GPS-based high-efficiency accumulation method for target echo of external radiation source based on PSO and LVD

Abstract

The application discloses a GPS external radiation source target echo efficient accumulation method based on PSO and LVD. The method comprises the following steps: acquiring echo signals, and performing cross-correlation processing on the echo signals to obtain pulse compression signals; according to the pulse compression signals, the velocity and acceleration of target motion are estimated by using a PSO algorithm to obtain estimated velocity and acceleration; according to the estimated velocity and acceleration, first-order range migration, second-order range curvature and Doppler frequency migration correction are performed on the pulse compression signals to obtain corrected pulse compression signals; and the corrected pulse compression signals are coherently accumulated by using LVD to obtain a target detection result. The application can obtain a higher signal-to-noise ratio and high gain.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of radar, and particularly relates to a GPS external source target echo efficient accumulation method based on PSO and LVD. BACKGROUND

[0002] Since the navigation satellite is located outside the atmosphere, the navigation satellite is used as an external source, and the clutter received by the radar is relatively small, which is conducive to target detection. In addition, the navigation satellite has obvious advantages of global coverage and stable operation. Taking the Global Positioning System (GPS) of the United States as an example, the satellite constellation is composed of more than 20 satellites, which can ensure that at least 4 satellites cover any place on the ground. In addition, it also provides time service for convenient time synchronization, so the external source radar based on GPS is particularly suitable for silent monitoring of key coastal areas, and the typical targets are large low-altitude penetration fighters and sea vessels.

[0003] The GPS external source radar also has defects. The main defect is that the power of the satellite transmitted signal reaching the ground is too small, which causes the target echo signal to be often submerged in noise and multi-path clutter, and the signal-to-noise ratio and signal-to-clutter ratio are low. This makes the external source radar based on GPS need a longer (tens of seconds) accumulation time to detect the target compared with the active radar. During the long-time accumulation process, the motion of the target will cause the problems of cross-range cell migration and cross-Doppler cell migration of the echo signal, which causes the echo energy to be dispersed and affects the detection performance of the radar. Therefore, the long-time accumulation technology for the case of existing range migration and Doppler frequency migration is of great significance to improve the detection power of the GPS external source radar.

[0004] The long-time accumulation algorithm is mainly divided into coherent accumulation and non-coherent accumulation according to whether the phase information of the echo signal is retained. Since the useful echo phase information is lost, the gain of the non-coherent accumulation algorithm is low, while the coherent accumulation algorithm has better detection performance due to the compensation of the phase difference.

[0005] In the coherent accumulation algorithm, the main problems to be solved are range migration and Doppler frequency migration. For range migration, the common processing method is to perform a keystone transformation. This method can correct the first-order range migration under the condition that the velocity is unknown. For Doppler frequency migration, the common method is to transform the signal to the frequency domain, and use time-frequency analysis tools to estimate and detect the signal parameters. After the range migration and Doppler frequency migration are corrected, the coherent accumulation is generally realized by using the slow-time as the dimension of FFT.

[0006] When long-time multi-pulse accumulation is performed, target motion will cause problems of range migration and Doppler frequency migration, wherein the range migration can be divided into first-order range migration and second-order range curvature. Generally, a traditional keystone transform only corrects the first-order range migration and does not correct the second-order range curvature. When the keystone transform is used to correct the first-order range migration and the FFT is used to perform coherent accumulation in a slow time dimension, the second-order range curvature and the Doppler frequency migration will cause signal energy to be dispersed on a range-Doppler spectrum (RD spectrum), thereby affecting the detection performance of the radar. Compared with the FFT, the LVD is only affected by the first-order range migration and the second-order range curvature, and is not affected by the Doppler frequency migration. However, the resolution of the LVD in the frequency modulation dimension in the CFCR domain is relatively low, the detection accuracy of the target motion acceleration is poor, and when the acceleration of the target motion corresponds to a frequency modulation frequency in the center range of the frequency modulation frequency resolution unit, the peak value will decrease. In summary, the existing coherent accumulation algorithm will have a gain decrease problem when the accumulation time is lengthened. SUMMARY

[0007] In order to solve the above problems existing in the prior art, the application provides a GPS external source target echo efficient accumulation method based on PSO and LVD.

