阅读说明：本技术 一种协同校正源观测信息的加权多维标度tdoa定位方法 (Weighted multi-dimensional scale TDOA (time difference of arrival) positioning method for cooperative correction source observation information ) 是由 王鼎 尹洁昕 王盛 杨宾 唐涛 郑娜娥 聂福全 张莉 王成 吕品品 于 2021-08-13 设计创作，主要内容包括：本发明公开了一种协同校正源观测信息的加权多维标度TDOA定位方法,该方法将校正源观测信息与加权多维标度TDOA定位方法相结合,共包含两个计算阶段,在阶段a,通过利用校正源观测信息提高对传感器位置向量的估计精度(相比于其先验观测精度而言),在阶段b,联合阶段a的估计结果以及目标源观测信息对目标源进行定位,并进一步提高对传感器位置向量的估计精度(相比于阶段a的估计精度而言)。本发明能够充分利用校正源观测信息,并将其与加权多维标度TDOA定位方法进行深度融合,可以更好地抑制传感器位置先验误差的影响,从而提高对目标源的定位精度,并且还具有渐近统计最优性。(The invention discloses a weighted multi-dimensional scale TDOA (time difference of arrival) positioning method for cooperatively correcting source observation information, which combines the correction source observation information with the weighted multi-dimensional scale TDOA positioning method and comprises two calculation stages, wherein in the stage a, the estimation precision of a sensor position vector (compared with the prior observation precision) is improved by using the correction source observation information, and in the stage b, a target source is positioned by combining the estimation result of the stage a and the target source observation information, and the estimation precision of the sensor position vector (compared with the estimation precision of the stage a) is further improved. The method can fully utilize the observation information of the correction source, and carry out depth fusion on the observation information and the weighted multi-dimensional scale TDOA positioning method, can better inhibit the influence of the prior error of the sensor position, thereby improving the positioning precision of the target source and having asymptotic statistical optimality.)

1. A method for weighted multi-dimensional scale TDOA location with coordinated correction of source observation information, the method comprising two stages of computation: the method comprises a stage a and a stage b, wherein the stage a comprises steps 1 to 9, the stage b comprises steps 10 to 20, and the specific steps are as follows:

step 1: placing M sensors in space, placing 1 correction source in a positioning area, then obtaining the time difference between the correction source signal reaching the M-th sensor and reaching the 1 st sensor, and multiplying the time difference by the signal propagation speed to obtain the observed quantity of the correction source distance difference

Step 2: using sensor positionA priori observationsAnd correcting source range difference observationsConstructing an M x M order scalar product matrix

And step 3: apriori observations using sensor positionAnd correcting source range difference observationsConstructing an Mx 4 order matrixBy a matrixObtaining a 5 x 1 order vectorAnd further obtain a scalar quantity(Vector)And a scalar quantity

And 4, step 4: let iteration index k:equalto 0, set iteration convergence threshold value delta^(a)And an iteration initial value

And 5: sequentially calculating Mx (M-1) order matrixAndand Mx 3 Mth order matrixAnd

step 6: calculating an Mx (M-1) order matrix according to the calculation result of the step 5And Mx 3 Mth order matrixAnd to the matrixPerforming singular value decomposition;

and 7: calculating (4M-1) × (4M-1) order optimal weighting matrix according to the calculation result of the step 6

And 8: by usingComputing a 3 Mx 1 order vectorIf it isThen an estimate of the sensor position vector at stage a is obtained and recorded asAnd go to step 9; otherwise, updating the iteration index k ═ k +1, and going to the step 5;

and step 9: calculating a 3 Mx 3M-order mean square error matrix MSE by using the estimation result in the step 8^(a)；

Step 10: obtaining the time difference between the source signal of the target to be positioned and the M sensor and the 1 st sensor by using the M sensors arranged in the step 1, and multiplying the time difference by the signal propagation speed to obtain the observed quantity of the distance difference of the target source

Step 11: estimation of phase a using sensor position vectorsObserved distance difference from target sourceConstructing an M x M order scalar product matrix

Step 12: estimation of phase a using sensor position vectorsObserved distance difference from target sourceConstructing an Mx 4 order matrixAnd is composed of a matrixObtaining a matrix

Step 13: let iteration index k:equalto 0, set iteration convergence threshold value delta^(b)And setting an iteration initial valueAnd

step 14: sequentially calculating Mx (M-1) order matrixAndand Mx 3 Mth order matrixAnd

step 15: calculating an M x (M-1) order matrix from the calculation results of step 14And Mx 3 Mth order matrixAnd to the matrixPerforming singular value decomposition;

step 16: based on mean square error matrix MSE in step 9^(a)Calculating an optimal weighting matrix of order (4M-1) × (4M-1)Then using the optimal weighting matrixCalculating the (3M +4) × (3M +4) order matrixAnd (3M +4) × 1 order vector

And step 17: constructing a (3M +4) × (3M +4) order matrix Λ^(b)Then to the matrixCarrying out eigenvalue decomposition;

step 18: calculating a (3M +4) x 1 order vector using the eigenvalue decomposition result in step 17Andthen calculates the scalar quantity

Step 19: using Newton's method to solveSelecting real roots and eliminating false roots, wherein the roots are roots of a unitary 6-degree polynomial of coefficients;

step 20: computing iterative results using the root selected in step 19Andif it isThen obtaining the estimation result of the target source position vector in the stage bAnd the estimation of the sensor position vector in phase bOtherwise, the iteration index k: ═ k +1 is updated, and the process goes to step 14.

