Near-field beamforming method and system for UAV cluster based on Kalman filtering

Abstract

The present invention provides a Kalman filter-based near-field beamforming method and system for drone clusters, belonging to the field of drone cluster near-field beamforming. The method comprises: constructing an array received signal phase error model under near-field conditions; simplifying the array received signal phase error model by Taylor expanding the measured value of the drone cluster array received signal phase and the phase value calculated based on the array element position navigation measurement value at the ideal position of the drone cluster array; constructing a phase difference state equation and measurement equation for the drone cluster; filtering the simplified array received signal phase error model using a Kalman filter to predict the received signal residual phase; and calculating an array received signal estimate using the predicted received signal residual phase to complete array beamforming. The present invention effectively suppresses the impact of errors on near-field array beamforming under the conditions of drone cluster array position error and signal phase measurement error.

Description

Technical Field

[0001] The present invention belongs to the field of UAV cluster near-field beamforming, and more specifically, relates to a UAV cluster near-field beamforming method and system based on Kalman filtering. Background Art

[0002] Due to limitations such as the spacing between drone swarms and the aperture of array antennas, electronic countermeasure targets for drone swarms are likely to be located in the near-field of the antenna arrays that form them. Conventional far-field antenna electromagnetic field theory is inapplicable. Therefore, beamforming technology is urgently needed to improve the quality of electronic countermeasure missions for drone swarms and achieve directional, high-gain beamforming from cluster antennas. To effectively form a beam, the spatial position accuracy of the drones must be within half the wavelength of the received or transmitted signal. However, due to the error between the actual and ideal drone positions and sensor measurement errors, the accuracy of drone position information obtained from navigation data is often greater than half the wavelength of the signal. Directly using position information obtained from navigation data still prevents the antenna array from effectively forming a beam. Therefore, given known navigation data, filtering and estimating the navigation data is necessary, or more directly, filtering and estimating the phase error of the drone received signals. After compensating for the error in each drone's received signal, array beamforming is performed. When the estimation system can be viewed as a linear system and the noise follows a Gaussian distribution, directly using a Kalman filter (KF) can achieve good parameter estimation results. Although the position sensor measurement noise and phase measurement noise during the linear motion of the drone can be regarded as Gaussian distribution, for the drone cluster array beamforming, the decisive factor is the array received signal phase. The transformation from the spatial domain to the phase domain is a nonlinear transformation. The Gaussian measurement error caused by the drone cluster position converted to the signal phase will cause the received signal phase noise to exhibit non-Gaussian characteristics. At this time, the KF correlation algorithm cannot be used for processing, and there is no basis for setting the filter parameters. Summary of the Invention

[0003] In view of the defects of the existing technology, the purpose of the present invention is to provide a near-field beamforming method and system for drone clusters based on Kalman filtering, aiming to solve the problems of the lack of application of existing beamforming algorithms in drone clusters, the inability to flexibly apply Kalman filtering algorithms, etc., which lead to the lack of near-field beamforming for drone clusters due to the fact that most beamforming algorithms solve weights based on far-field approximation conditions and the signal phase domain noise is non-Gaussian noise.

[0004] To achieve the above objectives, in a first aspect, the present invention provides a near-field beamforming method for a UAV cluster based on Kalman filtering, comprising the following steps:

[0005] D1: Construct the phase difference state equation and measurement equation of the UAV cluster based on the measured value of the received signal phase of the UAV cluster array, the phase state transfer noise of the UAV and the measurement noise;

[0006] D2: Based on the phase difference state equation and measurement equation of the UAV cluster, combined with phase noise and position noise, a Kalman filter is used to filter the simplified array received signal phase error model to predict the residual phase of the received signal;

[0007] D3: Calculate the array received signal estimate using the predicted received signal residual phase, and calculate the array beamforming based on the array weight vector.

[0008] The simplified method for constructing the array received signal phase error model specifically includes the following steps:

[0009] S1: Under near-field conditions, based on the setting of the UAV cluster array and the target radiation source, the array received signal phase error model is constructed according to the measured value of the UAV cluster array received signal phase and the phase value calculated based on the array element position navigation measurement value;

[0010] S2: Under the condition that the distance from the target radiation source to the center point of the UAV array is greater than the total length of the UAV cluster array, the array received signal phase error model is simplified by Taylor expanding the measured value of the UAV cluster array's received signal phase and the phase value calculated based on the array element position navigation measurement value at the ideal position of the UAV cluster array, so that the noise distribution of the residual measurement value of the received signal is approximately Gaussian distribution.