[0008] The technical problem to be solved by the application is solved by the following technical scheme:

[0009] The application provides a GPS external source target echo efficient accumulation method based on PSO and LVD, comprising:

[0010] An echo signal is acquired, and the echo signal is subjected to cross-correlation processing to obtain a pulse compression signal;

[0011] According to the pulse compression signal, the velocity and acceleration of target motion are estimated by using a PSO algorithm to obtain estimated velocity and acceleration;

[0012] According to the estimated velocity and acceleration, the pulse compression signal is corrected in terms of first-order range migration, second-order range curvature and Doppler frequency migration to obtain a corrected pulse compression signal;

[0013] The corrected pulse compression signal is subjected to coherent accumulation by using an LVD to obtain a target detection result.

[0014] Compared with the prior art, the application has the following beneficial effects:

[0015] The application makes accurate estimation on the initial velocity and acceleration of target motion by using the PSO algorithm, then makes first-order range migration and second-order range curvature correction on the cross-correlation spectrum data by using the obtained velocity and acceleration parameters, so that the signal energy can be concentrated in the CFCR domain of the LVD, and makes correction on the multiple pairs of Doppler frequency migration by using the obtained acceleration parameters, so that the peak value of the LVD in the CFCR domain appears at the zero frequency position of the frequency modulation rate, effectively alleviates the problem of LVD peak value decline, thereby obtaining higher signal-to-noise ratio and high gain.

[0016] The application will be further described in detail below in combination with the drawings and specific embodiments. BRIEF DESCRIPTION OF DRAWINGS

[0017] Figure 1 is a flowchart of a GPS external source target echo efficient accumulation method based on PSO and LVD provided by an embodiment of the application;

[0018] Figure 2 is a construction principle diagram of a target function provided by an embodiment of the application;

[0019] Figure 3 is a flowchart of an LVD algorithm provided by an embodiment of the application;

[0020] Figure 4 is a result of KT+FFT on the cross-correlation spectrum of different lengths under a signal-to-noise ratio of-40dB provided by an embodiment of the application;

[0021] Figure 5 is a result of KT+LVD on sequences of different lengths under a signal-to-noise ratio of-40dB provided by an embodiment of the application;

[0022] Figure 6 is a result of PSO+LVD on sequences of different lengths under a signal-to-noise ratio of-40dB provided by an embodiment of the application. DETAILED DESCRIPTION

[0023] The application will be further described in detail below in combination with specific embodiments, but the embodiments of the application are not limited thereto.

[0024] Figure 1 is a flowchart of a GPS external source target echo efficient accumulation method based on PSO and LVD provided by an embodiment of the application, as shown in the figure, the method comprises the following steps of: Figure 1

[0025] S101, obtaining an echo signal and performing cross-correlation processing on the echo signal to obtain a pulse compression signal.

[0026] ​S102, according to the pulse compression signal, the velocity and acceleration of the target motion are estimated by using the PSO algorithm, and the estimated velocity and acceleration are obtained.

[0027] S103, according to the estimated velocity and acceleration, the first-order range migration, the second-order range curvature and the Doppler frequency migration correction are carried out on the pulse compression signal, and the corrected pulse compression signal is obtained.

[0028] S104, the corrected pulse compression signal is coherently accumulated by using LVD, and the target detection result is obtained.

[0029] For the above S101, the reference signal is used for cross-correlation processing of the echo signal, so as to obtain the pulse compression signal (also called cross-correlation spectrum).

[0030] For example, the expression of the reference signal S ref (τ,η) and the echo signal S r (τ,η) are as follows:

[0031]

[0032] Wherein, A ref is the amplitude of the reference signal, A r is the amplitude of the echo signal, u is the envelope of the signal, c is the speed of light, λ is the wavelength, τ ∈ [0, T] is the fast time, T is the pulse repetition period, η ∈ [0, T D ] is the slow time and takes the integer multiple of T, T D is the pulse accumulation time, L(η) is the distance from the receiver to the satellite, R t (η) is the distance from the satellite to the target, R r (η) is the distance from the receiver to the target.

[0033] For example, after the reference signal S ref (τ,η) is used for cross-correlation processing of the echo signal S r (τ,η), the expression of the obtained pulse compression signal PC(τ,η) is as follows:

[0034]

[0035] Wherein, A PC is the amplitude of the pulse compression signal, CF is the periodic correlation function, ΔR(0) is the initial distance difference between the receiver and the target, ΔR(η) is the distance difference between the receiver and the target at the moment of the slow time η, v0 represents the real speed of the target motion, and a0 represents the real acceleration of the target motion.

