CN103293517B - Diagonal-loading robust adaptive radar beam forming method based on ridge parameter estimation - Google Patents

Abstract

The invention discloses a diagonal-loading robust adaptive radar beam forming method based on ridge parameter estimation. According to an implementation scheme, the method includes: receiving signals in real time by radar antennas; constructing adaptive weight vectors of a radar; defining output power of a radar antennal array; adopting a new estimation criterion for estimating unknown vectors; utilizing the estimated values of the unknown vectors for acquiring loading amount; and acquiring adaptive weight vectors for forming beams. The loading mount is determined in an adaptive diagonal loading method in the prior art by means of applying the new estimation criterion and a convex optimization tool. The method has the advantages that accuracy of weighted vectors of the radar antennas is improved, beams narrow in major lobe, low in minor lobe and capable of pointing to a target direction are formed, distortion of radar beams is avoided, desired signal receiving of the radar is enhanced, receiving of interference and noise is inhibited, errors in radar applications are resisted, radar targets can detected accurately, and false report or failure in report of targets by the radar is avoided.

Description

Diagonal loading robust adaptive radar beam forming method based on ridge parameter estimation

Technical Field

The invention belongs to the technical field of array signal processing, relates to a beam forming technology of radar signals, and particularly relates to a diagonal loading robust adaptive radar beam forming method based on ridge parameter estimation, which is mainly used for detecting radar targets.

Background

Array signal processing is an important branch of modern signal processing, and the application of the array signal processing relates to a plurality of technical fields such as radar, communication, biomedical engineering, sonar and the like. The beam forming is also called spatial filtering, is used for detecting a target in the radar field, is a main aspect of array processing, and achieves the purposes of enhancing a radar target signal and inhibiting a radar interference signal by performing weighted spatial filtering on each array element of a radar antenna. The adaptive beam forming can adaptively change the weighting factors of each array element of the radar according to the change of the signal environment. In recent 30 years, a great deal of research results have emerged in adaptive radar beamforming: a Sampling Matrix Inversion (SMI) method, a Linear Constraint Minimum Variance (LCMV) method, a diagonal loading method, a ridge regression-based adaptive radar beamforming method (HKB), a generalized linear combination-based covariance matrix correction (GLC), and the like.

The SMI method is a common method for adaptively detecting a target by a radar, and engineering implementation is relatively simple. The LCMV method is also a commonly used method for adaptively detecting a target by a radar, and belongs to the SMI field. In the practical application of the SMI method, various errors can cause main lobe deviation and side lobe level rise of radar beams, and in severe cases, the radar beams are distorted, so that the radar cannot accurately detect the position of a target, and sometimes even cannot detect the target or falsely report the target. Thus, a diagonally loaded radar beamforming method for suppressing radar pattern distortion arises. The diagonal loading technique is: before the covariance matrix of the radar receiving data is inverted, the covariance matrix is corrected, and the method for realizing correction is to load the value on the diagonal line of the covariance matrix of the radar receiving data. The diagonal loading technology can inhibit disturbance of small eigenvalues and corresponding eigenvectors, weaken influence of radar noise, improve distortion of a radar directional diagram, resist steering vector errors and have high robustness, and meanwhile, radar interference signals can be compressed, and convergence speed is increased.

The loading of the conventional diagonal loading adaptive radar beam forming method is determined by the estimated radar noise power, and the selection of the loading is not fixedly restricted and is usually selected by a radar user according to experience. Although the diagonal loading technology improves the distortion of a radar pattern to a certain extent, the following problems still exist: when the loading amount is too small, the effect of improving the distortion of a radar directional diagram is not obvious; secondly, when the loading amount is too large, the interference suppression strength of the radar is reduced; thirdly, the loading amount selected according to the experience of a radar user has the influence of human factors; and the method can not change in a fully self-adaptive manner along with the change of the actual received signal of the radar, has great limitation in the actual application of the radar, and needs a beam forming method which can adjust the radar beam in a fully self-adaptive manner according to the change of the actual signal in order to improve the real-time searching speed and accuracy of the radar to the target.