2. The method for TDOA location based on weighted multi-dimensional scale with co-correction of source observation information as recited in claim 1, wherein in said step 2, a M x M order scalar product matrix is constructed as follows

In the formula

3. The method for TDOA location based on weighted multi-dimensional scale with co-correction of source observation information as claimed in claim 1, wherein in said step 3, M x 4 order matrix is constructed as follows

By a matrixObtaining a 5 x 1 order vectorThe corresponding calculation formula is:

in the formulau_dIn order to correct the position vector of the source,a priori observations of the position of the 1 st sensor; 1_M×1Representing an mx 1 order all-1 vector; scalar quantityIs a vector1 st element in (1); vector quantityIs a vectorA column vector of the 2 nd to 4 th elements; scalar quantityIs a vectorThe 5 th element in (a);

4. the method for TDOA location based on weighted multi-dimensional scale with co-correction of source observation information as claimed in claim 1, wherein in said step 5, M x (M-1) order matrix is calculated sequentially as followsAndand Mx 3 Mth order matrixAnd

matrix arrayThe calculation formula of (2) is as follows:

in the formula

I_MRepresenting an M × M order identity matrix; i is_M-1Representing an identity matrix of order (M-1) × (M-1); o is_1×(M-1)Represents an all-zero matrix of order 1 × (M-1);representing a vectorThe column vector consisting of the 1 st to 3 rd elements;representing a vectorThe column vector consisting of the 4 th to 6 th elements;representing a vectorA column vector consisting of the 3M-2 to 3M-th elements;

matrix arrayThe calculation formula of (2) is as follows:

in the formula

O_3×MRepresenting a 3 × M order all-zero matrix;represents an identity matrix I of 5 × 5 order₅The 5 th column vector;

matrix arrayThe calculation formula of (2) is as follows:

in the formula

Matrix arrayThe calculation formula of (2) is as follows:

in the formula

Representing an M × M order identity matrix I_MThe 1 st column vector of (1); i is₃Representing a 3 × 3 order identity matrix; o is_1×3MRepresents a 1 × 3M order all-zero matrix; o is_4×3Representing a 4 x 3 order all-zero matrix;representing a vectorThe 2 nd to 4 th elements of the column vector.

5. The method for TDOA location based on weighted multi-dimensional scale with co-correction of source observation information as recited in claim 4, wherein in said step 6, M x (M-1) order matrix is calculated as followsAnd Mx 3 Mth order matrix

And to the matrixSingular value decomposition is carried out:

in the formulaRepresents an identity matrix I of 5 × 5 order₅The 5 th column vector;represents an M (M-1) order column orthogonal matrix;represents an orthogonal matrix of order (M-1) × (M-1);representing an (M-1) × (M-1) order diagonal matrix whose diagonal elements are matricesThe singular value of (a).

6. The method for TDOA location based on weighted multi-dimensional scale with co-correction of source observation information as claimed in claim 5, wherein in said step 7, the optimal weighting matrix of the order of (4M-1) × (4M-1) is calculated as follows

In the formula E_dRepresenting a covariance matrix of the corrected source range difference observation errors; e_sRepresenting the covariance matrix of the prior errors of the sensor locations.

7. The method for TDOA location based on weighted multi-dimensional scale with co-correction of source observation information as recited in claim 6, wherein in said step 8, a 3M x 1 order vector is computed as follows

In the formula

I_3MRepresenting a 3M × 3M order identity matrix;represents an identity matrix I of 5 × 5 order₅The 1 st column vector of (1).

8. The TDOA location method with weighted multi-dimensional scale for cooperatively correcting source observation information as claimed in claim 1, wherein in said step 9, the 3 mx 3M-order mean square error matrix MSE is calculated as follows^(a)：

In the formula

1_(M-1)×1Represents (M-1) x 1 order full 1 vector; u. of_dIs a position vector of the correction source;representing a vectorThe column vector consisting of the 1 st to 3 rd elements;representing a vectorThe column vector consisting of the 4 th to 6 th elements;representing a vectorThe column vector consisting of the 7 th to 9 th elements;representing a vectorA column vector consisting of the 3M-2 to 3M-th elements; e_dRepresenting a covariance matrix of the corrected source range difference observation errors; e_sRepresenting the covariance matrix of the prior errors of the sensor locations.

9. The method for TDOA location based on weighted multi-dimensional scale with co-correction of source observation information as recited in claim 8, wherein in said step 11, an M x M scalar product matrix is constructed as follows

In the formula

10. The method for TDOA location based on weighted multi-dimensional scale with co-correction of source observation information as recited in claim 1, wherein in said step 12, the M x 4 order matrix is constructed as follows

By a matrixObtaining an Mx 5 order matrixThe corresponding calculation formula is:

in the formula

11. The method of claim 10A method for weighted multi-dimensional scale TDOA location of cooperative correction source observation information is characterized in that in step 13, iteration initial values are adoptedAndthe corresponding expression is:

vector in the formulaRepresentation matrixThe 1 st column vector of (1); matrix arrayRepresentation matrixThe 2 nd to 5 th column vectors in (b).

