CN116482641A - Low-altitude multipath target super-resolution elevation estimation method based on block sparse modeling - Google Patents
Low-altitude multipath target super-resolution elevation estimation method based on block sparse modeling Download PDFInfo
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- G—PHYSICS
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- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
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Abstract
The invention discloses a low-altitude multipath target super-resolution elevation estimation method based on block sparse modeling, which comprises the following steps: based on the positioning and orientation information of the radar and the azimuth measurement value of the radar to the target, establishing a rectangular coordinate system in a plane where the echo propagation path is located; extracting a topographic curve in a certain distance range in the direction of a target from a geographic information system; grid division is carried out on the airspace of interest in the pitching dimension, the effectiveness of reflection paths corresponding to each pitching angle is analyzed by combining the distance measurement value and the topography curve, and the incidence pitching angle of the reflection waves is calculated; constructing a structured redundant dictionary by using direct echo steering vectors and reflected wave steering vectors corresponding to all pitch angles of interest; establishing a structured sparse representation model of radar array element domain/subarray domain/beam domain received data; solving a convex combination optimization problem by adopting a first-order rapid algorithm, and recovering a block sparse signal matrix; the elevation angle estimated value of the target is obtained based on the restored block sparse signal, so that the accuracy of the model can be effectively improved.
Description
Technical Field
The invention relates to the technical field of radar low-altitude target direction-finding positioning, in particular to a low-altitude multipath target super-resolution elevation estimation method based on block sparse modeling.
Background
Low altitude burst prevention is one of the important threats faced by the current air defense system, and high-precision elevation angle estimation/altitude measurement is always a difficult problem in the low altitude detection field due to the influence of multipath effects of radar target echoes.
In the aspect of a multipath propagation model, the method is more widely studied and adopted at present, and the heights/positions of reflection points and the incidence angles of reflected waves are inverted in a digital elevation map based on a specular reflection assumption, but a default mirror plane is generally parallel to a ground plane, and the influence of topography fluctuation on a reflection path is not considered; part of the recent research has also begun to take into account the effects of diffuse reflection, but the robustness to reflected wave angle of incidence errors/fluctuations is generally improved by optimizing the estimation algorithm.
In terms of estimation algorithms, with the rapid development of super-resolution direction-finding technology, algorithms for estimating elevation angle of a low-altitude target by applying super-resolution parameter estimation are endless, and more common algorithms can be divided into the following three types: the first type is an adaptive beam forming algorithm, which can weaken the influence of diffuse reflection on estimation performance by widening the null of a reflected wave, but generally requires sufficient snapshot numbers and incoherent signals, and can design multiple matrix inversion operations, so that the computational complexity is high; the second class is classical parameter estimation algorithm, such as subspace algorithm or maximum likelihood algorithm, the former has serious deterioration in performance under the conditions of less snapshot and strong correlation of signals, and the latter requires known or estimated target number; the third class is compressed sensing or sparse recovery class algorithms, which generally require adjustment of super-parameters to ensure estimation performance, and existing models and methods do not consider the paired nature of direct echo and reflected waves. In addition, existing studies typically concatenate multipath fading factor (or called complex reflection coefficient, etc.) estimates with elevation estimates, but due to coupling of parameters, the estimation errors of the two may affect each other, resulting in reduced estimation performance; to solve this problem, iterations are required in an alternating optimized manner, which in turn necessarily results in a significant increase in computational complexity.
In summary, the existing low-altitude target elevation angle estimation method is difficult to obtain a satisfactory compromise among model accuracy, estimation performance and implementation complexity, and cannot guarantee reliability under severe conditions such as fewer snapshots, strong correlation of echoes and the like.
Disclosure of Invention
The invention aims to solve the problem of deterioration of elevation measurement performance caused by multipath effect when a radar detects a low-altitude target in a complex geographic environment, and provides a low-altitude multipath target super-resolution elevation estimation method based on block sparse modeling. The method accurately builds a multipath propagation model on the basis of fully considering the actual topographic relief influence of the array, combines the airspace sparsity of the target and the paired characteristics of the direct echo and the reflected wave to build a structured sparse representation model, and provides a block sparse recovery model and algorithm which are free of super parameters and can be rapidly realized for parameter estimation. The model is more accurate, the number of targets and the surface reflection characteristic are not required to be known, the method has higher estimation precision and reliability under the conditions of strong correlation of echoes and few snapshots (even single snapshot), and can invert the information such as multipath attenuation factors, pulse-to-pulse amplitude and phase fluctuation characteristics of target echoes and the like while completing high-precision and super-resolution elevation estimation of a plurality of multipath targets, and the application is not limited by the arrangement mode and system of a radar receiving array, so that the method is wider in applicability.
In order to achieve the above object, the technical scheme adopted for solving the technical problems is as follows:
a low-altitude multipath target super-resolution elevation estimation method based on block sparse modeling comprises the following specific steps:
step 1: based on the positioning and orientation information of the radar and the azimuth measurement value of the radar to the target, establishing a rectangular coordinate system in a plane where the echo propagation path is located;
step 2: extracting a topographic curve in a certain distance range in the direction of a target from a Geographic Information System (GIS);
step 3: grid division is carried out on the airspace of interest in the pitching dimension, the effectiveness of reflection paths corresponding to each pitching angle is analyzed by combining the distance measurement value and the topography curve, and the incidence pitching angle of the reflection waves is calculated;
step 4: constructing a structured redundant dictionary by using direct echo steering vectors and reflected wave steering vectors corresponding to all pitch angles of interest;
step 5: establishing a structured sparse representation model of radar array element domain/subarray domain/beam domain received data;
step 6: solving a convex combination optimization problem by adopting a first-order rapid algorithm, and recovering a block sparse signal matrix;
step 7: the elevation angle estimated value of the target is obtained based on the restored block sparse signal, and the attenuation factor of the reflection path and the inter-pulse amplitude-phase fluctuation characteristic of the target echo can be further obtained according to the requirement.