[0036] Here, the above S102 can be realized by the following steps:

[0037] S1021, determine an expression of the number of cells to be translated in the opposite direction of the range migration along the fast time dimension when correcting the pulse compression signal for the range migration, according to the velocity and the acceleration of the target motion to be estimated.

[0038] Here, the range migration can be corrected by performing the translation envelope alignment on the pulse compression signal. Exemplarily, the expression of the number of cells is as follows: F S is the fast time sampling frequency, represents the velocity of the target motion used in the process of estimating v0, represents the acceleration of the target motion used in the process of estimating a0.

[0039] S1022, determine an expression of the signal obtained after correcting the pulse compression signal for the range migration, according to the expression of the number of cells.

[0040] S1023, construct a Doppler frequency migration compensation function according to the acceleration of the target motion to be estimated.

[0041] Exemplarily, the expression of the Doppler frequency migration compensation function is as follows:

[0042]

[0043] S1024, determine an expression of the corrected pulse compression signal obtained after correcting the pulse compression signal for the first-order range migration, the second-order range curvature and the Doppler frequency migration, according to the expression of the signal obtained after correcting the pulse compression signal for the range migration, and the Doppler frequency migration compensation function.

[0044] Here, the expression of the signal obtained after correcting the pulse compression signal for the range migration can be multiplied by the Doppler frequency migration compensation function to obtain the expression of the corrected pulse compression signal. Exemplarily, the expression of the corrected pulse compression signal is as follows:

[0045]

[0046] wherein η ∈ [0, T D ] is the slow time and takes an integer multiple of T, τ ∈ [0, T] is the fast time, T is the pulse repetition period, T D is the pulse accumulation time, ΔR(0) is the initial distance difference between the receiver and the target, λ is the wavelength, c is the speed of light, and CF is the periodic correlation function.

[0047] S1025, construct an objective function according to the expression of the corrected pulse compression signal.

[0048] Exemplarily,Figure 2 The schematic diagram of the objective function is shown in FIG. 2. Figure 2 The corrected pulse compression signal can be subjected to FFT along the slow time dimension η to convert the cross-correlation spectrum into the RD spectrum, and the peak energy on the RD spectrum is taken as the mapping value of the objective function f(X). If and Both the range migration and the Doppler frequency migration are completely corrected, the peak energy on the RD spectrum reaches the maximum, and the objective function f(X) also reaches the maximum. Therefore, the expression of the objective function is as follows: FFT{·} represents the fast Fourier transform along the slow time dimension.

[0049] S1026, according to the objective function, the velocity and acceleration of the target motion to be estimated are estimated by using the PSO algorithm, and the estimated velocity and acceleration are obtained.

[0050] Specifically, S1026 can be implemented through steps S1-S4:

[0051] S1, initializing the position vector, velocity vector and historical optimal position vector of n particles, obtaining the initial position vector initial velocity vector and initial historical optimal position vector of each particle, wherein the position vector of each particle is a two-dimensional parameter composed of the velocity and acceleration of the target motion.

[0052] Here, the position vector, velocity vector and historical optimal position vector of the n particles can be randomly initialized.

[0053] S2, when the kth iteration is performed and k=1, according to the initial historical optimal position vector of all particles and the objective function, the maximum function value of the kth iteration is determined the group historical optimal position vector of the kth iteration and the historical optimal position vector of the kth iteration of each particle of each particle is completed, wherein i is a positive integer, and i takes a value from 1 to n.

[0054] Specifically, the process of the first iteration is as follows:

[0055] 1) Substitute the initial historical optimal position vector of all particles into the objective function f(X) respectively, and obtain n objective function values;

[0056] 2) take the maximum value of the n objective function values as the maximum function value of the kth iteration;

[0057] 3) the initial historical optimal position vector corresponding to the maximum function value of the kth iteration is taken as the group historical optimal position vector of the kth iteration

[0058] 4) for each particle, the initial historical optimal position vector of the particle is taken as the historical optimal position vector of the kth iteration of the particle

[0059] S3, when the kth iteration is performed and k is greater than 1, for each particle, based on the maximum function value of the (k-1)th iteration the group historical optimal position vector of the (k-1)th iteration and the historical optimal position vector of the (k-1)th iteration of the particle the velocity vector of the (k-1)th iteration of the particle the position vector of the (k-1)th iteration and the historical optimal position vector of the (k-1)th iteration is updated to obtain the velocity vector of the kth iteration of the particle the position vector of the kth iteration and the historical optimal position vector of the kth iteration the kth iteration is completed, where k is a positive integer greater than or equal to 1.

