CN108761399B - Passive radar target positioning method and device - Google Patents

Passive radar target positioning method and device Download PDF

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CN108761399B
CN108761399B CN201810556996.2A CN201810556996A CN108761399B CN 108761399 B CN108761399 B CN 108761399B CN 201810556996 A CN201810556996 A CN 201810556996A CN 108761399 B CN108761399 B CN 108761399B
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胡德秀
赵勇胜
赵拥军
刘智鑫
赵闯
赵泽亚
张睿
黄东华
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Information Engineering University of PLA Strategic Support Force
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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
    • 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
    • G01S13/02—Systems using reflection of radio waves, e.g. primary radar systems; Analogous systems
    • G01S13/06—Systems determining position data of a target

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Abstract

The invention relates to a passive radar target positioning method and a passive radar target positioning device, wherein an observation equation of an angle and a time difference is linearized to obtain a group of linear equations, the rough estimation of a target position is obtained by using least square, an observation error and an external radiation source position error are simultaneously considered in the linear equations to obtain a constrained total least square model, the obtained least square solution is used as an initial solution, and Newton iteration is adopted to obtain the accurate estimation of the target position. The method considers the angle observation error, the time difference observation error and the position error of the external radiation source, the positioning result is the optimal estimation result when the external radiation source has errors, the nonlinear angle and time difference observation equation is subjected to linearization treatment to obtain the least square algebraic solution, and the least square algebraic solution is used as the initial solution of Newton iteration to ensure the convergence of the algorithm.

Description

Passive radar target positioning method and device
Technical Field
The invention belongs to the technical field of passive radar target positioning, and particularly relates to a passive radar target positioning method and device.
Background
The passive radar is a special bistatic radar, does not radiate source electromagnetic waves per se, and detects and positions a target by receiving and processing a reflected or scattered signal of the target to an existing external radiation source in the environment. Compared with the traditional active radar, the special working principle has the good characteristics of four-reactance (electronic interference, anti-radiation weapon attack, stealth target attack and low-altitude ultra-low altitude penetration prevention). Therefore, passive radar technology has been of great interest in the field of international radar for many years.
The position information of the external radiation source is an essential parameter for passive radar target positioning. However, for some radiation sources, such as enemy military radiation sources, the position of the radiation source is often not accurately obtained and can only be estimated by the ESM system, and the position of the obtained external radiation source contains large errors. For example, the author "single station DOA-TDOA passive positioning algorithm based on regularization constrained total least squares" published by zhao champion, zhu, usa, 9, 2016, 9, in the book 38, which reduces the positioning accuracy of a passive radar system due to the presence of external radiation source position errors, and therefore, it is necessary to consider the influence of the external radiation source position errors on the positioning accuracy and design a targeted target positioning algorithm.
The positioning of the joint angle and the time difference is a commonly used positioning system of the passive radar, and has better positioning precision than a positioning system only using the angle or the time difference. However, in the conventional positioning method, the position error of the external radiation source is not considered. Therefore, a multi-base passive radar target positioning method considering the position error of the external radiation source is needed, so that the optimal estimation of the target position is realized when the position of the external radiation source is inaccurate.
Disclosure of Invention
The invention aims to provide a passive radar target positioning method and a passive radar target positioning device, which are used for solving the problem that the target position estimation precision of the conventional passive radar target positioning method is low.
In order to solve the technical problem, the invention provides a passive radar target positioning method, which comprises the following steps:
1) constructing an observation equation of the angle and the time difference, carrying out linearization treatment on the observation equation of the angle and the time difference to obtain a linear equation, and solving the linear equation to obtain an initial estimation value of the target position;
2) expressing the angle measurement value as the difference between an angle true value and an angle observation error, expressing the time difference measurement value as the difference between the time difference true value and the time difference observation error, expressing the measurement position value of the external radiation source as the difference between the true position value and the position measurement error of the external radiation source, respectively substituting the angle measurement value and the time difference measurement value into the linear equation, and respectively obtaining a first function of taking the angle true value as a quantity to be solved and a second function of taking the time difference true value as the quantity to be solved; substituting the measured position value of the external radiation source as a new variable into the linear equation to obtain a third function of taking the real position value of the external radiation source as a quantity to be solved;
3) and constructing a least square model according to the first function, the second function and the third function, carrying out Taylor expansion on the model at the initial estimation value of the target position, solving to obtain a Newton iteration formula, carrying out iteration by using the initial estimation value of the target position and the Newton iteration formula until the iteration reaches a set number of times, and obtaining an accurate estimation value of the target position.