Further, step 1 includes the following:
the method comprises the steps of acquiring information such as longitude, latitude, altitude, antenna/array orientation and the like of a radar through positioning and orientation equipment of the radar, estimating the azimuth angle of a target by adopting technologies such as monopulse angle measurement and the like, establishing a rectangular coordinate system in a plane perpendicular to a ground plane in the direction, and taking the longitude/latitude and altitude of the radar as a coordinate origin. The radar coordinates are (x) R ,y R ) Wherein x is R ＝0，y R Corresponding to the altitude of the radar antenna/array.
Further, step 2 includes the following:
a topographical curve within the coordinate plane and within a range of distances of interest near the radar is extracted from a Geographic Information System (GIS). Due to the discreteness of the digital map, the curve is actually a set of points divided at a certain resolution: { (x) n ,y n )|n＝1,2,...,N}。
Further, step 3 includes the following:
dividing the airspace of interest into grids { theta } at certain intervals in the pitch dimension l I l=1, 2, &..l }, calculating the position coordinates (x T ,y T )＝(x R +Rcosθ,y R +Rsin θ) and further analyzing each grid angle θ in combination with the topography profile l Corresponding reflection path effectiveness and corresponding reflection wave incidence pitch angle theta l ′。
Specifically, the analysis method of the reflection path effectiveness and the reflection wave incidence pitch angle is as follows:
(1) defining a range of potential reflection points based on a range difference constraint of the target direct echo and the reflected wave: in view of the fact that the direct echo and the reflected wave can be distinguished by the distance when the wave path difference is large, the difference between the reflected path length and the target distance measurement value can be restrained to be not more than a plurality of distance resolution units, namely d R +d T ≤R+ΔR max Wherein d R D is the distance from the reflection point to the radar T For the distance of the reflection point to the target ΔR max Typically 1 to 3 times the distance resolution is available. Constrained set of potential reflection point coordinatesCan be expressed as:
(2) calculating the tangential slope at each point of the topographic curve: two convenient calculation modes are provided, one is that the distances from the left and right adjacent points of the point to the tangent line are equal, then (x n ,y n ) Tangential slope k at n ＝(y n+1 -y n-1 )/(x n+1 -x n-1 ) The method comprises the steps of carrying out a first treatment on the surface of the Taking average of the slopes of the connecting lines between the point and the left and right adjacent points, and the corresponding slope expression isFor general relief level and map resolution, the two calculation modes are basically equivalent.
(3) Determining reflection point position coordinates based on the geometric relationship: referring to fig. 3, under the assumption of ideal specular reflection, a point (x, y) is the condition of the reflection point that the bisector of the included line angle between the target and the reflection point and between the reflection point and the radar coincides with the normal of the topographic curve at the reflection point. The method is characterized in that the method is obtained by an angular bisector theorem and a fixed ratio point formula, and the coordinates of an intersection point of the angular bisector and a connecting line between the target and the radar are as follows:
if the line between this point and the reflection point (x, y) is perpendicular to the tangent of the topographic curve (slope k), then there are:
k(y C -y)＝x-x C ，
the finishing is available, and the filling conditions for reflecting points are as follows:
the position coordinates of the reflection point corresponding to the target with the pitch angle θ can be determined based on the following formula:
wherein,,representation set->An element that minimizes the absolute value of f.
(4) Calculating the precise coordinates of the reflection point by interpolation: if the map resolution does not meet the requirement, the terrain curve can be interpolated in the neighborhood of the reflection point with the expected high resolution, the sub-steps (1) - (3) are repeated, and finally the obtained coordinates of the reflection point are still recorded as (x) θ ,y θ )。
(5) Judging the effectiveness of the reflection path and calculating the incidence pitch angle of the reflection wave: considering that there may be a shadow on the reflection path, resulting in reflected waves not being received by the radar, the effective reflection path must satisfy: coordinate set of potential reflection pointsNot empty, and for any +.>The following equation holds.
Therefore, it can be determined based on this whether or not the multipath effect exists at the target pitch angle θ. If the reflection path is valid, the incident pitch angle θ' of the reflected wave is: θ' =arctan [ (y) θ -y R )/(x θ -x R )]。
As a special case of the above analysis, if the ground is roughly considered to be absolutely flat (i.e. the mirror plane is parallel to the ground plane: y=y n ) The above analysis method of the coordinates of the reflection point can be simplified as follows: the path difference constraint in substep (1) is rewritable asSubstep (2) may be omitted (consider k n Constant zero); the reflection point position coordinate expression in the substep (3) is rewritten as:
further, step 4 includes the following:
the following redundant dictionary is constructed by using the direct echo guide vectors and the reflected wave guide vectors corresponding to all pitch angle grid points (the grid point L is far greater than the target number D):
A＝[A 1 A 2 … A L ]
where a (θ) represents an mx 1-dimensional receive array steering vector of the radar when the pitch angle of the incident signal is θ, which may be either a time-array element domain steering vector (M corresponds to the number of antenna elements), a subarray domain steering vector (M corresponds to the number of subarrays), or a beam domain steering vector (M corresponds to the number of beams); record A l Is of the column number J l The column number of A is K, then J l ＝1,2，Whereas dictionary a is composed of blocks a with a column number of typically 2 l Regularly formed, a may be referred to as a structured dictionary.