Thus, beam forming methods have been proposed which can be changed fully adaptively according to changes in the actual conditions: HKB method and GLC method. The HKB method can adaptively determine the diagonal loading amount of data received by the radar according to the data received by the radar, does not need to select the diagonal loading amount manually, and can better detect the radar target when the radar sampling data is less. However, the HKB method also has its disadvantages: the loading amount in the HKB method can be increased along with the increase of the fast beat number, when the fast beat number is larger, the detection precision of the HKB method is reduced due to overlarge loading amount, and a radar cannot detect a target or falsely report the target in serious cases. The GLC method can directly search an optimal guide vector or an optimal radar data covariance matrix according to radar receiving data, so that the robustness of a radar beam former is improved. However, it still has many disadvantages: the model of the covariance matrix of the reestimated radar receiving data is as follows: the method comprises the following steps of linear combination of a radar data covariance matrix and an identity matrix, namely, assuming that noise received by a radar is white Gaussian noise, and if the noise received by the actual radar is color noise, the method cannot accurately estimate a radar target; secondly, in the process of solving the minimum mean square error of the covariance matrix, due to the lack of the prior distribution information knowledge of useful signals, a large error exists in the estimation operation, which causes a large error of a detected radar target; thirdly, when the snapshot number is large, a small diagonal loading amount can be generated, the robustness of resisting the guide vector error can be reduced by the GLC method, namely when the antenna deviates, the GLC method cannot accurately detect the target and even cannot detect the target.

In summary, in the existing schemes for detecting radar targets by using beam forming, the SMI method and the LCMV method have the problems of radar beam distortion and incapability of detecting radar targets in a fully adaptive manner according to environmental changes; the HKB method has the problems that the loading capacity is too large when the snapshot number is slightly large, and the radar detection performance is reduced or fails; the GLC method has the problems of sensitivity to prior information errors, loss of robustness for resisting radar guide vector errors within hours of snapshot and the like. These problems make it impossible for the radar to detect the target accurately and quickly, even if the target is not detected or false reported.

Disclosure of Invention

The invention aims to provide a ridge parameter estimation-based diagonal loading robust adaptive radar beam forming method which is adaptive, reasonable in loading amount, insensitive to prior information error and capable of resisting steering vector error on the basis of the existing adaptive radar beam forming method aiming at the defects in the existing method.

In order to achieve the purpose, the technical idea of the invention is as follows: the method directly and adaptively extracts information related to noise and errors from the received data of the radar, quickly obtains the load quantity of the covariance matrix of the received data of the radar which is more in line with the actual situation by using the extracted information and a new estimation criterion, and obtains the weighted vector of the radar array by using the load quantity to perform adaptive beam forming, thereby realizing the accurate and rapid detection of the radar target, and specifically comprises the following steps:

step 1), radar receives signals in real time, the radar receives signals are set as x (t), x (t) is sampled for N times in real time, and data x ═ x (t) of the radar received signals are obtained₁)，...，x(t_N)]Estimating covariance matrix of radar received data x by maximum likelihood estimationWhere N is the number of fast beats.

Step 2) setting the direction vector of the radar target signal as a_sAccording to a_sObtaining a signal space B orthogonal to a radar target signal space; using B, constraint w^Ha_sConstructing a radar weighting vector with 1 and an unknown vector etaWherein, (.)^HRepresenting the conjugate transpose, M is the number of elements of the antenna array, B is an M x (M-1) -dimensional complex matrix, w is an M x 1-dimensional complex vector, and η is an (M-1) x 1-dimensional complex vector.

Step 3) the radar beam forming model is as follows:

$\underset{w}{\min }{w}^H\hat{R}w$ s.t.w^Ha_s＝1

using radar weighted vectorsObtaining an objective function of radar beam forming:

<math> <mrow> <munder> <mi>min</mi> <mi>w</mi> </munder> <msup> <mi>w</mi> <mi>H</mi> </msup> <mover> <mi>R</mi> <mo>^</mo> </mover> <mi>w</mi> <mo>=</mo> <munder> <mi>min</mi> <mi>&eta;</mi> </munder> <msup> <mrow> <mo>(</mo> <mi>B&eta;</mi> <mo>-</mo> <mfrac> <msub> <mi>a</mi> <mi>s</mi> </msub> <mi>M</mi> </mfrac> <mo>)</mo> </mrow> <mi>H</mi> </msup> <mover> <mi>R</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mi>B&eta;</mi> <mo>-</mo> <mfrac> <msub> <mi>a</mi> <mi>s</mi> </msub> <mi>M</mi> </mfrac> <mo>)</mo> </mrow> <mo>=</mo> <munder> <mi>min</mi> <mi>&eta;</mi> </munder> <msubsup> <mrow> <mo>|</mo> <mo>|</mo> <msup> <mover> <mi>R</mi> <mo>^</mo> </mover> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msup> <mi>B&eta;</mi> <mo>-</mo> <msup> <mover> <mi>R</mi> <mo>^</mo> </mover> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msup> <mfrac> <msub> <mi>a</mi> <mi>s</mi> </msub> <mi>M</mi> </mfrac> <mo>|</mo> <mo>|</mo> </mrow> <mn>2</mn> <mn>2</mn> </msubsup> </mrow> </math>

order to And e-b-X η is a residual vector, the objective function of radar beam forming is simplified as follows:

<math> <mrow> <munder> <mi>min</mi> <mi>&eta;</mi> </munder> <msubsup> <mrow> <mo>|</mo> <mo>|</mo> <mi>X&eta;</mi> <mo>-</mo> <mi>b</mi> <mo>|</mo> <mo>|</mo> </mrow> <mn>2</mn> <mn>2</mn> </msubsup> </mrow> </math>

wherein,representing the value of w when the expression takes the minimum value,the expression is expressed as the value of eta when the expression takes the minimum value,representation matrixThe square root matrix of (1) |₂Representing a 2 norm.

Step 4) using the new estimation criterionTo estimate the unknown vector eta, and then apply the standard interior point method to satisfy the estimation criterionSearching for unknown vector etaRetrieve the estimateWherein | · | purple sweet₁Representing a 1 norm. In the existing beam forming method, the estimation criteria are all usedEstimation criteria for use in the inventionThe unknown vector eta can be estimated more reasonably according to actual conditions, and more reasonable loading capacity is obtained, so that the method has stronger self-adaptability.

Step 5) applying the estimator of step 4)Covariance matrix of radar received dataIs solved, where p is a scalar.

Step 6) using the covariance matrix of the radar receiving dataAnd a direction vector a of the radar target signal_sAnd obtaining a weighting vector w of the radar antenna, sending the obtained weighting vector w to the radar, updating the weighting coefficient of the radar antenna, and forming a beam which is narrow in main lobe, low in side lobe and capable of accurately pointing to the detection direction after signals received by the radar in real time are weighted by the coefficients. The invention enhances the receiving of the radar to the observation direction signal, inhibits the radar from receiving the incoming wave signals in other directions, and achieves the purpose of accurately detecting the radar target.

Compared with the prior art, the invention has the following advantages:

(1) the invention uses a new estimateCriterion of countingSolving the unknown vector eta by a convex optimization tool to obtain an estimator which is more practicalAnd then a more accurate weighting vector of the radar antenna array is obtained, and a beam formed by the weighting vector has a narrower main lobe and a lower side lobe and can be more accurately pointed to the detection direction. In practical application, the method can enhance the receiving of the radar antenna array to the radar expected signal, inhibit the receiving to the radar interference and noise, resist the error existing in the radar system and the prior information, and achieve the purpose of detecting the radar target more effectively and accurately;

(2) the invention carries out diagonal loading on the covariance matrix of the radar received data, reduces the dispersion degree of the characteristic value of the covariance matrix of the radar received data, reduces the main lobe width and the side lobe height of radar beams, and avoids the distortion of the radar beams, thereby avoiding false report or missed report of the radar in practical application;

(3) the invention can self-adaptively extract the information related to the environment directly from the radar receiving data, can self-adaptively change according to the change of the environment, achieves the aim of detecting the radar target in real time and has stronger self-adaptive capability.

