阅读说明：本技术 一种无人机阵列幅相误差与信号doa联合估计方法 (Unmanned aerial vehicle array amplitude and phase error and signal DOA joint estimation method ) 是由 李建峰 张淇婷 晋本周 张小飞 吴启晖 于 2021-11-24 设计创作，主要内容包括：本发明公开了一种无人机阵列幅相误差与信号DOA联合估计方法,包括：在每架无人机上搭载单个天线阵元,多架无人机组成的无人机群构成接收阵列以接收信源信号；在观测基线不变的情况下,通过无人机运动使阵列结构发生改变,每次阵列结构变化后对信源信号进行再次采集,得到多个信源信号；针对每个采集到的信源信号,计算其协方差矩阵,通过特征值分解得到相应的噪声子空间；通过噪声子空间和方向向量重构二次优化问题,构造代价函数,通过谱峰搜索得到幅相误差和DOA联合估计。本发明能够实现DOA和阵列幅相误差联合估计,校正幅相误差,提高无源定位的精准性。(The invention discloses a method for jointly estimating the amplitude-phase error and the DOA (direction of arrival) of an unmanned aerial vehicle array, which comprises the following steps: each unmanned aerial vehicle is provided with a single antenna array element, and an unmanned aerial vehicle cluster consisting of a plurality of unmanned aerial vehicles forms a receiving array to receive information source signals; under the condition that an observation base line is not changed, the array structure is changed through the movement of the unmanned aerial vehicle, and the information source signals are collected again after the array structure is changed every time to obtain a plurality of information source signals; calculating a covariance matrix of each acquired information source signal, and decomposing a characteristic value to obtain a corresponding noise subspace; and reconstructing a quadratic optimization problem through a noise subspace and a direction vector, constructing a cost function, and obtaining amplitude-phase error and DOA joint estimation through spectrum peak search. The method can realize the combined estimation of the DOA and the array amplitude and phase errors, correct the amplitude and phase errors and improve the accuracy of passive positioning.)

1. An unmanned aerial vehicle array amplitude and phase error and signal DOA joint estimation method is characterized by comprising the following steps:

s1, carrying a single antenna array element on each unmanned aerial vehicle, and forming a receiving array by an unmanned aerial vehicle cluster consisting of a plurality of unmanned aerial vehicles so as to receive information source signals;

s2, under the condition that an observation base line is not changed, the array structure is changed through the movement of the unmanned aerial vehicle, and the information source signals are collected again after the array structure is changed every time, so that a plurality of information source signals are obtained;

s3, calculating a covariance matrix of each acquired information source signal, and decomposing the covariance matrix through eigenvalues to obtain a corresponding noise subspace;

and S4, reconstructing a quadratic optimization problem through a noise subspace and a direction vector, constructing a cost function, and obtaining amplitude-phase error and DOA joint estimation through spectrum peak search.

2. The method for jointly estimating the amplitude-phase error and the signal DOA of the array of unmanned aerial vehicles according to claim 1, wherein in step S1, a single antenna array element is mounted on each unmanned aerial vehicle, and a process for forming a receiving array by a cluster of multiple unmanned aerial vehicles to receive a signal source signal includes the following steps:

s11, making M unmanned aerial vehicles evenly arranged, each unmanned aerial vehicle carrying an antenna array element, the array element spacing being unit interval，Represents a wavelength; m is a positive integer greater than 2;

s12, assuming that there are K parallel plane wavesThe light is incident in the direction of incidence,and K is a positive integer larger than 2, and when the array amplitude and phase error exists, the array receiving signal in the initial state is represented as:

wherein the content of the first and second substances,is a diagonal matrix of amplitude and phase errors,is represented by a vectorA diagonal matrix of the elements in (a);in order to be the vector of the signal,is an additive white gaussian noise, and is,a matrix of directions is represented, which is,representsA directional vector in the direction, expressed as:

in the formula (I), the compound is shown in the specification,the respective position information of the M unmanned aerial vehicles in the initial state is shown.