[0011] Further preferably, the array received signal phase error model is:

[0012]

[0013] in, is the position coordinate measurement value of the UAV array element n; x P and y P are the horizontal and vertical coordinates of the target radiation source; k is the wave number; φ n0 is the initial phase of the received signal; φ n is the phase difference of the received signal at the ideal position; Δφ n,ss is the phase measurement noise of the nth UAV at the ssth sampling moment; R n,ss =[Δx n,ss Δy n,ss Δz n,ss ] T is the 3×1 dimensional measurement noise of the position measurement sensor of the n-th UAV at the ss-th sampling moment.

[0014] Further preferably, the simplified array received signal phase error model is:

[0015]

[0016] Among them, r n is the ideal distance between the UAV array element and the target radiation source; H is the ideal vertical height of the UAV cluster array.

[0017] Further preferably, the phase difference state equation and measurement equation of the UAV cluster are:

[0018]

[0019] Among them, A n =1;H n =1;φ n,ss =φ n0 +φ n ; is φ n,ss The measured value of n n is the phase state transfer noise of the nth UAV, with a mean of 0 and a variance of Q n Gaussian noise; v n is the measurement noise caused by the motion measurement error of the x-axis, y-axis, and z-axis of the n-th UAV and the phase measurement error, which has a mean of 0 and a variance of R n Gaussian noise;

[0020]

[0021] Among them, R x0 、R y0 、R z0 are the position transfer error variances of the x-axis, y-axis, and z-axis of the drone cluster; R x 、R y 、R z are the position measurement error variances of the x-axis, y-axis, and z-axis of the UAV cluster; R φ is the phase measurement error variance.

[0022] In a second aspect, the present invention provides a UAV cluster near-field beamforming system based on Kalman filtering, comprising:

[0023] An equation building module is used to build a phase difference state equation and a measurement equation of the UAV cluster based on the measured value of the received signal phase of the UAV cluster array, the phase state transfer noise of the UAVs, and the measurement noise;

[0024] The prediction module for the residual phase of the received signal is used to filter the simplified array received signal phase error model using Kalman filtering based on the phase difference state equation and measurement equation of the drone cluster, combined with phase noise and position noise, to predict the residual phase of the received signal;

[0025] An array beamforming module is used to calculate an estimated value of the array received signal by using the predicted residual phase of the received signal and to complete array beamforming by combining the array weight vector;

[0026] The module for constructing the array received signal phase error model is used to construct the array received signal phase error model based on the UAV cluster array and the target radiation source under near-field conditions, according to the measured phase value of the UAV cluster array received signal and the phase value calculated based on the array element position navigation measurement value;

[0027] The simplified module of the array receiving signal phase error model is used to simplify the array receiving signal phase error model under the condition that the distance from the target radiation source to the center point of the drone array is greater than the total length of the drone cluster array. The measured value of the receiving signal phase of the drone cluster array and the phase value calculated based on the array element position navigation measurement value are Taylor expanded at the ideal position of the drone cluster array. This achieves that the noise distribution of the residual measurement value of the receiving signal is approximately Gaussian distribution.

[0028] Further preferably, the array received signal phase error model is:

[0029]

[0030] in, is the position coordinate measurement value of the UAV array element n; x P and y P are the horizontal and vertical coordinates of the target radiation source; k is the wave number; φ n0 is the initial phase of the received signal; φ n is the phase difference of the received signal at the ideal position; Δφ n,ss is the phase measurement noise of the nth UAV at the ssth sampling moment; R n,ss =[Δx n,ss Δy n,ss Δz n,ss ] T For the ss The 3×1 dimensional measurement noise of the position measurement sensor of the nth UAV at the sampling time.

[0031] Further preferably, the simplified array received signal phase error model is:

[0032]

[0033] Among them, r n is the ideal distance between the UAV array element and the target radiation source; H is the ideal vertical height of the UAV cluster array.

[0034] Further preferably, the phase difference state equation and measurement equation of the UAV cluster are:

[0035]

[0036] Among them, A n =1;H n =1;φ n,ss =φ n0 +φ n ; is φ n,ss The measured value of n n is the phase state transfer noise of the nth UAV, with a mean of 0 and a variance of Q n Gaussian noise; v n is the measurement noise caused by the motion measurement error of the x-axis, y-axis, and z-axis of the n-th UAV and the phase measurement error, which has a mean of 0 and a variance of R n Gaussian noise;

[0037]

[0038] Among them, R x0 、R y0 、R z0 are the position transfer error variances of the x-axis, y-axis, and z-axis of the drone cluster; R x 、R y 、R z are the position measurement error variances of the x-axis, y-axis, and z-axis of the UAV cluster; R φ is the phase measurement error variance.

