CN110058202B - High-performance hybrid positioning method based on angle and signal arrival time difference estimation and implementation device thereof - Google Patents

High-performance hybrid positioning method based on angle and signal arrival time difference estimation and implementation device thereof Download PDF

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CN110058202B
CN110058202B CN201910410716.1A CN201910410716A CN110058202B CN 110058202 B CN110058202 B CN 110058202B CN 201910410716 A CN201910410716 A CN 201910410716A CN 110058202 B CN110058202 B CN 110058202B
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angle
array
target
estimation
arrival
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CN110058202A (en
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熊海良
庄众
侯强
任美婷
龚舒
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Shandong University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • 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
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/021—Auxiliary means for detecting or identifying radar signals or the like, e.g. radar jamming signals
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • 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
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/003—Bistatic radar systems; Multistatic radar systems
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00—Reducing energy consumption in communication networks
    • Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks

Abstract

The invention relates to a high-performance hybrid positioning method based on angle and signal arrival time difference estimation and a realization device thereof, which comprises the following steps: (1) Realizing the estimation of the angle of arrival of the target based on the MIMO bistatic radar, and describing the estimation error of the target position caused by the estimation of the angle of arrival; (2) Considering the signal arrival time difference of the system, and describing the relation between the signal arrival distance error and the target coordinate in the TDOA estimation; (3) And constructing a loss function by utilizing least square, and obtaining a target coordinate. According to the invention, a unitary matrix is introduced based on a signal model of the bistatic radar, so that the operation efficiency is improved; the accuracy of angle estimation is improved through sharing the feature vector; the algorithm of the joint positioning of two parameters of angle and signal reaching time difference improves the accuracy of target position estimation and reduces the requirement on the number of the receiving arrays.

Description

High-performance hybrid positioning method based on angle and signal arrival time difference estimation and implementation device thereof
Technical Field
The invention relates to a high-performance hybrid positioning method based on angle and signal arrival time difference estimation and an implementation device thereof, belonging to the technical field of navigation and positioning.
Background
The positioning method is widely applied to various fields of military war, urban management, civilian use, geology, rescue and relief work and the like. Among them, radio detection and positioning technology is concerned by students at home and abroad. The radio detection and positioning technology based on electromagnetic wave parameters mainly comprises angle estimation (DOA), signal arrival time difference estimation (TDOA) and received signal strength estimation (RSS), and the three methods can realize independent positioning. The signal arrival time difference estimation requires clock synchronization and at least 3 receiving arrays, the receiving signal intensity estimation is sensitive to the channel environment, and the joint positioning algorithm aiming at the angle estimation generally requires angle pairing of the transmitting array and the receiving array, so that higher operation complexity can be generated, and the joint positioning combines the advantages of each positioning technology and avoids the defects as much as possible, thereby playing an increasingly important role in simultaneously improving the positioning accuracy and the operation efficiency.
The angle estimation algorithm mainly comprises the following steps: multiple signal classification (MUSIC) algorithms find the target angle by searching spatial spectral peaks, but also result in higher complexity, and subsequent scholars have developed several expansion algorithms such as orthogonal vector method, root MUSIC algorithm, etc. taking these drawbacks into account. The rotation invariant subspace (ESPRIT) algorithm refines angle information by rotating the invariant matrix, and is divided into a least square ESPRIT algorithm and a total least square ESPRIT algorithm according to the difference of the modes of acquiring the angle information. And then, introducing a unitary matrix to develop into a unitary ESPRIT algorithm, and reducing the operation complexity by converting a complex matrix in the operation process into a real matrix. In MIMO bistatic radar systems, a joint estimation method of the angle of departure (DOD) and the angle of arrival is generally adopted. Aiming at the problem of angle estimation of joint DOD and DOA in a radar system, a MUSIC algorithm and an ESPRIT algorithm are respectively developed into a 2D MUSIC algorithm and a 2D ESPRIT algorithm. The 2D MUSIC algorithm significantly reduces the operation efficiency, and later further develops into an RD MUSIC algorithm that reduces the operation complexity.