Further, step 5 includes the following:
based on the mxk-dimensional dictionary a given in step 4, the radar (array element domain/subarray domain/beam domain) reception data X can be modeled as:
X＝AS+N
wherein, X is composed of distance domain data (unit of distance R) after pulse pressure of each channel, and the column number corresponds to pulse number P (also called sampling snapshot number); n is M x P Viga Gaussian white noise; s is a KXP dimensional signal matrix, and can be divided into blocks according to rows by referring to the block rule of AS l Is J l The x P-dimensional signal matrix, the operator "T" represents the transpose of the matrix. S is S l Line 1 s of (2) l1 Corresponding pitch angle is theta l P samples of target echo of J l =2, then S l Line 2 s of (2) l2 P samples corresponding to its reflected wave; since the target echo is homologous to the reflected wave, the two ideally differ by only a complex constant ρ (called multipath fading factor), s, determined by the spatial propagation characteristics and the surface reflection characteristics l2 ＝ρs l1 . It can be seen that when the grid angleθ l When there is a target on the S l The system consists of a target echo and a reflected wave thereof, and is a non-zero matrix; otherwise, S l =0. Because the number of targets D is limited, the number of self-defined grid points L can be far greater than D, and S is necessarily a block sparse matrix with most blocks being zero, so that as long as the signal matrix S is restored, the target pitch angle theta can be determined through the positions of non-zero blocks, and the information such as multipath fading factors rho, target inter-pulse amplitude-phase fluctuation characteristics and the like can be obtained based on the data of the non-zero blocks.
Further, step 6 includes the following:
to recover the block sparse signal matrix S, the following convex combination optimization problem is established:
wherein I F The Frobenius norm representing the matrix (degenerated to l for vectors 2 A norm); weights w for penalty terms for each block l Given by the formula:
wherein the operator "tr { }" represents the trace of the matrix, the covariance matrix estimate R is given by:
wherein,,diag (p) represents a diagonal matrix constructed with vector p as a diagonal element; power vector p= [ p ] 1 p 2 … p k ] T The elements in (a) are->The optimization model does not need manual workAnd the adjusted or optimized super parameters avoid complex operations such as cross verification and the like.
In particular, the above-mentioned fast solution of the convex optimization problem may employ a first-order value optimization algorithm, such as an improved block coordinate descent method, a linearization alternate direction multiplier method (L-ADMM, or P-ADMM), an original dual hybrid gradient method (PDHG), or a related improved algorithm, which has the advantage that the solution process does not involve complex operations such as matrix inversion, and the computational complexity does not explosively increase with the increase of dictionary dimensions and snapshot numbers. In addition, before the algorithm iteration starts, the initial value S of the matrix S to be restored (0) Can be given by a linear minimum mean square error estimator (LMMSE): s is S (0) ＝Diag(p)·A H R -1 X。
Further, step 7 includes the following:
block sparse signal matrix based on recoveryThe spatial spectrum can be given by:
or->Pitch angle estimation for D targetsCan be according to Z (theta) l ) Position of the larger peak in ∈ ->Determination, i.e.)>Further, the signal matrix estimate may be modified as follows:
wherein the method comprises the steps ofThe inter-pulse fluctuation characteristic of the d-th target echo can be determined by +.>Line 1 (denoted +.>) Is given; if->The number of lines of (i.e. the object has a reflection path) is 2, the 2 nd behavior is recorded +.>The corresponding multipath fading factor can be defined by +.>Given.
Compared with the prior art, the invention has the following advantages and positive effects due to the adoption of the technical scheme:
(1) The method fully considers the influence of the conditions of actual terrain gradient, ground object shielding and the like on the target echo propagation path, and can effectively improve the accuracy of the model.
(2) According to the method, elevation angle estimation is converted into a block sparse signal recovery problem through structural sparse representation modeling of radar received data, the number of targets and the surface reflection characteristic are not required to be known, manual parameter adjustment and complete data self-adaption are not required, and the method has higher precision and reliability under the conditions of strong correlation of echoes and few shots (even single shots).
(3) The optimization problem designed by the method can be solved quickly by adopting a first-order numerical optimization algorithm, and the calculation complexity can be reduced remarkably.
(4) The method can complete high-precision super-resolution elevation estimation of a plurality of multipath targets, and can simultaneously acquire attenuation factors of corresponding reflection paths and inter-pulse amplitude-phase fluctuation characteristics of target echoes.
(5) The method has no special requirements on the arrangement mode and system of the radar receiving array, and has wide applicability.
Drawings
FIG. 1 is a flow chart of the method according to the present invention;
FIG. 2 is a schematic diagram of the technical idea of analyzing echo propagation paths according to the present invention;
FIG. 3 is a schematic diagram of the geometrical relationship of the direct echo and reflected wave propagation paths of the object of the present invention;
FIG. 4 is a graph showing the analysis result of the method of the present invention on a low-altitude target multipath effect under actual topography;
FIG. 5 is a spatial spectrum of the method of the present invention given at a signal-to-noise ratio of 10dB and a snapshot count of 64;
FIG. 6 is an estimation of the amplitude fluctuation characteristics of the target echo according to the method of the present invention;
FIG. 7 is a graph showing the estimation of the phase fluctuation characteristics of the target echo according to the method of the present invention;
FIG. 8 is a spatial spectrum of the method of the present invention given at a signal-to-noise ratio of-5 dB and a snapshot count of 64;
fig. 9 is a spatial spectrum given by the method of the present invention at a signal-to-noise ratio of 10dB and a snapshot number of 1.