3. The method of claim 2, wherein in step S3, for each collected source signal, calculating a covariance matrix thereof, and obtaining a corresponding noise subspace through eigenvalue decomposition comprises the following steps:

s21, under the condition that the base line is not changed, the corresponding array element positions are changed through the movement of the unmanned aerial vehicle to form new arrays, and for each newly formed array, corresponding information source signals are collected;

s22, for the ith collected source signalThe covariance matrix is calculated according to the following formula:

wherein L represents the fast beat number of the data;indicating a desire;represents a conjugate transpose operation;is shown aslTaking a snap shot;

s23, forPerforming eigenvalue decomposition on the covariance matrix, wherein the eigenvalue decomposition is expressed as:

wherein the content of the first and second substances,represents oneA diagonal matrix of dimensions whose diagonal elements are made up of the larger K eigenvalues resulting from eigenvalue decomposition,is a diagonal matrix formed by M-K smaller eigenvalues;is a matrix formed by eigenvectors corresponding to the K larger eigenvalues,then the feature vector is a matrix formed by the feature vectors corresponding to other feature values;andreferred to as signal subspace and noise subspace, respectively; i =1,2, …, p, p is the total number of observations.

4. The unmanned aerial vehicle array amplitude-phase error and signal DOA joint estimation method according to claim 3, wherein in step S4, a quadratic optimization problem is reconstructed through a noise subspace and a direction vector, a cost function is constructed, and the process of obtaining the amplitude-phase error and DOA joint estimation through spectral peak search comprises the following steps:

s41, constructing a secondary optimization problem:

wherein the content of the first and second substances,in order to obtain the error of the amplitude and the phase,，to representThe operation of the transposition is carried out,representing the DOA parameter to be estimated;

in the formula (I), the compound is shown in the specification,a steering vector representing the ith observation,is represented by a vectorI =1,2, …, p;

s42, constructing a cost function:

in the formula (I), the compound is shown in the specification,is a constant;

s43, forCalculating a partial derivative:

wherein the content of the first and second substances,，is a constant;

and S44, obtaining an estimated value of the angle and amplitude-phase error:

；

s45, mixingSubstitution of expression (c)And calculating to obtain an estimated value of DOA:

。

5. the method for jointly estimating the amplitude-phase error and the signal DOA of the unmanned aerial vehicle array according to claim 1, further comprising the steps of:

evaluating the effectiveness of the estimation result by using the root mean square error as a performance estimation index; the corresponding root mean square error is calculated according to the following formula:

wherein N represents the number of Monte Carlo simulations,representing the true angle of incidence of the kth signal,represents the angle estimation value of the k signal in the n simulation experiment,representing the true value of the mth magnitude-phase error coefficient,and (4) representing the estimated value of the mth amplitude-phase error coefficient in the nth simulation experiment.

Technical Field

The invention relates to the technical field of array signal processing, in particular to a Direction of Arrival (DOA) and amplitude and phase error joint estimation method based on an unmanned aerial vehicle population array.

Background

Array signal processing is an important branch of modern signal processing, is a technical field which is developed rapidly in recent decades, and is widely applied to military and civil fields such as radar, sonar, wireless communication and the like. Direction-of-arrival estimation is one of the key techniques of array signal processing technology, and its main purpose is to estimate spatial source position. The DOA estimation technology is developed rapidly, and related theories and technologies are still in continuous perfection.

The ubiquitous existence of array errors is a significant reason for the difficulty of applying spatial spectrum estimation techniques to practical engineering. In general, almost all DOA estimation algorithms are based on the premise that the flow pattern of the array is accurately known, and in order to obtain a good algorithm estimation effect, the actual array and a standard array model in theoretical research must be ensured to be completely consistent. In practice, however, both the device itself and the actual environment may cause errors in the array. When using ideal array flow patterns for actual DOA estimation, it is inevitable that direction finding results with large errors are obtained, or that direction finding results are not valid at all. Most of the effects of array errors can eventually be attributed to array magnitude-phase errors. Therefore, the research on the DOA estimation algorithm under the condition that the array amplitude-phase error exists has important significance for the practical application of the spatial spectrum estimation technology.