[0039] In a third aspect, the present invention provides an electronic device comprising: at least one memory for storing programs; and at least one processor for executing the programs stored in the memory. When the program stored in the memory is executed, the processor is used to execute the method described in the first aspect or any possible implementation of the first aspect.

[0040] In a fourth aspect, the present invention provides a computer-readable storage medium storing a computer program. When the computer program runs on a processor, the processor executes the method described in the first aspect or any possible implementation of the first aspect.

[0041] In a fifth aspect, the present invention provides a computer program product, which, when executed on a processor, enables the processor to execute the method described in the first aspect or any possible implementation of the first aspect.

[0042] It can be understood that the beneficial effects of the second to fifth aspects mentioned above can be found in the relevant description of the first aspect mentioned above, and will not be repeated here.

[0043] In general, the above technical solutions conceived by the present invention have the following advantages compared with the prior art:

[0044] Beneficial effects:

[0045] The present invention provides a UAV cluster near-field beamforming method and system based on Kalman filtering. The present invention first constructs an array receiving signal phase error model based on the setting of the UAV cluster array and the target radiation source under near-field conditions, according to the measured value of the received signal phase of the UAV cluster array and the phase value calculated according to the array element position navigation measurement value; uses Taylor expansion to simplify the model, and converts the compensated received signal phase non-Gaussian noise into Approximately Gaussian noise Then, based on the phase difference state equation and measurement equation of the UAV cluster, combined with phase noise and position noise, the simplified array received signal phase error model is filtered by Kalman filtering to predict the residual phase of the received signal; finally, the array received signal estimation value is calculated by using the predicted residual phase of the received signal, and the array beamforming is completed in combination with the array weighting vector; the feasibility of the UAV cluster near-field beamforming method provided by the present invention is proved through simulation, and under the conditions of the existence of UAV cluster array position error and signal phase measurement error, the influence of the error on the near-field array beamforming is effectively suppressed. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 This is a flow chart of a near-field beamforming method for a UAV cluster based on Kalman filtering provided by an embodiment of the present invention;

[0047] Figure 2 is a schematic diagram of a near-field array geometric model provided by an embodiment of the present invention;

[0048] FIG3(a) is a diagram of σ provided by an embodiment of the present invention. R =0.4m,σ X Schematic diagram of phase estimation of the 16th UAV when =0.2rad;

[0049] FIG3( b ) is a graph showing the σ provided by an embodiment of the present invention. R =0.4m,σ X = 0.4rad; Phase estimation diagram of the 16th UAV;

[0050] FIG3(c) is a graph showing the σ provided by an embodiment of the present invention. R =0.4m,σ X Schematic diagram of phase estimation of the 16th UAV when =0.6rad;

[0051] FIG3(d) is a graph showing the σ provided by an embodiment of the present invention. R =0.4m,σ X = 0.8rad;

[0052] FIG4(a) is a diagram of σ provided by an embodiment of the present invention. X =0.4rad,σ R Schematic diagram of phase estimation of the 16th UAV when =0.2m;

[0053] FIG4( b ) is a graph showing the σ provided by an embodiment of the present invention. X =0.4rad,σ R = 0.4m when the phase estimation diagram of the 16th UAV;

[0054] FIG4(c) is a graph showing the σ provided by an embodiment of the present invention. X =0.4rad,σ R = 0.6m;

[0055] FIG4(d) is a graph showing the σ provided by an embodiment of the present invention. X =0.4rad,σ R = 0.8m when the phase estimation diagram of the 16th UAV;

[0056] FIG5(a) is a graph showing the embodiment of the present invention with θ=0°, σ R =0.2m and σ X =Beamforming diagram when 0.2rad;

[0057] FIG5(b) is a graph showing the embodiment of the present invention with θ=6° and σ R =0.2m and σ X =Beamforming diagram when 0.2rad;

[0058] FIG5(c) is a graph showing the embodiment of the present invention with θ=0°, σ R =0.4m and σ X =Beamforming diagram when 0.4rad;

[0059] FIG5(d) is a graph showing the embodiment of the present invention with θ=6° and σ R =0.4m and σ X =Beamforming diagram when 0.4rad;

[0060] FIG5(e) is a graph showing the embodiment of the present invention with θ=0°, σ R =0.6m and σ X =Beamforming diagram when 0.6rad;

