阅读说明：本技术 一种频控阵雷达角度-距离参数解耦合方法 (Frequency control array radar angle-distance parameter decoupling method ) 是由 洪升 杨凯凯 赵志欣 朱琪 叶延恒 于 2020-06-04 设计创作，主要内容包括：本发明属于雷达技术领域,公开了一种利用多径信号的频控阵雷达角度-距离解耦合方法,主要解决频控阵雷达在进行角度-距离估计时,目标角度和距离参数耦合导致参数估计失败的问题。其实现步骤为：S1,建立频控阵列雷达的发射模型；S2,根据S1频控阵列发射模型以及目标空间环境,建立目标回波信号模型；S3,利用多径信号模型实现角度-距离参数解耦合；S4,采用可解相干的阵列谱估计方法对角度和距离参数进行联合估计。本发明优点是无需对频控阵列的阵元间隔、频率间隔、发射方式进行特殊设计,仅利用探测环境反射的目标多径回波实现频控阵的角度-距离参数解耦合,降低了发射端的设计复杂度及硬件成本,解决了多径环境下的目标参数估计问题。(The invention belongs to the technical field of radars, and discloses an angle-distance decoupling method for a frequency control array radar by using multipath signals, which mainly solves the problem that parameter estimation fails due to the coupling of target angle and distance parameters when the frequency control array radar carries out angle-distance estimation. The method comprises the following implementation steps: s1, establishing a transmitting model of the frequency control array radar; s2, establishing a target echo signal model according to the S1 frequency control array emission model and the target space environment; s3, decoupling the angle-distance parameters by using a multipath signal model; and S4, jointly estimating the angle and distance parameters by adopting a decoherence array spectrum estimation method. The method has the advantages that special design on array element intervals, frequency intervals and a transmitting mode of the frequency control array is not needed, angle-distance parameter decoupling of the frequency control array is realized only by using target multipath echoes reflected by a detection environment, the design complexity and hardware cost of a transmitting end are reduced, and the problem of target parameter estimation in a multipath environment is solved.)

1. A frequency control array radar angle-distance decoupling method using multipath signals is characterized in that a frequency control array is not required to be specially designed, only multipath echo signals in the environment are used for realizing target angle-distance decoupling, and the specific implementation steps comprise:

s1: establishing a transmitting model of the frequency control array radar;

s2: establishing a target echo signal model according to the S1 frequency control array emission model and a target space environment;

s3: utilizing a multipath signal model to realize angle-distance parameter decoupling;

s4: and jointly estimating angle and distance parameters by adopting a decoherence array spectrum estimation method.

2. The method of claim 1, wherein the frequency-controlled array radar angle-distance decoupling comprises: the S1 includes:

(1) the method comprises the steps that a narrow-band frequency control array radar transmitting signal model is characterized in that a transmitting array of the narrow-band frequency control array radar transmitting signal model is a linear array with M array elements, a first array element is used as a reference array element, and the transmitting frequency of the first array element is used as a reference frequency; the array transmits M signals s (t) s with different frequencies₁(t),s₂(t),…,s_m(t),…,s_M(t)]^T(ii) a The signal transmitted by the mth array element is:

s_m(t)＝exp(j2πf_mt)s₀(t),0≤t≤T,m＝1,2,…,M (1)

where T is the transmit pulse duration, s₀(t) is a transmit waveform, f_mIs the transmitting carrier of the m-th array element antennaFrequency, which can be expressed as:

f_m＝f₁+Δf_m,m＝1,2,…,M (2)

wherein f is₁Is the reference frequency, Δ f_mIs the carrier frequency difference of the mth array element relative to the reference array element, and satisfies the carrier frequency f of the reference array element₁Much larger than the frequency increment deltaf_m；

(2) The process of deriving the transmitting array guide vector of the narrow-band frequency control array radar is as follows:

the transmitting signal of the narrow-band frequency control array radar irradiates on a certain target in a detection environment, and if the angle of the target relative to the frequency control array is theta and the distance relative to the array reference array element is r, the distance r of the target relative to the mth array element of the array is_mComprises the following steps:

r_m≈r-d_msin(θ),m＝1,2,…,M (3)

wherein d is_mRepresents the spacing of the m-th array element from the reference array element, and r₁R; at time t, the phase of the signal transmitted by the reference array element at the target is:

wherein c is the speed of light, and at this time, the phase difference of the mth array element relative to the reference array element transmitting signal at the target is:

let t be equal to zero in equation (5), and the corresponding time-invariant phase difference is:

the frequency control array radar emission guide vector obtained by the method is as follows:

wherein the content of the first and second substances,

(3) the method disclosed by the invention is characterized in that no special requirements are required for the form and parameters of the frequency control transmitting array, and the method can be widely applied to different frequency control array forms, such as different array types, different array element intervals, different array element frequencies and the like;

taking uniform frequency intervals as an example in the form of uniform linear arrays, at this time, the array element distance intervals and the array element frequency intervals are respectively:

d_m＝(m-1)d,m＝1,2,…,M (8)

Δf_m＝(m-1)Δf,m＝1,2,…,M (9)

wherein d is the distance interval between adjacent array elements, Δ f is the frequency increment of the adjacent array elements, and the formula (8) and the formula (9) are substituted into the formula (6), and the non-time-varying phase difference becomes:

wherein phi is (2 pi/c) (f)₁dsin (theta) -delta fr) represents the echo phase difference of adjacent array elements, and the formula (10) is replaced into the formula (7), so that the uniform frequency control array transmitting array steering vector of the uniform linear array is obtained as follows:

a(φ)＝a(θ,r)＝[1,exp(jφ),…,exp(j(m-1)φ),…,exp(j(M-1)φ)]^T(11)。

3. the method of claim 1, wherein the frequency-controlled array radar angle-distance decoupling comprises: the S2 includes:

in the space detection environment, the angle of a detected target relative to a transmitting array and the distance relative to a reference array element are assumed to be (theta)_d,r_d) (ii) a M signals with different frequencies transmitted by the frequency control array are received and processed after being reflected by a target; assuming that the receiver is band-limited, the receiving array comprises M array elements, the M-th receiving array element only receives and processes the signal with the frequency f_mOf (2) a signal(ii) a Thus, the frequency controlled array receives discrete signals of

Where L is 1,2, …, L is a discrete sampling point, n is_d(l) Representing the discrete noise received by the receiving array,representing a discrete sample of the target echo; the phase difference of the expected target echoes received by adjacent array elements is

φ_d＝g_d(θ_d,r_d)＝(2π/c)(f₁dsin(θ_d)-Δfr_d) (13)

Wherein, g_d(. represents by (θ)_d,r_d) Mapping to phi_dA mapping function of (a);

frequency control array radar receives echo x to target_d(l) Array signal processing is carried out to estimate the angle and distance parameters of the target, and almost all array parameter estimation methods are essentially to receive the phase difference phi of the array_dEstimate and then by_dFurther obtaining the angle theta of the target_dAnd a distance r_d；

In a conventional phased array (non-frequency controlled array), phi_dIs the unknown angle parameter theta_dA one-dimensional function of, and_dand theta_dAre in one-to-one correspondence, and phi is estimated_dThe unknown angle parameter theta can be directly obtained_d(ii) a However, in the frequency-controlled array, φ_dIs the parameter angle theta_dAnd a distance r_dOf a joint two-dimensional function of (a) and an unknown parameter theta_dAnd r_dAre mutually coupled and cannot be derived from the estimated phi_dDirect mapping to obtain the angle theta_dAnd a distance r_dThe angle and distance parameter estimation fails.