The method includes the steps of linearizing observation equations of angles and time differences to obtain a group of linear equations, obtaining rough estimation of a target position by using least square, simultaneously considering observation errors and external radiation source position errors into the linear equations to obtain a constrained total least square model, using the obtained least square solution as an initial solution, and obtaining accurate estimation of the target position by adopting Newton iteration. The method considers the angle observation error, the time difference observation error and the position error of the external radiation source, and the positioning result is the optimal estimation result when the external radiation source has errors; the method linearizes the nonlinear angle and time difference observation equation to obtain a least square algebraic solution, and uses the least square algebraic solution as an initial solution of Newton iteration to ensure the convergence of the algorithm.
As a further definition of the least squares model, step 3) further comprises the following sub-steps of constructing the least squares model:
(1) whitening processing is carried out on the angle observation error in the first function, the time difference observation error in the second function and the position measurement error in the third function, and functional relations of whitening noise vectors with the angle observation error, the time difference observation error and the position measurement error are obtained after processing;
(2) and establishing a constraint condition according to the functional relation and the first function, the second function and the third function, and taking the norm-squared minimum of the whitening noise vector as a target function.
Further, the method also comprises the following steps: and transforming the target function under the constraint condition into a minimization target function without the constraint condition to be used as a final least square model.
In order to solve the above technical problem, the present invention further provides a passive radar target positioning device, including a calculation processing module, where the calculation processing module is configured to implement the following steps:
1) constructing an observation equation of the angle and the time difference, carrying out linearization treatment on the observation equation of the angle and the time difference to obtain a linear equation, and solving the linear equation to obtain an initial estimation value of the target position;
2) expressing the angle measurement value as the difference between an angle true value and an angle observation error, expressing the time difference measurement value as the difference between the time difference true value and the time difference observation error, expressing the measurement position value of the external radiation source as the difference between the true position value and the position measurement error of the external radiation source, respectively substituting the angle measurement value and the time difference measurement value into the linear equation, and respectively obtaining a first function of taking the angle true value as a quantity to be solved and a second function of taking the time difference true value as the quantity to be solved; substituting the measured position value of the external radiation source as a new variable into the linear equation to obtain a third function of taking the real position value of the external radiation source as a quantity to be solved;
3) and constructing a least square model according to the first function, the second function and the third function, carrying out Taylor expansion on the model at the initial estimation value of the target position, solving to obtain a Newton iteration formula, carrying out iteration by using the initial estimation value of the target position and the Newton iteration formula until the iteration reaches a set number of times, and obtaining an accurate estimation value of the target position.
Further, step 3) further comprises the following sub-steps of constructing a least squares model:
(1) whitening processing is carried out on the angle observation error in the first function, the time difference observation error in the second function and the position measurement error in the third function, and functional relations of whitening noise vectors with the angle observation error, the time difference observation error and the position measurement error are obtained after processing;
(2) and establishing a constraint condition according to the functional relation and the first function, the second function and the third function, and taking the norm-squared minimum of the whitening noise vector as a target function.
Further, the method also comprises the following steps: and transforming the target function under the constraint condition into a minimization target function without the constraint condition to be used as a final least square model.
Drawings
FIG. 1 is a schematic flow chart of the present invention for estimating a target location;
FIG. 2 is a schematic diagram of the geometric positions of an external radiation source and an observation station in the experimental simulation of the present invention;
FIG. 3 is a comparison graph of simulation of target position estimation error versus time difference measurement error in accordance with the present invention;
FIG. 4 is a simulated contrast plot of target position estimation error as a function of angle measurement error in accordance with the present invention;
FIG. 5 is a simulated contrast plot of target position estimation error as a function of external radiation source position error in accordance with the present invention.
Detailed Description
The following further describes embodiments of the present invention with reference to the drawings.
The invention provides a passive radar target positioning method, which comprises the following steps:
1) and constructing an observation equation of the angle and the time difference, carrying out linearization treatment on the observation equation of the angle and the time difference to obtain a linear equation, and solving the linear equation to obtain an initial estimation value of the target position.
2) Expressing the angle measurement value as the difference between an angle true value and an angle observation error, expressing the time difference measurement value as the difference between the time difference true value and the time difference observation error, expressing the measurement position value of the external radiation source as the difference between the true position value and the position measurement error of the external radiation source, respectively substituting the angle measurement value and the time difference measurement value into the linear equation, and respectively obtaining a first function of taking the angle true value as a quantity to be solved and a second function of taking the time difference true value as the quantity to be solved; and substituting the measured position value of the external radiation source as a new variable into the linear equation to obtain a real position value of the external radiation source as a third function of the quantity to be solved.