Detailed Description
The following description of the embodiments of the present invention will be made apparent and fully in view of the accompanying drawings, in which some, but not all embodiments of the invention are shown. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Referring to the flowchart of fig. 1, the embodiment discloses a low-altitude multipath target super-resolution elevation estimation method based on block sparse modeling, which comprises the following steps:
step 1: based on the positioning and orientation information of the radar and the azimuth measurement value of the radar to the target, establishing a rectangular coordinate system in a plane where the echo propagation path is located;
step 2: extracting a topographic curve in a certain distance range in the direction of a target from a Geographic Information System (GIS);
step 3: grid division is carried out on the airspace of interest in the pitching dimension, the effectiveness of reflection paths corresponding to each pitching angle is analyzed by combining the distance measurement value and the topography curve, and the incidence pitching angle of the reflection waves is calculated;
step 4: constructing a structured redundant dictionary by using direct echo steering vectors and reflected wave steering vectors corresponding to all pitch angles of interest;
step 5: establishing a structured sparse representation model of radar array element domain/subarray domain/beam domain received data;
step 6: solving a convex combination optimization problem by adopting a first-order rapid algorithm, and recovering a block sparse signal matrix;
step 7: the elevation angle estimated value of the target is obtained based on the restored block sparse signal, and the attenuation factor of the reflection path and the inter-pulse amplitude-phase fluctuation characteristic of the target echo can be further obtained according to the requirement.
The steps are specifically described as follows:
further, step 1 includes the following:
the method comprises the steps of acquiring information such as longitude, latitude, altitude, antenna/array orientation and the like of a radar through positioning and orientation equipment of the radar, establishing a rectangular coordinate system in a plane perpendicular to a ground plane on the azimuth of a target (a target azimuth angle measured value is acquired by technologies such as monopulse angle measurement and the like), taking the position of the longitude/latitude and the altitude of the radar as a coordinate origin, taking the 0 altitude as an x-axis and taking the zenith as a y-axis positive direction. The radar coordinates are (x) R ,y R ) Wherein x is R ＝0，y R Corresponding to the altitude of the radar antenna/array.
Further, step 2 includes the following:
and extracting a topographic curve in the coordinate plane and in a range of a distance of interest near the radar based on digital elevation information provided by a Geographic Information System (GIS). Due to the discreteness of the digital map, the curve is actually composed ofA set of points divided at a certain resolution (e.g. 30m, 90 m): { (x) n ,y n ) n=1, 2,..n }. The digital map resolution employed in this embodiment is 30 meters.
Further, step 3 includes the following:
dividing the airspace of interest into grids { theta } at a certain interval in a pitch dimension (pitch angle is defined as that the horizontal direction is 0, the upper direction is positive, and the lower direction is negative) l I l=1, 2, &..l }, calculating the position coordinates (x T ,y T )＝(x R +Rcosθ,y R +Rsin θ) and further analyzing each grid angle θ in combination with the topography profile l Corresponding reflection path effectiveness and corresponding reflection wave incidence pitch angle theta l '. Here, the pitching grid only needs to cover a low-altitude airspace by combining with the actual beam width of the radar, and can be divided at equal angular intervals or equally at sinusoidal spaces of pitch angles; the present embodiment chooses to grid-divide between-2.5 to 5 times beamwidth with 1/80 beamwidth as the interval. Fig. 2 intuitively presents the technical idea of the step, namely that a curve formed by all reflection points meeting the assumption of specular reflection between a target and a radar and an actual topographic curve often have only very individual intersection points, and the specific position of the intersection points can be deduced according to the geometric relationship.
Specifically, the analysis method of the reflection path effectiveness and the reflection wave incidence pitch angle is as follows:
(1) defining a range of potential reflection points based on a range difference constraint of the target direct echo and the reflected wave: in view of the fact that the direct echo and the reflected wave can be distinguished by the distance when the wave path difference is large, the difference between the reflected path length and the target distance measurement value can be restrained to be not more than a plurality of distance resolution units, namely d R +d T ≤R+ΔR max Wherein d R D is the distance from the reflection point to the radar T Distance from the reflection point to the target; deltaR max The distance resolution is generally 1-3 times that of the radar, and the distance measurement error and the topographic curve are the reason that a certain margin is neededPrecision limitations, the potential for energy leakage from neighboring distance cells, etc. Constrained set of potential reflection point coordinatesCan be expressed as:
(2) calculating the tangential slope at each point of the topographic curve: two convenient calculation modes are provided, one is that the distances from the left and right adjacent points of the point to the tangent line are equal, then (x n ,y n ) Tangential slope k at n ＝(y n+1 -y n-1 )/(x n+1 -x n-1 ) The method comprises the steps of carrying out a first treatment on the surface of the Taking average of the slopes of the connecting lines between the point and the left and right adjacent points, and the corresponding slope expression isThe present embodiment uses the latter to calculate the tangential slope.
