CN108761399A - A kind of passive radar object localization method and device - Google Patents

Abstract

The present invention relates to a kind of passive radar object localization method and devices, the observational equation of angle and the time difference are linearized, obtain one group of linear equation, and obtain the rough estimate of target location using least square, by observation error and external sort algorithm site error simultaneously in view of in linear equation, it obtains constraint total least square model and the accurate estimation of target location is obtained using Newton iteration using obtained least square solution as initial solution.The present invention considers angular observation error, the site error of time difference observation error and external sort algorithm, positioning result is that there are optimal estimation results when error for external sort algorithm, by nonlinear angle and time difference observational equation linearization process, least square algebraic solution is obtained, and as the initial solution of Newton iteration, it ensure that convergence.

Description

A passive radar target location method and device

technical field

The invention belongs to the technical field of passive radar target positioning, and in particular relates to a passive radar target positioning method and device.

Background technique

As a special kind of bistatic radar, passive radar itself does not radiate electromagnetic waves, but detects and locates targets by receiving and processing the reflected or scattered signals of targets to existing external radiation sources in the environment. This special working principle makes it have good four-resistance (electronic interference, anti-radiation weapon attack, stealth target attack, low-altitude and ultra-low-altitude penetration) characteristics compared with traditional active radars. Therefore, passive radar technology has been receiving much attention in the international radar field for many years.

The position information of the external radiation source is a necessary parameter for passive radar target location. However, for some radiation sources, such as enemy military radiation sources, their positions cannot be obtained accurately, and can only be estimated through the ESM system, and the obtained external radiation source positions contain large errors. For example, the author Zhao Yongjun published the paper "Single Station DOA-TDOA Passive Location Algorithm Based on Regularized Constrained Total Least Squares" in "Journal of Electronics and Information Technology" Volume 38 Issue 9 in September 2016. Due to the existence of external radiation Therefore, it is necessary to consider the influence of the location error of the external radiation source on the positioning accuracy and design a targeted target positioning algorithm.

Positioning combined with angle and time difference is a commonly used positioning system for passive radar, and it has better positioning accuracy than positioning systems that only use angle or time difference. However, in the existing positioning methods, the position error of the external radiation source is not considered. Therefore, there is an urgent need for a multistatic passive radar target location method that considers the position error of the external radiation source, so as to achieve the optimal estimation of the target position when the position of the external radiation source is inaccurate.

Contents of the invention

The object of the present invention is to provide a passive radar target positioning method and device, which are used to solve the problem of low accuracy of estimating the target position in the existing passive radar target positioning method.

In order to solve the above technical problems, the present invention proposes a passive radar target positioning method, comprising the following steps:

1) Construct the observation equation of angle and time difference, and linearize the observation equation of angle and time difference to obtain a linear equation, and solve the linear equation to obtain the initial estimated value of the target position;

2) Express the angle measurement value as the difference between the true angle value and the angle observation error, express the time difference measurement value as the difference between the time difference true value and the time difference observation error, and express the measured position value of the external radiation source as the real position of the external radiation source The difference between the value and the position measurement error, the measured value of the angle and the measured value of the time difference are respectively substituted into the linear equation, and the real value of the angle is obtained as the first function of the quantity to be sought, and the real value of the time difference is used as the second function of the quantity to be sought ; Substituting the measured position value of the external radiation source into the linear equation as a new variable, obtaining the real position value of the external radiation source as the third function of the quantity to be sought;

3) Construct the least squares model according to the first function, the second function, and the third function, expand the model at the initial estimated value of the target position by Taylor expansion, and obtain the Newton iterative formula by solving it, and use the initial estimate of the target position The value and the Newton iteration formula are iterated to the set number of iterations to obtain an accurate estimate of the target position.

The invention linearizes the observation equations of angle and time difference to obtain a set of linear equations, and uses least squares to obtain a rough estimate of the target position, and takes the observation error and the position error of the external radiation source into consideration in the linear equations to obtain the minimum constraint overall The square model takes the obtained least square solution as the initial solution, and uses Newton iteration to obtain an accurate estimate of the target position. The invention 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 there is an error in the external radiation source; the present invention linearizes the non-linear angle and time difference observation equations to obtain The least squares algebraic solution is obtained, and it is used as the initial solution of Newton iteration, which ensures the convergence of the algorithm.