3) And constructing a least square model according to the first function, the second function and the third function, carrying out Taylor expansion on the model at the initial estimation value of the target position, solving to obtain a Newton iteration formula, carrying out iteration by using the initial estimation value of the target position and the Newton iteration formula until the iteration reaches the set times, and obtaining an accurate estimation value of the target position.
The method includes the steps of linearizing observation equations of angles and time differences to obtain a group of linear equations, obtaining rough estimation of a target position by using least square, simultaneously considering observation errors and external radiation source position errors into the linear equations to obtain a constrained total least square model, using the obtained least square solution as an initial solution, and obtaining accurate estimation of the target position by adopting Newton iteration. The method considers the angle observation error, the time difference observation error and the position error of the external radiation source, and the positioning result is the optimal estimation result when the external radiation source has errors; the method linearizes the nonlinear angle and time difference observation equation to obtain a least square algebraic solution, and uses the least square algebraic solution as an initial solution of Newton iteration to ensure the convergence of the algorithm.
Specifically, the invention provides a multi-base passive radar target positioning method considering the joint angle and the time difference of the position error of an external radiation source aiming at a passive radar system under the condition that the position error of the external radiation source exists, as shown in fig. 1, the steps are as follows:
firstly, linearizing an observation equation of the angle and the time difference to obtain a group of linear equations, and obtaining a rough estimation of the target position by using least square. The specific solving method is as follows:
assume that there are N external radiation sources, 1 target, and 1 observation station in the scene. And two pairs of antennas are distributed on the observation station and are respectively used for receiving the direct signal from the external radiation source and the target echo signal. And establishing a space rectangular coordinate system by taking the observation station as an origin. Assume that the target position to be estimated X ═ Xo,yo,zo]T. True position of external radiation source
Figure BDA0001682692730000061
Unknown, only obtaining a measurement s containing an errork＝[xk,yk,zk]T(k ═ 1, 2.., N), i.e.
Figure BDA0001682692730000062
Wherein, Δ skThe positions of the N external radiation sources are represented in a matrix form, resulting in a matrix of 3N × 1 as follows:
s＝so+Δs
in the formula (I), the compound is shown in the specification,
Figure BDA0001682692730000063
Figure BDA0001682692730000064
the true distance of the target from the observation station is
Figure BDA0001682692730000065
True distance of target to radiation source k
Figure BDA0001682692730000066
The true distance of the radiation source k from the observation station is
Figure BDA0001682692730000067
Assuming that the signal propagation speed is c, the time difference between the direct signal of the external radiation source k and the echo signal after the direct signal and the echo signal after the echo signal are reflected by the target arrive at the observation station is:
Figure BDA0001682692730000068
the azimuth angle and the pitch angle of the target to the observation station are respectively set as thetaoAnd
Figure BDA0001682692730000069
then according to the geometric relationship between the target and the observation station:
Figure BDA00016826927300000610
through a series of transformations, the observation equation for angle and time difference can be expressed in linear form as follows:
Figure BDA0001682692730000071
the system of linear equations is expressed in matrix form as:
HoX＝bo
wherein the content of the first and second substances,
Figure BDA0001682692730000072
Figure BDA0001682692730000073
by using a weighted least square estimation method, the coarse estimation of the target position is obtained as follows:
Figure BDA0001682692730000074
secondly, simultaneously considering the observation error and the position error of the external radiation source into a linear equation to obtain a least square model, and the steps are as follows:
(1) and whitening the angle observation error in the first function, the time difference observation error in the second function and the position measurement error in the third function to obtain a functional relation between the whitening noise vector and the angle observation error, the time difference observation error and the position measurement error respectively.
(2) And establishing a constraint condition according to the functional relation and the first function, the second function and the third function, wherein the minimum norm square of the whitening noise vector is taken as a target function.
Further, the least square model may be transformed to convert an objective function under a constraint condition into a minimized objective function without a constraint condition as a final least square model.