With the increasing wide application of array signal processing technology, improvement and popularization of the method are proposed by academia. Wu Qihui et al of the university of Lewy et al propose a generic, reciprocal planar array and propose a local spectral search method to estimate the two-dimensional angle of arrival, but spectral search can lead to a dramatic increase in computation. Yang Xiaopeng et al of Beijing university propose DOA estimation methods based on joint singular value decomposition, effectively reducing the computation time and improving the robustness of angle estimation. Zheng Wang et al of Nanjing aerospace university uses the ESPRIT algorithm to initialize DOA and combines the received data of multiple sub-arrays to provide an AF MUSIC algorithm, thereby further improving the degree of freedom and the accuracy of DOA estimation. The scholars of the western electronic technology university combine the time reversal technology and the coherent signal subspace method to provide a low-pitch angle estimation algorithm aiming at a multipath environment, and the method has better robustness aiming at the conditions of a slow moving target, channel mismatch, other channel noise and the like, but the change of the topography in a complex environment can influence the angle estimation.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a high-performance hybrid positioning method based on angle and signal arrival time difference estimation;
the invention also provides a device for realizing the hybrid positioning method;
the scheme provides an innovative algorithm with lower operation complexity based on a unitary ESPRIT algorithm, and reduces the influence of terrain on estimation performance through a bistatic deployment model and far-field target setting. The invention aims to improve the accuracy and the operation efficiency of target position estimation, and provides a joint estimation algorithm for eliminating a pairing process around a multi-input multi-output bistatic radar improved wave separation direction and wave arrival direction joint estimation technology, and the target position is positioned jointly by combining two parameters of angle and signal arrival time difference, so that the positioning performance is effectively improved.
Term interpretation:
1. MIMO (Multiple-Input Multiple-Output) refers to using Multiple transmitting antennas and receiving antennas at a transmitting end and a receiving end, respectively, so that signals are transmitted and received through the Multiple antennas at the transmitting end and the receiving end, thereby improving communication quality.
2. U-ESPRIT algorithm, unitary rotation invariant subspace algorithm;
3. DOD, wave separation angle;
4. DOA, angle of arrival.
The technical scheme of the invention is as follows:
a high-performance hybrid positioning method based on angle and signal arrival time difference estimation comprises the following steps:
(1) Realizing the estimation of the angle of arrival of the target based on the MIMO bistatic radar, and describing the estimation error of the target position caused by the estimation of the angle of arrival; the MIMO bistatic radar system is based on a unitary matrix, a classical high-resolution angle estimation algorithm is improved into a DOA estimation method with lower operation complexity and higher positioning accuracy by sharing feature vectors of a transmitting end and a receiving end, and meanwhile, the relation between a target coordinate and a position error is determined according to a relational expression of a wave arrival angle, a transmitting array coordinate and the target coordinate.
(2) Considering the signal arrival time difference of the radar deployment model, and describing the relationship between the signal arrival distance error and the target coordinates in the TDOA estimation;
(3) And constructing a loss function by utilizing least square, and obtaining a target coordinate.
The invention utilizes the relation between the angle information, the signal arrival time difference parameter and the estimated time error to correlate the position error and the signal arrival distance error with the target coordinates, and utilizes least square to realize the target position positioning.
According to a preferred embodiment of the invention, step (1) comprises the steps of:
obtaining an estimated value of the angle of arrival through a D0D and DOA joint estimation algorithm;
analyzing the relation among the arrival angle, the target coordinates and the receiving array coordinates by the triangular structures of the transmitting array, the target and the receiving array;
and describing a relation among the target coordinates, the target position error and the angle of arrival.
According to a preferred embodiment of the present invention, step (2) means:
obtaining signal arrival time difference and time arrival time error according to a TD0A algorithm;
analyzing the signal arrival distance height error according to the signal arrival time error;
the relation between the signal arrival distance error and the target coordinates is described.
According to a preferred embodiment of the invention, step (1) comprises the steps of:
A. based on the MIMO bistatic radar, a radar deployment model is deployed, the radar deployment model comprises a target, a transmitting array, a 1 st receiving array and a 2 nd receiving array, the transmitting array, the 1 st receiving array and the 2 nd receiving array are respectively arranged in different areas, the transmitting array, the 1 st receiving array and the 2 nd receiving array all comprise a plurality of array elements, the target is set as a far-field target, namely, the azimuth angles of each array element in the transmitting array, the 1 st receiving array and the 2 nd receiving array are regarded as equal, and a receiving array output signal model X is established, as shown in a formula (I):
in the formula (I), X 1 Refers to the output signal of the 1 st receiving array, X 2 Refers to the output signal of the 2 nd receiving array, A 1 Refers to a guide matrix of a system formed by a 1 st receiving array and a transmitting array, A 2 The system is characterized in that the system comprises a 2 nd receiving array and a transmitting array, S refers to a source signal matrix, and N refers to a sampling sample of additional sensor noise;