Drawings

FIG. 1 is a flow chart of an implementation of the present invention;

FIG. 2 is a graph of the output SINR of radar antenna arrays of different methods as a function of the fast beat number of the received signals of the arrays under ideal conditions;

FIG. 3 is a graph of the output SINR of the radar antenna array of different methods as a function of the fast beat number of the received signal of the array under non-ideal conditions;

FIG. 4 is a graph of output signal-to-interference-and-noise ratio of a radar antenna array as a function of input signal-to-noise ratio for the array for different approaches;

fig. 5 is a graph of radar antenna array output signal-to-interference-and-noise ratio as a function of array pointing error for different approaches.

Detailed Description

Example 1:

the invention relates to a diagonal loading robust self-adaptive radar beam forming method based on ridge parameter estimation, which is used for detecting a radar target, and is shown in the beam forming process of figure 1, and the specific implementation of the method comprises the following steps:

step 1: the method comprises the steps of receiving signals by a radar in real time, setting the received signals x (t), carrying out real-time sampling on x (t) for N times to obtain data x of the received signals by the radar, and estimating a covariance matrix of the received data x by using a maximum likelihood estimation methodThe solving process comprises the following steps:

(1a) according to the structural model of the radar antenna receiving signals, the radar receiving signals x (t) of the radar antenna with the array element number M at the time t are represented as follows:

<math> <mrow> <mi>x</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>s</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <mi>i</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <mi>n</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mo>[</mo> <msub> <mi>a</mi> <mi>s</mi> </msub> <msub> <mi>a</mi> <msub> <mi>i</mi> <mn>1</mn> </msub> </msub> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <msub> <mi>a</mi> <msub> <mi>i</mi> <mi>p</mi> </msub> </msub> <mo>]</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mi>s</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <msub> <mi>i</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>i</mi> <mi>p</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>+</mo> <mi>n</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </math>

wherein N is the fast beat number, p is the number of interference signals received by the radar,radar antenna array manifold matrix of dimension M x (p +1), a_sIs the steering vector of radar target signal s (t),are respectively radar interference signals i₁(t)，i₂(t)，…，i_p(t) a steering vector, n (t) is a noise signal received by the radar, a_s，…，n (t) are all M × 1-dimensional complex vectors;

(1b) sampling the radar receiving signal x (t) for N times to obtain the receiving data of the radar antenna:

x＝[x(t₁)，...，x(t_N)]

(1c) the covariance matrix of the data x received by the radar antenna is calculated by using the following formulaComprises the following steps:

<math> <mrow> <mover> <mi>R</mi> <mo>^</mo> </mover> <mo>=</mo> <mfrac> <mn>1</mn> <mi>N</mi> </mfrac> <munderover> <mi>&Sigma;</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <mi>x</mi> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>n</mi> </msub> <mo>)</mo> </mrow> <msup> <mi>x</mi> <mi>H</mi> </msup> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>n</mi> </msub> <mo>)</mo> </mrow> </mrow> </math>

wherein, (.)^HRepresenting a conjugate transpose.

By step 1, real-time information of the radar signal is already obtained, and then information required in the implementation process of the present invention is extracted from the obtained real-time information.

Step 2: constructing an expression of a weighting vector w of the radar antenna array:

(1a)let the direction vector of the radar target signal be a_sAccording to the radar target signal direction vector a_sSolving to satisfy the constraint condition: b is^Ha_s＝0，B^HB is the orthogonal complement B of the radar target signal space of I; wherein, (.)^HDenotes a conjugate transpose, B is an M × (M-1) -dimensional complex matrix;

(1b) according to the condition that the orthogonal complement space B and the self-adaptive weighting vector w of the radar antenna array should meet: w is a^Ha_sThe linear combination to get the weighting vector of the radar antenna array is 1:

<math> <mrow> <mi>w</mi> <mo>=</mo> <mfrac> <msub> <mi>a</mi> <mi>s</mi> </msub> <mi>M</mi> </mfrac> <mo>-</mo> <mi>B&eta;</mi> </mrow> </math>

wherein eta is (M-1) multiplied by 1 dimension complex vector to be solved, and M is the array element number of the antenna array.