4. The method of claim 1, wherein the frequency-controlled array radar angle-distance decoupling comprises: in the step S3, in the step S,

when the target detection environment has obstacles such as buildings, forests, ground, lake surfaces and the like, the transmitting-target path and the target-receiving path are reflected by the obstacles at a high probability and are positioned at (theta)_s,r_s) The multipath echo signal reflected by the obstacle corresponding to the target can be written as:

wherein the angle of the target multipath echo signal relative to the transmitting array and the distance relative to the reference array element are (theta)_s,r_s)，n_s(l) Representing the discrete noise received by the receiving array, and rho representing the multipath reflection coefficient; the phase difference of target multipath echoes received by adjacent array elements is

φ_s＝g_s(θ_s,r_s)＝(2π/c)(f₁dsin(θ_s)-Δfr_s) (15)

Wherein, g_s(. represents by (θ)_s,r_s) Mapping to phi_sA mapping function of (a);

at the receiving end, the direct wave signal x of the target echo_d(l) And multipath reflected wave signal x_s(l) Are added together to form a total target echo of

Wherein a ═ a (θ)_d,r_d),a(θ_s,r_s)]Is an array flow pattern matrix, n (l) ═ n_d(l)+n_s(l) Is a white noise signal obeying complex Gaussian distribution, L is the signal fast beat number, and as can be known from the formula (12) and the formula (14), the direct wave signal and the multipath reflection signal in the target echo x (L) in the formula (16) are coherent;

estimating target parameters by using an array signal processing method in a multipath environment firstly requires de-coherent processing of direct wave signals and reflected wave signals in echo signals, and then direct wave signals are respectively estimatedThe angle distance parameter and the angle distance parameter of the reflected wave signal are obtained by firstly carrying out coherent de-processing and estimating to obtain the phase difference phi of the direct wave in the frequency control array radar_dAnd a phase difference phi of the reflected wave_s(ii) a Then, by_dMapping to obtain the angle and distance of the direct wave

5. The method of claim 1, wherein the frequency-controlled array radar angle-distance decoupling comprises: in the step S3, in the step S,

when the target multipath signal is mainly in the form of specular reflection, a direct wave component and a reflected wave component in the target echo have a certain mathematical relationship, and taking the specular reflection on the ground as an example, a multipath reflection model is shown in fig. 1:

h in the figure_aDenotes the array height, h_tAn angular distance parameter (theta) of the direct wave signal according to the basic principle of specular reflection_d,r_d) And an angular distance parameter (theta) of the reflected wave signal_s,r_s) There is a mathematical mapping relationship (θ)_s,r_s)＝H(θ_d,r_d) The method comprises the following steps:

wherein the content of the first and second substances,

h₁(θ_d,r_d)≈-arcsin(sin(θ_d)+2h_a/r_d) (18)

(3) mapping function g on original frequency control array phase difference by using multipath signal model_d(. and g)_sOn the basis of (-) the mapping function H (-) between the direct wave parameter and the reflected wave parameter is added, the angle-distance coupling, namely the joint type (13), (15) and (17), can be effectively eliminated, and the equation set can be obtained

g_d(θ_d,r_d)＝φ_d(20a)

g_s(θ_s,r_s)＝φ_s(20b)

h₁(θ_d,r_d)＝θ_s(20c)

h₂(θ_s,θ_d,r_d)＝r_s(20d)

As can be readily derived from equations (13), (15) and (17), the four equations in equation (20) are linearly independent, i.e., the remaining fourth equation cannot be derived from any three equations, and the system of equations contains four unknown variables (θ)_d,r_d,θ_s,r_s) And the four equations are linearly independent, the system of equations in equation (20) can therefore yield a unique solution (θ)_d,r_d,θ_s,r_s) And through simultaneous solution of equations, decoupling of angle and distance parameters can be realized.

6. The method of claim 1, wherein the frequency-controlled array radar angle-distance decoupling comprises: in the step S4, in the step S,

by adopting a spatial spectrum estimation method with a decoherence capability, taking a generalized multi-signal classification (G-MUSIC) algorithm and a Maximum Likelihood Estimation (MLE) algorithm as examples, the method realizes the joint estimation without coupling of angle and distance parameters, and has two implementation schemes:

the first scheme is as follows: using the method of space spectrum estimation to direct wave phase difference phi_dAnd a phase difference phi of the reflected wave_sPerforming joint search; search for phi_dAnd phi_sThen, the four equations are simultaneously solved by substituting the four equations into an equation set formula (20), and an angular distance parameter (theta) of the direct wave and the reflected wave is further obtained_d,r_d,θ_s,r_s)；

In the first embodiment, the equations (20c) and (20d) in the equation set of equation (20) may be substituted into the equations (20a) and (20b), so that the variable (θ) is eliminated_s,r_s) To obtain a value related to (theta)_d,r_d) The binary equation set of two variables is solved, the quaternary equation is solved and the dimension is reduced to the binary equation, so that the calculation complexity can be reduced to a certain extent, but the simplified equation set contains a compound function of a trigonometric function, so that an analytic solution cannot be directly obtained, and the numerical solution complexity is still high;

scheme II: firstly, substituting the mathematical relation between the angle and the distance of the direct wave and the reflected wave in the formula (17) into a space spectrum estimation function, removing the angle and the distance parameters of the reflected wave to obtain a space spectrum function taking the angle and the distance parameters of the direct wave as unknown variables, and realizing the first dimension reduction (equivalent to dimension reduction of a quaternary equation into a binary equation); then, directly estimating the angle and the distance of the decoupled direct wave by using a spectrum estimation method, wherein the second dimensionality reduction can be realized by adopting a dimensionality reduction searching method such as alternate projection;

the existence of multipath signals can effectively remove the coupling between angles and distances, but at the same time, the problem of coherence between the target direct wave signal and the multipath signals is also brought, so that before angle and distance estimation, a decorrelation process must be performed, and common decorrelation methods mainly include two methods: one is array smoothing, and the other is a spatial spectrum estimation method with decorrelation capability, wherein the former method has the defect that the aperture of an array needs to be lost, so that the parameter estimation precision is reduced; the latter has the defects that the multi-dimensional search of direct waves and reflected waves needs to be realized, the calculated amount is large, and in order to ensure the parameter estimation precision, the invention adopts a second coherent solution method;

by adopting the second scheme, the method can ensure the parameter estimation precision while realizing decoherence, and effectively realize the decoupling estimation of the angle and the distance in the frequency control array radar by using smaller calculated amount;

by adopting the second scheme, the concrete implementation process of utilizing the G-MUSIC algorithm to realize the angle-distance coupling-free joint estimation comprises the following steps:

estimating covariance matrix of received signal

Secondly, characteristic decomposition is carried out on the covariance matrix of the received signals to obtain a noise subspace