B. introducing unitary matrix Q to convert the output signals of 1 st receiving array and 2 nd receiving array into real matrix Y 1 、Y 2 The compounds are respectively shown as a formula (II) and a formula (III):
in the formulas (II) and (III),refers to the conjugate transpose of unitary matrix with dimension M of the number of elements of the transmit array, +.>Is the number N of the receiving array elements with the dimension of 1 st 1 Conjugation of unitary matrix of (2)Transpose (S)>Refers to the number N of array elements of the 2 nd receiving array 2 Is a conjugate transpose of the unitary matrix of (a);
C. according to a classical U-ESPRIT algorithm, a matrix containing DOD and DOA information is obtained, wherein the matrix is respectively shown as a formula (IV) and a formula (V):
in the formulas (IV) and (V), Σ t Refers to a matrix containing the information of the angle of departure, K i1 And K i2 Respectively representI=1, 2, < ->0 represents a matrix with elements 0, I represents a unit matrix, E si Representing a signal subspace constructed by a system consisting of a transmitting array and an ith receiving array, the signal subspace being obtained by: by matrix Y i Performing eigenvalue decomposition, arranging eigenvalues obtained by eigenvalue decomposition from large to small, taking eigenvectors corresponding to the previous P eigenvalues to form signal components, and constructing signal subspace, Σ ri Refers to a matrix containing angle of arrival information for signals arriving at the ith receive array, and K i3 And K i4 Respectively indicate->Real and imaginary parts of>
The relational expression is shown as the formula (VI) and the formula (VII):
in the formulas (VI) and (VII),and is also provided with
Λ t Including the wave separation angle, lambda ri Angle of arrival, d, comprising the ith receive array t Represents the distance between adjacent array elements in the transmitting array, d r Represents the distance between the adjacent array elements of the ith receiving array, the distances between the adjacent array elements in the 1 st receiving array and the 2 nd receiving array are the same, lambda represents the wavelength, theta p The wave separation angle of the P-th target, p=1, 2,..p, P represents the number of targets;representing the angle of arrival of the p-th target at the i-th receive array;
performing eigenvalue decomposition on the formula (VI) and the formula (VII) to obtain direct estimated values of DOD and DOA; at the same time, use sigma t Sum sigma ri In the same matrix T i Reducing pairing, i.e. computing the matrix T generated when DOA i Substituting formula (VI) to solve the matching estimation value of DOD, and calculating matrix T generated in DOD process i Substituting formula (VII) to calculateSolving a matching estimation value of DOA;
carrying out arithmetic average on the direct estimated value of DOD and the matching estimated value of DOD to obtain a final estimated value of the wave separation angle; and carrying out arithmetic average on the direct DOA estimated value and the DOA matching estimated value to obtain a final estimated value of the angle of arrival.
D. According to the radar deployment model, the transmitting array, the real target and the ith receiving array are regarded as triangles, and a relation exists, as shown in a formula (VIII):
in the formula (VIII), the length of the corner edge of the estimated value of the actual target distance wave arrival angle is marked as d i The distance of the target from the ith receive array is denoted by r i The angle of arrival of the ith receive array has a true value ofThe estimated value of the angle of arrival is marked as +.>
Setting the coordinates of the target to (x) t ,y t ) The coordinates of the ith receive array are (x i ,y i ) Expanding formula (VIII) to formula (IX):
according to the preferred embodiment of the present invention, step (2), the signal arrival time difference of the radar deployment model is considered, and the signal arrival distance error in the TDOA estimation (i.e., n mentioned below is described TDOA ) The relation with the target coordinates comprises the following steps:
assume that the time required for the electromagnetic wave transmitted by the transmitting end to be received by the ith receiving end after being reflected by the unmanned aerial vehicle is t i The time required for the electromagnetic wave to be directly received by the ith receiving end after being transmitted by the transmitting end is t' i The difference between the time taken by the two propagation modes is Deltaτ i ＝t i -t′ i The distance difference between the two propagation modes is s Δi ＝cΔτ i The method comprises the steps of carrying out a first treatment on the surface of the c is the propagation speed of electromagnetic wave and has the relation s Δi +s i ＝s+r i +n TDOA ，n TDOA Representing the error in the propagation process, and the distance between the target and the transmitting end is s and meets the following requirementsThe distance between the transmitting array and the ith receiving array is s i ；
Let s be Δi,O ＝s Δi +s, willSubstitution of s Δi,O ＝s Δi +s i ＝s+r i +n TDOA And assume
Substitution into formula s Δi,O ＝s Δi +s i ＝s+r i +n TDOA And simultaneously square the two sides of the equal sign, as shown in formula (X):
constructing a relational expression according to formulas (IX) and (X), and obtaining a relational expression describing the arrival distance error of the signal and the target coordinates, wherein the relational expression is shown as a formula (XI):
Ax T +q＝b (Ⅺ)
in the formula (XI),
according to the present invention, preferably, step (3) of constructing a loss function by least squares and obtaining the target coordinates means:
constructing a loss function as shown in formula (XII):
in the formula (XII),
C TDOA a covariance matrix representing errors in the TDOA estimation process;
according to a preferred embodiment of the present invention, in step (3), the target coordinates are obtained by:
obtaining an estimated value of the target position coordinate, namely the target coordinate by utilizing a least square idea; as shown in formula (XIII):
thus, the invention can realize the position positioning of the target by utilizing one transmitting array and two receiving arrays.