And step 3: the model for radar beamforming is:

$\underset{w}{\min }{w}^H\hat{R}w$ s.t.w^Ha_s＝1

using radar weighted vectorsObtaining an objective function of radar beam forming:

<math> <mrow> <munder> <mi>min</mi> <mi>w</mi> </munder> <msup> <mi>w</mi> <mi>H</mi> </msup> <mover> <mi>R</mi> <mo>^</mo> </mover> <mi>w</mi> <mo>=</mo> <munder> <mi>min</mi> <mi>&eta;</mi> </munder> <msup> <mrow> <mo>(</mo> <mi>B&eta;</mi> <mo>-</mo> <mfrac> <msub> <mi>a</mi> <mi>s</mi> </msub> <mi>M</mi> </mfrac> <mo>)</mo> </mrow> <mi>H</mi> </msup> <mover> <mi>R</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mi>B&eta;</mi> <mo>-</mo> <mfrac> <msub> <mi>a</mi> <mi>s</mi> </msub> <mi>M</mi> </mfrac> <mo>)</mo> </mrow> <mo>=</mo> <munder> <mi>min</mi> <mi>&eta;</mi> </munder> <msubsup> <mrow> <mo>|</mo> <mo>|</mo> <msup> <mover> <mi>R</mi> <mo>^</mo> </mover> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msup> <mi>B&eta;</mi> <mo>-</mo> <msup> <mover> <mi>R</mi> <mo>^</mo> </mover> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msup> <mfrac> <msub> <mi>a</mi> <mi>s</mi> </msub> <mi>M</mi> </mfrac> <mo>|</mo> <mo>|</mo> </mrow> <mn>2</mn> <mn>2</mn> </msubsup> </mrow> </math>

order to And e-b-X η is a residual vector, the objective function of radar beam forming is simplified as follows:

<math> <mrow> <munder> <mi>min</mi> <mi>&eta;</mi> </munder> <msubsup> <mrow> <mo>|</mo> <mo>|</mo> <mi>X&eta;</mi> <mo>-</mo> <mi>b</mi> <mo>|</mo> <mo>|</mo> </mrow> <mn>2</mn> <mn>2</mn> </msubsup> </mrow> </math>

wherein,representing the value of w when the expression takes the minimum value,the expression is expressed as the value of eta when the minimum value is taken, s.t. represents the constraint condition as follows,representation matrixThe square root matrix, | | | | luminance₂Representing a 2 norm.

And 4, step 4: using new estimation criteriaTo estimate the unknown vector eta, and then apply the standard interior point method to satisfy the estimation criterionThe unknown vector eta is searched, and the specific solving method is as follows:

the method uses the mature CVX in the convex optimization field to satisfy the objective functionThe unknown vector eta of the radar is searched to obtain the estimator of etaWherein | · | purple sweet₁Representing a 1 norm.

And 5: using the estimator in step 4Covariance matrix for radar received dataThe loading coefficient rho is solved, and the concrete solving method is as follows:

estimating the quantities in step 4Covariance matrix substituted into radar reception dataExpression of the diagonal loading factor ofIn (1) obtainingIs determined by the diagonal loading coefficient p, wherein | | | | | non-calculation₂Representing a 2 norm.

Step 6: covariance matrix using radar received dataAnd a direction vector a of the radar target signal_sAnd obtaining a weighting vector w of the radar antenna, wherein the specific solving method comprises the following steps:

(6a) covariance matrix using radar received dataAnd a direction vector a of the radar target signal_sObtaining the weighted vector of the radar antenna array

<math> <mrow> <mi>w</mi> <mo>=</mo> <mfrac> <mrow> <msup> <mrow> <mo>(</mo> <mover> <mi>R</mi> <mo>^</mo> </mover> <mo>+</mo> <mi>&rho;I</mi> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <msub> <mi>a</mi> <mi>s</mi> </msub> </mrow> <mrow> <msup> <msub> <mi>a</mi> <mi>s</mi> </msub> <mi>H</mi> </msup> <mrow> <mo>(</mo> <mover> <mi>R</mi> <mo>^</mo> </mover> <mo>+</mo> <mi>&rho;I</mi> <mo>)</mo> </mrow> <msub> <mi>a</mi> <mi>s</mi> </msub> </mrow> </mfrac> </mrow> </math>

Wherein, (.)^HRepresenting a conjugate transpose, (.)^-1Representing matrix inversion, I is an M-dimensional unit matrix.

