(l) represent the real part of a pseudo-random sequence of length L, where l = 0, 1, ..., L-1, and T. c f is the spread spectrum chip spacing. c Let g(t) be the center frequency of the transmitted signal carrier, and g(t) be the pulse shaping function. If g(t) is a rectangular pulse, then...

[0034] Beneficial effects:

[0035] 1. This invention provides a Doppler estimation method for underwater acoustic signals based on an improved firefly algorithm. The method employs a pseudo-random sequence to construct the transmitted signal, improving its resistance to multipath interference and broadband Doppler effects in mobile underwater acoustic communication scenarios. At the receiving end, a coarse Doppler estimation is first performed using a large step size. Within a narrowed Doppler factor search range, the firefly algorithm is improved based on a variable-scale chaotic strategy. An objective function is constructed using the correlation between the received signal and a local reference signal carrying different Doppler factors. The fitness value is calculated, transforming Doppler estimation into a continuous optimization problem. This achieves Doppler estimation accuracy that meets the synchronization requirements of underwater acoustic communication with lower computational complexity. Simultaneously, the Doppler-sensitive nature of the algorithm ensures estimation stability over a larger Doppler range.

[0036] 2. This invention provides a Doppler estimation method for underwater acoustic signals based on an improved firefly algorithm, which utilizes the autocorrelation characteristics of pseudo-random sequences to suppress multipath interference and improve the anti-multipath performance of the signal.

[0037] 3. This invention provides a method for Doppler estimation of underwater acoustic signals based on an improved firefly algorithm. It uses a variable-scale chaotic strategy to continuously adjust the light absorption coefficient, thus solving the problems of premature convergence and slow iteration speed in the later stages of the standard firefly algorithm. Attached Figure Description

[0038] Figure 1 The flowchart shows the improved firefly algorithm in the Doppler estimation method for underwater acoustic signals.

[0039] Figure 2 The graph shows the search results for the objective function generated using the reference signal amplitude and Doppler frequency offset as variables.

[0040] Figure 3 To improve the convergence performance of the Doppler estimation iteration in the firefly algorithm;

[0041] Figure 4 A comparison chart showing the Doppler estimation accuracy of the least squares method and the method of this invention under Gaussian and multipath channels;

[0042] Figure 5 A graph showing the effect of different signal lengths on the accuracy of Doppler estimation;

[0043] Figure 6 This is a graph showing the impact of different Doppler factors on the accuracy of Doppler estimation under low signal-to-noise ratio. Detailed Implementation

[0044] To enable those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings.

[0045] This invention uses pseudo-random codes to construct broadband underwater acoustic signals. At the receiving end, Doppler coarse estimation and fine estimation are performed sequentially. In the fine estimation process, the firefly algorithm with random search is introduced to replace the exhaustive fuzzy function method. That is, the Doppler fine estimation is transformed into a continuous optimization problem of finding the maximum value. The stability of the firefly algorithm is enhanced by a variable-scale chaotic strategy.

[0046] Specifically, such as Figure 1 As shown, a method for Doppler estimation of underwater acoustic signals based on an improved firefly algorithm includes the following steps:

[0047] S1: The broadband underwater acoustic signal constructed based on the pseudo-random sequence is modulated onto the transmission frequency band by a carrier wave to obtain the transmitted signal s(t) as follows:

[0048]

[0049] in, Let c(l) represent the real part of a pseudo-random sequence of length L, where l = 0, 1, ..., L-1, and T. c f is the spread spectrum chip spacing. c Let g(t) be the center frequency of the transmitted signal carrier, and g(t) be the pulse shaping function. If g(t) is a rectangular pulse, then...

[0050] S2: After the transmitted signal passes through the underwater acoustic channel, it reaches the receiver and is correlated with local reference signals carrying different Doppler factors. The Doppler factor corresponding to the maximum correlation is used as the coarse estimate of the Doppler factor, and the Doppler fine search interval is constructed using the coarse estimate of the Doppler factor as the midpoint of the interval.

[0051] The specific method for calculating correlation is as follows:

[0052]

[0053] in, To preset the Doppler factor, Δ step To preset the search step size, and These are the preset minimum and preset maximum values, respectively. For local reference signal and Doppler factor The correlation coefficient, where N is the number of sampling points, and r(n) is the receiver's correlation coefficient at 1 / T. c T is the digital signal obtained by sampling frequency. c It is the chip duration, T s Let T be the symbol duration, c(l) be a pseudo-random sequence of length L, and l = 0, 1, ..., L-1. c f is the spread spectrum chip spacing. c Let g(t) be the center frequency of the transmitted signal carrier, and g(t) be the pulse shaping function. If g(t) is a rectangular pulse, then... |·| represents taking the absolute value;

[0054] By comparing the various correlation results, the Doppler factor corresponding to the one with the highest correlation is taken as the coarse estimate of the Doppler factor. Represented as:

[0055]

[0056] At the same time, the Doppler fine search range is denoted as

[0057] S3: Determine the initial position of each firefly in the firefly population within the Doppler fine search range, and calculate the luminous intensity of each firefly under the initial position conditions.