12. The method for TDOA location based on weighted multi-dimensional scale with co-correction of source observation information as recited in claim 11, wherein in said step 14, M x (M-1) order matrices are computed sequentially as followsAndand Mx 3 Mth order matrixAnd

matrix arrayThe calculation formula of (2) is as follows:

in the formula

WhereinRepresenting a vectorThe column vector consisting of the 1 st to 3 rd elements;representing a vectorThe column vector consisting of the 4 th to 6 th elements;representing a vectorA column vector consisting of the 3M-2 to 3M-th elements;

matrix arrayThe calculation formula of (2) is as follows:

in the formula

Wherein

Matrix arrayThe calculation formula of (2) is as follows:

in the formula

Matrix arrayThe calculation formula of (2) is as follows:

in the formula

1_M×1Representing an mx 1 order all-1 vector;represents an identity matrix I of 5 × 5 order₅The 5 th column vector;representing a vectorThe 2 nd to 4 th elements of the column vector.

13. The method for TDOA location based on weighted multi-dimensional scale with co-correction of source observation information as recited in claim 12, wherein in said step 15, the matrix is alignedSingular value decomposition is carried out to obtain:

in the formulaRepresents an M (M-1) order column orthogonal matrix;represents an orthogonal matrix of order (M-1) × (M-1);representing an (M-1) × (M-1) order diagonal matrix whose diagonal elements are matricesThe singular value of (a).

14. The method for TDOA location based on weighted multi-dimensional scale with co-correction of source observation information as recited in claim 13, wherein in said step 16, an optimal weighting matrix of the order of (4M-1) × (4M-1) is calculated as follows

In the formula E_tRepresenting a target source range difference observation error covariance matrix;

then using the optimal weighting matrixCalculating the (3M +4) × (3M +4) order matrixAnd (3M +4) × 1 order vectorThe corresponding calculation formula is:

in the formula O_4×3MRepresenting a 4 x 3M order all-zero matrix; o is_3M×4Representing a 3 mx 4 order all-zero matrix; o is_3M×(M-1)Represents a 3 Mx (M-1) order all-zero matrix; o is_(M-1)×3MRepresenting an (M-1). times.3M order all-zero matrix.

15. The method for weighted multi-dimensional scale TDOA location based on collaborative correction of source observation information as recited in claim 1, wherein in said step 17, a matrix Λ of (3M +4) × (3M +4) order is constructed as follows^(b)：

In the formula I₃Representing a 3 × 3 order identity matrix; o is_3(M-1)×1Represents a 3(M-1) × 1 order all-zero matrix; o is_1×3(M-1)Represents an all-zero matrix of order 1 × 3 (M-1); o is_{3(M-1)×3(M-1)}Represents a 3(M-1) × 3(M-1) order all-zero matrix;

then to the matrixThe characteristic value decomposition is carried out to obtain:

in the formulaIs a matrix made up of eigenvectors;whereinThe eigenvalues are represented and arranged in descending order of absolute value from large to small, only the first 4 eigenvalues are non-zero eigenvalues, and the rest are zero eigenvalues.

16. The method for TDOA location based on weighted multi-dimensional scale with co-correction of source observation information as recited in claim 15, wherein in said step 18, a (3M +4) x 1 order vector is computed as followsAnd

the scalar is then calculated as follows

In the formula

WhereinRepresenting a vectorThe jth element in (a).

17. The method for TDOA location based on weighted multi-dimensional scale with co-correction of source observation information as claimed in claim 1, wherein in said step 19, Newton's method is used for solvingFor the root of a univariate 6 th order polynomial of the coefficients, the corresponding polynomial equation can be expressed as:

let the root of the polynomial equation beAnd selects the real root using the following criteria

In the formulaE_tRepresenting a target source range difference observation error covariance matrix;

andrespectively indicate the utilization of the jth rootThe obtained position vector of the m-th sensor and the position vector of the target source are calculated according to the following formula:

wherein I₃Representing a 3 × 3 order identity matrix; o is_3×(3M+1)Represents a 3 × (3M +1) order all-zero matrix; o is_3×4Representing a 3 × 4 order all-zero matrix;representing an M × M order identity matrix I_MThe m-th column vector of (1).

18. The method for weighted multi-dimensional scale TDOA location based on collaborative correction of source observation information as recited in claim 1, wherein in said step 20, the calculation is performed as followsAnd

in the formula O_4×4Representing a 4 x 4 order all-zero matrix; i is₄Representing a 4 x 4 order identity matrix.

Technical Field

The invention belongs to the technical field of target source positioning, and particularly relates to a weighted multi-dimensional scale TDOA (time difference of arrival) positioning method for cooperative correction source observation information.

Background

As is well known, the target source positioning technology plays an important role in the fields of target monitoring, navigation telemetry, seismic surveying, radio astronomy, emergency rescue, safety management and other industrial and electronic information. The positioning (i.e. position parameter estimation) of the target source can be accomplished by using active devices such as radar, laser, sonar and the like, which are called active positioning technologies and have the advantages of all weather, high precision and the like. However, the active positioning system usually needs to transmit a high-power electromagnetic signal to implement, so that the position of the active positioning system is very easy to expose, and the active positioning system is easy to be found by the other party, and is affected by the electronic interference of the other party, so that the positioning performance is greatly deteriorated, and even the safety and reliability of the system are compromised.

Target source localization may also be achieved using target (actively) radiated or (passively) scattered radio signals, a technique referred to as passive localization technique, which refers to estimating target location parameters by receiving target radiated or scattered radio signals without the observation station actively transmitting electromagnetic signals. Compared with an active positioning system, the passive positioning system has the advantages of no active transmission of electromagnetic signals, strong viability, long reconnaissance action distance and the like, thereby being widely concerned and deeply researched by scholars at home and abroad. The passive positioning system can be divided into a single-station passive positioning system and a multi-station passive positioning system according to the number of observation stations (or sensors), wherein the multi-station passive positioning system generally has higher positioning precision. In a multi-station location system, TDOA (which may be equivalently a range difference) is a type of observation that is applied more frequently. The TDOA positioning technology is to perform positioning by using time difference of arrival of target source signals acquired by a plurality of sensors in a space, wherein the time difference of arrival of the target source signals at two different sensors can determine 1 hyperboloid (line), and the position coordinates of the target source can be obtained by intersecting a plurality of hyperboloids (lines). With the continuous development of modern communication technology and time difference measurement technology, TDOA positioning technology has become one of the most mainstream target source positioning means.