The device for realizing the hybrid positioning method comprises a signal preliminary processing module, a target azimuth angle estimation module, a TDOA estimation module and a joint estimation module; the signal preliminary processing module is respectively connected with the target azimuth angle estimation module and the TDOA estimation module, and the target azimuth angle estimation module and the TDOA estimation module are both connected with the joint estimation module;
the signal preliminary processing module is used for: sampling echo signals, representing array output signals into a matrix form, and carrying out real-number operation on the matrix;
the target azimuth estimation module is used for: obtaining a matrix containing DOD and DOA information by using a U-ESPRIT algorithm, decomposing a characteristic value of the matrix to obtain an azimuth direct estimated value, carrying out sharing operation on the characteristic vector to obtain an azimuth matching estimated value, and averaging the direct and matching estimated values to obtain a final azimuth estimated value; and analyzing the spatial relationship among the transmitting array, the airplane and the receiving array, extracting the relationship among the arrival angle, the target coordinate and the receiving array coordinate, and obtaining the relationship among the target coordinate, the airplane position error and the arrival angle.
The TDOA estimation module is used for: and obtaining a signal arrival time difference and a signal arrival time error according to the TDOA algorithm, analyzing a signal arrival distance error according to the signal arrival time error, and describing a relation between the signal arrival distance error and the target coordinates.
The joint estimation module is used for: and processing the relation between the target azimuth angle estimation module and the TDOA estimation module, and obtaining the position coordinates of the target by using a least square method.
The beneficial effects of the invention are as follows:
1. according to the method, the radar deployment characteristics are utilized, the characteristic vector is shared in the angle estimation process, the matching process of the transmitting array and the receiving array in DOD and DOA joint estimation is reduced, and further the operation efficiency and the angle estimation accuracy are improved.
2. The invention utilizes the spatial position relation among the transmitting array, the target and the receiving array, combines the angle estimation and the signal arrival time difference estimation, describes the relation between the target coordinates and the errors, utilizes least square to obtain the target position, and improves the target positioning performance compared with TDOA estimation.
3. The number of the receiving arrays is required to be not less than 3 when the TDOA is estimated, but the invention reduces the requirement on the number of the receiving arrays by introducing the angle parameter, and can realize target positioning when only two receiving arrays are arranged.
Drawings
FIG. 1 is a schematic diagram of a radar deployment of the present invention;
FIG. 2 is a schematic flow chart of DOD and DOA joint angle estimation;
FIG. 3 is a flow chart of a high performance hybrid positioning method based on angle and signal arrival time difference estimation according to the present invention;
FIG. 4 is a block diagram of a device for implementing the hybrid positioning method of the present invention;
FIG. 5 is a schematic diagram of a radar deployment according to an embodiment of the present invention;
FIG. 6 is a schematic diagram of an embodiment of the invention for estimating performance.
Detailed Description
The invention is further defined by, but is not limited to, the following drawings and examples in conjunction with the specification.
Example 1
A high performance hybrid positioning method based on angle and signal arrival time difference estimation, as shown in fig. 3, comprising the steps of:
(1) Realizing the estimation of the angle of arrival of the target based on the MIMO bistatic radar, and describing the estimation error of the target position caused by the estimation of the angle of arrival; the MIMO bistatic radar system is based on a unitary matrix, a classical high-resolution angle estimation algorithm is improved into a DOA estimation method with lower operation complexity and higher positioning accuracy by sharing feature vectors of a transmitting end and a receiving end, and meanwhile, the relation between a target coordinate and a position error is determined according to a relational expression of a wave arrival angle, a transmitting array coordinate and the target coordinate. The method comprises the following steps:
obtaining an estimated value of the angle of arrival through a D0D and DOA joint estimation algorithm;
analyzing the relation among the arrival angle, the target coordinates and the receiving array coordinates by the triangular structures of the transmitting array, the target and the receiving array;
and describing a relation among the target coordinates, the target position error and the angle of arrival.
(2) Considering the signal arrival time difference of the radar deployment model, and describing the relationship between the signal arrival distance error and the target coordinates in the TDOA estimation; the method comprises the following steps:
obtaining signal arrival time difference and time arrival time error according to a TD0A algorithm;
analyzing the signal arrival distance height error according to the signal arrival time error;
the relation between the signal arrival distance error and the target coordinates is described.
(3) And constructing a loss function by utilizing least square, and obtaining a target coordinate.
The invention utilizes the relation between the angle information, the signal arrival time difference parameter and the estimated time error to correlate the position error and the signal arrival distance error with the target coordinates, and utilizes least square to realize the target position positioning.