Wherein, U_SIs the signal-to-noise subspace, U_NIs the noise subspace, Λ_SIs a diagonal matrix of large eigenvalues, Λ_NIs a diagonal matrix formed by small eigenvalues;

③ use an array flow pattern matrix A ═ a (theta)_d,r_d),a(θ_s,r_s)]Constructing the G-MUSIC spatial spectrum function as

④ the equation (20c) and the equation (20d) in the formula (17) are substituted into the G-MUSIC spatial spectrum function in the formula (23), and the G-MUSIC spatial spectrum function after the first dimensionality reduction is obtained as

⑤ further adopting dimension reduction search method

wherein the content of the first and second substances,representing the direct wave distance obtained by the ith iteration;representing the angle of the direct wave obtained by the ith iteration, and performing alternate iteration according to an equation (24a) and an equation (24b) until convergence;

(4) by adopting the second scheme, the specific implementation process of utilizing the MLE algorithm to realize the angle-distance coupling-free joint estimation comprises the following steps:

estimating covariance matrix of received signal

② use an array flow pattern matrix A ═ a (theta)_d,r_d),a(θ_s,r_s)]Construct a projection matrix of

P(θ_d,r_d,θ_s,r_s)＝(Aτ)((Aτ)^HAτ)^-1(Aτ)^H(25)

③ constructing a maximum likelihood MLE space spectrum function of

P_MLE(θ_d,r_d,θ_s,r_s)＝Tr(P(θ_d,r_d,θ_s,r_s)R_x) (26)

Wherein Tr (·) represents the trace of the matrix;

④ the MLE space spectrum function in formula (26) is substituted by equation (20c) and equation (20d) in formula (17) to obtain the MLE space after the first dimension reductionA cross spectrum function of

⑤ Using a dimension reduction search method, will

the specific dimension reduction searching process comprises the following steps:

wherein the content of the first and second substances,representing the direct wave distance obtained by the ith iteration;

Technical Field

The invention belongs to the technical field of radars, and relates to a decoupling method for angle-distance parameters of a frequency control array radar.

Background

The concept of Frequency-controlled array (FDA) was first proposed by p.antonik et al in the 2006 IEEE radar annual meeting. Frequency-controlled array means that a small frequency increment is introduced between adjacent array element carrier frequencies (the frequency increment is far smaller than the reference array element carrier frequency). The frequency increment causes phases on some distance units to be mutually superposed to form wave crests, and the phases on some distance units are mutually offset to form wave troughs, so that a beam pattern is caused to be not only related to angles but also related to distances, which is the main difference between a frequency control array and a phased array and is the most main characteristic of the frequency control array. By utilizing the characteristics, the distance-dependent beam forming and the distance-dependent interference suppression can be realized, so that the radar target detection performance is improved.

Target localization is an important target in radar detection. The traditional phased array radar can only realize the angle estimation of a target; the distance dependency of the frequency control array radar enables the angle and the distance parameter of the target to be mutually coupled, so that the target positioning in the frequency control array radar is difficult to achieve. How to decouple the angle and the distance of a target in a frequency control array radar and realize the joint estimation of the angle and the distance of the target is a key and difficult problem.

The reason for the angle-distance parameter coupling in the frequency control array radar is that the phase difference of the received echoes among the frequency control array elements not only depends on the angle value of a target, but also depends on the distance value of the target. In a frequency control array radar, the existing angle-distance decoupling method mainly comprises the methods of transmitting double pulses, dividing sub-arrays, random frequency modes and the like. The method for transmitting double pulses refers to that the frequency control array continuously transmits pulses with two different frequency increments, and has higher requirements on time resources because the number of the transmitted pulses needs to be increased. The method for dividing the subarray is to divide the array into a plurality of different subarrays, wherein different subarrays have different array intervals or different array frequency increments, and the method needs to specially design and change the structure of the transmitting array, so that the aperture of the transmitting array is lost, and the parameter estimation precision is reduced. The random frequency mode method means that the frequency increment among array elements is random and irregular, and whether the decoupling success of the method has randomness or not is achieved due to random selection of the transmitting frequency.

The existing angle-distance decoupling method in the frequency control array radar has the defects that: firstly, a pulse transmitting form, a transmitting array form, a transmitting frequency form and the like need to be specially designed at a transmitting end, so that the design and implementation complexity of a radar transmitting system is improved; extra physical resources such as time, aperture, frequency and the like need to be consumed, so that the estimation precision of the parameters is reduced under the condition of limited physical resources; and thirdly, whether the angle-distance decoupling is successful or not depends on whether the design of the transmitting end is reasonable or not.

The existing angle-distance decoupling method in the frequency control array radar can not be separated from the special design of a transmitting end; and can not be widely applied to frequency control arrays.

Disclosure of Invention

The invention aims to provide a method for realizing target angle-distance decoupling by utilizing multipath signals in a detection environment, which can realize angle-distance decoupling in hundreds of certainty without depending on special design of a transmitting end, additional consumption of physical resources and improvement of system design complexity and can be widely applied to frequency control arrays in different forms.

The invention is realized by the following technical solutions:

a frequency control array radar angle-distance decoupling method using multipath signals comprises the following steps:

s1, determining parameters such as the number of transmitting array elements, array element intervals, transmitting carriers, array frequency increment and the like of a frequency control array according to the actual application scene of the radar and the characteristics of a frequency control array system, and establishing a transmitting model of the frequency control array radar;

s2, under the set frequency control array, establishing a target echo signal model according to the target space environment;

s3, decoupling the angle-distance parameters by using a multipath signal model;

s4, jointly estimating the distance and the angle of the target by using a decoherence array parameter spectrum estimation method, such as a generalized multiple signal classification (G-MUSIC) algorithm, a Maximum Likelihood Estimation (MLE) algorithm and the like, and obtaining the distance and angle parameters after decoupling.

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

1) the method realizes the angle-distance decoupling sum of the frequency control array radar by using the multipath echo signals without special design at a transmitting end; physical resources do not need to be consumed additionally, the complexity of a radar system does not need to be increased, and meanwhile, the decoupling success probability is one hundred percent.

2) The method of the invention does not depend on the special design of the transmitting end, and can be widely applied to frequency control arrays in different forms.