Disclosure of Invention

Aiming at the defects in the prior art, the invention provides a method for jointly estimating the amplitude and phase errors and the DOA (direction of arrival) signals of the unmanned aerial vehicle array, which realizes array position change based on an unmanned aerial vehicle cluster, can realize the joint estimation of the DOA and the amplitude and phase errors of the array, corrects the amplitude and phase errors and improves the accuracy of passive positioning.

In order to achieve the purpose, the invention adopts the following technical scheme:

an unmanned aerial vehicle array amplitude and phase error and signal DOA joint estimation method comprises the following steps:

s1, carrying a single antenna array element on each unmanned aerial vehicle, and forming a receiving array by an unmanned aerial vehicle cluster consisting of a plurality of unmanned aerial vehicles so as to receive information source signals;

s2, under the condition that an observation base line is not changed, the array structure is changed through the movement of the unmanned aerial vehicle, and the information source signals are collected again after the array structure is changed every time, so that a plurality of information source signals are obtained;

s3, calculating a covariance matrix of each acquired information source signal, and decomposing the covariance matrix through eigenvalues to obtain a corresponding noise subspace;

and S4, reconstructing a quadratic optimization problem through a noise subspace and a direction vector, constructing a cost function, and obtaining amplitude-phase error and DOA joint estimation through spectrum peak search.

In order to optimize the technical scheme, the specific measures adopted further comprise:

further, in step S1, the process of mounting a single antenna array element on each drone and forming a receiving array by a group of multiple drones to receive the signal source signal includes the following steps:

s11, making M unmanned aerial vehicles evenly arranged, each unmanned aerial vehicle carrying an antenna array element, the array element spacing being unit interval，Represents a wavelength; m is a positive integer greater than 2;

s12, assuming that there are K parallel plane wavesThe light is incident in the direction of incidence,and K is a positive integer larger than 2, and when the array amplitude and phase error exists, the array receiving signal in the initial state is represented as:

wherein the content of the first and second substances,is a diagonal matrix of amplitude and phase errors,is represented by a vectorA diagonal matrix of the elements in (a);in order to be the vector of the signal,is an additive white gaussian noise, and is,a matrix of directions is represented, which is,representsA directional vector in the direction, expressed as:

in the formula (I), the compound is shown in the specification,the respective position information of the M unmanned aerial vehicles in the initial state is shown.

Further, in step S3, the process of calculating a covariance matrix of each collected source signal and obtaining a corresponding noise subspace through eigenvalue decomposition includes the following steps:

s21, under the condition that the base line is not changed, the corresponding array element positions are changed through the movement of the unmanned aerial vehicle to form new arrays, and for each newly formed array, corresponding information source signals are collected;

s22, for the ith collected source signalThe covariance matrix is calculated according to the following formula:

wherein L represents the fast beat number of the data;indicating a desire;represents a conjugate transpose operation;is shown aslTaking a snap shot;

s23, forPerforming eigenvalue decomposition on the covariance matrix, wherein the eigenvalue decomposition is expressed as:

wherein the content of the first and second substances,represents oneA diagonal matrix of dimensions whose diagonal elements are made up of the larger K eigenvalues resulting from eigenvalue decomposition,is a diagonal matrix formed by M-K smaller eigenvalues;is a matrix formed by eigenvectors corresponding to the K larger eigenvalues,then the feature vector is a matrix formed by the feature vectors corresponding to other feature values;andreferred to as signal subspace and noise subspace, respectively; i =1,2, …, p, p is the total number of observations.

Further, in step S4, reconstructing a quadratic optimization problem through a noise subspace and a direction vector, constructing a cost function, and obtaining a combined estimation of amplitude-phase error and DOA through a spectral peak search includes the following steps:

s41, constructing a secondary optimization problem:

wherein the content of the first and second substances,in order to obtain the error of the amplitude and the phase,，it is shown that the transpose operation,representing the DOA parameter to be estimated;

in the formula (I), the compound is shown in the specification,a steering vector representing the ith observation,is represented by a vectorI =1,2, …, p;

s42, constructing a cost function:

in the formula (I), the compound is shown in the specification,is a constant;

s43, forCalculating a partial derivative:

wherein the content of the first and second substances,，is a constant;

and S44, obtaining an estimated value of the angle and amplitude-phase error:

；

s45, mixingSubstitution of expression (c)And calculating to obtain an estimated value of DOA:

。

further, the method further comprises the steps of:

evaluating the effectiveness of the estimation result by using the root mean square error as a performance estimation index; the corresponding root mean square error is calculated according to the following formula:

wherein N represents the number of Monte Carlo simulations,representing the true angle of incidence of the kth signal,represents the angle estimation value of the k signal in the n simulation experiment,representing the true value of the mth magnitude-phase error coefficient,and (4) representing the estimated value of the mth amplitude-phase error coefficient in the nth simulation experiment.