Example 2
A high performance hybrid positioning method based on angle and signal arrival time difference estimation according to embodiment 1, which is different in that:
step (1), comprising the steps of:
A. based on the MIMO bistatic radar, a radar deployment model is deployed, as shown in fig. 1, the radar deployment model comprises a target, a transmitting array, a 1 st receiving array and a 2 nd receiving array, the transmitting array, the 1 st receiving array and the 2 nd receiving array are respectively arranged in different areas, the transmitting array, the 1 st receiving array and the 2 nd receiving array all comprise a plurality of array elements, the target is set as a far-field target, namely, the azimuth angle of each array element in the transmitting array, the 1 st receiving array and the 2 nd receiving array is regarded as equal, and a receiving array output signal model X is established, as shown in a formula (I):
in the formula (I), X 1 Refers to the output signal of the 1 st receiving array, X 2 Refers to the output signal of the 2 nd receiving array, A 1 Refers to a guide matrix of a system formed by a 1 st receiving array and a transmitting array, A 2 The system is characterized in that the system comprises a 2 nd receiving array and a transmitting array, S refers to a source signal matrix, and N refers to a sampling sample of additional sensor noise;
B. as shown in fig. 2, unitary is introducedMatrix Q converts the output signals of the 1 st receiving array and the 2 nd receiving array into a real matrix Y 1 、Y 2 The compounds are respectively shown as a formula (II) and a formula (III):
in the formulas (II) and (III),refers to the conjugate transpose of unitary matrix with dimension M of the number of elements of the transmit array, +.>Is the number N of the receiving array elements with the dimension of 1 st 1 Conjugate transpose of unitary matrix of +.>Refers to the number N of array elements of the 2 nd receiving array 2 Is a conjugate transpose of the unitary matrix of (a);
C. according to a classical U-ESPRIT algorithm, a matrix containing DOD and DOA information is obtained, wherein the matrix is respectively shown as a formula (IV) and a formula (V):
in the formulas (IV) and (V), Σ t Refers to a matrix containing the information of the angle of departure, K i1 And K i2 Respectively representI=1, 2, < ->0 represents a matrix with elements 0, I represents a unit matrix, E si Representing a signal subspace constructed by a system consisting of a transmitting array and an ith receiving array, the signal subspace being obtained by: by matrix Y i Performing eigenvalue decomposition, arranging eigenvalues obtained by eigenvalue decomposition from large to small, taking eigenvectors corresponding to the previous P eigenvalues to form signal components, and constructing signal subspace, Σ ri Refers to a matrix containing angle of arrival information for signals arriving at the ith receive array, and K i3 And K i4 Respectively indicate->Real and imaginary parts of>
The relational expression is shown as the formula (VI) and the formula (VII):
in the formulas (VI) and (VII),and is also provided with
Λ t Including the wave separation angle, lambda ri Angle of arrival, d, comprising the ith receive array t Represents the distance between adjacent array elements in the transmitting array, d r Represents the distance between the adjacent array elements of the ith receiving array, the distances between the adjacent array elements in the 1 st receiving array and the 2 nd receiving array are the same, lambda represents the wavelength, theta p The wave separation angle of the P-th target, p=1, 2,..p, P represents the number of targets;representing the angle of arrival of the p-th target at the i-th receive array;
performing eigenvalue decomposition on the formula (VI) and the formula (VII) to obtain direct estimated values of DOD and DOA; at the same time, use sigma t Sum sigma ri In the same matrix T i Reducing pairing, i.e. computing the matrix T generated when DOA i Substituting formula (VI) to solve the matching estimation value of DOD, and calculating matrix T generated in DOD process i Substituting the DOA into a formula (VII) to solve the matching estimation value of the DOA;
carrying out arithmetic average on the direct estimated value of DOD and the matching estimated value of DOD to obtain a final estimated value of the wave separation angle; and carrying out arithmetic average on the direct DOA estimated value and the DOA matching estimated value to obtain a final estimated value of the angle of arrival.