Based on the algebraic characteristics of TDOA observation equations, foreign and domestic researchers have proposed many superior TDOA locating methods, wherein the weighted multi-dimensional scale TDOA locating method has certain representativeness (Wei H W, WanQ, Chen Z X, Ye S F.A novel weighted multidimensional scaling analysis for time-of-arrival-based mobile location [ J ]. IEEE Transactions on Signal Processing,2008,56(7):3018 and 3022.) (Ho K C, Lu X, Kovaservirus L. Source location using A and FDOA measures in the prediction of location errors: analysis and analysis [ J ] on signaling Processing,2007, schematic [ J ] Processing,2007, W55, W-boundary, W-55, W-simulation [ J ] for weighted multi-dimensional scale TDOA locating analysis for time-of time-arrival Processing, systems, and Signal Processing,2017,36(11): 1754-. On the other hand, in practical applications, when sensors are randomly arranged or mounted on platforms such as an aircraft or a ship, a priori errors of the sensor positions inevitably occur, and the priori errors have great influence on the positioning accuracy of the TDOA (Zhu Guaiui, Von Dazheng, Nee Weike, the equation of time difference positioning algorithm [ J ] electronics, 2016,44(1):21-26.) based on multi-dimensional scale analysis in the case of the sensor position errors.

Disclosure of Invention

Aiming at the problem that the prior error of the sensor position has a large influence on the TDOA positioning precision in practical application, the invention provides a weighted multi-dimensional scale TDOA positioning method for cooperatively correcting source observation information, which combines the correction source observation information and can better inhibit the influence of the prior error of the sensor position, thereby improving the positioning precision of a target source and further improving the estimation precision of a sensor position vector (compared with the prior observation precision).

In order to achieve the above object, the present invention provides a method for weighted multi-dimensional scale TDOA location with cooperative correction of source observation information, which comprises two computation stages, stage a and stage b, wherein stage a comprises steps 1 to 9, and stage b comprises steps 10 to 20. The purpose of stage a is to improve the accuracy of the estimate of the sensor position vector (compared to its a priori accuracy of observation) using the corrected source observation information. In stage a, first obtaining TDOA observations (equivalent to range-difference observations) about a corrected source signal using a plurality of sensors in space and constructing a scalar product matrix using the range-difference observations, thereby forming a multi-dimensional scaled linear equation about a sensor position vector; then, quantitatively deducing an error covariance matrix in the linear equation by using a first-order error analysis method, and designing an optimal weighting matrix for obtaining a closed-form solution of a sensor position vector; and finally, deriving an estimated mean square error matrix of the closed-form solution. The purpose of the stage b is to combine the estimation result of the stage a and the observation information of the target source to locate the target source, and further improve the estimation accuracy of the sensor position vector (compared with the estimation accuracy of the stage a). In stage b, first obtaining TDOA observations (equivalent to range-difference observations) about the target source signals using the same sensors in space and constructing a scalar product matrix using the range-difference observations, thereby forming multi-dimensional scaled linear equations about the target source location vectors and the sensor location vectors; then, combining the estimated mean square error of the stage a, quantitatively deducing an error covariance matrix in the linear equation by using a first-order error analysis method, and designing an optimal weighting matrix; and finally, constructing a parameter solving model by combining the estimation result given in the stage a, converting the parameter solving problem into a polynomial root solving problem by utilizing a Lagrange multiplier technology, and obtaining a joint estimation value of a target source position vector and a sensor position vector by a Newton root solving method. Compared with the existing weighted multi-dimensional scale TDOA positioning method, the new method combines the correction source observation information, can better inhibit the influence of the prior error of the sensor position, thereby improving the positioning precision of the target source and having asymptotic statistical optimality. The invention specifically adopts the following technical scheme:

step 1: placing M sensors in space, placing 1 correction source in a positioning area, then obtaining the time difference between the correction source signal reaching the M-th sensor and reaching the 1 st sensor, and multiplying the time difference by the signal propagation speed to obtain the observed quantity of the correction source distance difference

Step 2: apriori observations using sensor positionAnd correcting source range difference observationsConstructing an M x M order scalar product matrix

And step 3: apriori observations using sensor positionAnd correcting source range difference observationsConstructing an Mx 4 order matrixBy a matrixTo obtain5 x 1 order vectorAnd further obtain a scalar quantity(Vector)And a scalar quantity

And 4, step 4: let iteration index k:equalto 0, set iteration convergence threshold value delta^(a)And an iteration initial value

And 5: sequentially calculating Mx (M-1) order matrixAndand Mx 3 Mth order matrixAnd

step 6: calculating an Mx (M-1) order matrix according to the calculation result of the step 5And Mx 3 Mth order matrixAnd to the matrixPerforming singular value decomposition;

and 7: calculating (4M-1) × (4M-1) order optimal weighting matrix according to the calculation result of the step 6