The specific process is as follows:
let the true of observation vectorReal value
Figure BDA0001682692730000081
Measured value thereof is
Figure BDA0001682692730000082
Measurement error
Figure BDA0001682692730000083
Then there are:
θ＝θo+Δθ
merge s and θ into one column vector α of (4N +2) × 1 ═ θT,sT]TAs a total observed quantity, the corresponding observation error is n ═ Δ θT,ΔsT]T. Simultaneously considering angle, time difference observation error delta theta and external radiation source position error delta s to matrix HoAnd boInfluence of (b) then HoX＝boMay be expressed as a function of the observed quantity α:
Ho(α-n)＝bo(α-n)
h is to beo(α -n) and bo(α -n) Taylor expansion at measurement α and neglecting second order and above error terms yields the following equation:
Ho＝H-ΔH,bo＝b-Δb
then Ho(α-n)＝bo(α -n) can be expressed as:
(H-ΔH)X＝b-Δb
in the formula (I), the compound is shown in the specification,
ΔH＝[F1n,F2n,F3n],Δb＝F4n
Fl1,2,3,4 can be calculated according to the following formula:
Figure BDA0001682692730000091
calculating according to the formula to obtain a matrix Fl1,2,3,4 are each:
Figure BDA0001682692730000092
Figure BDA0001682692730000093
wherein, sigma1,Σ2,Σ4,Σ5Is N × 3N, Σ3A matrix of N × 2, whose elements are as follows:
Figure BDA0001682692730000094
Figure BDA0001682692730000101
Figure BDA0001682692730000102
Figure BDA0001682692730000103
Figure BDA0001682692730000111
if the errors in n have correlation or have different variance, it needs to be whitened. Let Q be E [ nnT]Cholesky decomposition (triangular decomposition) is performed on Q to obtain Q ═ PPTObtaining a whitened noise vector u ═ P-1n, then, order
Figure BDA0001682692730000112
Then
FlPu＝Glu
Let WX＝xG1+yG2+zG3-G4Then (H- Δ H) X ═ b- Δ b can be expressed as:
HX-b＝WXu
solving the CTLS solution of the target position when the constraint condition HX-b is satisfiedXu.s.A suitable solution vector X is determined such thatObjective function | | u | | non-conducting phosphor2And minimum. The mathematical expression is as follows:
Figure BDA0001682692730000113
the above formula is a minimization problem of a quadratic function under the constraint of a quadratic constraint equation, and can be transformed into an unconstrained minimization problem of a minimized variable X:
Figure BDA0001682692730000114
in the formula
Figure BDA0001682692730000115
A representation matrix WXThe Moore-Penrose inverse of (1). Will be provided with
Figure BDA0001682692730000116
Substituting into the target function of the CTLS model (least square model), the CTLS solution (least square solution) of the target position is a variable X which satisfies the minimization of the following target function, therefore, the measurement error and the position error of the external radiation source are both considered in the equation, and the constraint total least square model of the target position is constructed as follows:
Figure BDA0001682692730000121
and finally, taking the obtained least square solution as an initial solution, and obtaining accurate estimation of the target position by adopting Newton iteration. The specific process is as follows:
using the least square solution obtained as the initial solution
Figure BDA0001682692730000122
The addition of J (X) to X0And (3) processing Taylor expansion, and neglecting error terms of the third order and above to obtain:
Figure BDA0001682692730000123
in the formula (I), the compound is shown in the specification,
Figure BDA0001682692730000124
and is
Figure BDA0001682692730000125
Figure BDA0001682692730000126
Wherein the content of the first and second substances,
Figure BDA0001682692730000127
Figure BDA0001682692730000128
Figure BDA0001682692730000129
Figure BDA00016826927300001210
order to
Figure BDA00016826927300001211
Obtaining:
A+B(X-X0)＝0
solving the above formula to obtain a Newton iteration formula as follows:
X＝X0-B-1A
and obtaining accurate estimation of the target position by using a Newton iteration formula, and converging to a global optimal solution by iterating for 2-3 times.
The simulation experiment of the invention was simulated using the passive radar system of fig. 2 and the geometric position diagram of the target. Fig. 3, fig. 4, and fig. 5 show simulation comparisons of the target position estimation error with time difference measurement error, angle measurement error, and external radiation source position error change, respectively, and it can be seen that the estimation performance of the present invention is significantly better than a positioning algorithm that ignores the external radiation source position error under the condition that the external radiation source position error exists, and the estimation error is closest to the cramer-perot boundary.
The invention also provides a passive radar target positioning device, which comprises a calculation processing module, wherein the calculation processing module is used for realizing the following steps:
1) and constructing an observation equation of the angle and the time difference, carrying out linearization treatment on the observation equation of the angle and the time difference to obtain a linear equation, and solving the linear equation to obtain an initial estimation value of the target position.
2) Expressing the angle measurement value as the difference between an angle true value and an angle observation error, expressing the time difference measurement value as the difference between the time difference true value and the time difference observation error, expressing the measurement position value of the external radiation source as the difference between the true position value and the position measurement error of the external radiation source, respectively substituting the angle measurement value and the time difference measurement value into the linear equation, and respectively obtaining a first function of taking the angle true value as a quantity to be solved and a second function of taking the time difference true value as the quantity to be solved; and substituting the measured position value of the external radiation source as a new variable into the linear equation to obtain a real position value of the external radiation source as a third function of the quantity to be solved.