D. According to the radar deployment model, the transmitting array, the real target and the ith receiving array are regarded as triangles, and a relation exists, as shown in a formula (VIII):
in the formula (VIII), the length of the corner edge of the estimated value of the actual target distance wave arrival angle is marked as d i The distance of the target from the ith receive array is denoted by r i The angle of arrival of the ith receive array has a true value ofAngle of arrival estimateMarked as->
Setting the coordinates of the target to (x) t ,y t ) The coordinates of the ith receive array are (x i ,y i ) Expanding formula (VIII) to formula (IX):
example 3
A high performance hybrid positioning method based on angle and signal arrival time difference estimation according to embodiment 1 or 2, which is different in that:
step (2), consider the signal arrival time difference of the radar deployment model and describe the signal arrival distance error in the TDOA estimation (i.e., n mentioned below TDOA ) The relation with the target coordinates comprises the following steps:
assume that the time required for the electromagnetic wave transmitted by the transmitting end to be received by the ith receiving end after being reflected by the unmanned aerial vehicle is t i The time required for the electromagnetic wave to be directly received by the ith receiving end after being transmitted by the transmitting end is t' i The difference between the time taken by the two propagation modes is Deltaτ i ＝t i -t′ i The distance difference between the two propagation modes is s Δi ＝cΔτ i The method comprises the steps of carrying out a first treatment on the surface of the c is the propagation speed of electromagnetic wave and has the relation s Δi +s i ＝s+r i +n TDOA ，n TDOA Representing the error in the propagation process, and the distance between the target and the transmitting end is s and meets the following requirementsThe distance between the transmitting array and the ith receiving array is s i ；
Let s be Δi,O ＝s Δi +s, willSubstitution of s Δi,O ＝s Δi +s i ＝s+r i +n TDOA And assume
Substitution into formula s Δi,O ＝s Δi +s i ＝s+r i +n TDOA And simultaneously square the two sides of the equal sign, as shown in formula (X):
constructing a relational expression according to formulas (IX) and (X), and obtaining a relational expression describing the arrival distance error of the signal and the target coordinates, wherein the relational expression is shown as a formula (XI):
Ax T +q＝b (Ⅺ)
in the formula (XI),
example 4
A high performance hybrid positioning method based on angle and signal arrival time difference estimation according to embodiment 1 or 2, which is different in that: step (3), constructing a loss function by utilizing least squares, and obtaining target coordinates, which are:
constructing a loss function as shown in formula (XII):
in the formula (XII),
C TDOA a covariance matrix representing errors in the TDOA estimation process;
obtaining target coordinates, namely:
obtaining an estimated value of the target position coordinate, namely the target coordinate by utilizing a least square idea; as shown in formula (XIII):
thus, the invention can realize the position positioning of the target by utilizing one transmitting array and two receiving arrays.
Example 5
A high performance hybrid positioning method based on angle and signal arrival time difference estimation according to embodiment 2, which is different in that: the embodiment model is shown in fig. 5, a transmitting end and three receiving ends are provided, wherein the coordinates of a radar antenna array of the transmitting end are (0, 0) m, the coordinates of a radar antenna array of the 1 st receiving end are (4000,0) m, the coordinates of a radar antenna array of the 2 nd receiving end are (5000, -500) m, and the coordinates of a radar antenna array of the 3 rd receiving end are (5500, -500) m. The target is set as an aircraft, the coordinates of which are (2000,4000) meters.
Electromagnetic waves are emitted by a sending end, reflected by an airplane to form echoes, received by three receiving ends, and subjected to data processing by the method to obtain the coordinates of the airplane, wherein the specific steps of the data processing are as follows:
1) The unitary matrix is utilized to convert the output signal matrix of the receiving array into a real matrix, the autocorrelation matrix of the real matrix is calculated, the real matrix is subjected to eigenvalue decomposition, eigenvalues obtained by eigenvalue decomposition are arranged from large to small, eigenvectors corresponding to the previous P eigenvalues are taken to form signal components, and a signal subspace is constructed.
2) And (3) calculating a formula (IV) and a formula (V), decomposing the characteristic values of the formula (IV) and the formula (V) to obtain a shared matrix T and a direct angle estimated value, and obtaining a matching angle estimated value by using the shared matrix.
3) And respectively carrying out arithmetic average on the wave separation angle and the wave arrival angle to obtain final estimated values of DOD and DOA.
4) The triangle structures of the transmitting array, the airplane and the receiving array analyze the relation among the arrival angle, the airplane coordinate and the receiving array coordinate, and describe the relation among the airplane coordinate, the airplane position error and the arrival angle.
5) And obtaining a signal arrival time difference and a signal arrival time error according to the TDOA algorithm, analyzing a signal arrival distance error according to the signal arrival time error, and describing a relation between the signal arrival distance error and the aircraft coordinates.
6) And obtaining the position coordinates of the aircraft by using a least square method for the relation in the step 5) and the step 6).
The estimated performance obtainable by computer simulation is shown in fig. 6. The abscissa σ represents the signal arrival distance error floating value in the TDOA estimation process, and the ordinate is the root mean square error of the aircraft position. As can be seen from fig. 6, as σ increases, the aircraft position estimation error is larger, but even if the signal arrival distance error in the TDOA estimation process is 18 meters, the aircraft position estimation error of the present invention is less than 10 meters, and the influence caused by the TDOA estimation error is greatly reduced.