And 8: by usingComputing a 3 Mx 1 order vectorIf it isThen an estimate of the sensor position vector at stage a is obtained and recorded asAnd go to step 9; otherwise, updating the iteration index k ═ k +1, and going to the step 5;

and step 9: calculating a 3 Mx 3M-order mean square error matrix MSE by using the estimation result in the step 8^(a)；

Step 10: obtaining the time difference between the source signal of the target to be positioned and the M sensor and the 1 st sensor by using the M sensors arranged in the step 1, and multiplying the time difference by the signal propagation speed to obtain the observed quantity of the distance difference of the target source

Step 11: estimation of phase a using sensor position vectorsObserved distance difference from target sourceConstructing an M x M order scalar product matrix

Step 12: estimation of phase a using sensor position vectorsObserved distance difference from target sourceConstructing an Mx 4 order matrixAnd is composed of a matrixObtaining a matrix

Step 13: let iteration index k:equalto 0, set iteration convergence threshold value delta^(b)And setting an iteration initial valueAnd

step 14: sequentially calculating Mx (M-1) order matrixAndand Mx 3 Mth order matrixAnd

step 15: calculating an M x (M-1) order matrix from the calculation results of step 14And Mx 3 Mth order matrixAnd to the matrixPerforming singular value decomposition;

step 16: based on mean square error matrix MSE in step 9^(a)Calculating an optimal weighting matrix of order (4M-1) × (4M-1)Then using the optimal weighting matrixCalculating the (3M +4) × (3M +4) order matrixAnd (3M +4) × 1 order vector

And step 17: constructing a (3M +4) × (3M +4) order matrix Λ^(b)Then to the matrixCarrying out eigenvalue decomposition;

step 18: calculating a (3M +4) x 1 order vector using the eigenvalue decomposition result in step 17Andthen calculates the scalar quantity

Step 19: using Newton's method to solveSelecting real roots and eliminating false roots, wherein the roots are roots of a unitary 6-degree polynomial of coefficients;

step 20: computing iterative results using the root selected in step 19Andif it isThen obtaining the estimation result of the target source position vector in the stage bAnd the estimation of the sensor position vector in phase bOtherwise, the iteration index k: ═ k +1 is updated, and the process goes to step 14.

Further, in the step 2, an M × M order scalar product matrix is constructed as follows

In the formula

Further, in the step 3, an mx 4 order matrix is constructed as follows

By a matrixObtaining a 5 x 1 order vectorThe corresponding calculation formula is:

in the formulau_dIn order to correct the position vector of the source,a priori observations of the position of the 1 st sensor; 1_M×1Representing an mx 1 order all-1 vector; scalar quantityIs a vector1 st element in (1); vector quantityIs a vectorA column vector of the 2 nd to 4 th elements; scalar quantityIs a vectorThe 5 th element in (a);

further, in the step 5, the M × (M-1) order matrix is sequentially calculated as followsAndand Mx 3 Mth order matrixAnd

matrix arrayThe calculation formula of (2) is as follows:

in the formula

I_MRepresenting an M × M order identity matrix; i is_M-1Representing an identity matrix of order (M-1) × (M-1); o is_1×(M-1)Represents an all-zero matrix of order 1 × (M-1);representing a vectorThe column vector consisting of the 1 st to 3 rd elements;representing a vectorThe column vector consisting of the 4 th to 6 th elements;representing a vectorA column vector consisting of the 3M-2 to 3M-th elements;

matrix arrayThe calculation formula of (2) is as follows:

in the formula

O_3×MRepresenting a 3 × M order all-zero matrix;represents an identity matrix I of 5 × 5 order₅The 5 th column vector;

matrix arrayThe calculation formula of (2) is as follows:

in the formula

Matrix arrayThe calculation formula of (2) is as follows:

in the formula

Representing an M × M order identity matrix I_MThe 1 st column vector of (1); i is₃Representing a 3 × 3 order identity matrix; o is_1×3MRepresents a 1 × 3M order all-zero matrix; o is_4×3Representing a 4 x 3 order all-zero matrix;representing a vectorThe 2 nd to 4 th elements of the column vector.

Further, in the step 6, the M × (M-1) order matrix is calculated as followsAnd Mx 3 Mth order matrix

And to the matrixSingular value decomposition is carried out:

in the formulaRepresents an identity matrix I of 5 × 5 order₅The 5 th column vector;represents an M (M-1) order column orthogonal matrix;represents an orthogonal matrix of order (M-1) × (M-1);representing an (M-1) × (M-1) order diagonal matrix whose diagonal elements are matricesThe singular value of (a).

Further, in the step 7, the optimal weighting matrix of the (4M-1) × (4M-1) order is calculated as follows

In the formula E_dRepresenting a covariance matrix of the corrected source range difference observation errors; e_sRepresenting the covariance matrix of the prior errors of the sensor locations.

Further, in step 8, a 3 mx 1 order vector is calculated as follows

In the formula

I_3MRepresenting a 3M × 3M order identity matrix;represents an identity matrix I of 5 × 5 order₅The 1 st column vector of (1).

Further, in step 9, a 3 mx 3M-order mean square error matrix MSE is calculated as follows^(a)：

In the formula

1_(M-1)×1Represents (M-1) x 1 order full 1 vector; u. of_dIs a position vector of the correction source;representing a vectorThe column vector consisting of the 1 st to 3 rd elements;representing a vectorThe column vector consisting of the 4 th to 6 th elements;representing a vectorThe column vector consisting of the 7 th to 9 th elements;representing a vectorA column vector consisting of the 3M-2 to 3M-th elements; e_dRepresenting a covariance matrix of the corrected source range difference observation errors; e_sRepresenting the covariance matrix of the prior errors of the sensor locations.