[0061] FIG5(f) is a graph showing the embodiment of the present invention with θ=6° and σ R =0.6m and σ X =Beamforming diagram when 0.6rad;

[0062] FIG5(g) is a graph showing the case where θ=0°, σ is provided in an embodiment of the present invention. R =0.8m and σ X =Beamforming diagram when 0.8rad;

[0063] FIG5(h) is a graph showing the embodiment of the present invention with θ=6° and σ R =0.8m and σ X =0.8rad when the beam forming diagram. DETAILED DESCRIPTION

[0064] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0065] Example 1

[0066] like Figure 1 As shown, the embodiment of the present invention provides a near-field beamforming method for a UAV cluster based on Kalman filtering. The specific description is as follows:

[0067] Under near-field conditions, the assumption that electromagnetic waves propagate in space in the form of plane waves is not valid, and spherical waves need to be used to describe them; Figure 2 As shown in the figure, suppose that the N-element near-field antenna array composed of N drones is linearly distributed at equal intervals along the axis parallel to the x-axis at a height H. The total length of the drone cluster array is L. The ideal position coordinates of the nth, n=1, 2, ..., Nth drone array elements are (x n ,y n ,z n ), y n =0,z n =H, -L / 2≤x n ≤L / 2, the real position coordinates are P is the target radiation source of the UAV cluster array in any near-field space, located in the xOy plane, with coordinates P(x P ,y P,0), C is the center point of the ideal array, D is the projection of P on the y-axis, R is the distance from P to the center point C of the array, R0 is the distance from the center point C to D of the array, θ is the angle between CP and CD, β is the angle between CD and CO, and R0=Rcosθ,x P =Rsinθ,y P =R0sinβ,H=R0cosβ,r n It represents the ideal distance from antenna element n to point P, Δr n The difference between the ideal distance from antenna element n to point P and R is Δr n =r n -R, Represents the actual distance from antenna element n to point P, It represents the difference between the actual distance from antenna element n to point P and the ideal distance,

[0068] For the radiation signal from the radiation source P, the true value of the signal received at the center point C of the array can be expressed as Where j is the imaginary unit, φ n0 is the initial phase of the received signal. Taking this signal as the reference signal, the true value of the radiation signal received by array element n can be expressed as:

[0069]

[0070] Among them, φ n is the phase difference caused by the difference between the distance from the ideal value of the array element n position to point P and R, φ n =-kΔr n , k = 2π / λ is the wave number; Δφ n is the phase synchronization error caused by the time synchronization error between UAVs; The phase difference is caused by the distance difference between the actual value of the array element n position and the ideal value to point P, which can be expressed as:

[0071]

[0072] Then the true value of the signal phase received by array element n is It can be expressed as:

[0073]

[0074] The phase error of array beamforming comes from the phase error caused by the error between the actual value and the ideal value of the array element position and the phase error caused by the phase measurement of the received signal. At the ssth sampling time (ss = 1, 2, ..., SS), the measured value of the phase of the received signal of array element n is:

[0075]

[0076] Among them, Δφ n,ss is the phase measurement noise of the nth UAV at the ssth sampling moment; Substituting formula (2) into formula (4), the measured value of the received signal phase is It can be expressed as:

[0077]

[0078] The array position error is composed of the error between the true value and the ideal value of the array position and the position measurement error. According to formula (4), at the ssth sampling time, let The phase value is calculated based on the array element position navigation measurement value. It is the phase difference caused by converting the spatial domain to the phase domain and can be expressed as:

[0079]

[0080] in, is the difference between the actual distance from array element n to point P and the ideal distance at the ssth sampling moment; is the position coordinate measurement value of array element n at the ssth sampling time, which is:

[0081]

[0082] Among them, R n,ss =[Δx n,ss Δy n,ss Δz n,ss ] T is the 3×1-dimensional measurement noise of the position measurement sensor of the n-th UAV at the ss-th sampling time;

[0083] After compensating Equation (5) with the position measurement value shown in Equation (6), the residual phase of the received signal of the n-th UAV at the ss sampling time is obtained:

[0084]

[0085] Formula (8) shows that the position measurement value of the UAV group is considered as its true value to roughly compensate for the phase error caused by the position difference between the true position and the ideal position. During the compensation process, position measurement error will be introduced. Obviously, due to the existence of phase error caused by position measurement and phase measurement, if the N×1 array weight vector W=[w1 w2 … w N ] T , where w n =exp(-jkΔr n ), weighted summation of the received signals of each array element is performed, which makes it impossible to effectively perform beamforming;