Example 6
The apparatus for implementing a high performance hybrid positioning method based on angle and signal arrival time difference estimation according to any one of embodiments 1 to 5, as shown in fig. 4, includes a signal preliminary processing module, a target azimuth estimating module, a TDOA estimating module, and a joint estimating module; the signal preliminary processing module is respectively connected with the target azimuth angle estimation module and the TDOA estimation module, and the target azimuth angle estimation module and the TDOA estimation module are both connected with the joint estimation module;
the signal preliminary processing module is used for: sampling echo signals, representing array output signals into a matrix form, and carrying out real-number operation on the matrix; the target azimuth estimation module is used for: obtaining a matrix containing DOD and DOA information by using a U-ESPRIT algorithm, decomposing a characteristic value of the matrix to obtain an azimuth direct estimated value, carrying out sharing operation on the characteristic vector to obtain an azimuth matching estimated value, and averaging the direct and matching estimated values to obtain a final azimuth estimated value; and analyzing the spatial relationship among the transmitting array, the airplane and the receiving array, extracting the relationship among the arrival angle, the target coordinate and the receiving array coordinate, and obtaining the relationship among the target coordinate, the airplane position error and the arrival angle. The TDOA estimation module is used for: and obtaining a signal arrival time difference and a signal arrival time error according to the TDOA algorithm, analyzing a signal arrival distance error according to the signal arrival time error, and describing a relation between the signal arrival distance error and the target coordinates. The joint estimation module is used for: and processing the relation between the target azimuth angle estimation module and the TDOA estimation module, and obtaining the position coordinates of the target by using a least square method.

Claims (6)

1. The high-performance hybrid positioning method based on angle and signal arrival time difference estimation is characterized by comprising the following steps of:
(1) Realizing the estimation of the angle of arrival of the target based on the MIMO bistatic radar, and describing the estimation error of the target position caused by the estimation of the angle of arrival;
(2) Considering a signal arrival time difference TDOA of a radar deployment model, and describing the relationship between a signal arrival distance error and a target coordinate in TDOA estimation;
(3) Constructing a loss function by utilizing least square, and obtaining a target coordinate;
step (1), comprising the steps of:
A. based on the MIMO bistatic radar, a radar deployment model is deployed, the radar deployment model comprises a target, a transmitting array, a 1 st receiving array and a 2 nd receiving array, the transmitting array, the 1 st receiving array and the 2 nd receiving array are respectively arranged in different areas, the transmitting array, the 1 st receiving array and the 2 nd receiving array all comprise a plurality of array elements, the target is set as a far-field target, namely, the azimuth angles of each array element in the transmitting array, the 1 st receiving array and the 2 nd receiving array are regarded as equal, and a receiving array output signal model X is established, as shown in a formula (I):
in the formula (I), X 1 Refers to the output signal of the 1 st receiving array, X 2 Refers to the output signal of the 2 nd receiving array, A 1 Refers to a guide matrix of a system formed by a 1 st receiving array and a transmitting array, A 2 The system is characterized in that the system comprises a 2 nd receiving array and a transmitting array, S refers to a source signal matrix, and N refers to a sampling sample of additional sensor noise;
B. introducing unitary matrix Q to convert the output signals of 1 st receiving array and 2 nd receiving array into real matrix Y 1 、Y 2 The compounds are respectively shown as a formula (II) and a formula (III):
in the formulas (II) and (III),refers to the conjugate transpose of unitary matrix with dimension M of the number of elements of the transmit array, +.>Is the number N of the receiving array elements with the dimension of 1 st 1 Conjugate transpose of unitary matrix of +.>Refers to the number N of array elements of the 2 nd receiving array 2 Is a conjugate transpose of the unitary matrix of (a);
C. according to the U-ESPRIT algorithm, a matrix containing information of the wave separation angle and the wave arrival angle is obtained, wherein the matrix is respectively shown as a formula (IV) and a formula (V):
in the formulas (IV) and (V), Σ t Refers to a matrix containing the information of the angle of departure, K i1 And K i2 Respectively representI=1, 2, < ->0 represents a matrix with elements 0, I represents a unit matrix, E si Representing a signal subspace constructed by a system consisting of a transmitting array and an ith receiving array, the signal subspace being obtained by: by matrix Y i Performing eigenvalue decomposition, arranging eigenvalues obtained by eigenvalue decomposition from large to small, taking eigenvectors corresponding to the previous P eigenvalues to form signal components, and constructing signal subspace, Σ ri Refers to a matrix containing angle of arrival information for signals arriving at the ith receive array, and K i3 And K i4 Respectively indicate->Is used for the real and imaginary parts of (a),
the relational expression is shown as the formula (VI) and the formula (VII):
Σ t ＝T i -1 Λ t T i (Ⅵ)
Σ ri ＝T i -1 Λ ri T i (Ⅶ)
in the formulas (VI) and (VII),and is also provided with
Λ t Including the wave separation angle, lambda ri Angle of arrival, d, comprising the ith receive array t Represents the distance between adjacent array elements in the transmitting array, d r Represents the distance between the adjacent array elements of the ith receiving array, the distances between the adjacent array elements in the 1 st receiving array and the 2 nd receiving array are the same, lambda represents the wavelength, theta p The wave separation angle of the P-th target, p=1, 2,..p, P represents the number of targets;representing the angle of arrival of the p-th target at the i-th receive array;
performing eigenvalue decomposition on the formula (VI) and the formula (VII) to obtain direct estimated values of the wave separation angle and the wave arrival angle; the matrix T generated when calculating the angle of arrival i Substituting formula (VI) to solve the matching estimation value of the wave separation angle, and calculating the matrix T generated in the wave separation angle process i Substituting the matching estimation value of the arrival angle into a formula (VII);
carrying out arithmetic average on the direct estimated value of the wave separation angle and the matching estimated value of the wave separation angle to obtain a final estimated value of the wave separation angle; carrying out arithmetic average on the direct estimation value of the angle of arrival and the matching estimation value of the angle of arrival to obtain the final estimation value of the angle of arrival;
D. according to the radar deployment model, the transmitting array, the real target and the ith receiving array are regarded as triangles, and a relation exists, as shown in a formula (VIII):
in the formula (VIII), the length of the corner edge of the estimated value of the actual target distance wave arrival angle is marked as d i The distance of the target from the ith receive array is denoted by r i The angle of arrival of the ith receive array has a true value ofThe estimated value of the angle of arrival is marked as +.>
Setting the coordinates of the target to (x) t ,y t ) The coordinates of the ith receive array are (x i ,y i ) Expanding formula (viii) to formula (IX):
2. the method of high performance hybrid positioning based on angle and signal arrival time difference estimation according to claim 1, wherein step (2) is:
obtaining signal arrival time difference and arrival time error according to a TD0A algorithm;
analyzing a signal arrival distance error according to the signal arrival time error;
the relation between the signal arrival distance error and the target coordinates is described.