Further, in the step 11, an M × M order scalar product matrix is constructed as follows

In the formula

Further, in the step 12, an mx 4 order matrix is constructed as follows

By a matrixObtaining an Mx 5 order matrixThe corresponding calculation formula is:

in the formula

Further, in the step 13, an initial value is iteratedAndthe corresponding expression is:

vector in the formulaRepresentation matrixThe 1 st column vector of (1); matrix arrayRepresentation matrixThe 2 nd to 5 th column vectors in (b).

Further, in the step 14, the M × (M-1) order matrix is sequentially calculated as followsAndand Mx 3 Mth order matrixAnd

matrix arrayThe calculation formula of (2) is as follows:

in the formula

WhereinRepresenting a vectorThe column vector consisting of the 1 st to 3 rd elements;representing a vectorThe column vector consisting of the 4 th to 6 th elements;representing a vectorA column vector consisting of the 3M-2 to 3M-th elements;

matrix arrayThe calculation formula of (2) is as follows:

in the formula

Wherein

Matrix arrayThe calculation formula of (2) is as follows:

in the formula

Matrix arrayThe calculation formula of (2) is as follows:

in the formula

1_M×1Representing an mx 1 order all-1 vector;represents an identity matrix I of 5 × 5 order₅The 5 th column vector;representing a vectorThe 2 nd to 4 th elements of the column vector.

Further, in the step 15, the matrix is alignedSingular value decomposition is carried out to obtain:

in the formulaRepresents an M (M-1) order column orthogonal matrix;represents an orthogonal matrix of order (M-1) × (M-1);representing an (M-1) × (M-1) order diagonal matrix whose diagonal elements are matricesThe singular value of (a).

Further, in the step 16, the optimal weighting matrix of the (4M-1) × (4M-1) order is calculated as follows

In the formula E_tRepresenting a target source range difference observation error covariance matrix;

then using the optimal weighting matrixCalculating the (3M +4) × (3M +4) order matrixAnd (3M +4) × 1 order vectorThe corresponding calculation formula is:

in the formula O_4×3MRepresenting a 4 x 3M order all-zero matrix; o is_3M×4Representing a 3 mx 4 order all-zero matrix; o is_3M×(M-1)Represents a 3 Mx (M-1) order all-zero matrix; o is_(M-1)×3MRepresenting an (M-1). times.3M order all-zero matrix.

Further, in the step 17, a matrix Λ of (3M +4) × (3M +4) order is constructed as follows^(b)：

In the formula I₃Representing a 3 × 3 order identity matrix; o is_3(M-1)×1Represents a 3(M-1) × 1 order all-zero matrix; o is_1×3(M-1)Represents an all-zero matrix of order 1 × 3 (M-1); o is_{3(M-1)×3(M-1)}Represents a 3(M-1) × 3(M-1) order all-zero matrix;

then to the matrixThe characteristic value decomposition is carried out to obtain:

in the formulaIs a matrix made up of eigenvectors;whereinThe eigenvalues are represented and arranged in descending order of absolute value from large to small, only the first 4 eigenvalues are non-zero eigenvalues, and the rest are zero eigenvalues.

Further, in the step 18, a (3M +4) × 1 order vector is calculated as followsAnd

the scalar is then calculated as follows

In the formula

WhereinRepresenting a vectorThe jth element in (a).

Further, in the step 19, the solution is solved by using Newton's method toFor the root of a univariate 6 th order polynomial of the coefficients, the corresponding polynomial equation can be expressed as:

let the root of the polynomial equation beAnd selects the real root using the following criteria

In the formulaE_tRepresenting a target source range difference observation error covariance matrix;

andrespectively indicate the utilization of the jth rootThe obtained position vector of the m-th sensor and the position vector of the target source are calculated according to the following formula:

wherein I₃Representing a 3 × 3 order identity matrix; o is_3×(3M+1)Represents a 3 × (3M +1) order all-zero matrix; o is_3×4Representing a 3 × 4 order all-zero matrix;representing an M × M order identity matrix I_MThe m-th column vector of (1).

Further, in the step 20, the calculation is performed as followsAnd

in the formula O_4×4Representing a 4 x 4 order all-zero matrix; i is₄Representing a 4 x 4 order identity matrix.

Compared with the prior art, the invention has the following beneficial effects:

the patent provides a weighted multi-dimensional scale TDOA positioning method for cooperatively correcting source observation information aiming at the scene where the prior error of the sensor position exists, combines the correction source observation information with the weighted multi-dimensional scale TDOA positioning method, can fully utilize the correction source observation information, and carries out depth fusion on the correction source observation information and the weighted multi-dimensional scale TDOA positioning method, can better inhibit the influence of the prior error of the sensor position, thereby improving the positioning precision of a target source, and further improving the estimation precision of a sensor position vector (compared with the prior observation precision).