[0086] For the antenna array composed of UAV clusters, although the targets of interest such as wireless communication, electronic reconnaissance, and jamming are generally located in the near field area of ​​the array, the distance from the target of interest to the antenna center is usually still much larger than the antenna aperture. Using this condition, we can assume that R>>L and solve the equation (5) Doing Taylor series expansion at the ideal position gives:

[0087]

[0088] in, are the differences between the actual position value of the nth UAV and the corresponding ideal position value on the three coordinate axes;

[0089] Similarly, the phase measurement value of the nth UAV at the ssth sampling time as shown in formula (6) is Taylor expansion at the ideal position is:

[0090]

[0091] Substituting equations (9) and (10) into equation (8), the residual measurement value of the received signal phase is It can be approximated as:

[0092]

[0093] It can be seen from formula (11) that since the position measurement errors of the x-axis, y-axis, and z-axis are independent of each other and obey the Gaussian distribution, the residual measurement value noise distribution of the received signal phase shown in formula (11) can be approximated to a Gaussian distribution after Taylor expansion, and the measurement noise variance characteristic can also be derived from formula (11). Then, the Kalman filter (KF) can be used to filter it, and the predicted

[0094] The residual value of the received signal phase is obtained by the filtering algorithm as the estimated value of the received signal phase of the nth UAV The array output is then obtained by performing a weighted summation of the received signals of each array element, which is also known as array beamforming:

[0095]

[0096] in,[·] H represents the conjugate transpose of the matrix; is the estimated value of the array received signal, which can be expressed as:

[0097]

[0098] The following describes the specific operation of KF:

[0099] The operation of KF consists of two stages: prediction and update. In the prediction stage, the filter uses the estimate of the previous state to make an estimate of the current state and the error covariance. In the update stage, the Kalman gain is updated using the prior error covariance. The filter uses the observation value of the current state to optimize the predicted value obtained in the prediction stage to obtain a more accurate new estimate and update the error covariance matrix, as shown in Equation (14).

[0100]

[0101] Among them, u ss is the input vector of the ssth sampling, u ss =0; B is the system control matrix, B=0; g ss,ss-1 is the system state g sampled at the ss-1th time ss-1 The predicted system state g of the ssth sampling ss , in the present invention, represents the phase value converted from the signal received according to the position of the UAV; P ss-1 is the covariance matrix of the ss-1th sampling; P ss,ss-1 is the covariance matrix P based on the ss-1th sampling ss-1 The covariance matrix P of the predicted ssth sampling ss ;m ss is the observed value of the ssth sampling, that is, the measured H is the measurement matrix, which is 1 in the present invention; Q is the noise matrix introduced by the position sensor measurement; R is the measurement noise matrix, which represents the phase noise introduced by the sensor; K ss is the Kalman gain matrix of the ssth sampling; I is the identity matrix; A is the state transition matrix. In the present invention, A indicates that the UAV is hovering and in the electronic countermeasure state;

[0102] In the array received signal phase error model of the present invention, according to formula (13), the phase difference state equation and measurement equation of the UAV cluster are constructed based on the residual measurement value of the received signal phase, and there is

[0103]

[0104] Among them, A n =1;H n =1;φ n,ss =φ n0 +φ n ; is φ n,ss The measured value of n n is the phase state transfer noise of the nth UAV, with a mean of 0 and a variance of Q n Gaussian noise; v nis the measurement noise caused by the motion measurement error of the x-axis, y-axis, and z-axis of the n-th UAV and the phase measurement error, which has a mean of 0 and a variance of R n Gaussian noise, it can be deduced from formula (11):

[0105]

[0106] Among them, R x0 、R y0 、R z0 are the position transfer error variances of the x-axis, y-axis, and z-axis respectively; R x 、R y 、R z are the position measurement error variances of the x-axis, y-axis, and z-axis respectively; R φ is the phase measurement error variance.

[0107] Example 2

[0108] The present invention provides a UAV cluster near-field beamforming system based on Kalman filtering, comprising:

[0109] An equation building module is used to build a phase difference state equation and a measurement equation of the UAV cluster based on the measured value of the received signal phase of the UAV cluster array, the phase state transfer noise of the UAVs, and the measurement noise;

[0110] The prediction module for the residual phase of the received signal is used to filter the simplified array received signal phase error model using Kalman filtering based on the phase difference state equation and measurement equation of the drone cluster, combined with phase noise and position noise, to predict the residual phase of the received signal;

[0111] An array beamforming module is used to calculate an estimated value of the array received signal by using the predicted residual phase of the received signal and to complete array beamforming by combining the array weight vector;