The invention has the beneficial effects that:

compared with the prior art, the method breaks through the limitation of DOA estimation on amplitude and phase errors in the prior art, can obtain an accurate angle estimation value, and has more accurate positioning performance; under the condition that the amplitude and phase errors exist, the method can estimate and correct the amplitude and phase error value without an auxiliary calibration information source, an auxiliary calibration array element and iterative solution, and can obtain high-resolution estimation.

Drawings

Fig. 1 is a flow chart of the unmanned aerial vehicle array amplitude-phase error and signal DOA joint estimation method of the invention.

Fig. 2 is a view of a receiving array scenario formed by the drone swarm of the present invention.

FIG. 3 is a graph comparing uncorrected amplitude phase error with a spectral peak corrected using the method of the present invention.

Fig. 4 is a graph comparing the performance of DOA estimation of the present invention at different signal-to-noise ratios.

FIG. 5 is a graph comparing the real and imaginary part estimation performance of the amplitude phase error under different signal-to-noise ratios.

Detailed Description

The present invention will now be described in further detail with reference to the accompanying drawings.

It should be noted that the terms "upper", "lower", "left", "right", "front", "back", etc. used in the present invention are for clarity of description only, and are not intended to limit the scope of the present invention, and the relative relationship between the terms and the terms is not limited by the technical contents of the essential changes.

For convenience of description, the symbols in the present embodiment have the following meanings:it is shown that it is desirable to,which represents the conjugate transpose operation,it is shown that the transpose operation,is represented by a vectorThe elements in (a) constitute a diagonal matrix.

Fig. 1 is a flow chart of the unmanned aerial vehicle array amplitude-phase error and signal DOA joint estimation method of the invention. The method uses a plurality of unmanned aerial vehicles as a platform to carry array elements, and the array elements form an array receiving signal. The method comprises the following steps:

s1, each unmanned aerial vehicle is provided with a single antenna array element, and the unmanned aerial vehicle cluster formed by a plurality of unmanned aerial vehicles forms a receiving array to receive the information source signals.

And S2, under the condition that the observation base line is not changed, the array structure is changed through the movement of the unmanned aerial vehicle, and the signal source signals are collected again after the array structure is changed every time, so that a plurality of signal source signals are obtained.

And S3, calculating a covariance matrix of each acquired source signal, and decomposing an eigenvalue to obtain a corresponding noise subspace.

And S4, reconstructing a quadratic optimization problem through a noise subspace and a direction vector, constructing a cost function, and obtaining amplitude-phase error and DOA joint estimation through spectrum peak search.

The concrete implementation is as follows:

step 1: signal reception

Uniformly arranging unmanned aerial vehicles, carrying one antenna array element on each unmanned aerial vehicle, and taking the array element interval as unit interval，Indicating the wavelength. Suppose there are K parallel plane wavesAt incident, when array amplitude and phase errors existIn time, the array receive signal may be expressed as:

whereinIs a diagonal matrix of amplitude and phase errors,in order to be the vector of the signal,is an additive white gaussian noise, and is,a matrix of directions is represented, which is,representsA directional vector in the direction, expressed as:

in the formula (I), the compound is shown in the specification,indicating the drone position at this time.

The received signal information can be obtained according to a data model, and a covariance matrix is calculated:

in the formula, L represents the fast beat number of data. To pairPerforming eigenvalue decomposition on the covariance matrix, which can be expressed as:

wherein the content of the first and second substances,represents oneA diagonal matrix of dimensions whose diagonal elements are made up of the larger K eigenvalues resulting from eigenvalue decomposition,is a diagonal matrix made up of M-K smaller eigenvalues.Is a matrix formed by eigenvectors corresponding to the K larger eigenvalues,it is a matrix formed by eigenvectors corresponding to other eigenvalues.Andreferred to as signal subspace and noise subspace, respectively.