[0060] Specifically, in addition to the first iteration, the process of each iteration is as follows:

[0061] 1) for each particle, based on the group historical optimal position vector of the (k-1)th iteration the historical optimal position vector of the (k-1)th iteration of the particle the velocity vector of the (k-1)th iteration of the particle the position vector of the (k-1)th iteration of the particle the inertia weight, the acceleration coefficient and the preset coefficient, to generate the velocity vector of the kth iteration of the particle

[0062] For example, the expression of the velocity vector of the kth iteration of the particle is as follows:

[0063]

[0064] where ω is the inertia weight, c1 and c2 are the acceleration coefficients, r1 and r2 are the preset coefficients, and r1 and r2 are random numbers between 0 and 1, the value range of v max represents a preset maximum velocity vector.

[0065] 2) according to the velocity vector of the kth iteration of the particle and the position vector of the (k-1)th iteration of the particle generating the position vector of the kth iteration of the particle

[0066] The expression of the position vector of the kth iteration of the particle is:

[0067] 3) using the objective function, calculating the function value of the position vector of the kth iteration of the particle and the function value of the (k-1)th iteration of the history optimal position vector of the particle

[0068] 4) according to the size relationship between the function value and the function value , determining the history optimal position vector of the kth iteration of the particle

[0069] The expression of the history optimal position vector of the kth iteration of the particle is:

[0070]

[0071] 5) substituting the history optimal position vector of the kth iteration of all particles into the objective function f(X) respectively, obtaining n objective function values, taking the maximum value of the n objective function values as the maximum function value of the kth iteration, and taking the history optimal position vector of the kth iteration corresponding to the maximum function value of the kth iteration as the group history optimal position vector of the kth iteration

[0072] S4, judging whether the result of the kth iteration or k reaches the iteration termination condition, if not, then k=k+1, and continue to iterate until the iteration termination condition is finally reached, and the group history optimal position vector obtained when the iteration termination condition is reached is taken as the estimated velocity and acceleration.

[0073] ​​​​Here, the termination condition can be determined by checking if the historical optimal position vectors of the group obtained in several consecutive iterations are the same. For example, if the historical optimal position vectors of the group are the same in several consecutive iterations, it indicates that the termination condition has been met; otherwise, the termination condition has not been met and iterations need to continue until the termination condition is met. Alternatively, the termination condition can be determined by checking if the iteration number k is less than or equal to the preset iteration number N. For example, if k is N, it indicates that the termination condition has been met; otherwise, iterations need to continue until the termination condition is met.

[0074] For the above S103, once the velocity and acceleration are estimated, the pulse compression signal can be corrected sequentially by first-order distance migration, second-order distance curvature, and Doppler frequency migration based on the estimated velocity and acceleration, thereby obtaining the corrected pulse compression signal.

[0075] Specifically, for S103 above, the Doppler frequency migration compensation function is determined based on the estimated velocity and acceleration; based on the Doppler frequency migration compensation function, the initially corrected signal is subjected to Doppler frequency migration correction to obtain the corrected pulse compression signal.

[0076] Here, as Figure 3 As shown, the above S104 can be implemented through the following steps:

[0077] S1041. Select the slow time sequence of each distance unit from the corrected pulse compression signal.

[0078] For example, the slow time series PC(η) for each distance unit m The expression for ) is as follows:

[0079] v0 represents the true velocity of the target motion, that is, the velocity of the target motion estimated through the above process, and a0 represents the true acceleration of the target motion, that is, the acceleration of the target motion estimated through the above process.

[0080] S1042. Calculate the parameterized instantaneous symmetric autocorrelation function of the slow time series for each selected distance unit.

[0081] For example, the expression for the parametric instantaneous symmetric autocorrelation function of the slow time series of each distance unit is as follows:

[0082]

[0083] Wherein, the time delay variable μ∈[-b,T] Db], the change interval of the delay variable is 2T, and b is a preset delay parameter, generally taking a value of 1.