Drawings

FIG. 1 is a basic flowchart of a method for weighted multi-dimensional scale TDOA location of collaborative correction of source observation information in accordance with an embodiment of the present invention;

FIG. 2 is a target source positioning result scatter plot and a positioning error elliptic curve (X-Y plane coordinates); wherein 2(a) is a target source positioning result scatter diagram and a positioning error elliptic curve (X-Y plane coordinate) corresponding to the weighted multidimensional scaling positioning method disclosed by the patent; 2(b) a target source positioning result scatter diagram and a positioning error elliptic curve (X-Y plane coordinates) corresponding to the existing weighted multidimensional scaling positioning method;

FIG. 3 is a target source positioning result scatter plot and a positioning error elliptic curve (Y-Z plane coordinates); wherein 3(a) is a target source positioning result scatter diagram and a positioning error elliptic curve (Y-Z plane coordinate) corresponding to the weighted multidimensional scaling positioning method disclosed by the patent; 3(b) a target source positioning result scatter diagram and a positioning error elliptic curve (Y-Z plane coordinate) corresponding to the existing weighted multidimensional scaling positioning method;

FIG. 4 shows the estimated root mean square error of the target source location vector as a function of the standard deviation σ_tThe variation curve of (d);

FIG. 5 is a graph of the root mean square error of the sensor position vector estimate as a function of the standard deviation σ_tThe variation curve of (d);

FIG. 6 shows the estimated root mean square error of the target source location vector as a function of the standard deviation σ_sThe variation curve of (d);

FIG. 7 is a graph of the root mean square error of the sensor position vector estimate as a function of the standard deviation σ_sThe change curve of (2).

Detailed Description

The invention is further illustrated by the following examples in conjunction with the accompanying drawings:

as shown in FIG. 1, a method for weighted multi-dimensional scale TDOA location with collaborative correction of source observation information includes two stages of computation: the method comprises a stage a and a stage b, wherein the stage a comprises steps 1 to 9, the stage b comprises steps 10 to 20, and the specific steps are as follows:

step 1: placing M sensors in space, placing 1 correction source in a positioning area, then obtaining the time difference between the signal of the correction source reaching the M (M is more than or equal to 2 and less than or equal to M) th sensor and the signal reaching the 1 st sensor, and multiplying the time difference by the signal propagation speed to obtain the observed quantity of the distance difference of the correction source

Step 2: apriori observations using sensor positionAnd correcting source range difference observationsConstructing an M x M order scalar product matrix

And step 3: apriori observations using sensor positionAnd correcting source range difference observationsConstructing an Mx 4 order matrixBy a matrixObtaining a 5 x 1 order vectorAnd further obtain a scalar quantity(Vector)And a scalar quantity

And 4, step 4: let iteration index k:equalto 0, set iteration convergence threshold value delta^(a)And an iteration initial value

And 5: sequentially calculating Mx (M-1) order matrixAndand Mx 3 Mth order matrixAnd

step 6: calculating an Mx (M-1) order matrix according to the calculation result of the step 5And Mx 3 Mth order matrixAnd to the matrixPerforming singular value decomposition;

and 7: calculating the (4M-1) × (4M-1) order of the best according to the calculation result of the step 6Optimal weighting matrix

And 8: by usingComputing a 3 Mx 1 order vectorIf it isThen an estimate of the sensor position vector at stage a is obtained and recorded asAnd go to step 9; otherwise, updating the iteration index k ═ k +1, and going to the step 5;

and step 9: calculating a 3 Mx 3M-order mean square error matrix MSE by using the estimation result in the step 8^(a)；

Step 10: obtaining the time difference between the source signal of the target to be positioned and the M (M is more than or equal to 2 and less than or equal to M) sensor and the 1 st sensor by using the M sensors placed in the step 1, and multiplying the time difference by the signal propagation speed to obtain the observed quantity of the distance difference of the target source

Step 11: estimation of phase a using sensor position vectorsObserved distance difference from target sourceConstructing an M x M order scalar product matrix

Step 12: estimation at stage a using sensor position vectorsResult countingObserved distance difference from target sourceConstructing an Mx 4 order matrixAnd is composed of a matrixObtaining a matrix

Step 13: let iteration index k:equalto 0, set iteration convergence threshold value delta^(b)And setting an iteration initial valueAnd

step 14: sequentially calculating Mx (M-1) order matrixAndand Mx 3 Mth order matrixAnd

step 15: calculating an M x (M-1) order matrix from the calculation results of step 14And Mx 3 Mth order matrixAnd to the matrixPerforming singular value decomposition;

step 16: based on mean square error matrix MSE in step 9^(a)Calculating an optimal weighting matrix of order (4M-1) × (4M-1)Then using the optimal weighting matrixCalculating the (3M +4) × (3M +4) order matrixAnd (3M +4) × 1 order vector

And step 17: constructing a (3M +4) × (3M +4) order matrix Λ^(b)Then to the matrixCarrying out eigenvalue decomposition;

step 18: calculating a (3M +4) x 1 order vector using the eigenvalue decomposition result in step 17Andthen calculates the scalar quantity

Step 19: using Newton's method to solveIs one of coefficientSelecting real roots and eliminating false roots from roots of the 6 th-order polynomial;

step 20: computing iterative results using the root selected in step 19Andif it isThen obtaining the estimation result of the target source position vector in the stage bAnd the estimation of the sensor position vector in phase bOtherwise, the iteration index k: ═ k +1 is updated, and the process goes to step 14.

Further, in the step 1, M sensors are placed in the space, wherein the position vector of the M (2 ≦ M ≦ M) sensor is1 correction source is arranged in the positioning area, and the position vector of the correction source is(known quantity), and then obtaining the time difference between the arrival of the correction source signal at the m-th sensor and the arrival at the 1 st sensorAnd multiplying the time difference by the signal propagation speed to obtain a corrected source range difference observed quantityThe corresponding expression is:

in the formula of_dmRepresenting the corrected source range difference observation error.