[0058] It should be noted that this invention requires initializing the firefly algorithm parameters based on the transmitter synchronization signal parameters and the Doppler coarse estimation results. Specifically, this involves initializing the light absorption coefficient γ, maximum attraction β0, step size α, current iteration number q, total iteration number MaxGeneration, and random coefficient rand. iLet m be the number of fireflies in the firefly population, then the initial position x of each firefly is... i The setup method is as follows:

[0059]

[0060] Where i = 1, 2, ..., m, rand i It is a random number between [0,1].

[0061] Meanwhile, the calculation method for the luminous intensity of each firefly under the initial position conditions is as follows:

[0062]

[0063] Among them, I i For the i-th firefly at the initial position x i The luminous intensity is given by N, where N is the number of sampling points, and r(n) is the luminous intensity at the receiver at a frequency of 1 / T. c T is the digital signal obtained by sampling frequency. c It is the chip duration, T s Let T be the symbol duration, c(l) be a pseudo-random sequence of length L, and l = 0, 1, ..., L-1. c f is the spread spectrum chip spacing. c Let g(t) be the center frequency of the transmitted signal carrier, and g(t) be the pulse shaping function. If g(t) is a rectangular pulse, then... |·| represents taking the absolute value.

[0064] Therefore, this invention uses the correlation between the local reference signal and the received signal carrying different Doppler factors as the objective function to calculate the fitness value J(x). i ), that is, the luminous intensity I of each firefly. i .

[0065] S4: Determine whether the maximum number of iterations has been reached. If yes, the position corresponding to the firefly with the strongest current luminous intensity is the Doppler factor precise estimation result. If no, proceed to step S5.

[0066] It should be noted that after entering the loop iteration, fireflies with low light intensity will be attracted by fireflies with high light intensity, causing them to move. The attraction between fireflies will decrease as the distance between them increases. Check whether the iteration termination condition is met, that is, check whether the maximum number of iterations has been reached. If not, update the position and light intensity of each firefly; if so, output the optimal position and light intensity of the fireflies and end the loop process.

[0067] Each firefly approaches the firefly with the strongest current light intensity according to the following set rules:

[0068]

[0069] in, Let x be the updated position of the i-th firefly. j For the firefly with the strongest luminosity, j = 1, 2, ..., m, α is the set step size, β(d ij Let d be the attraction of the firefly j with the strongest luminosity to the i-th firefly. ij Let be the distance between the firefly j with the strongest current luminosity and the i-th firefly.

[0070] It should be noted that when the firefly with the strongest light intensity updates its position, if we let i = j in the above formula, then we have:

[0071]

[0072] in, This shows the updated position of the firefly j, which currently emits the strongest light.

[0073] Furthermore, attraction β(d ij The calculation method for ) is as follows:

[0074]

[0075] Where β0 is the attractive force at the light source, and β0 is a set constant, γ is the light absorption coefficient based on the chaotic variable scaling transformation, and we have:

[0076] γ=τu k+1

[0077]

[0078] The scaling transformation of chaotic variables is represented as:

[0079] u k+1 =τQ(u A )

[0080] Where τ = q / MaxGeneration, q is the current iteration number in the Firefly Algorithm, MaxGeneration is the maximum iteration number set in the Firefly Algorithm, k is the current iteration number in the chaotic variable scaling transformation, and Q(·) is the chaotic mapping operator.

[0081] S5: The firefly with the strongest current luminosity randomly changes its position, and the other fireflies move closer to the firefly with the strongest current luminosity according to the set rules, completing the position update of all fireflies. Then, under the conditions of each updated position, the luminosity of each firefly is recalculated, and step S4 is repeated.

[0082] Therefore, the underwater acoustic signal Doppler estimation method proposed in this invention, based on the improved firefly algorithm, uses pseudo-random codes to construct the transmitted signal and leverages their excellent autocorrelation characteristics to suppress multipath interference in the underwater acoustic channel. Simultaneously, it utilizes the Doppler sensitivity of the code to ensure estimation stability over a large Doppler range. It introduces a random search firefly algorithm to replace the exhaustive fuzzy function method, improving its computational complexity. Furthermore, it employs a variable-scale chaotic strategy to continuously adjust the light absorption coefficient, addressing the problems of premature convergence and slow iteration speed in the later stages of the standard firefly algorithm.