(6b) And (3) sending the weighting vector w obtained in the step (6a) to a radar, updating the weighting coefficients of the radar antenna, weighting the signals received by the radar in real time by the coefficients to form a beam with a narrow main lobe and a low side lobe and capable of accurately pointing to a detection direction, enhancing the reception of the radar to signals in an observation direction, inhibiting the reception of the radar to incoming wave signals in other directions, and achieving the purpose of accurately detecting a radar target.

Example 2:

the diagonal loading robust adaptive radar beam forming method based on ridge parameter estimation is the same as embodiment 1, and the effect of the method is further explained by combining simulation experiments as follows:

simulation 1: and (3) comparing the relation between the output signal-to-interference-and-noise ratio and the snapshot number:

simulation conditions are as follows: the radar antenna array model is a uniform linear array with the space of half wavelength, the array element number is 10, the number of radar target signals is 1, the number of interference signals is 2, the signal-to-noise ratio SNR is 0dB, and the dry-to-noise ratio INR₁＝INR₂10dB, the incoming wave direction of the radar target signal is theta_s20 °, the direction of the incoming wave of the interference signal 1 is θ_i1At-30 °, the spatial frequency of the interference signal 2 direction vector isWherein γ is 0.9, and the monte carlo number is 200.

Simulation content:

under ideal conditions, namely under the condition of no radar guide vector error, the existing conventional beam forming method, the HKB beam forming method, the generalized linear combination GLC robust beam forming method and the method of the invention are used for simulating the signal-to-interference-and-noise ratio output by the radar antenna array along with the change of the fast beat number of the received signal of the radar antenna array, and the simulation result is shown in figure 2. As can be seen from fig. 2, the present invention has significantly improved detection performance compared to the existing beamforming method, because the present invention improves the accuracy of the radar antenna weighting vector. In practical application, the radar antenna array can enhance the reception of radar expected signals, inhibit the reception of radar interference and noise, and achieve the purpose of more effectively and accurately detecting radar targets.

Example 3:

the diagonal loading robust adaptive radar beam forming method based on ridge parameter estimation is the same as embodiment 1, and the effect of the method is further explained by combining simulation experiments as follows:

simulation 2: and (3) comparing the relation between the output signal-to-interference-and-noise ratio and the snapshot number:

simulation conditions are as follows: radar steering vector errorThe other simulation conditions were the same as simulation 1.

Simulation content: under the non-ideal condition, namely under the condition that the radar has the guide vector error, the existing conventional beam forming method, the HKB beam forming method, the generalized linear combination GLC steady beam forming method and the method of the invention are used for simulating the output signal-to-interference-and-noise ratio of the radar antenna array along with the input signal-to-noise ratio of the radar antenna array, and the simulation result is shown in figure 3. As can be seen from fig. 3, under non-ideal conditions, the performance of other algorithms is reduced significantly, but the present invention still has better performance, which indicates that the present invention has stronger robustness against radar steering vector errors.

Example 4:

the diagonal loading robust adaptive radar beam forming method based on ridge parameter estimation is the same as embodiment 1, and the effect of the method is further explained by combining simulation experiments as follows:

simulation 3: comparing the relation between the output signal-to-interference-and-noise ratio and the input signal-to-noise ratio:

simulation conditions are as follows: assuming that the fast beat number N is 20, the SNR varies, and other simulation conditions are the same as those of simulation 1.

Simulation content: the simulation results are shown in fig. 4, in which the conventional beam forming method, the HKB beam forming method, the generalized linear combination GLC robust beam forming method and the method of the present invention are used to simulate the output signal-to-interference-and-noise ratio of the radar antenna array as the input signal-to-noise ratio of the radar antenna array changes. As can be seen from FIG. 4, the invention avoids the distortion of radar beams by carrying out adaptive diagonal loading on the covariance matrix of radar receiving data, and compared with other methods, the performance is obviously improved.

Example 5:

the diagonal loading robust adaptive radar beam forming method based on ridge parameter estimation is the same as embodiment 1, and the effect of the method is further explained by combining simulation experiments as follows:

and (4) simulation: and comparing the output signal-to-interference-and-noise ratio with the array pointing error relation:

simulation conditions are as follows: assuming that the fast beat number N is 20, the pointing error of the radar array is theta_errorThe other simulation conditions are the same as simulation 1, with-2 to 2 °.