3) The method of the invention can simultaneously solve the problem of target parameter estimation in the multipath environment.

Drawings

The invention is further described below with reference to the figures and the detailed description.

FIG. 1 is a schematic diagram of a geometric model of a multipath echo signal according to the present invention;

FIG. 2 is a schematic diagram of angle-distance decoupling and principle of the present invention under a uniform frequency increment frequency control array model of a uniform linear array;

FIG. 3 is a G-MUSIC two-dimensional space spectrogram when the signal-to-noise ratio SNR is 20dB in a second scheme of the present invention under the uniform frequency increment frequency control array of the uniform linear array;

FIG. 4 is a MLE two-dimensional space spectrogram when the signal-to-noise ratio SNR is 20dB in a second scheme under the uniform linear array uniform frequency increment frequency control array of the present invention;

FIG. 5 is an angle estimation root mean square error performance curve obtained by the G-MUSIC and MLE algorithms before and after AP dimensionality reduction in a second scheme of the present invention under the uniform frequency increment frequency control array of the uniform linear array;

FIG. 6 is a distance estimation root mean square error performance curve obtained by the G-MUSIC and MLE algorithms before and after AP dimensionality reduction in a second scheme of the present invention under the uniform frequency increment frequency control array of the uniform linear array;

FIG. 7 is a schematic diagram of an angle-distance decoupling principle of the present invention under the nonuniform frequency increment frequency control array of the nonuniform linear array;

FIG. 8 is a contour line schematic diagram of a G-MUSIC spectrogram in a non-multipath signal model in a second scheme of the invention under a non-uniform frequency increment frequency control array of a non-uniform linear array;

FIG. 9 is a contour line schematic diagram of a G-MUSIC spectrogram in a second scheme under a multipath signal model under the non-uniform frequency increment frequency control array of the non-uniform linear array of the invention;

FIG. 10 is a G-MUSIC two-dimensional space spectrogram in the case of an inhomogeneous frequency increment frequency control array of an inhomogeneous linear array and a signal-to-noise ratio SNR of 20dB in a second scheme of the present invention;

FIG. 11 is a MLE two-dimensional space spectrogram in the case of an inhomogeneous frequency increment frequency control array of an inhomogeneous linear array and a signal-to-noise ratio SNR of 20dB in a second scheme of the present invention;

FIG. 12 is an angle estimation root mean square error performance curve obtained by G-MUSIC and MLE algorithms before and after AP dimension reduction in a second scheme of the invention under the nonuniform frequency increment frequency control array of the nonuniform linear array;

FIG. 13 is a distance estimation root mean square error performance curve obtained by G-MUSIC and MLE algorithms before and after AP dimension reduction in a second scheme of the invention under the nonuniform frequency increment frequency control array of the nonuniform linear array;

FIG. 14 is a diagram of the steps of the method of the present invention.

Detailed Description

The technical scheme of the invention is further explained by the specific implementation mode in combination with the attached drawings.

A frequency control array radar angle-distance decoupling method using multipath signals is characterized by comprising the following steps:

s1, establishing a frequency control array radar emission model:

(1) the method comprises the steps that a narrow-band frequency control array radar transmitting signal model is characterized in that a transmitting array of the narrow-band frequency control array radar transmitting signal model is a linear array with M array elements, a first array element is used as a reference array element, and the transmitting frequency of the first array element is used as a reference frequency; the array transmits M signals s (t) s with different frequencies₁(t),s₂(t),…,s_m(t),…,s_M(t)]^T(ii) a The signal transmitted by the mth array element is:

s_m(t)＝exp(j2πf_mt)s₀(t),0≤t≤T,m＝1,2,…,M (1)

where T is the transmit pulse duration, s₀(t) is a transmit waveform, f_mThe transmission carrier frequency of the mth array element antenna can be expressed as:

f_m＝f₁+Δf_m,m＝1,2,…,M (2)

wherein f is₁Is the reference frequency, Δ f_mIs the carrier frequency difference of the mth array element relative to the reference array element, and satisfies the carrier frequency f of the reference array element₁Much larger than the frequency increment deltaf_m。

(2) The process of deriving the transmitting array guide vector of the narrow-band frequency control array radar is as follows:

the transmitting signal of the narrow-band frequency control array radar irradiates on a certain target in a detection environment, and if the angle of the target relative to the frequency control array is theta and the distance relative to the array reference array element is r, the distance r of the target relative to the mth array element of the array is_mComprises the following steps:

r_m≈r-d_msin(θ),m＝1,2,…,M (3)

wherein d is_mRepresents the spacing of the m-th array element from the reference array element, and r₁R; at time t, the phase of the signal transmitted by the reference array element at the target is:

where c is the speed of light. At this time, the phase difference of the mth array element relative to the reference array element transmitting signal at the target is:

let t be equal to zero in equation (5), and the corresponding time-invariant phase difference is:

the frequency control array radar emission guide vector obtained by the method is as follows:

wherein the content of the first and second substances,

(3) the method disclosed by the invention is characterized in that no special requirements are required for the form and parameters of the frequency control transmitting array, and the method can be widely applied to different frequency control array forms, such as different array types, different array element intervals, different array element frequencies and the like.

Taking the uniform frequency increment as an example in the form of a uniform linear array, at this time, the array element distance interval and the array element frequency interval are respectively:

d_m＝(m-1)d,m＝1,2,…,M (8)

Δf_m＝(m-1)Δf,m＝1,2,…,M (9)

wherein d is the distance interval of adjacent array elements, and Δ f is the frequency interval of adjacent array elements. When formula (6) is substituted with formula (8) or formula (9), the non-time-varying phase difference is:

wherein phi is (2 pi/c) (f)₁dsin (theta) - Δ fr) represents the phase difference of the echoes of adjacent array elements. The formula (10) is substituted into the formula (7), and the steering vector of the uniform frequency control array transmitting array of the uniform linear array is obtained by the following steps:

a(φ)＝a(θ,r)＝[1,exp(jφ),…,exp(j(m-1)φ),…,exp(j(M-1)φ)]^T(11)

s2, establishing a target echo signal model according to the S1 frequency control array emission model and the target space environment:

in the space detection environment, the angle of a detected target relative to a transmitting array and the distance relative to a reference array element are assumed to be (theta)_d,r_d) (ii) a M signals with different frequencies transmitted by the frequency control array are received and processed after being reflected by a target;assuming that the receiver is band-limited, the receiving array comprises M array elements, the M-th receiving array element only receives and processes the signal with the frequency f_mThe signal of (a); thus, the frequency controlled array receives discrete signals of

Where L is 1,2, …, L is a discrete sampling point, n is_d(l) Representing the discrete noise received by the receiving array,representing a discrete sample of the target echo; the phase difference of the expected target echoes received by adjacent array elements is

φ_d＝g_d(θ_d,r_d)＝(2π/c)(f₁dsin(θ_d)-Δfr_d) (13)

Wherein, g_d(. represents by (θ)_d,r_d) Mapping to phi_dThe mapping function of (2).