3. The method of claim 1, wherein the step (2) considers the signal arrival time difference of the radar deployment model and describes the relationship between the signal arrival distance error and the target coordinates in the TDOA estimation, and comprises the steps of:
assume that the time required for the electromagnetic wave emitted by the transmitting array to be received by the ith receiving array after being reflected by the unmanned aerial vehicle is t i The time required for the electromagnetic wave to be directly received by the ith receiving array after being transmitted by the transmitting array is t' i The difference between the two propagation modes is Deltaτ i ＝t i -t′ i ，
The distance difference between the two propagation modes is s △i ＝c△τ i The method comprises the steps of carrying out a first treatment on the surface of the c is the propagation speed of electromagnetic wave and has the relation s △i +s i ＝s+r i +n TDOA ，n TDOA Representing errors in the propagation process, the distance between the target and the transmitting array is s, and the distance between the transmitting array and the ith receiving array is s i ；
Let s be △i,O ＝s △i +s i And assume
Substitution into formula s △i,O ＝s △i +s i ＝s+r i +n TDOA And simultaneously square operation is carried out on two sides of the equal sign, as shown in the formula (X):
constructing a relational expression according to formulas (IX) and (X), and obtaining a relational expression describing the arrival distance error of the signal and the target coordinates, wherein the relational expression is shown as a formula (XI):
Ax T +q＝b (XI)
in the formula (XI) of the present invention,
4. the method of claim 3, wherein the step (3) of constructing a loss function by least squares and obtaining the target coordinates is:
constructing a loss function as shown in formula (XII):
in the formula (XII),
C TDOA a covariance matrix representing errors in the TDOA estimation process.
5. The method of high performance hybrid positioning based on angle and signal arrival time difference estimation according to claim 4, wherein the step (3) of obtaining the target coordinates is:
obtaining an estimated value of the target position coordinate, namely the target coordinate by utilizing a least square idea; as shown in formula (XIII):
6. the apparatus for implementing a hybrid positioning method according to any one of claims 1 to 5, comprising a signal preliminary processing module, a target azimuth estimating module, a TDOA estimating module, and a joint estimating module; the signal preliminary processing module is respectively connected with the target azimuth angle estimation module and the TDOA estimation module, and the target azimuth angle estimation module and the TDOA estimation module are both connected with the joint estimation module;
the signal preliminary processing module is used for: sampling echo signals, representing array output signals into a matrix form, and carrying out real-number operation on the matrix;
the target azimuth estimation module is used for: acquiring a matrix containing the information of the wave separation angle D0D and the wave arrival angle DOA by using a U-ESPRIT algorithm, decomposing the eigenvalue of the matrix to obtain an azimuth direct estimated value, carrying out sharing operation on the eigenvector to obtain an azimuth matching estimated value, and averaging the direct and matching estimated values to obtain a final azimuth estimated value; analyzing the spatial relationship among the transmitting array, the target and the receiving array, extracting the relationship among the arrival angle, the target coordinate and the receiving array coordinate, and obtaining a relational expression among the target coordinate, the target position error and the arrival angle;
the TDOA estimation module is used for: obtaining a signal arrival time difference and a signal arrival time error according to a TDOA algorithm, analyzing a signal arrival distance error according to the signal arrival time error, and describing a relation between the signal arrival distance error and a target coordinate;
the joint estimation module is used for: and processing the relation between the target azimuth angle estimation module and the TDOA estimation module, and obtaining the position coordinates of the target by using a least square method.
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