(3) Determining reflection point position coordinates based on the geometric relationship: referring to fig. 3, under the assumption of ideal specular reflection, a point (x, y) is the condition of the reflection point that the bisector of the included line angle between the target and the reflection point and between the reflection point and the radar coincides with the normal of the topographic curve at the reflection point. The method is characterized in that the method is obtained by an angular bisector theorem and a fixed ratio point formula, and the coordinates of an intersection point of the angular bisector and a connecting line between the target and the radar are as follows:
if the line between this point and the reflection point (x, y) is perpendicular to the tangent of the topographic curve (slope k), then there are:
k(y C -y)＝x-x C
the finishing is available, and the filling conditions for reflecting points are as follows:
the position coordinates of the reflection point corresponding to the target with the pitch angle θ can be determined based on the following formula:
wherein,,representation set->An element that minimizes the absolute value of f.
(4) Calculating the precise coordinates of the reflection point by interpolation: if the map resolution does not meet the requirement, the terrain curve can be interpolated in the neighborhood of the reflection point with the expected high resolution, the sub-steps (1) - (3) are repeated, and finally the obtained coordinates of the reflection point are still recorded as (x) θ ,y θ ). In this embodiment, the neighborhood range is ±60 meters, the resolution of the map after interpolation is 1 meter, and the interpolation method is cubic spline interpolation.
(5) Judging the effectiveness of the reflection path and calculating the incidence pitch angle of the reflection wave: considering that there may be a shadow on the reflection path, resulting in reflected waves not being received by the radar, the effective reflection path must satisfy: coordinate set of potential reflection pointsNot empty, and for any x n ＜x θl 、/>The following equation holds.
Therefore, it can be determined based on this whether or not the multipath effect exists at the target pitch angle θ. If the reflection path is valid, the incident pitch angle θ' of the reflected wave is: θ' =arctan [ (y) θ -y R )/(x θ -x R )]。
As a special case of the above analysis, if the ground is roughly considered to be absolutely flat (i.e. the mirror plane is parallel to the ground plane: y=y n ) The above analysis method of the coordinates of the reflection point can be simplified as follows: the path difference constraint in substep (1) is rewritable asSubstep (2) may be omitted (consider k n Constant zero); the reflection point position coordinate expression in the substep (3) is rewritten as:
fig. 4 shows the result of analyzing the multipath effect of the target with 8 km from the radar and a pitch angle of-0.5 DEG based on the step, wherein the elevation of the ground at the radar is 252.414 meters, the distance from the radar receiving array to the ground is 5 meters, and the distance resolution of the radar is 3 meters. It can be seen that after the difference of the wave path is limited to be within 6 meters, the potential reflection point is limited to be within about 5.76 kilometers; the final reflection point position coordinate obtained after interpolation of the map is (813 meters, 245.058 meters), the incidence pitch angle of the reflection wave is-0.105 degrees, and no shielding exists on the propagation path of the reflection wave.
Further, step 4 includes the following:
the following redundant dictionary is constructed by using the direct echo guide vectors and the reflected wave guide vectors corresponding to all pitch angle grid points (the grid point L is far greater than the target number D):
A＝[A 1 A 2 … A L ]
where a (θ) represents an mx 1-dimensional receive array steering vector of the radar when the pitch angle of the incident signal is θ, which may be either a time-array element domain steering vector (M corresponds to the number of antenna elements), a subarray domain steering vector (M corresponds to the number of subarrays), or a beam domain steering vector (M corresponds to the number of beams); record A l Is of the column number J l The column number of A is K, then J l ＝1,2，Whereas dictionary a is composed of blocks a with a column number of typically 2 l Regularly formed, a may be referred to as a structured dictionary.
In fact, the basic situation (L.ltoreq.K.ltoreq.2L) that there is no reflection path and only one reflection path is considered here, if the actual topography is more complex, there may be multiple reflection paths, and only the dictionary needs to be correspondingly expanded at this time. The number of grid points L adopted in the embodiment is 601, and after reflection path analysis, the final dictionary column number K is 1174; the radar receiving array is a uniform linear array which is vertically arranged, the number M of antenna units is 256, the unit spacing is half wavelength, and the specific expression of the guiding vector is as follows:
further, step 5 includes the following:
based on the mxk-dimensional dictionary a given in step 4, the radar (array element domain/subarray domain/beam domain) reception data X can be modeled as:
X＝AS+N
wherein, X is composed of distance domain data (unit of distance R) after pulse pressure of each channel, and the column number corresponds to pulse number P (also called sampling snapshot number); n is MxP Vegarian GaussianWhite noise; s is a KXP dimensional signal matrix, and can be divided into blocks according to rows by referring to the block rule of AS l Is J l The x P-dimensional signal matrix, the operator "T" represents the transpose of the matrix. S is S l Line 1 s of (2) l1 Corresponding pitch angle is theta l P samples of target echo of J l =2, then S l Line 2 s of (2) l2 P samples corresponding to its reflected wave; since the target direct echo is homologous to the reflected wave, the two ideally differ by only a complex constant ρ (called multipath fading factor), s l2 ≈ρs l1 (usually |ρ| < 1), ρ is actually the result of the combination of attenuation due to the difference in wave path and propagation medium, surface reflection characteristics, reception gains at different angles of incidence, and the like. It can be seen that when the grid angle θ l When there is a target on the S l The system consists of a target echo and a reflected wave thereof, and is a non-zero matrix; otherwise, S l =0. Because the number of targets D is limited, the number of self-defined grid points L can be far greater than D, and S is necessarily a block sparse matrix with most blocks being zero, so that as long as the signal matrix S is restored, the target pitch angle theta can be determined through the positions of non-zero blocks, and the information such as multipath fading factors rho, target inter-pulse amplitude-phase fluctuation characteristics and the like can be obtained based on the data of the non-zero blocks.