[0112] The module for constructing the array received signal phase error model is used to construct the array received signal phase error model based on the UAV cluster array and the target radiation source under near-field conditions, according to the measured phase value of the UAV cluster array received signal and the phase value calculated based on the array element position navigation measurement value;

[0113] The simplified module of the array receiving signal phase error model is used to simplify the array receiving signal phase error model under the condition that the distance from the target radiation source to the center point of the drone array is greater than the total length of the drone cluster array. The measured value of the receiving signal phase of the drone cluster array and the phase value calculated based on the array element position navigation measurement value are Taylor expanded at the ideal position of the drone cluster array. This achieves that the noise distribution of the residual measurement value of the receiving signal is approximately Gaussian distribution.

[0114] Further preferably, the array received signal phase error model is:

[0115]

[0116] in, is the position coordinate measurement value of the UAV array element n; x P and y P are the horizontal and vertical coordinates of the target radiation source; k is the wave number; φ n0 is the initial phase of the received signal; φ n is the phase difference of the received signal at the ideal position; Δφ n,ss is the phase measurement noise of the nth UAV at the ssth sampling moment; R n,ss =[Δx n,ss Δy n,ss Δz n,ss ] T is the 3×1 dimensional measurement noise of the position measurement sensor of the n-th UAV at the ss-th sampling moment.

[0117] Further preferably, the simplified array received signal phase error model is:

[0118]

[0119] Among them, r n is the ideal distance between the UAV array element and the target radiation source; H is the ideal vertical height of the UAV cluster array.

[0120] Further preferably, the phase difference state equation and measurement equation of the UAV cluster are:

[0121]

[0122] Among them, A n =1;H n =1;φ n,ss =φ n0 +φ n ; is φ n,ss The measured value of n n is the phase state transfer noise of the nth UAV, with a mean of 0 and a variance of Q n Gaussian noise; v n is the measurement noise caused by the motion measurement error of the x-axis, y-axis, and z-axis of the n-th UAV and the phase measurement error, which has a mean of 0 and a variance of R n Gaussian noise;

[0123]

[0124] Among them, Rx0 、R y0 、R z0 are the position transfer error variances of the x-axis, y-axis, and z-axis of the drone cluster; R x 、R y 、R z are the position measurement error variances of the x-axis, y-axis, and z-axis of the UAV cluster; R φ is the phase measurement error variance.

[0125] Example 3

[0126] Assume that the signal frequency f0 = 300 MHz, the wavelength λ = 1 m, the number of array elements N = 26, the array aperture L = 500 λ, the ideal height of the array elements H = 1000 m, R0 = 30 km, θ = 0° or θ = 6°, R = cosθR0, and the ideal position of the array is to be evenly spaced linearly distributed along an axis parallel to the x-axis at the height H and symmetrical about the y-axis, with the main lobe of the beam pointing to the known radiation source P(x P, y P ,0), where x P =Rsinθ,y P =R0sinβ, signal sampling number SS=100, the position measurement error of the drone on the x-axis, y-axis, and z-axis R n,ss Subject to mean 0, variance σ R The phase measurement error has a mean of 0 and is Gaussian with a range of 0.2m to 0.8m. X is a Gaussian distribution with an interval of 0.2 rad, ranging from 0.2 rad to 0.8 rad; the beamforming algorithm based on KF (abbreviated as KFB) proposed in the present invention is compared with the beamforming algorithms based on unscented Kalman filter and extended Kalman filter (abbreviated as UKFB and EKFB, respectively). In UKFB, the state dimension is 1, the scaling ratio ρ=6, and the initial value of KFB is consistent with the observed value. In beamforming, the array generally scans and searches for signals within a certain spatial range. According to the expected direction of the wave, the array selects the corresponding weighted value to perform weighted summation on the wave signals received by the array. When there is a signal in the expected direction of the wave, the array will form a beam; all data are generated by simulation, the simulation-generated measurement value is abbreviated as SM, and the true value is abbreviated as TV; taking the beamforming parameter estimation when the array does not scan the direction of θ=0° and there is a signal as an example, when σ R =0.4m, the signal phase is estimated using the KFB, EKFB and UKFB proposed in the present invention, and the phase estimation value is obtained as follows: Figures 3(a) to 3(d) ; When σ X =0.4rad, the phase estimation value is obtained as Figures 4(a) to 4(d) , where the measurement value is the sensor's measurement of the true value, the position sensor measurement value error obeys the mean of 0, and the variance σR The Gaussian distribution of the phase sensor measurement error has a mean of 0 and a variance of σ X Gaussian distribution;