Frequency control array radar receives echo x to target_d(l) Array signal processing is performed to estimate the angle and distance parameters of the target. Almost all array parameter estimation methods are essentially phase differences phi of receiving arrays_dEstimate and then by_dFurther obtaining the angle theta of the target_dAnd a distance r_d。

In a conventional phased array (non-frequency controlled array), phi_dIs the unknown angle parameter theta_dA one-dimensional function of, and_dand theta_dAre in one-to-one correspondence, and phi is estimated_dThe unknown angle parameter theta can be directly obtained_d(ii) a However, in the frequency-controlled array, φ_dIs the parameter angle theta_dAnd a distance r_dOf a joint two-dimensional function of (a) and an unknown parameter theta_dAnd r_dAre mutually coupled and cannot be derived from the estimated phi_dDirect mapping to obtain the angle theta_dAnd a distance r_dThe angle and distance parameter estimation fails.

S3, angle-distance parameter decoupling is realized by using a multipath signal model:

(1) when the target detection environment has obstacles such as buildings, forests, ground, lake surfaces and the like, the transmitting-target path and the target-receiving path are reflected by the obstacles at a high probability and are positioned at (theta)_s,r_s) The multipath echo signal reflected by the obstacle corresponding to the target can be written as:

wherein the angle of the target multipath echo signal relative to the transmitting array and the distance relative to the reference array element are (theta)_s,r_s)，n_s(l) Representing the discrete noise received by the receiving array, and rho representing the multipath reflection coefficient; the phase difference of target multipath echoes received by adjacent array elements is

φ_s＝g_s(θ_s,r_s)＝(2π/c)(f₁dsin(θ_s)-Δfr_s) (15)

Wherein, g_s(. represents by (θ)_s,r_s) Mapping to phi_sThe mapping function of (2). At the receiving end, the direct wave signal x of the target echo_d(l) And multipath reflected wave signal x_s(l) Are added together to form a total target echo of

Wherein a ═ a (θ)_d,r_d),a(θ_s,r_s)]Is an array flow pattern matrix, n (t) n_d(l)+n_s(l) Is a white noise signal obeying a complex gaussian distribution, and L is the number of fast beats of the signal. As can be seen from equations (12) and (14), the direct wave signal and the multipath reflected signal in the target echo x (l) in equation (16) are coherent.

Estimating target parameters by using an array signal processing method in a multipath environment firstly requires de-coherent processing of a direct wave signal and a reflected wave signal in an echo signal, and then respectively estimates an angular distance parameter of the direct wave signal and an angular distance parameter of the reflected wave signalAnd (4) counting. In the frequency control array radar, the processing procedure is that firstly, the direct wave phase difference phi is obtained through the coherent resolving processing_dAnd a phase difference phi of the reflected wave_s(ii) a Then, by_dMapping to obtain the angle and distance of the direct wave

By phi_sMapping to obtain the angle and distance of the reflected waveIn the frequency-controlled array, g is mapped, as described in S2_d(. and g)_s(.) is a two-dimensional joint mapping, namely angle and distance parameter coupling, and the angle and distance estimation of the direct wave and the reflected wave fails.

(2) When the target multipath signal is mainly in the form of mirror reflection, a certain mathematical relationship exists between the direct wave component and the reflected wave component in the target echo. Taking the specular reflection on the ground as an example, the multipath reflection model is shown in fig. 1.

H in the figure_aDenotes the array height, h_tRepresenting the target height. According to the basic principle of specular reflection,

angular distance parameter (theta) of direct wave signal_d,r_d) And an angular distance parameter (theta) of the reflected wave signal_s,r_s) There is a mathematical mapping relationship (θ)_s,r_s)＝H(θ_d,r_d) The method comprises the following steps:

wherein the content of the first and second substances,

h₁(θ_d,r_d)≈-arcsin(sin(θ_d)+2h_a/r_d) (18)

(3) mapping function g on original frequency control array phase difference by using multipath signal model_d(. and g)_sAnd (DEG) on the basis of increasing a mapping function H (DEG) between the direct wave parameter and the reflected wave parameter, the angle-distance coupling can be effectively eliminated. I.e., simultaneous equations (13), (15) and (17), a system of equations is obtained

g_d(θ_d,r_d)＝φ_d(20a)

g_s(θ_s,r_s)＝φ_s(20b)

h₁(θ_d,r_d)＝θ_s(20c)

h₂(θ_s,θ_d,r_d)＝r_s(20d)

It is not difficult to derive from equations (13), (15) and (17) that the four equations in equation (20) are independent of each other, i.e., the remaining fourth equation cannot be derived from any three equations. The system of equations contains four unknown variables (theta)_d,r_d,θ_s,r_s) And the four equations are independent of each other, the system of equations in equation (20) can be uniquely solved by (θ)_d,r_d,θ_s,r_s). By simultaneously solving the equation, the decoupling of the angle and distance parameters can be realized.

And S4, jointly estimating the angle and distance parameters by adopting a decoherence array spectrum estimation method.

(1) The existence of multipath signals can effectively remove the coupling between angles and distances, but at the same time, brings the problem of coherence between the target direct wave signal and the multipath signals. Therefore, a de-coherence process must be performed before the angle and distance estimates are made. Common methods of decoherence mainly include two types: one is array smoothing, and the other is a spatial spectrum estimation method with the coherent resolving capability. The former has the disadvantage that the array aperture needs to be lost, thereby reducing the parameter estimation precision; the latter has the disadvantage that the calculation amount is large because multi-dimensional search of direct waves and reflected waves needs to be realized. In order to ensure the parameter estimation accuracy, the invention adopts a second coherent solution method.

(2) A spatial spectrum estimation method with decoherence capability (taking generalized MUSIC and a maximum likelihood MLE algorithm as examples) is adopted to realize the angle and distance parameter coupling-free joint estimation, and two implementation schemes are provided:

the first scheme is as follows: using the method of space spectrum estimation to direct wave phase difference phi_dAnd a phase difference phi of the reflected wave_sPerforming joint search; search for phi_dAnd phi_sThen the four equations are simultaneously solved by being substituted into an equation set formula (20), and the angular distance parameters (theta) of the direct wave and the reflected wave are further obtained_d,r_d,θ_s,r_s)。

In the first embodiment, the equations (20c) and (20d) in the equation set of equation (20) may be substituted into the equations (20a) and (20b), so that the variable (θ) is eliminated_s,r_s) To obtain a value related to (theta)_d,r_d) A system of two-dimensional equations for the two variables, which is then solved. The dimension reduction of the quaternary equation solution to the binary equation solution can reduce the calculation complexity to a certain extent. However, the simplified equation set contains a complex function of a trigonometric function, an analytic solution cannot be directly obtained, and the complexity of numerical solution is still high.