Simulation content: the simulation result of the simulation of the output signal-to-interference-and-noise ratio of the radar antenna array with the change of the pointing error of the radar antenna array is shown in fig. 5 by using the conventional beam forming method, the HKB beam forming method, the generalized linear combination GLC robust beam forming method and the method of the invention. As can be seen from FIG. 5, the method has stronger capability of resisting the prior information error than other methods; meanwhile, when the number of snapshots is only 20, the method still has good performance, which shows that the method can change in real time according to the change of the environment, achieves the purpose of detecting the radar target in real time, and has stronger self-adaptive capacity.

In summary, the implementation scheme of the diagonal loading robust adaptive radar beam forming method based on ridge parameter estimation of the present invention includes: receiving signals by a radar antenna in real time; constructing a radar adaptive weight vector; defining output power of a radar antenna array; estimating an unknown vector by adopting a new cost function; acquiring the loading capacity by using the unknown vector estimation value; and obtaining the self-adaptive weight vector to perform beam forming. The invention applies a new estimation criterion and a convex optimization tool to solve the problem of determining the loading amount in the self-adaptive diagonal loading method in the prior art. The invention improves the precision of the radar antenna weighting vector, forms the wave beam which has narrow main lobe and low side lobe and can self-adaptively point to the target direction, avoids the distortion of the radar wave beam, enhances the receiving of the radar to the expected signal, inhibits the receiving of interference and noise, resists the error existing in the radar application, can more accurately detect the radar target and avoids the false report or the missing report of the target by the radar.

Claims (3)

1. A diagonal loading robust adaptive radar beam forming method based on ridge parameter estimation is used for detecting radar targets, and is characterized in that: the method comprises the following steps:

step 1) setting a radar receiving signal as x (t), carrying out N times of real-time sampling on the x (t) to obtain data x of the radar receiving signal, and estimating a covariance matrix of the radar receiving data x by using a maximum likelihood estimation methodWherein N is the number of fast beats;

step 2) setting the direction vector of the radar target signal as a_sAccording to a_sObtaining a space B orthogonal to the radar target signal space; using B and constraint w^Ha_s1, expressing radar weight vector w by linear combination of unknown vector etaIs shown, wherein^HRepresenting conjugate transposition, wherein M is the array element number of the antenna array;

step 3) the model of the radar beam forming problem is:

$\begin{array}{cc}\underset{w}{\min }{w}^H\hat{R}w& s.t.w^H{a}_s=1\end{array}$

using radar weighted vectorsObtaining an objective function of a radar beamforming problem:

<math> <mrow> <munder> <mi>min</mi> <mi>w</mi> </munder> <msup> <mi>w</mi> <mi>H</mi> </msup> <mover> <mi>R</mi> <mo>^</mo> </mover> <mi>w</mi> <mo>=</mo> <munder> <mi>min</mi> <mi>&eta;</mi> </munder> <msup> <mrow> <mo>(</mo> <mi>B&eta;</mi> <mo>-</mo> <mfrac> <msub> <mi>a</mi> <mi>s</mi> </msub> <mi>M</mi> </mfrac> <mo>)</mo> </mrow> <mi>H</mi> </msup> <mover> <mi>R</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mi>B&eta;</mi> <mo>-</mo> <mfrac> <msub> <mi>a</mi> <mi>s</mi> </msub> <mi>M</mi> </mfrac> <mo>)</mo> </mrow> <mo>=</mo> <munder> <mi>min</mi> <mi>&eta;</mi> </munder> <msubsup> <mrow> <mo>|</mo> <mo>|</mo> <msup> <mover> <mi>R</mi> <mo>^</mo> </mover> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msup> <mi>B&eta;</mi> <mo>-</mo> <msup> <mover> <mi>R</mi> <mo>^</mo> </mover> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msup> <mfrac> <msub> <mi>a</mi> <mi>s</mi> </msub> <mi>M</mi> </mfrac> <mo>|</mo> <mo>|</mo> </mrow> <mn>2</mn> <mn>2</mn> </msubsup> </mrow> </math>

order toIf e-X η is the residual vector, the objective function of the radar beamforming problem is simplified as:

<math> <mrow> <munder> <mi>min</mi> <mi>&eta;</mi> </munder> <msubsup> <mrow> <mo>|</mo> <mo>|</mo> <mi>X&eta;</mi> <mo>-</mo> <mi>b</mi> <mo>|</mo> <mo>|</mo> </mrow> <mn>2</mn> <mn>2</mn> </msubsup> </mrow> </math>

wherein,representing the value of w when the expression takes the minimum value,the expression is expressed as the value of eta when the minimum value is taken, s.t. represents the constraint condition as follows,representation matrixThe square root matrix, | | | | luminance₂Represents a 2 norm;

step 4) using the new estimation criterionTo estimate the unknown vector eta, and then apply the standard interior point method to satisfy the estimation criterionIs searched to obtain the estimatorWherein | · | purple sweet₁Represents a norm of 1;

step 5) application estimatorCovariance matrix for obtaining radar receiving dataIs given by a diagonal loading factor p, where p is a scalar; will estimateCovariance matrix of radar receiving data in applicationExpression of the diagonal loading factor ofIn (1) obtainingWhere M is the number of array elements of the antenna array, | | | | n computation₂Represents a 2 norm;

step 6) using the covariance matrix of the radar receiving dataAnd a direction vector a of the radar target signal_sAnd obtaining a weighting vector w of the radar antenna, sending the obtained weighting vector w to the radar, updating the weighting coefficients of the radar antenna, and forming a beam pointing to the detection direction after the signals received by the radar in real time are weighted by the coefficients.

2. The method of claim 1, wherein the method comprises: wherein in step 1): real-time receiving data x of radar and covariance matrix of xThe solving process comprises the following steps:

(1a) according to the structural model of the radar antenna receiving signals, the receiving signals x (t) of the radar antenna with the array element number M at the time t are represented as follows:

$x\left(t\right)=s\left(t\right)+i\left(t\right)+n\left(t\right)=\left[\begin{array}{cccc}{a}_s& a_{i_1}& ...& a_{i_p}\end{array}\right]\left[\begin{array}{c}s\left(t\right)\\ i_1\left(t\right)\\ ...\\ i_p\left(t\right)\end{array}\right]+n\left(t\right)$

wherein p is the number of interference signals received by the radar, $A=\left[\begin{array}{cccc}{a}_s& a_{i_1}& ...& a_{i_p}\end{array}\right]$ radar antenna array flow pattern matrix of dimension M x (p +1), a_sIs the steering vector of radar target signal s (t),are respectively radar interference signals i₁(t)，i₂(t)，…，i_p(t), n (t) is a noise signal received by the radar, n (t) are all M × 1-dimensional complex vectors;

(1b) sampling the radar receiving signal x (t) for N times to obtain the receiving data of the radar antenna:

x＝[x(t₁)，...，x(t_N)]

(1c) calculating a covariance matrix of the data x received by the radar antenna by using a maximum likelihood estimation method:

<math> <mrow> <mover> <mi>R</mi> <mo>^</mo> </mover> <mo>=</mo> <mfrac> <mn>1</mn> <mi>N</mi> </mfrac> <munderover> <mi>&Sigma;</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <mi>x</mi> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>n</mi> </msub> <mo>)</mo> </mrow> <msup> <mi>x</mi> <mi>H</mi> </msup> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mi>n</mi> </msub> <mo>)</mo> </mrow> </mrow> </math>

wherein N represents the number of beats (.)^HRepresenting a conjugate transpose.

3. The ridge parameter estimation based diagonal loading robust adaptive radar beamforming method according to claim 2, wherein: wherein in step 6): covariance matrix using radar received dataAnd a direction vector a of the radar target signal_sAnd obtaining a weighting vector w of the radar antenna, wherein the specific solving method comprises the following steps:

covariance matrix using radar received dataAnd a direction vector a of the radar target signal_sObtaining the weighted vector of the radar antenna arrayApplying w to a radar antenna for beamforming to achieve detection of a radar target, wherein ·^HRepresenting a conjugate transpose, (.)^-1Representing matrix inversion, I is an M-dimensional identity matrix.