[0127] Depend on Figures 3(a) to 3(d) As shown in Figures 4(a) to 4(d), both the KF algorithm and the UKF algorithm can converge to the true value within dozens of samples. The jitter amplitude of the estimated value of KFB is smaller than that of UKFB. The reason is that KFB approximates the probability density function of the estimated phase as a linear function, which is consistent with the simulation model. Directly using KFB can achieve a better estimation effect, while UKFB uses sigma points to approximate the probability density function of the estimated value, which increases the complexity of the calculation. The phase value estimated by EKFB jitters around the true value. Although the jitter amplitude is smaller than the measured value, it is difficult to converge to the true value within 100 snapshots.

[0128] The main lobe width, average side lobe level and algorithm duration of the beam formed after compensating the phase error of the three algorithms mentioned above are simulated and compared. The simulation parameters remain unchanged and the median filter algorithm (MF) is added for beamforming comparison. By performing 100 Monte Carlo simulations on each algorithm, the beamforming diagram is shown as follows: Figures 5(a) to 5(h) As shown in the figure, the average sidelobe level is defined as the average value of the sidelobe part below -10dB, and the main lobe width is the width between the half-power points of the main lobe. The algorithm average time, average sidelobe level and main lobe width are shown in Table 1;

[0129] Table 1

[0130]

[0131] Depend on Figures 5(a) to 5(h)As shown in Table 1, regardless of whether the beam is scanned or not, the array cannot be formed into a beam by using the measurement value for compensation; the EKFB beam formation is greatly affected by the measurement error. As the measurement error increases, the EKFB sidelobe level increases significantly. The reason is that the EKFB estimated phase tracks the phase measurement value change and jitters around the true phase value. It can be seen from the simulation that within 100 sampling cycles, the EKFB estimated phase has not converged to the true value, resulting in uncertainty in the final phase estimate caused by the influence of the measurement value. As the measurement error increases, the uncertainty also increases, resulting in errors in the phase compensation value. Among the three algorithms, the KFB average The duration is the shortest; although the sidelobe level of UKFB is slightly lower than that of KFB in most cases, the duration used is almost 15 times that of KFB, and the duration used by EKFB is almost 30 times that of KFB. The reason is that whether using Sigma points to simulate the posterior probability density distribution function or estimating the Jacobian matrix of the observation function for each sampling, there is a problem of large computational complexity; as the measurement error increases, the sidelobe levels of the beams formed by KFB and UKFB tend to increase, but within the measurement error variation range of the present invention, the beam can still be effectively formed, which reflects that KFB and UKFB are better robust to measurement errors.

[0132] It will be easily understood by those skilled in the art that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A near-field beamforming method for UAV clusters based on Kalman filtering, characterized in that: The following steps are involved: D1: Construct the phase difference state equation and measurement equation of the UAV cluster based on the measured value of the received signal phase of the UAV cluster array, the phase state transfer noise of the UAV and the measurement noise; D2: Based on the phase difference state equation and measurement equation of the UAV cluster, combined with phase noise and position noise, a Kalman filter is used to filter the simplified array received signal phase error model to predict the residual phase of the received signal; D3: Calculate the array received signal estimate using the predicted received signal residual phase, and combine it with the array weight vector to complete array beamforming; The simplified method for constructing the array received signal phase error model specifically includes the following steps: S1: Under near-field conditions, based on the setting of the UAV cluster array and the target radiation source, the array received signal phase error model is constructed according to the measured value of the UAV cluster array received signal phase and the phase value calculated based on the array element position navigation measurement value; S2: Under the condition that the distance from the target radiation source to the center point of the UAV array is greater than the total length of the UAV cluster array, the array received signal phase error model is simplified by Taylor expanding the measured value of the UAV cluster array's received signal phase and the phase value calculated based on the array element position navigation measurement value at the ideal position of the UAV cluster array, so that the noise distribution of the residual measurement value of the received signal is approximately Gaussian distribution.

2. The UAV cluster near-field beamforming method according to claim 1, characterized in that: The array received signal phase error model is: in, is the position coordinate measurement value of the UAV array element n; x P and y P are the horizontal and vertical coordinates of the target radiation source; k is the wave number; φ n0 is the initial phase of the received signal; φ n is the phase difference of the received signal at the ideal position; Δφ n,ss is the phase measurement noise of the nth UAV at the ssth sampling moment; R n,ss =[Δx n,ss Δy n,ss Δz n,ss ] T is the 3×1 dimensional measurement noise of the position measurement sensor of the n-th UAV at the ss-th sampling moment.