Scheme II: first, the angle-distance mathematical relationship between the direct wave and the reflected wave in equation (17) is substituted into the spatial spectrum estimation function to remove the angle and distance parameters (θ) of the reflected wave_s,r_s) Obtaining the angle and distance parameters (theta) of the direct wave_d,r_d) For a spatial spectrum function of an unknown variable, realizing first dimension reduction (equivalent to dimension reduction of a quaternary equation into a binary equation); then, the angle and distance of the decoupled direct wave are directly estimated by using a spectrum estimation method, wherein a second dimensionality reduction can be realized by adopting a dimensionality reduction search method such as Alternating Projection (AP).

The method recommends the scheme II, can ensure the parameter estimation precision while realizing decoherence, and effectively realizes the decoupling estimation of the angle and the distance in the frequency control array radar by using smaller calculated amount.

(3) By adopting the second scheme, the concrete implementation process of utilizing the G-MUSIC algorithm to realize the angle-distance coupling-free joint estimation comprises the following steps:

the covariance matrix of the received signal can be estimated from the array received signal as

Performing characteristic decomposition on the covariance matrix of the received signal to obtain a noise subspace

Wherein, U_SIs the signal-to-noise subspace, U_NIs the noise subspace, Λ_SIs a diagonal matrix of large eigenvalues, Λ_NIs a diagonal matrix of small eigenvalues.

According to the orthogonal principle of signal subspace and noise subspace, an array flow pattern matrix A ═ a (theta)_d,r_d),a(θ_s,r_s)]The G-MUSIC spatial spectrum function can be constructed as

Wherein [ ·]^HIs a matrix conjugate device { · }^-1The reciprocal is calculated.

The spatial spectrum function in the formula (23) can be equivalent to

Where det (. circle-solid.) represents determinant.

According to theta_dAnd theta_sCan obtain a matrix

Is a singular matrix, so λ ═ 0 is always a solution to equation (24), so the spatial spectral function can be further rewritten as:

the mathematical relation of angle and distance between the direct wave and the reflected wave in the formula (17) is used for substituting the space spectrum estimation function in the formula (25) to finally reduce the dimension to be related to (theta)_d,r_d) Two-dimensional spatial spectral function of

Compared with a four-dimensional space spectrum function, the calculation amount is greatly reduced.

(4) By adopting the second scheme, the specific implementation process of utilizing the MLE algorithm to realize the angle-distance coupling-free joint estimation comprises the following steps:

under the assumption that the noise is complex Gaussian distribution, the array received signal satisfies the following probability distribution function

Wherein, X ═ X (1), …, X (l), …, X (L)]，

The parameter to be estimated isσ²Is the variance of the complex gaussian distribution of the noise.

Logarithm of the probability distribution function (31), and²derivative to obtain sigma²Is estimated as

By substituting equation (32) into equation (31) and taking the logarithm of equation (31), the likelihood function of

From the equation (33), the likelihood function satisfies the following relationship

The formula (16) relates toFrom a maximum likelihood estimate of the linear modelIs estimated as

Substituting the formula (35) into the formula (34) and simplifying, the MLE spectrum function can be obtained as

P_MLE(θ_d,r_d,θ_s,r_s)＝Tr(P(θ_d,r_d,θ_s,r_s)R_x) (36)

Wherein Tr (·) represents the trace of the matrix, P ═ A τ ((A τ)^HAτ)^-1(Aτ)^HIs a projection matrix.

Similarly, the mathematical relationship between the angle and the distance between the direct wave and the reflected wave in equation (17) is used to substitute the equation for (θ)_d,r_d,θ_s,r_s) In the four-dimensional space spectrum function of (a), the final dimension is reduced to (theta)_d,r_d) Two-dimensional space spectrum ofThe amount of calculation can be reduced.

G-MUSIC spectral function after first dimensionality reduction by using formula (17)And MLE spectral functionIs a two-dimensional function of the target angle and distance, and is required for the angle theta_dAnd a distance r_dA two-dimensional search is performed. In order to further reduce the calculation amount, secondary reduction can be carried out by using a dimension reduction search algorithm such as AP (access point)Dimension, converting two-dimensional search into one-dimensional iterative search. Here will beAndis denoted as P (theta)_d,r_d) The AP algorithm comprises the following steps:

step ①, parameter initialization, initializing the initial variables (angle and distance) to be searched, and recording the initial values as

②, angle search, i.e. the distance obtained by the i-1 st iteration

Substitution into the spectral function P (theta)_d,r_d) In the angle theta_dOne-dimensional search is carried out on the variable to obtain the angle of the ith iterative solution

③, search for distance by finding the angle of the ith iteration

Substitution into the spectral function P (theta)_d,r_d) In the range of r_dOne-dimensional search is performed on the variable to obtain the distance of the ith iterative solution

Step four, iteration termination judgment: and judging whether an iteration stopping condition is met, if so, obtaining final estimated values of the angle and the distance, and if not, returning to the step II, and performing iteration solving according to the formula (38) and the formula (39).

The iteration stop conditions comprise two conditions, namely, the maximum iteration times are reached, and the following conditions are met

Where the sum represents the error threshold for angle and distance, respectively.

In the method, the two-dimensional search is avoided by the AP dimension reduction iterative search method, the calculated amount can be further reduced, and the secondary dimension reduction of the spectral function method is realized.

Simulation content and results

The effect of the technical scheme can be further illustrated by the following simulation results:

simulation scenario 1: and the frequency control array is an algorithm simulation verification and performance evaluation under the uniform linear array and linear frequency increment.

The transmitting array in the frequency control array radar adopts an even linear array with 12 array elements, adopts even frequency increment, and the carrier frequency f of the first array element₁150Mhz, frequency increment Δ f 3000Hz, and array element spacing d 1 m. Suppose array overhead h_a25m, with one target at height h_t＝4500m，r_d70km, multipath reflection coefficient p 0.9exp (j pi), direct wave angle θ_dAbout 3.67, reflected wave angle θ_dAnd is approximately equal to-3.71. The distance dimension search step is 100m and the angle dimension search step is 0.05 °.

Simulation content and results:

simulation 1: the implementation process and implementation result of the first scheme in S4 are specifically implemented. Firstly, a binary equation set is obtained by dimensionality reduction of the quaternary equation set, namely, the equation (20c) and the equation (20d) are substituted into the equation (20b) to obtain an equation g_s(θ_d,r_d)＝φ_sAnd equation g in formula (20a)_d(θ_d,r_d)＝φ_dAnd (5) simultaneous solution. Then, the phase difference phi of the direct wave received between the frequency control array elements is solved and obtained by utilizing a common coherent spectrum estimation solving method in the phased array radar_dAnd a phase difference phi of the reflected wave_s. Based on the above simulation parameters, phi can be obtained_d＝2.0877，φ_s-1.6789. Finally, solve for g_s(θ_d,r_d)＝φ_sAnd g_d(θ_d,r_d)＝φ_dThe system of equations, being binary, requires numerical solution since the system of equations has no solution. Plotting the equation g on the angle-distance plane_d(θ_d,r_d) 2.0877, as shown by the black curve in fig. 2; draw equation g_s(θ_d,r_d) -1.6789, as shown by the red curve in fig. 2. The unique intersection point of the two curves is the solution of the equation set and corresponds to the solved target angle theta_dAnd a distance r_dThe solving precision depends on the searching step length of the angle and the distance.