[0084] S1043, variable substitution is performed on the parametric instantaneous symmetric autocorrelation function of the slow time sequence of each distance unit, to obtain a transformed parametric instantaneous symmetric autocorrelation function.

[0085] Specifically, η k = η m (μ+b) Variable substitution is performed on the parametric instantaneous symmetric autocorrelation function of the slow time sequence of each distance unit, and the expression of the transformed parametric instantaneous symmetric autocorrelation function obtained is as follows:

[0086]

[0087] S1044, FFT is performed on each transformed parametric instantaneous symmetric autocorrelation function in the delay dimension, to convert to a CFCR domain, and an LVD result is obtained correspondingly.

[0088] Specifically, the expression of each LVD result is as follows:

[0089]

[0090] wherein, represents each LVD result, f c is a center frequency, is a frequency modulation rate, CF is a periodic correlation function, b is a preset delay parameter, and δ represents an impact function.

[0091] S1045, the obtained LVD results are merged, and an LVD result with the highest peak value is selected from all the obtained LVD results.

[0092] S1046, target detection is performed according to the LVD result with the highest peak value, to obtain a target detection result.

[0093] Specifically, 2D-CFAR (2D-CFAR) detection can be performed on the LVD result with the highest peak value, if a target is detected, the estimated speed and acceleration are the speed and acceleration of the target in motion, and the distance difference from the target can be determined according to the distance unit corresponding to the LVD result with the highest peak value, so as to realize detection of the target.

[0094] The effect of the method is verified through a simulation experiment.

[0095] 1. Simulation conditions

[0096] The initial target distance is set to 2000m, the target relative radar radial motion initial speed is 19m / s, the target motion acceleration is 0.045m / s2, the pulse repetition period is 1ms, the sampling rate is 20.46MHz, the carrier frequency is 1576.42MHz, the signal-to-noise ratio is -40dB, and the total residence time is 10s.

[0097] 2. Simulation experiment content and result analysis

[0098] Figure 4 is the result of KT+FFT of the cross-correlation spectrum under different time lengths with a signal-to-noise ratio of -40dB, wherein, the a graph is a 2-second (s) plane RD spectrum, the c graph is a 5s plane RD spectrum, and the e graph is a complete 10s plane RD spectrum. Figure 5 is the result of KT+LVD of the sequence under different time lengths with a signal-to-noise ratio of -40dB, wherein, the a graph is a 2s plane CFCR spectrum, the c graph is a 5s plane CFCR spectrum, and the e graph is a complete 10s plane CFCR spectrum. Figure 6 is the result of PSO+LVD of the sequence under different time lengths with a signal-to-noise ratio of -40dB, wherein, the a graph is a 2s plane CFCR spectrum, the c graph is a 5s plane CFCR spectrum, and the e graph is a complete 10s plane CFCR spectrum. Figure 4 、 5 , 6, wherein, the b graph is a 2s frequency profile, the d graph is a 5s frequency profile, and the f graph is a complete 10s frequency profile. Table 1 is the result of 2D-CFAR of the sequence under different time lengths with a signal-to-noise ratio of -40dB after processing by the three methods.

[0099] Table 1 is the result of 2D-CFAR detection of the sequence under different time lengths with a signal-to-noise ratio of -40dB.

[0100] Duration (s) KT + FFT KT + LVD PSO + LVD 2 17.859 dB 21.570 dB 22.536 dB 5 17.633 dB 24.967 dB 25.325 dB 10 15.729 dB 22.304 dB 27.453 dB

[0101] As can be seen from the simulation results, with the increase of the accumulation time, the gain of KT+FFT will continuously decrease due to the influence of the second-order distance curvature and the Doppler frequency migration. Although LVD is not affected by the Doppler frequency migration, when the accumulation time is 10s, the frequency resolution is 0.1Hz / s, the target acceleration corresponds to a frequency of 0.2365Hz / s, and the theoretical peak value of LVD is located near the center of the third resolution unit in the CFCR domain frequency dimension. At this time, the peak value decreases obviously. Under the same conditions, the PSO+LVD method not only has the highest peak noise ratio, but also the peak noise ratio increases with the increase of the accumulation time, and it is an efficient long-time accumulation method.