As a further limitation of the least squares model, step 3) also includes the following substeps of building the least squares model:

(1) 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 are whitened, and after processing, the whitening noise vector is respectively associated with the angle observation error, time difference observation error, The functional relationship of the position measurement error;

(2) According to the functional relational expression, and the first function, the second function and the third function, a constraint condition is established, and the minimum norm square of the whitening noise vector is taken as the objective function.

Further, the method further includes the following step: transforming the objective function under the constraints into an unconstrained minimized objective function as the final least squares model.

In order to solve the above technical problems, the present invention also proposes a passive radar target positioning device, including a calculation processing module, which is used to implement the following steps:

1) Construct the observation equation of angle and time difference, and linearize the observation equation of angle and time difference to obtain a linear equation, and solve the linear equation to obtain the initial estimated value of the target position;

2) Express the angle measurement value as the difference between the true angle value and the angle observation error, express the time difference measurement value as the difference between the time difference true value and the time difference observation error, and express the measured position value of the external radiation source as the real position of the external radiation source The difference between the value and the position measurement error, the measured value of the angle and the measured value of the time difference are respectively substituted into the linear equation, and the real value of the angle is obtained as the first function of the quantity to be sought, and the real value of the time difference is used as the second function of the quantity to be sought ; Substituting the measured position value of the external radiation source into the linear equation as a new variable, obtaining the real position value of the external radiation source as the third function of the quantity to be sought;

3) Construct the least squares model according to the first function, the second function, and the third function, expand the model at the initial estimated value of the target position by Taylor expansion, and obtain the Newton iterative formula by solving it, and use the initial estimate of the target position The value and the Newton iteration formula are iterated to the set number of iterations to obtain an accurate estimate of the target position.

Further, step 3) also includes the following substeps of constructing the least squares model:

(1) 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 are whitened, and after processing, the whitening noise vector is respectively associated with the angle observation error, time difference observation error, The functional relationship of the position measurement error;

(2) According to the functional relational expression, and the first function, the second function and the third function, a constraint condition is established, and the minimum norm square of the whitening noise vector is taken as the objective function.

Further, the method further includes the following step: transforming the objective function under the constraints into an unconstrained minimized objective function as the final least squares model.

Description of drawings

Fig. 1 is a schematic flow chart of estimating target position in the present invention;

Fig. 2 is a schematic diagram of the geometric positions of external radiation sources and observation stations in the experimental simulation of the present invention;

Fig. 3 is the simulation comparison diagram of the variation of the target position estimation error with the time difference measurement error of the present invention;

Fig. 4 is the simulation contrast diagram that the target position estimation error of the present invention changes with the angle measurement error;

Fig. 5 is a simulation comparison diagram of the variation of the target position estimation error with the position error of the external radiation source according to the present invention.

Detailed ways

The specific embodiments of the present invention will be further described below in conjunction with the accompanying drawings.

The invention provides a passive radar target positioning method, comprising the following steps:

1) Construct the observation equation of angle and time difference, and linearize the observation equation of angle and time difference to obtain a linear equation, and solve the linear equation to obtain the initial estimate of the target position.

2) Express the angle measurement value as the difference between the true angle value and the angle observation error, express the time difference measurement value as the difference between the time difference true value and the time difference observation error, and express the measured position value of the external radiation source as the real position of the external radiation source The difference between the value and the position measurement error, the measured value of the angle and the measured value of the time difference are respectively substituted into the above-mentioned linear equation, and the real value of the angle is obtained as the first function of the quantity to be sought, and the real value of the time difference is used as the second function of the quantity to be sought; Substitute the measured position value of the external radiation source into the above linear equation as a new variable, and obtain the real position value of the external radiation source as the third function of the quantity to be sought.

3) Construct the least squares model according to the first function, the second function, and the third function, expand the model at the initial estimated value of the target position, and obtain the Newton iteration formula by solving it, and use the initial estimated value of the target position and the Newton iteration The formula is iterated to a set number of iterations to obtain an accurate estimate of the target position.