Further, step 6 includes the following:
to recover the block sparse signal matrix S, the following convex combination optimization problem is established:
wherein I F The Frobenius norm representing the matrix (degenerated to l for vectors 2 A norm); weights w for penalty terms for each block l Given by the formula:
wherein the operator "tr { }" represents the trace of the matrix, the covariance matrix estimate R is given by:
wherein,,diag (p) represents a diagonal matrix constructed with vector p as a diagonal element; power vector p= [ p ] 1 p 2 … p k ] T The elements in (a) are->The optimization model has no super parameters which need to be manually adjusted or optimized, and complex operations such as cross verification and the like are avoided.
In particular, the above-mentioned fast solution of the convex optimization problem may employ a first-order value optimization algorithm, such as an improved block coordinate descent method, a linearization alternate direction multiplier method (L-ADMM, or P-ADMM), an original dual hybrid gradient method (PDHG), or a related improved algorithm, which has the advantage that the solution process does not involve complex operations such as matrix inversion, and the computational complexity does not explosively increase with the increase of dictionary dimensions and snapshot numbers. In addition, before the algorithm iteration starts, the initial value S of the matrix S to be restored (0) Can be given by a linear minimum mean square error estimator (LMMSE): s is S (0) ＝Diag(p)·A H R -1 X is a metal alloy. The embodiment adopts PDHG algorithm based on correction penalty function and Nesterov method acceleration to solve.
Further, step 7 includes the following:
block sparse signal matrix based on recoveryThe spatial spectrum can be given by:
or->Pitch angle estimation of D targets +.>Can be according to Z (theta) l ) Position of the larger peak in ∈ ->Determination, i.e.)>Further, the signal matrix estimate may be modified as follows:
wherein,,the inter-pulse fluctuation characteristic of the d-th target echo can be determined by +.>Line 1 (denoted +.>) Is given; if->The number of lines of (i.e. the object has a reflection path) is 2, the 2 nd behavior is recorded +.>The corresponding multipath fading factor can be defined by +.>Given.
In conclusion, the low-altitude multipath target super-resolution elevation estimation method based on block sparse modeling is suitable for radar low-altitude target high-precision direction finding positioning under complex terrain conditions. The method effectively utilizes the topographic information to improve the accuracy of a multipath propagation model, establishes a structured sparse representation model, and proposes a rapid self-adaptive block sparse recovery algorithm to ensure the estimation performance and reliability under the conditions of strong correlation of echoes and few shots (even single shots); the method does not need to know the number of targets and the surface reflection characteristic, can provide information such as multipath attenuation factors, inter-pulse fluctuation characteristics and the like while finishing high-precision and super-resolution elevation estimation of multiple targets, and is not limited by the arrangement mode and system of a radar receiving array.
The effects of the present invention were confirmed by the following examples and simulation experiments.
FIG. 5 shows spatial spectral contrast for different methods with a target number of 2, a signal-to-noise ratio of 10dB, and a snapshot number of 64, wherein the target distance is 8 km from the radar, the pitch angles of the radar are respectively + -0.05 DEG, the receiving array is a uniform linear array with 256 units and half-wavelength intervals, and the beam width is about 0.4 DEG; the signal-to-noise ratio is defined as the ratio of the direct echo to the noise power of a certain target in a single receive channel; because the radar receiving data is the distance domain data of the specific unit after pulse compression, the snapshot number corresponds to the pulse number; "unstructured model" refers to the inclusion of all possible target pitch angles and reflected wave pitch angles indiscriminately into the grid ("structured model" and "unstructured model" grid ranges of-1 deg. -2 deg. and-2.87 deg. -2 deg., respectively), and the unified view of them as targets for elevation estimation. It can be seen that when an unstructured model is adopted, no matter a multi-signal classification (MUSIC) algorithm or a sparse recovery algorithm is adopted for angle estimation, although a spatial spectrum has spectrum peaks on a pitch angle where a target is located and a pitch angle where a reflected wave is located (located at-0.98 degrees and-1.35 degrees), higher false peaks can occur on other angles (especially the noise bottom of the MUSIC algorithm is obviously raised, which is caused by strong correlation between a homologous direct echo and the reflected wave), and the judgment of a final estimation result is affected; in contrast, when the "structured model" mentioned in this patent is adopted, both the MUSIC algorithm and the proposed algorithm can be used to obtain a "clean" spatial spectrum and accurate super-resolution angle estimation (target spacing of about 1/4 beam width), and the proposed method has almost no spurious peaks.
Fig. 6 and 7 show the target echo amplitude-phase heave characteristics estimated by the method presented in this patent under the simulation conditions of fig. 5. It can be seen that the proposed method can accurately invert the amplitude and phase fluctuation characteristics of the target echo while obtaining the elevation angle estimation. In addition, in the simulation, the amplitude and the phase of the two target multipath fading factors are (0.5918, 103.3593 degrees) and (0.5303-55.2548 degrees), and the estimation values given by the method are (0.5918, 103.3104 degrees) and (0.5314-55.3880 degrees), respectively, so that the multipath fading factors of all targets can be accurately estimated by the method.
Figure 8 shows the spatial spectrum of the proposed method with a signal to noise ratio of-5 dB and a snapshot number of 64. It can be seen that under the condition of low signal-to-noise ratio, although the spatial spectrum given by the MUSIC algorithm based on the unstructured model and the sparse recovery algorithm based on the structured model has spectrum peaks at the target angles, a large number of pseudo peaks exist at other angles at the same time, and the heights of the pseudo peaks may even exceed the heights of the target spectrum peaks, so that reliable elevation estimation results cannot be obtained; in contrast, the method provided by the invention can still realize reliable and accurate super-resolution elevation angle estimation.