The effective implementation of the first scheme in the simulation 1 can also verify the effectiveness of decoupling of the target angle and the distance in the frequency control array radar by using the multipath signals. As can be seen from the figure, the target angle θ cannot be obtained from the black curve or the red curve alone_dAnd a distance r_dThe corresponding equation has an infinite number of solutions, i.e. in the case of only direct waves or only multipath reflected waves, due to the angle θ_dAnd a distance r_dCannot realize accurate estimation of target parameters. However, as can be seen from the figure, the black curve and the red curve have only one intersection point, and the angle and the distance corresponding to the intersection point are consistent with those set by the simulation, which shows that the target angle θ can be obtained by the simultaneous equations_dAnd a distance r_dThe unique solution of (2) that is, the target angle theta in the frequency control array radar can be effectively realized by using the multipath echo signals_dAnd a distance r_dDecoupling and accurate estimation.

Simulation 2: the implementation process and implementation result of the second scheme in S4 are specifically implemented. Firstly, the equation (20c) and the equation (20d) in the formula (17) are substituted into the G-MUSIC spatial spectrum function in the formula (25) and the MLE spatial spectrum function in the formula (36) to obtain the G-MUSIC spatial spectrum function after the first dimensionality reductionAs shown in FIG. 3, the MLE space spectrum after the first dimensionality reduction is obtainedAs shown in fig. 4. In fig. 3 and 4, the G-MUSIC spectrogram and the MLE spectrogram have unique spectral peaks, and the angles and distances corresponding to the spectral peaks are consistent with the angles and distances set by simulation, which indicates that the method of the present invention can effectively implement angle and distance decoupling in the frequency controlled array radar by using multipath signals.

Simulation 3: the parameter estimation performance evaluation of the second scheme in S4 is specifically implemented. And evaluating the parameter estimation performance of the second G-MUSIC algorithm and the MLE algorithm which are specifically implemented in the S4 and have no AP dimension reduction and AP dimension reduction, wherein the estimation performance index is Root Mean Square Error (RMSE) of angle and distance estimation. Specifically, the angle and distance RMSE calculation expression is:

wherein the content of the first and second substances,represents the estimated angle value of the p-th target at the d-th time,

and (3) representing the P-th target distance value estimated at the D-th time, wherein P represents the number of targets, D represents the simulation frequency of the Monte Carlo, and the simulation frequency of the Monte Carlo is 200.

Fig. 5 shows the variation of the angle estimate RMSE with signal to noise ratio (SNR) for different algorithms. As can be seen from the graph, the angle estimation RMSE before and after the dimension reduction of the AP of the G-MUSIC algorithm and the MLE algorithm is smaller and smaller with the increase of the SNR; the estimation performance of the G-MUSIC algorithm is equivalent to that of the MLE algorithm, and the estimation performance after the AP dimension reduction is slightly lower than that of two-dimensional search before the dimension reduction. The distance estimate RMSE versus signal to noise ratio SNR for different algorithms is given in fig. 6. As can be seen from the graph, the distance estimation RMSE before and after dimension reduction of the AP of the G-MUSIC algorithm and the MLE algorithm is smaller and smaller with the increase of SNR; the estimation performance of the G-MUSIC algorithm is approximately equivalent to that of the MLE algorithm, and the estimation performance after the AP dimension reduction is slightly lower than that of two-dimensional search before dimension reduction. Simulation shows that the G-MUSIC algorithm and the MLE algorithm can realize decoupling estimation of the angle and the distance of the frequency control array radar under the multipath model by the methods before and after AP dimension reduction, and have better estimation accuracy.

Simulation scenario 2: the frequency control array is algorithm simulation verification and performance evaluation under the non-uniform linear array and the non-linear frequency increment.

Suppose an array has 4 array elements with an interval d₁＝3m，d₂＝1m，d₃2m, frequency increments of Δ f₁＝1000Hz，Δf₂＝9000Hz，Δf₃The remaining parameter settings are consistent with simulation scenario 1 at 2000 Hz.

Simulation content and results:

and (4) simulation: and specifically implementing the implementation process and implementation result of the first scheme in the step S4 under the nonlinear frequency increment frequency control array of the non-uniform linear array. Firstly, under the non-uniform frequency increment frequency control array of the non-uniform linear array, the phase difference of direct waves among array elements to be estimated isM, n is 1,2, …, M ≠ n, in common

A plurality of; the phase difference of the reflected wave between the array elements to be estimated is

M, n is 1,2, …, M ≠ n, in common

And (4) respectively. According to

Can obtain the relation theta_d,r _d6 equations ofM, n ≠ n, 1,2, …, M; similarly, according to

Can obtain the relation theta_s,r _s6 equations ofM, n ≠ n, 1,2, …, M ≠ n. Then, the united type (17) can be obtained to contain 14 pieces of theta_d,r_d,θ_s,r_sThe system of equations in quaternion is

h₁(θ_d,r_d)＝θ_s(44c)

h₂(θ_s,θ_d,r_d)＝r_s(44d)

By substituting the formula (44c) and the formula (44d) into the formula (44b), an equation can be obtainedEquation in the sum formula (44a)Simultaneous solving to obtain the reduced dimension containing 12 values about theta_d,r_dThe system of equations of the binary equation is

Then, solving and obtaining the inter-array element direct wave phase difference received by the frequency control array by utilizing a common coherent spectrum estimation solving method in the phased array radarPhase difference with reflected wave

Based on the above simulation parameters, the method can obtain

Substituting the above phase difference value into equation set (45) for θ_d,r_dAnd (6) solving. Since the system of equations has no analytic solution, a numerical solution is required. Meanwhile, the finding in the solving process is thatThe same two equations exist in the equation set (45), and the equation set (45) actually contains ten equations, with redundant equations removed. The curves corresponding to the ten equations after redundancy removal are plotted, as shown in fig. 7. As can be seen from the figure, the ten curves have unique intersection points, which are the solutions of the equation set (45) after redundancy removal, and the target angles theta corresponding to the intersection points_dAnd a distance r_dNamely the target angle and distance set by simulation, and the solving precision of the target angle and distance depends on the searching step length of the angle and distance.