The invention linearizes the observation equations of angle and time difference to obtain a set of linear equations, and uses least squares to obtain a rough estimate of the target position, and takes the observation error and the position error of the external radiation source into consideration in the linear equations to obtain the minimum constraint overall The square model takes the obtained least square solution as the initial solution, and uses Newton iteration to obtain an accurate estimate of the target position. The invention 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 there is an error in the external radiation source; the present invention linearizes the non-linear angle and time difference observation equations to obtain The least squares algebraic solution is obtained, and it is used as the initial solution of Newton iteration, which ensures the convergence of the algorithm.

Specifically, the present invention aims at the passive radar system under the condition that there is an error in the position of the external radiation source, and proposes a multi-static passive radar target positioning method that considers the joint angle and time difference of the position error of the external radiation source, as shown in Figure 1. Proceed as follows:

First, the observation equations of angle and time difference are linearized to obtain a set of linear equations, and a rough estimate of the target position is obtained using least squares. The specific solution method is as follows:

Suppose there are N external radiation sources, 1 target, and 1 observation station in the scene. Two antennas are arranged on the observation station, which are respectively used to receive the direct signal from the external radiation source and the target echo signal. With the observation station as the origin, a space rectangular coordinate system is established. Assume that the estimated target position X=[x ^o , y ^o , z ^o ] ^T . The true position of the external radiation source unknown, only its measured value with error s _k =[x _k ,y _k ,z _k ] ^T (k=1,2,...,N), namely

Among them, Δs _k is the corresponding measurement error vector. The positions of N external radiation sources are expressed in matrix form, and the following 3N×1 matrix is obtained:

s=s ^o +Δs

In the formula,

The real distance from the target to the observation station is The real distance from the target to the radiation source k The real distance from the radiation source k to the observation station is Assuming that the signal propagation speed is c, then the time difference between the direct signal of the external radiation source k and the echo signal reflected by the target arriving at the observation station is:

Let the azimuth and elevation angles from the target to the observation station be θ ^o and According to the geometric relationship between the target and the observation station:

After a series of transformations, the observation equations of angle and time difference can be expressed in the following linear form:

Express the system of linear equations in matrix form as:

H ^o X = b ^o

in,

Using the weighted least squares estimation method, the rough estimate of the target position is obtained as:

Secondly, taking the observation error and the position error of the external radiation source into the linear equation at the same time to obtain the least squares model, the steps are as follows:

(1) 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 are whitened, and after processing, the whitening noise vector is respectively associated with the angle observation error, time difference observation error, Functional relation for position measurement error.

(2) According to the functional relational expression, and the first function, the second function and the third function, a constraint condition is established, and the minimum square norm of the whitening noise vector is taken as the objective function.

Further, the above least squares model can also be transformed, and the objective function under the constraint condition can be transformed into an unconstrained minimized objective function as the final least squares model.

The specific process is:

Let the true value of the observation vector be Its measured value is Measurement error Then there are:

θ＝θ ^o +Δθ

Combine s and θ into a (4N+2)×1 column vector α=[θ ^T ,s ^T ] ^T as the total observation quantity, and the corresponding observation error is n=[Δθ ^T ,Δs ^T ] ^T . Considering the influence of angle, time difference observation error Δθ and external radiation source position error Δs on matrices H ^o and b ^o at the same time, then H ^o X = b ^o can be expressed as a function of observation α:

H ^o (α-n)=b ^o (α-n)

Taylor expansion of H ^o (α-n) and b ^o (α-n) at the measured value α, and ignoring the second-order and above error terms, the following formula is obtained:

H ^o ＝H-ΔH, b ^o ＝b-Δb

Then H ^o (α-n)=b ^o (α-n) can be expressed as:

(H-ΔH)X=b-Δb

In the formula,

ΔH=[F ₁ n, F ₂ n, F ₃ n], Δb=F ₄ n

F _l , l=1,2,3,4 can be calculated according to the following formula:

Calculated according to the above formula, the obtained matrix F _l , l=1, 2, 3, 4 are respectively:

Among them, Σ ₁ , Σ ₂ , Σ ₄ , Σ ₅ are N×3N, Σ ₃ is a matrix of N×2, and its elements are as follows:

If the errors in n are correlated or have different variances, they need to be whitened. Make Q=E[nn ^T ], do Cholesky decomposition (triangular decomposition) to Q to get Q=PP ^T , obtain the noise vector u=P ^-1 n of whitening, then, make but

F _l Pu = G _l u

Let W _X =xG ₁ +yG ₂ +zG ₃ -G ₄ , then (H-ΔH)X=b-Δb can be expressed as:

HX-b＝W _X u

Solve the CTLS solution of the target position, that is, determine a suitable solution vector X under the constraint condition HX-b=W _X u, so that the objective function ||u|| ² is the smallest. Its mathematical expression is:

The above formula is a minimization problem of a quadratic function under the constraints of a quadratic constraint equation, which can be transformed into an unconstrained minimization problem for the minimization variable X:

In the formula Represents the Moore-Penrose inverse of matrix W _X. Will Substituting into the objective function of the CTLS model (least squares model), the CTLS solution (least squares solution) of the target position is the variable X that satisfies the minimization of the following objective function. Therefore, the measurement error and the position error of the external radiation source are taken into account in the equation, the constrained overall least squares model of the target position is constructed as:

Finally, the obtained least squares solution is used as the initial solution, and the precise estimation of the target position is obtained by Newton iteration. The specific process is:

The least squares solution obtained above is used as the initial solution Taylor expansion of J(X) at X ₀ , and ignoring the third-order and above error terms, we get:

In the formula, and in,

make get:

A+B(XX ₀ )＝0

Solving the above formula, the Newton iteration formula is obtained as:

X＝X ₀ -B ^-1 A

Using Newton's iterative formula to get an accurate estimate of the target position, it only needs to iterate 2-3 times to converge to the global optimal solution.

Using the schematic diagram of the geometric position of the passive radar system and the target in Fig. 2, the simulation experiment of the present invention is simulated. Fig. 3, Fig. 4, Fig. 5 have respectively shown the simulation comparison of the target position estimation error of the present invention with time difference measurement error, angle measurement error, external radiation source position error change, can find out that under the condition that there is external radiation source position error, The estimation performance of the invention is obviously better than the positioning algorithm which ignores the position error of the external radiation source, and the estimation error is closest to the Cramereau boundary.

The present invention also proposes a passive radar target positioning device, including a calculation processing module, and the calculation processing module is used to realize the following steps:

1) Construct the observation equation of angle and time difference, and linearize the observation equation of angle and time difference to obtain a linear equation, and solve the linear equation to obtain the initial estimate of the target position.

2) Express the angle measurement value as the difference between the true angle value and the angle observation error, express the time difference measurement value as the difference between the time difference true value and the time difference observation error, and express the measured position value of the external radiation source as the real position of the external radiation source The difference between the value and the position measurement error, the measured value of the angle and the measured value of the time difference are respectively substituted into the above-mentioned linear equation, and the real value of the angle is obtained as the first function of the quantity to be sought, and the real value of the time difference is used as the second function of the quantity to be sought; Substitute the measured position value of the external radiation source into the above linear equation as a new variable, and obtain the real position value of the external radiation source as the third function of the quantity to be sought.

3) Construct the least squares model according to the first function, the second function, and the third function, and Taylor expand the model at the initial estimated value of the target position to solve the Newton iteration formula, and use the initial estimated value of the target position and Newton iteration The formula is iterated to a set number of iterations to obtain an accurate estimate of the target position.

The passive radar target positioning device referred to in the above-mentioned embodiments is actually a computer solution based on the method flow of the present invention, that is, a software framework that can be applied to a computer, and the above-mentioned device is corresponding to the method flow. processing process. Since the introduction of the above method is clear enough and complete, it will not be described in detail.

The above descriptions are only preferred embodiments of the present invention, and are not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and changes. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included within the scope of the claims of the present invention.

Claims (6)

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) 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.

2. The passive radar target locating method according to claim 1, wherein step 3) further comprises the sub-steps of constructing a least squares model by:

(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.

3. The passive radar target locating method of claim 2, 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.

4. 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) 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.

5. The passive radar target locating apparatus of claim 4, wherein step 3) further comprises the sub-steps of constructing a least squares model by:

(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.

6. The passive radar target locating apparatus of claim 5, 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.