Fig. 9 shows the spatial spectrum of the proposed method with a signal-to-noise ratio of 10dB and a snapshot number of 1. It can be seen that under the single snapshot condition, the sparse recovery algorithm based on the structured model still has the problem of false peaks, and cannot provide a reliable elevation estimation result; while MUSIC algorithms based on "unstructured models" are even totally ineffective due to covariance matrix rank deficiency (in this case, pretreatment by spatial smoothing etc. is needed, but such operations will lead to aperture loss); in contrast, the method provided by the patent can still provide reliable and accurate estimation results, and single-pulse super-resolution elevation estimation of the low-altitude target is realized.
The present invention is not limited to the above-mentioned embodiments, and any changes or substitutions that can be easily understood by those skilled in the art within the technical scope of the present invention are intended to be included in the scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.
Claims (9)
1. The low-altitude multipath target super-resolution elevation estimation method based on block sparse modeling is characterized by comprising the following steps of:
step 1, establishing a rectangular coordinate system in a plane where an echo propagation path is located based on positioning and orientation information of a radar and azimuth measurement value of the radar to a target;
step 2, extracting a topographic curve in a preset distance range in the direction of a target from a geographic information system;
step 3: grid division is carried out on the airspace of interest in the pitching dimension, the effectiveness of reflection paths corresponding to each pitching angle is analyzed by combining the distance measurement value and the topography curve, and the incidence pitching angle of the reflection waves is calculated;
step 4: constructing a structured redundant dictionary by using direct echo steering vectors and reflected wave steering vectors corresponding to all pitch angles of interest;
step 5: establishing a structured sparse representation model of radar array element domain, subarray domain or beam domain received data;
step 6: solving a convex combination optimization problem by adopting a first-order rapid algorithm, and recovering a block sparse signal matrix;
step 7: and obtaining an elevation angle estimated value of the target based on the restored block sparse signal matrix, and further obtaining an attenuation factor of the reflection path and inter-pulse amplitude-phase fluctuation characteristics of the target echo according to requirements.
2. The low-altitude multipath target super-resolution elevation estimation method based on block sparse modeling according to claim 1, wherein step 1 comprises:
acquiring longitude, latitude, altitude and antenna array orientation information of a radar positioning and orientation device, estimating azimuth angle of a target by adopting a monopulse angle measurement technology, and acquiring the azimuth angle of the target in the directionAnd establishing a rectangular coordinate system in a plane perpendicular to the ground plane, wherein the coordinate origin is the position with the longitude/latitude and the altitude of 0 of the radar. The radar coordinates are (x) R ,y R ) Wherein x is R ＝0，y R Corresponding to the altitude of the radar antenna/array.
3. The low-altitude multipath target super-resolution elevation estimation method based on block sparse modeling according to claim 2, wherein step 2 comprises:
extracting from the geographic information system a topographic curve within the coordinate plane and within a range of distances of interest in the vicinity of the radar, said topographic curve being a set of points divided at a resolution due to the discreteness of the digital map: { (x) n ,y n )|n＝1,2,...,N}。
4. The low-altitude multipath target super-resolution elevation estimation method based on block sparse modeling of claim 3, wherein step 3 comprises:
dividing the airspace of interest into grids { theta } at certain intervals in the pitch dimension l I l=1, 2, &..l }, calculating the position coordinates (x T ,y T )＝(x R +Rcosθ,y R +Rsin θ) and further analyzing each grid angle θ in combination with the topography profile l Corresponding reflection path effectiveness and corresponding reflection wave incidence pitch angle theta l ′；
The method for analyzing the effectiveness of the reflection path and the incidence pitch angle of the reflection wave comprises the following steps:
(1) defining a range of potential reflection points based on a range difference constraint of the target direct echo and the reflected wave: in view of the fact that the direct echo and the reflected wave can be distinguished by the distance when the wave path difference is large, the difference between the constrained reflection path length and the target distance measurement value is not more than a plurality of distance resolution units, namely d R +d T ≤R+ΔR max Wherein d R D is the distance from the reflection point to the radar T For the distance of the reflection point to the target ΔR max Distance resolutionThe ratio is 1-3 times. Constrained set of potential reflection point coordinatesExpressed as:
(2) calculating the tangential slope at each point of the topographic curve: let the distances from the adjacent points to the tangent line are equal, then (x n ,y n ) Tangential slope k at n ＝(y n+1 -y n-1 )/(x n+1 -x n-1 ) The method comprises the steps of carrying out a first treatment on the surface of the Or taking the average of the slopes of the connecting lines between the point and the left and right adjacent points respectively, and the corresponding slope expression is
(3) Determining reflection point position coordinates based on the geometric relationship: under the assumption of ideal specular reflection, a certain point (x, y) is the condition that an angular bisector of the connecting line included angle between the target and the reflecting point and between the reflecting point and the radar coincides with the normal line of a terrain curve at the reflecting point, the angular bisector and the connecting line between the target and the radar are obtained by an angular bisector theorem and a fixed ratio dividing point formula, and the intersection point coordinates of the angular bisector and the connecting line between the target and the radar are as follows:
if the line between the point and the reflection point (x, y) is perpendicular to the tangent of the topographic curve, the slope of the tangent is k, then there is:
k(y C -y)＝x-x C ，