Step 2: obtaining multiple noise subspaces

Under the condition that the base line is unchanged (namely, the signal incidence angle is unchanged), the corresponding array element positions are changed through the movement of the unmanned aerial vehicle, and a new array is formed. The same processing is performed to receive the signal again at this time, and a noise subspace can be obtained. Continuing to move to form a new array to obtain the p-th noise subspaceSuppose P total observations.

And step 3: DOA and amplitude-phase error joint estimation

In the presence of amplitude-phase errors, the MUSIC function becomes:

whereinIs the amplitude phase error.

Order toAnd constructing a secondary optimization problem:

wherein. Constructing a cost function:

。

to pairCalculating a partial derivative:，whereinIs a constant. Due to the fact thatIs obtained by. Thus, we can obtain an estimate of c:

will be provided withSubstitution of expression (c)The estimate of DOA can be expressed as:

。

to verify the effectiveness of the algorithm of the present invention, the following verification is performed by MATLAB simulation analysis, and the performance estimation indicator is Root Mean Square Error (RMSE), defined as:

where N represents the number of monte carlo simulations,representing the true angle of incidence of the kth signal,represents the angle estimation value of the k signal in the n simulation experiment,representing the true value of the mth magnitude-phase error coefficient,and (4) representing the estimated value of the mth amplitude-phase error coefficient in the nth simulation experiment.

As shown in fig. 2, which is a scene diagram of the present invention, the number of drones selected in the simulation is M =6, P =2,，，indicating the wavelength.

Fig. 3 shows a comparison of the spectral peaks of the amplitude and phase errors before and after correction by the method of the invention. The simulation assumes that the signal-to-noise ratio SNR is set to 20dB and the number of snapshots is set to J = 500. It can be seen from the spectrum peak diagram that the position and amplitude size of the spatial spectrum peak are affected by the amplitude-phase error. The estimation performance of the MUSIC algorithm is reduced when amplitude and phase errors exist, and if the errors are large, the algorithm can even fail.

FIG. 4 is a graph comparing DOA estimation performance of the method of the present invention with uncorrected methods at different signal-to-noise ratios. The simulation result shows that the method has high estimation precision, and the estimation precision of the unmanned aerial vehicle group array-based joint amplitude and phase error and signal DOA estimation method can be improved by a method for properly improving the signal to noise ratio.

FIG. 5 is a diagram of the performance of amplitude and phase error estimation under different SNR. The simulation result shows that the method can accurately estimate the real part and the imaginary part.

The invention discloses a joint amplitude and phase error and signal DOA estimation method based on an unmanned aerial vehicle group array, and belongs to the technical field of array signal processing. According to the invention, each unmanned aerial vehicle carries a single antenna array element, the unmanned aerial vehicle cluster consisting of a plurality of unmanned aerial vehicles forms a receiving array, and the positions of corresponding array elements can be changed by changing the individual positions in the unmanned aerial vehicle cluster, so that the array structure is changed. And (4) calculating a covariance matrix of the signals received by the arrays for multiple times, and performing eigenvalue decomposition to obtain a plurality of signal noise subspaces. And reconstructing a quadratic optimization problem through a noise subspace and a direction vector, constructing a cost function, finally determining DOA through spectral peak search, and simultaneously obtaining amplitude-phase error estimation. The invention breaks through the defect that the DOA estimation precision in the traditional unmanned aerial vehicle group cooperative sensing is limited by the fence of the amplitude and phase error between the unmanned aerial vehicles, does not need an auxiliary information source and an array element, does not need iterative solution, can obtain the high-precision DOA and amplitude and phase error combined estimation, and has important application value.

The above is only a preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above-mentioned embodiments, and all technical solutions belonging to the idea of the present invention belong to the protection scope of the present invention. It should be noted that modifications and embellishments within the scope of the invention may be made by those skilled in the art without departing from the principle of the invention.