[0102] It should be noted that the terms "first", "second", etc. are used only for descriptive purpose and should not be construed as indicating or implying relative importance or a specific order of limiting the indicated technical features. Thus, features defined with "first", "second" can explicitly or implicitly include one or more features. In the description of the present application, the meaning of "a plurality" is two or more, unless otherwise expressly and specifically limited.

[0103] In the description of the present application, the description of the terms "one embodiment", "some embodiments", "an example", "a specific example", or "some examples" etc. means that the specific features or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present application. In the present description, the illustrative description of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features or characteristics described can be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art can combine and combine different embodiments or examples described in the present description.

[0104] In the description, the word "comprising" does not exclude other components or steps, and "one" or "an" does not exclude a plurality. Some measures are described in mutually different embodiments, but this does not mean that these measures cannot be combined to produce good results.

[0105] The above is a further detailed description of the present application in combination with specific preferred embodiments, and cannot be considered as limiting the specific implementation of the present application to these descriptions. For those skilled in the art to which the present application belongs, without departing from the concept of the present application, a number of simple deductions or substitutions can be made, which should be considered as belonging to the protection scope of the present application.

Claims

1. A method for efficient accumulation of GPS external radiation source target echoes based on PSO and LVD, characterized in that, include: The echo signal is acquired, and cross-correlation processing is performed on the echo signal to obtain a pulse compression signal; Based on the pulse compression signal, the velocity and acceleration of the target motion are estimated using the PSO algorithm to obtain the estimated velocity and acceleration; Based on the estimated velocity and acceleration, the pulse compression signal is corrected by first-order distance migration, second-order distance curvature, and Doppler frequency migration to obtain the corrected pulse compression signal. The corrected pulse compression signal is coherently accumulated using LVD to obtain the target detection result; Specifically, based on the pulse compression signal, the velocity and acceleration of the target motion are estimated using the PSO algorithm to obtain the estimated velocity and acceleration, including: Based on the estimated velocity and acceleration of the target motion, determine the expression for the number of units translated in the opposite direction of distance migration along the fast time dimension when performing distance migration correction on the pulse compression signal; Based on the expression for the number of units, determine the expression for the signal obtained after distance migration correction of the pulse compression signal; Based on the estimated acceleration of the target motion, a Doppler frequency migration compensation function is constructed. Based on the expression of the signal obtained after distance migration correction of the pulse compression signal, and the Doppler frequency migration compensation function, the expression of the corrected pulse compression signal obtained after first-order distance migration, second-order distance curvature and Doppler frequency migration correction of the pulse compression signal is determined. Based on the expression of the corrected pulse compression signal, construct the objective function; Based on the objective function, the PSO algorithm is used to estimate the velocity and acceleration of the target motion to be estimated, and the estimated velocity and acceleration are obtained. The objective function is expressed as follows: ； ； in, Denotes the objective function, This indicates performing a Fast Fourier Transform on a slow time dimension. This indicates the velocity of the target motion that needs to be estimated. This represents the acceleration of the target motion that needs to be estimated. Indicating in the The velocity of the target motion used in the estimation process Indicating in the The acceleration of the target motion used in the estimation process, For slow time and with a value of T Integer multiples of, To save time, The pulse repetition period, For pulse accumulation time, The initial distance difference between the receiver and the target. For wavelength, At the speed of light, CF It is a periodic correlation function.

2. The method for efficient accumulation of GPS external radiation source target echoes based on PSO and LVD according to claim 1, characterized in that, The step of estimating the velocity and acceleration of the target motion based on the objective function using the PSO algorithm to obtain the estimated velocity and acceleration includes: Initialize the position vectors, velocity vectors, and historical best position vectors of n particles to obtain the initial position vector for each particle. Initial velocity vector and the initial historical optimal position vector In this context, the position vector of each particle is a two-dimensional parameter composed of the velocity and acceleration of the target motion; In the k-th iteration, where k=1, based on the initial historical optimal position vector of all particles... Given the objective function, determine the maximum function value for the kth iteration. The k-th group historical optimal position vector And the k-th historical best position vector of each particle. Complete the k-th iteration, where i is a positive integer and the value of i ranges from 1 to n; In the k-th iteration, where k is greater than 1, for each particle, the maximum function value based on the (k-1)-th iteration is... The group's historical optimal position vector in the (k-1)th iteration And the historical optimal position vector of the particle at the (k-1)th time. The velocity vector of the particle at the (k-1)th time. The position vector of the (k-1)th time and the historical best position vector of the (k-1)th time The velocity vector of the particle is updated to the kth time. The position vector of the kth time and the historical best position vector of the kth time Based on the k-th historical best position vector of all particles Using the objective function, determine the k-th group historical optimal position vector. Complete the k-th iteration, where k is a positive integer greater than or equal to 1; Determine whether the result of the k-th iteration or k has reached the iteration termination condition. If not, let k = k + 1 and continue iterating until the iteration termination condition is finally reached. The group's historical best position vector obtained when the iteration termination condition is reached is used as the estimated velocity and acceleration.