the finishing results are that (x, y) is the following condition:
the position coordinates of the reflection point corresponding to the target with the pitch angle theta are determined based on the following formula:
wherein,,representation set->An element that minimizes the absolute value of f;
(4) calculating the precise coordinates of the reflection point by interpolation: if the map resolution does not meet the requirement, interpolating the topographic curve in the neighborhood of the reflection point with the expected high resolution, and repeating the sub-steps (1) - (3), wherein the finally obtained coordinates of the reflection point are still recorded as (x) θ ,y θ )；
(5) Judging the effectiveness of the reflection path and calculating the incidence pitch angle of the reflection wave: considering that there may be a shadow on the reflection path, resulting in reflected waves not being received by the radar, the effective reflection path must satisfy: coordinate set of potential reflection pointsNot empty, and for any +.>The following holds:
therefore, it is determined based on this whether or not the multipath effect exists at the target pitch angle θ. If the reflection path is valid, the incident pitch angle θ' of the reflected wave is: θ' =arctan [ (y) θ -y R )/(x θ -x R )]；
Wherein, if roughly considered to be absolutely flat, i.e. the mirror plane is parallel to the ground plane: y=y n The above analysis method of the coordinates of the reflection point is simplified as follows: the wave path difference constraint in the substep (1) is rewritten asSubstep (2) omitted, consider k n Constant zero; the reflection point position coordinate expression in the substep (3) is rewritten as:
5. the low-altitude multipath target super-resolution elevation estimation method based on block sparse modeling of claim 4, wherein step 4 comprises:
the direct echo guide vector and the reflected wave guide vector corresponding to all pitch angle grid points are utilized to construct the following redundant dictionary, and the grid number L is far greater than the target number D:
A＝[A 1 A 2 … A L ]
wherein a (theta) represents an M multiplied by 1 dimension receiving array steering vector of the radar when the pitch angle of the incident signal is theta, and if a (theta) is an array element domain steering vector, M corresponds to the number of antenna elements; if a (θ) isThe subarray domain guide vector is M corresponding to the number of subarrays; if a (θ) is a beam domain steering vector, M corresponds to the number of beams; record A l Is of the column number J l The column number of A is K, then J l ＝1,2，Whereas dictionary a is composed of blocks a with a column number of typically 2 l Regularly formed, a may be referred to as a structured dictionary.
6. The low-altitude multipath target super-resolution elevation estimation method based on block sparse modeling of claim 5, wherein step 5 comprises:
based on the m×k dimensional dictionary a given in step 4, the received data X of the radar array element domain, the subarray domain, or the beam domain is modeled as:
X＝AS+N，
wherein X is composed of distance domain data after pulse pressure of each channel, and the column number corresponds to the pulse number P; n is M x P Viga Gaussian white noise; s is a KXP dimensional signal matrix, and can be divided into blocks according to rows by referring to the block rule of AS l Is J l X P dimensional signal matrix, operator "T" representing the transpose of the matrix; s is S l Line 1 s of (2) l1 Corresponding pitch angle is theta l P samples of target echo of J l =2, then S l Line 2 s of (2) l2 P samples corresponding to its reflected wave; due to the homology of the target echo to the reflected wave, the two ideally differ by only one complex constant ρ, s, determined by the spatial propagation characteristics and the surface reflection characteristics l2 ＝ρs l1 The method comprises the steps of carrying out a first treatment on the surface of the When the grid angle theta l When there is a target on the S l The system consists of a target echo and a reflected wave thereof, and is a non-zero matrix; otherwise, S l =0; because the target number D is limited and the number L of the self-defined grid points is far greater than D, S is necessarily a block sparse matrix with most of blocks being zero, the target pitch angle theta can be determined by the positions of non-zero blocks in the matrix S as long as the signal matrix S is restoredAnd acquiring multipath fading factor rho and target inter-pulse amplitude-phase fluctuation characteristic information based on the data of the non-zero blocks.
7. The low-altitude multipath target super-resolution elevation estimation method based on block sparse modeling of claim 6, wherein step 6 comprises:
to recover the block sparse signal matrix S, the following convex combination optimization problem is established:
wherein I F The Frobenius norm representing the matrix degenerates to l for the vector 2 A norm; weights w for penalty terms for each block l Given by the formula:
wherein the operator "tr { }" represents the trace of the matrix, the covariance matrix estimate R is given by:
wherein,,diag (p) represents a diagonal matrix constructed with vector p as a diagonal element; power vector p= [ p ] 1 p 2 … p k ] T The elements in (a) are->
8. The low-altitude multipath target super-resolution elevation angle based on block sparse modeling of claim 7The estimation method is characterized in that a first-order value optimization algorithm is adopted for rapid solution of the convex optimization problem, and the estimation method comprises the following steps: an improved block coordinate descent method, a linearization alternate direction multiplier method and an original dual mixed gradient method; before algorithm iteration starts, the initial value S of matrix S to be recovered (0) Given by a linear minimum mean square error estimator (LMMSE): s is S (0) ＝Diag(p)·A H R -1 X。
9. The low-altitude multipath target super-resolution elevation estimation method based on block sparse modeling according to claim 1, wherein step 7 comprises:
block sparse signal matrix based on recoveryThe spatial spectrum is given by:
or->
Pitch angle estimation for D targetsCan be according to Z (theta) l ) Position of the larger peak in ∈ ->Determination, i.e.The signal matrix estimate is modified as follows:
wherein,,the inter-pulse fluctuation characteristic of the d-th target echo is marked by + ->Is->Is given in line 1; if->The number of lines of (2), i.e. the object has a reflection path, the 2 nd behavior is recorded +.>The corresponding multipath fading factor is defined by +.>Given.
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