[0083] Furthermore, Figure 2 The image shows the search results for the objective function generated using the reference signal amplitude and Doppler frequency offset as variables, as provided in the embodiments of this application. Under a 0dB signal-to-noise ratio condition, an m-sequence with L = 127 chips is used as the transmitted signal, and the carrier frequency is f. c =3000Hz, chip duration T c =0.5ms. When the amplitude gain of the local reference signal varies in the range of [0, 1] and the Doppler frequency offset varies in the range of [-36Hz, 36Hz], the objective function constructed by the correlation method has a small sidelobe. It can make full use of the autocorrelation characteristics of the pseudo-random sequence to suppress multipath interference in the underwater acoustic channel. At the same time, it can be found that the amplitude change of the local reference signal does not affect the trend of the Doppler factor change, that is, it does not affect the Doppler factor estimation result.

[0084] Figure 3 The Doppler estimation iterative convergence effect of the improved firefly algorithm provided in this application embodiment is shown. The transmitted signal parameters are the same as... Figure 2 Under the conditions of 0dB signal-to-noise ratio and multipath channel in the pool, the Doppler factor is first coarsely estimated at -0.006 by searching at equal intervals within the Doppler frequency offset range of [-36Hz, 36Hz] with a step size of 6Hz. Then, a fine Doppler factor estimation is performed within the search range of -0.006 ± 0.002, i.e., [-0.008, -0.004], yielding a true Doppler factor of -0.007. When using the firefly algorithm with a variable-scale chaotic strategy for the search, the firefly population size is set to 20, based on x... i = -0.006 - 0.002 + 0.002 × 2rand i Initialize the firefly positions. Calculate the luminous intensity (fitness value) of each firefly according to step S3. Initialize parameters as follows: light absorption coefficient 1.8, maximum attraction 0.5, step size 0.00005, total iterations 50, and random number rand randomly selected from [0, 1]. Set the variable-scale chaotic mapping parameters as follows: u0 = 0.7, u... k+1 =τsin(πu) k), where τ = q / MaxGeneration, q is the current iteration number, and MaxGeneration is the maximum iteration number, 50. Figure 3 The results show that the firefly algorithm converges and obtains a stable Doppler estimation result in less than 10 iterations, -7.013×10⁻⁶. -3 , with the true Doppler factor -7×10 -3 Very close, the Doppler estimation accuracy meets the synchronization requirements of underwater acoustic communication.

[0085] Meanwhile, this invention constructs objective functions and calculates fitness values ​​under Gaussian and multipath channel conditions using the least squares method and the correlation method proposed in this invention, respectively. The Doppler factor estimation results are as follows: Figure 4 As shown, the pseudo-random sequence used has a length of 200 and a signal duration of 100ms. Under both channel conditions, the Doppler factor estimation accuracy of the method for constructing the objective function proposed in this invention is higher than that of the least squares method. This is because the method described in this invention utilizes the autocorrelation characteristics of the pseudo-random sequence to suppress multipath interference and improve the anti-multipath performance of the signal.

[0086] Figure 5 When constructing the objective function method for this invention, the impact of different sequence length gains on the Doppler estimation accuracy is discussed. As the length of the pseudo-random sequence increases, the signal time-bandwidth product increases, and its Doppler estimation performance becomes better.

[0087] Figure 6 The diagram shows the simulation results of different Doppler factor estimation accuracy under -5dB and -10dB conditions. It can be seen that the method proposed in this invention shows good estimation stability under the influence of broadband Doppler effect. At the same time, it is found that if the objective function is constructed by the least squares method for Doppler estimation, the estimation performance will be affected by the change of the signal time domain scale. When the Doppler factor is large, the Doppler estimation accuracy deteriorates significantly.

[0088] In summary, this invention proposes a Doppler estimation method for underwater acoustic signals based on an improved firefly algorithm for mobile underwater acoustic communication scenarios. It constructs a broadband underwater acoustic signal using a pseudo-random sequence. At the receiver, a coarse Doppler factor estimation is first performed using a large search step size. Within a narrowed search range, an objective function is constructed based on the correlation between the received signal and local reference signals with different Doppler factors. The improved firefly algorithm is then used to search for and obtain the Doppler factor estimation results. Through this heuristic algorithm, this invention can achieve Doppler estimation accuracy that meets the synchronization requirements of underwater acoustic communication with relatively low computational complexity. Simulation results also demonstrate that the method of constructing the transmitted signal and objective function in this invention can effectively improve the estimation accuracy error caused by multipath interference and temporal scale variations of broadband signals in mobile underwater acoustic communication.

[0089] Of course, the present invention may have other various embodiments. Without departing from the spirit and essence of the present invention, those skilled in the art can make various corresponding changes and modifications according to the present invention, but these corresponding changes and modifications should all fall within the protection scope of the appended claims.