3) And constructing a least square model according to the first function, the second function and the third function, carrying out Taylor expansion on the model at the initial estimation value of the target position, solving to obtain a Newton iteration formula, carrying out iteration by using the initial estimation value of the target position and the Newton iteration formula until the iteration reaches the set times, and obtaining an accurate estimation value of the target position.
The passive radar target positioning device referred to in the above embodiments is actually a computer solution based on the method flow of the present invention, that is, a software framework, and can be applied to a computer, and the above device is a processing process corresponding to the method flow. The above-described method will not be described in detail since it is sufficiently clear and complete.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the claims of the present invention.

Claims (4)

1. A passive radar target positioning method is characterized by comprising the following steps:
1) constructing an observation equation of the angle and the time difference, carrying out linearization treatment on the observation equation of the angle and the time difference to obtain a linear equation, and solving the linear equation to obtain an initial estimation value of the target position;
2) expressing the angle measurement value as the difference between an angle true value and an angle observation error, expressing the time difference measurement value as the difference between the time difference true value and the time difference observation error, expressing the measurement position value of the external radiation source as the difference between the true position value and the position measurement error of the external radiation source, respectively substituting the angle measurement value and the time difference measurement value into the linear equation, and respectively obtaining a first function of taking the angle true value as a quantity to be solved and a second function of taking the time difference true value as the quantity to be solved; substituting the measured position value of the external radiation source as a new variable into the linear equation to obtain a third function of taking the real position value of the external radiation source as a quantity to be solved;
3) constructing a least square model according to the first function, the second function and the third function, performing Taylor expansion on the model at the initial estimation value of the target position, solving to obtain a Newton iteration formula, performing iteration by using the initial estimation value of the target position and the Newton iteration formula until the iteration reaches a set number of times to obtain an accurate estimation value of the target position,
step 3) further comprises the following sub-steps of constructing a least squares model:
(1) whitening processing is carried out on the angle observation error in the first function, the time difference observation error in the second function and the position measurement error in the third function, and functional relations of whitening noise vectors with the angle observation error, the time difference observation error and the position measurement error are obtained after processing;
(2) and establishing a constraint condition according to the functional relation and the first function, the second function and the third function, and taking the norm-squared minimum of the whitening noise vector as a target function.
2. The passive radar target locating method of claim 1, further comprising the steps of: and transforming the target function under the constraint condition into a minimization target function without the constraint condition to be used as a final least square model.
3. A passive radar target locating device is characterized by comprising a calculation processing module, wherein the calculation processing module is used for realizing the following steps:
1) constructing an observation equation of the angle and the time difference, carrying out linearization treatment on the observation equation of the angle and the time difference to obtain a linear equation, and solving the linear equation to obtain an initial estimation value of the target position;
2) expressing the angle measurement value as the difference between an angle true value and an angle observation error, expressing the time difference measurement value as the difference between the time difference true value and the time difference observation error, expressing the measurement position value of the external radiation source as the difference between the true position value and the position measurement error of the external radiation source, respectively substituting the angle measurement value and the time difference measurement value into the linear equation, and respectively obtaining a first function of taking the angle true value as a quantity to be solved and a second function of taking the time difference true value as the quantity to be solved; substituting the measured position value of the external radiation source as a new variable into the linear equation to obtain a third function of taking the real position value of the external radiation source as a quantity to be solved;
3) constructing a least square model according to the first function, the second function and the third function, performing Taylor expansion on the model at the initial estimation value of the target position, solving to obtain a Newton iteration formula, performing iteration by using the initial estimation value of the target position and the Newton iteration formula until the iteration reaches a set number of times to obtain an accurate estimation value of the target position,
step 3) further comprises the following sub-steps of constructing a least squares model:
(1) whitening processing is carried out on the angle observation error in the first function, the time difference observation error in the second function and the position measurement error in the third function, and functional relations of whitening noise vectors with the angle observation error, the time difference observation error and the position measurement error are obtained after processing;
(2) and establishing a constraint condition according to the functional relation and the first function, the second function and the third function, and taking the norm-squared minimum of the whitening noise vector as a target function.
4. The passive radar target locating apparatus of claim 3, further comprising the steps of: and transforming the target function under the constraint condition into a minimization target function without the constraint condition to be used as a final least square model.
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