The effective implementation of the first scheme in the simulation 4 can also verify the effectiveness of decoupling of the target angle and the distance in the frequency control array radar by using the multipath signals under the non-uniform frequency increment frequency control array of the non-uniform linear array. If no reflection is present, equation (45b) is removed, leaving equation (45 a). After redundancy removal(45a) Comprising 5 equations, the corresponding curves being as in FIG. 7

The five curves show that the five wide line width curves have 4 intersection points in total, and it is impossible to determine which intersection point corresponds to the estimated target angle θ_dAnd a distance r_dThe decoupling fails. However, the target angle θ to be estimated is relative to the uniform frequency increment frequency control array of the uniform linear array_dAnd a distance r_dThere are numerous solutions; under the non-uniform frequency increment frequency control array of the non-uniform linear array, the target angle theta to be estimated_dAnd a distance r_dThere are 4 ambiguity solutions. This also shows that it is possible to achieve decoupling as long as the non-uniform array non-frequency increment frequency control array is specially designed; however, if the array spacing and frequency increment are not properly designed, decoupling may still fail, as in the case of parameter setting herein.

Under the nonuniform frequency increment frequency control array of the nonuniform array, if a reflected wave is introduced, namely equation (45b) is added on the basis of (45a), the frequency increment frequency control array can be obtained

On the basis of the corresponding 5 wide linewidth curves (corresponding to equation 45a), another 5 narrow linewidth curves corresponding to equation (45b) are added, as shown in FIG. 7Five curves are shown. As can be seen, after the reflected wave is introduced, the ten curves have unique intersection points, i.e., the equation set (45) has a unique solution corresponding to the target angle θ set by the simulation_dAnd a distance r_d. Meanwhile, the unique intersection point is one of the 4 intersection points corresponding to the direct wave formula (45a), which shows that the introduction of the target reflected wave can remove the ambiguity of the 4 ambiguity solutions obtained by the target direct wave. In a word, under the non-frequency incremental frequency control array of the non-uniform linear array, if the transmitting array is not specially designed, under the condition that only direct waves exist, other fuzzy estimation points except a real target exist, and accurate estimation of target parameters cannot be achieved. When reflection is introducedAfter the wave, the real position of the target can be solved by solving an equation set consisting of the reflected wave and the direct wave. Simulation shows that under the non-uniform frequency increment frequency control array of the non-uniform linear array, a transmitting array does not need to be specially designed, and a target angle theta in the frequency control array radar can be effectively realized by utilizing multipath echo signals_dAnd a distance r_dDecoupling and accurate estimation.

And (5) simulation: under the nonlinear frequency increment frequency control array of the non-uniform linear array, the G-MUSIC spectrum comparison is carried out under the condition of no multipath and the condition of multipath in the second scheme in the specific experiment S4. Assuming that there is no multipath reflected wave, the target angle theta is obtained_dAnd a distance r_dThe contour plot of the G-MUSIC spatial spectrum function of (a) is shown in fig. 8; introducing multipath reflected waves, and substituting equation (44c) and equation (44d) in formula (44) into G-MUSIC spatial spectrum function in formula (25) to obtain G-MUSIC spatial spectrum function after first dimension reductionThe corresponding contour plot is shown in fig. 9. Under a non-multipath signal model, in fig. 8, a plurality of contour peak points exist on a G-MUSIC spectral contour line, that is, a plurality of fuzzy solution positions exist, and the fuzzy solution positions correspond to the real target, the fuzzy target 1, the fuzzy target 2 and the fuzzy target 3 in fig. 7, so that the ambiguity of the solution cannot be eliminated. Under the multi-path signal model, in fig. 9, the G-MUSIC spectral contour line only has one peak point, and the peak point corresponds to the unique intersection point position of the ten curves in fig. 7, that is, the true angle θ of the target_dAnd a distance r_d. Comparing fig. 8 and fig. 9, it can be further shown that under the non-uniform frequency increment of the non-uniform linear array, the target angle θ in the frequency controlled array radar can be effectively realized by using the multi-path echo signal_dAnd a distance r_dDecoupling and accurate estimation.

And (6) simulation: and specifically implementing the implementation process and implementation result of the second scheme in the S4 under the nonlinear frequency increment frequency control array of the non-uniform linear array. Under the nonlinear frequency increment frequency control array of the non-uniform linear array, by using the target multi-path model, firstly, equation (34c) and equation (34d) in formula (34) are substituted into the G-MUSIC spatial spectrum function in formula (25) and formula (36)MLE space spectrum function to obtain G-MUSIC space spectrum after first dimensionality reduction

As shown in FIG. 10, the MLE space spectrum after the first dimensionality reduction is obtainedAs shown in fig. 11. In fig. 10 and 11, the G-MUSIC spectrogram and the MLE spectrogram have unique spectral peaks, and the maximum value is searched through a two-dimensional spectrum to obtain a unique target angle and distance value, which indicates that the method of the present invention is not limited to the form of a frequency control array, and angle and distance decoupling in a frequency control array radar can be effectively realized by using multipath signals under a non-uniform linear array and a non-linear frequency increment frequency control array.

And (7) simulation: and specifically implementing parameter estimation performance evaluation of the second scheme in S4 under the nonlinear frequency increment frequency control array of the non-uniform linear array. And evaluating the parameter estimation performance of two processing methods of the second G-MUSIC algorithm and the MLE algorithm in the specific implementation S4, namely AP-free dimension reduction and AP-dimension reduction.

Fig. 12 shows the variation curve of the angle estimation RMSE with the signal-to-noise ratio SNR of different algorithms under the nonlinear frequency increment frequency control array of the nonlinear array. As can be seen from the graph, the angle estimation RMSE before and after the dimension reduction of the AP of the G-MUSIC algorithm and the MLE algorithm is smaller and smaller with the increase of the SNR; the estimation performance of the G-MUSIC algorithm is equivalent to that of the MLE algorithm, and the estimation performance after the AP dimension reduction is slightly lower than that of two-dimensional search before the dimension reduction. The distance estimate RMSE versus signal to noise ratio SNR for the different algorithms is given in fig. 13.

As can be seen from the graph, the distance estimation RMSE before and after dimension reduction of the AP of the G-MUSIC algorithm and the MLE algorithm is smaller and smaller with the increase of SNR; the estimation performance of the G-MUSIC algorithm is approximately equivalent to that of the MLE algorithm, and the estimation performance after the AP dimension reduction is slightly lower than that of two-dimensional search before dimension reduction. Simulation shows that under the nonlinear frequency increment frequency control array of the non-uniform linear array, the method before and after AP dimension reduction of the G-MUSIC algorithm and the MLE algorithm can effectively realize the decoupling estimation of the angle and the distance of the frequency control array radar under the multipath model, and has better estimation precision.

While the invention has been described with reference to a preferred embodiment, it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted for elements thereof without departing from the spirit and scope of the invention. The present invention is not to be limited by the specific embodiments disclosed herein, and other embodiments that fall within the scope of the claims of the present application are intended to be within the scope of the present invention.