Claims

1. A method for Doppler estimation of underwater acoustic signals based on an improved firefly algorithm, characterized in that, Includes the following steps: S1: The broadband underwater acoustic signal constructed based on the pseudo-random sequence is modulated onto the transmission frequency band by a carrier wave to obtain the transmitted signal; S2: After the transmitted signal passes through the underwater acoustic channel, it reaches the receiver and is correlated with local reference signals carrying different Doppler factors. The Doppler factor corresponding to the maximum correlation is used as the coarse estimate of the Doppler factor, and the Doppler fine search interval is constructed using the coarse estimate of the Doppler factor as the midpoint of the interval. S3: Determine the initial position of each firefly in the firefly population within the Doppler fine search range, and calculate the luminous intensity of each firefly under the initial position conditions. S4: Determine whether the maximum number of iterations has been reached. If yes, the position corresponding to the firefly with the strongest current luminous intensity is the Doppler factor precise estimation result. If no, proceed to step S5. S5: The firefly with the strongest current luminosity randomly changes its position, and the other fireflies move closer to the firefly with the strongest current luminosity according to the set rules, completing the position update of all fireflies. Then, under the conditions of each updated position, the luminosity of each firefly is recalculated, and step S4 is repeated.

2. The underwater acoustic signal Doppler estimation method based on the improved firefly algorithm as described in claim 1, characterized in that, The correlation calculation method in step S2 is as follows: in, To preset the Doppler factor, Δ step To preset the search step size, and These are the preset minimum and preset maximum values, respectively. For local reference signal and Doppler factor The correlation coefficient, where N is the number of sampling points, and r(n) is the receiver's correlation coefficient at 1 / T. c T is the digital signal obtained by sampling frequency. c It is the chip duration, T s Let T be the symbol duration, c(l) be a pseudo-random sequence of length L, and l = 0, 1, ..., L-1. c f is the spread spectrum chip spacing. c Let g(t) be the center frequency of the transmitted signal carrier, and g(t) be the pulse shaping function. If g(t) is a rectangular pulse, then... |·| represents taking the absolute value; The Doppler factor corresponding to the highest correlation is used as the rough estimate of the Doppler factor. Represented as: At the same time, the Doppler fine search range is denoted as 3. The underwater acoustic signal Doppler estimation method based on the improved firefly algorithm as described in claim 1, characterized in that, Assume the Doppler fine search range is denoted as in, This is a rough estimate of the Doppler factor, Δ step Let m be the number of fireflies in the firefly population, and let x be the initial position of each firefly. i The setup method is as follows: Where i = 1, 2, ..., m, rand i It is a random number between [0,1]. Meanwhile, the calculation method for the luminous intensity of each firefly under the initial position conditions is as follows: Among them, I i For the i-th firefly at the initial position x i The luminous intensity is given by N, where N is the number of sampling points, and r(n) is the luminous intensity at the receiver at a frequency of 1 / T. c T is the digital signal obtained by sampling frequency. c It is the chip duration, T s Let T be the symbol duration, c(l) be a pseudo-random sequence of length L, and l = 0, 1, ..., L-1. c f is the spread spectrum chip spacing. c Let g(t) be the center frequency of the transmitted signal carrier, and g(t) be the pulse shaping function. If g(t) is a rectangular pulse, then... |·| represents taking the absolute value.

4. The underwater acoustic signal Doppler estimation method based on the improved firefly algorithm as described in claim 3, characterized in that, The remaining fireflies, according to the set rules, approach the firefly with the strongest current light intensity, specifically: in, Let x be the updated position of the i-th firefly. j For the firefly with the strongest luminosity, j = 1, 2, ..., m, α is the set step size, β(d ij Let d be the attraction of the firefly j with the strongest luminosity to the i-th firefly. ij Let be the distance between the firefly j with the strongest current luminosity and the i-th firefly.

5. The underwater acoustic signal Doppler estimation method based on the improved firefly algorithm as described in claim 4, characterized in that, Attraction β(d) ij The calculation method for ) is as follows: Where β0 is the attractive force at the light source, and β0 is a set constant, γ is the light absorption coefficient based on the chaotic variable scaling transformation, and we have: y=τu k+1 and k+1 =τQ(u k ) Where τ = q / MaxGeneration, q is the current iteration number in the Firefly Algorithm, MaxGeneration is the maximum iteration number set in the Firefly Algorithm, k is the current iteration number in the chaotic variable scaling transformation, and Q(·) is the chaotic mapping operator.

6. A method for underwater acoustic signal Doppler estimation based on an improved firefly algorithm as described in any one of claims 1 to 5, characterized in that, The transmitted signal s(t) is: in, Let c(l) represent the real part of a pseudo-random sequence of length L, where l = 0, 1, ..., L-1, and T. c f is the spread spectrum chip spacing. c Let g(t) be the center frequency of the transmitted signal carrier, and g(t) be the pulse shaping function. If g(t) is a rectangular pulse, then...

Images