3. The UAV cluster near-field beamforming method according to claim 2, characterized in that: The simplified array receiving signal phase error model is: Among them, r n is the ideal distance between the UAV array element and the target radiation source; H is the ideal vertical height of the UAV cluster array.

4. The UAV cluster near-field beamforming method according to claim 2 or 3, characterized in that: The phase difference state equation and measurement equation of the UAV cluster are: Among them, A n =1;H n =1;φ n,ss =φ n0 +φ n ; is φ n,ss The measured value of n n is the phase state transfer noise of the nth UAV, with a mean of 0 and a variance of Q n Gaussian noise; v n is the measurement noise caused by the motion measurement error of the x-axis, y-axis, and z-axis of the n-th UAV and the phase measurement error, which has a mean of 0 and a variance of R n Gaussian noise; Among them, R x0 、R y0 、R z0 are the position transfer error variances of the x-axis, y-axis, and z-axis of the drone cluster; R x 、R y 、R z are the position measurement error variances of the x-axis, y-axis, and z-axis of the UAV cluster; R φ is the phase measurement error variance.

5. A near-field beamforming system for UAV clusters based on Kalman filtering, characterized in that: include: An equation building module is used to build a phase difference state equation and a measurement equation of the UAV cluster based on the measured value of the received signal phase of the UAV cluster array, the phase state transfer noise of the UAVs, and the measurement noise; The prediction module for the residual phase of the received signal is used to filter the simplified array received signal phase error model using Kalman filtering based on the phase difference state equation and measurement equation of the drone cluster, combined with phase noise and position noise, to predict the residual phase of the received signal; An array beamforming module is used to calculate an estimated value of the array received signal by using the predicted residual phase of the received signal and to complete array beamforming by combining the array weight vector; The module for constructing the array received signal phase error model is used to construct the array received signal phase error model based on the UAV cluster array and the target radiation source under near-field conditions, according to the measured phase value of the UAV cluster array received signal and the phase value calculated based on the array element position navigation measurement value; The simplified module of the array receiving signal phase error model is used to simplify the array receiving signal phase error model under the condition that the distance from the target radiation source to the center point of the drone array is greater than the total length of the drone cluster array. The measured value of the receiving signal phase of the drone cluster array and the phase value calculated based on the array element position navigation measurement value are Taylor expanded at the ideal position of the drone cluster array. This achieves that the noise distribution of the residual measurement value of the receiving signal is approximately Gaussian distribution.

6. The UAV cluster near-field beamforming system according to claim 5, characterized in that: The array received signal phase error model is: in, is the position coordinate measurement value of the UAV array element n; x P and y P are the horizontal and vertical coordinates of the target radiation source; k is the wave number; φ n0 is the initial phase of the received signal; φ n is the phase difference of the received signal at the ideal position; Δφ n,ss is the phase measurement noise of the nth UAV at the ssth sampling moment; R n,ss =[Δx n,ss Δy n,ss Δz n,ss ] T is the 3×1 dimensional measurement noise of the position measurement sensor of the n-th UAV at the ss-th sampling moment.

7. The UAV cluster near-field beamforming system according to claim 6, characterized in that: The simplified array receiving signal phase error model is: Among them, r n is the ideal distance between the UAV array element and the target radiation source; H is the ideal vertical height of the UAV cluster array.

8. The UAV cluster near-field beamforming system according to claim 6 or 7, characterized in that: The phase difference state equation and measurement equation of the UAV cluster are: Among them, A n =1;H n =1;φ n,ss =φ n0 +φ n ; is φ n,ss The measured value of n n is the phase state transfer noise of the nth UAV, with a mean of 0 and a variance of Q n Gaussian noise; v n is the measurement noise caused by the motion measurement error of the x-axis, y-axis, and z-axis of the n-th UAV and the phase measurement error, which has a mean of 0 and a variance of R n Gaussian noise; Among them, R x0 、R y0 、R z0 are the position transfer error variances of the x-axis, y-axis, and z-axis of the drone cluster; R x 、R y 、R z are the position measurement error variances of the x-axis, y-axis, and z-axis of the UAV cluster; R φ is the phase measurement error variance.

9. A computer-readable storage medium storing a computer program, wherein when the computer program is executed on a processor, the processor is caused to execute the method according to any one of claims 1 to 4.

10. A computer program product, characterized in that When the computer program product is run on a processor, the processor is enabled to perform the method according to any one of claims 1 to 4.

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