3. The efficient accumulation method for GPS external radiation source target echoes based on PSO and LVD according to claim 2, characterized in that, In the k-th iteration, where k=1, the initial historical optimal position vector of all particles is used as the basis. Given the objective function, determine the maximum function value for the kth iteration. The k-th group historical optimal position vector And the k-th historical best position vector of each particle. ,include: In the k-th iteration, where k=1, the initial historical optimal position vectors of all particles are determined. Substituting each value into the objective function yields a total of n objective function values; The maximum value among the n objective function values ​​is taken as the maximum function value of the kth iteration. The initial historical optimal position vector corresponding to the maximum function value of the kth iteration is used as the group historical optimal position vector for the kth iteration. ; For each particle, the initial historical best position vector of the particle is... , as the k-th historical best position vector of the particle .

4. The efficient accumulation method for GPS external radiation source target echoes based on PSO and LVD according to claim 1, characterized in that, The expression for the corrected pulse compression signal includes: the velocity of the target motion that needs to be estimated. and acceleration In the The velocity of the target motion used in the estimation process In the The acceleration of the target motion used in the estimation process The step of constructing the objective function based on the expression of the corrected pulse compression signal includes: An FFT is performed on the expression of the corrected pulse compression signal along the slow time dimension to convert the cross-correlation spectrum into an RD spectrum; The objective function is obtained by using the peak energy on the RD spectrum as the mapping value of the objective function, where, if and If this is achieved, both distance migration and Doppler frequency migration will be fully corrected, the peak energy on the RD spectrum will reach its maximum, and the objective function will also reach its maximum value.

5. The efficient accumulation method for GPS external radiation source target echoes based on PSO and LVD according to claim 4, characterized in that, The expression for the number of units is as follows: ； in, For fast sampling frequency.

6. The method for efficient accumulation of GPS external radiation source target echoes based on PSO and LVD according to claim 1, characterized in that, The step involves performing first-order range migration, second-order range curvature, and Doppler frequency migration corrections on the pulse compression signal based on the estimated velocity and acceleration to obtain a corrected pulse compression signal, including: Based on the estimated velocity and acceleration, the pulse compression signal is subjected to first-order distance migration and second-order distance bending to obtain the initially corrected signal. The Doppler frequency migration compensation function is determined based on the estimated velocity and acceleration; The Doppler frequency migration compensation function is used to correct the Doppler frequency migration of the initially corrected signal to obtain the corrected pulse compression signal.

7. The efficient accumulation method for GPS external radiation source target echoes based on PSO and LVD according to claim 1, characterized in that, The step of using LVD to coherently accumulate the corrected pulse compression signal to obtain the target detection result includes: A slow time sequence for each distance unit is selected from the corrected pulse compression signal; Calculate the parameterized instantaneous symmetric autocorrelation function of the slow time series for each selected distance unit; By substituting variables into the parameterized instantaneous symmetric autocorrelation function of the slow time series for each distance unit, a transformed parameterized instantaneous symmetric autocorrelation function is obtained. For each of the transformed parameterized instantaneous symmetric autocorrelation functions, perform an FFT in the time delay dimension to transfer to the CFCR domain, and obtain a corresponding LVD result; Select the LVD result with the highest peak value from all the obtained LVD results; Target detection is performed based on the LVD result with the highest peak value to obtain the target detection result.

8. The efficient accumulation method for GPS external radiation source target echoes based on PSO and LVD according to claim 7, characterized in that, The expression for each LVD result is as follows: ； in, This represents each LVD result. For the center frequency, To adjust the frequency, CF It is a periodic correlation function. The preset delay parameters, Represents the impulse function. This represents the estimated velocity of the target motion. This represents the estimated acceleration of the target motion.

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