Further, in the step 2, the observed quantity is observed a priori by using the position of the sensorAnd correcting source range difference observationsConstructing an M x M order scalar product matrixThe corresponding calculation formula is:

in the formula

Further, in step 3, the observed quantity is observed a priori by using the sensor positionAnd correcting source range difference observationsConstructing an Mx 4 order matrixThe corresponding expression is:

by a matrixObtaining a 5 x 1 order vectorThe corresponding calculation formula is:

in the formulau_dIn order to correct the position vector of the source,a priori observations of the position of the 1 st sensor; 1_M×1Representing an mx 1 order all-1 vector; scalar quantityIs a vector1 st element in (1); vector quantityIs a vectorA column vector of the 2 nd to 4 th elements; scalar quantityIs a vectorThe 5 th element in (a);

further, in step 4, let the iteration index k:equalto 0, and set the iteration convergence threshold value δ^(a)And is combined withApriori observations using sensor positionSetting an iteration initial valueThe corresponding expression is:

further, in the step 5, M × (M-1) order matrix is calculated in sequenceAndand Mx 3 Mth order matrixAnd

matrix arrayThe calculation formula of (2) is as follows:

in the formula

I_MRepresenting an M × M order identity matrix; i is_M-1Representing an identity matrix of order (M-1) × (M-1); o is_1×(M-1)Represents an all-zero matrix of order 1 × (M-1);representing a vectorThe column vector consisting of the 1 st to 3 rd elements;representing a vectorThe column vector consisting of the 4 th to 6 th elements;representing a vectorA column vector consisting of the 3M-2 to 3M-th elements;

matrix arrayThe calculation formula of (2) is as follows:

in the formula

O_3×MRepresenting a 3 × M order all-zero matrix;represents an identity matrix I of 5 × 5 order₅The 5 th column vector; matrix arrayThe calculation formula of (2) is as follows:

in the formula

Matrix arrayThe calculation formula of (2) is as follows:

in the formula

Representing an M × M order identity matrix I_MThe 1 st column vector of (1); i is₃Representing a 3 × 3 order identity matrix; o is_1×3MRepresents a 1 × 3M order all-zero matrix; o is_4×3Representing a 4 x 3 order all-zero matrix;representing a vectorThe 2 nd to 4 th elements of the column vector.

Further, in the step 6, an M × (M-1) order matrix is calculatedAnd Mx 3 Mth order matrixAnd to the matrixSingular value decomposition is carried out to obtain:

in the formulaRepresents an identity matrix I of 5 × 5 order₅The 5 th column vector;represents an M (M-1) order column orthogonal matrix;represents an orthogonal matrix of order (M-1) × (M-1);representing an (M-1) × (M-1) order diagonal matrix whose diagonal elements are matricesThe singular value of (a).

Further, in the step 7, an optimal weighting matrix of (4M-1) × (4M-1) order is calculatedThe corresponding calculation formula is:

in the formula E_dRepresenting a covariance matrix of the corrected source range difference observation errors; e_sRepresenting the covariance matrix of the prior errors of the sensor locations.

Further, in the step 8, a 3 mx 1 order vector is calculatedThe corresponding calculation formula is:

in the formula

I_3MRepresenting a 3M × 3M order identity matrix;represents an identity matrix I of 5 × 5 order₅The 1 st column vector of (1).

Further, in step 9, a 3 mx 3M-order mean square error matrix MSE is calculated by using the estimation result in step 8^(a)The corresponding calculation formula is:

in the formula

1_(M-1)×1Represents (M-1) x 1 order full 1 vector; u. of_dIs a position vector of the correction source;representing a vectorThe column vector consisting of the 1 st to 3 rd elements;representing a vectorThe column vector consisting of the 4 th to 6 th elements;representing a vectorThe column vector consisting of the 7 th to 9 th elements;representing a vectorA column vector consisting of the 3M-2 to 3M-th elements; e_dRepresenting a covariance matrix of the corrected source range difference observation errors; e_sRepresenting the covariance matrix of the prior errors of the sensor locations.

Further, in the step 10, the step 1 is utilizedThe M sensors obtain the time difference between the arrival of the source signal of the target to be positioned at the mth sensor and the arrival at the 1 st sensorAnd multiplying the time difference by the signal propagation speed to obtain the target source range difference observed quantityThe corresponding expression is:

in the formula of_mRepresenting the target source range difference observation error.

Further, in step 11, the estimation result of the sensor position vector in stage a is usedObserved distance difference from target sourceConstructing an M x M order scalar product matrixThe corresponding calculation formula is:

in the formula

Further, in the step 12, the estimation result of the sensor position vector in the stage a is usedObserved distance difference from target sourceConstructing an Mx 4 order matrixThe corresponding expression is:

by a matrixObtaining an Mx 5 order matrixThe corresponding calculation formula is:

in the formula

Further, in step 13, let the iteration index k:equalto 0, and set the iteration convergence threshold value δ^(b)And setting an iteration initial valueAndthe corresponding expression is:

vector in the formulaRepresentation matrixThe 1 st column vector of (1); matrix arrayRepresentation matrixThe 2 nd to 5 th column vectors in (b).

Further, in the step 14, M × (M-1) order matrix is calculated in sequenceAndand Mx 3 Mth order matrixAnd

matrix arrayThe calculation formula of (2) is as follows:

in the formula

WhereinRepresenting a vectorThe column vector consisting of the 1 st to 3 rd elements;representing a vectorThe column vector consisting of the 4 th to 6 th elements;representing a vectorA column vector consisting of the 3M-2 to 3M-th elements;

matrix arrayThe calculation formula of (2) is as follows:

in the formula

Wherein

Matrix arrayThe calculation formula of (2) is as follows:

in the formula

Matrix arrayThe calculation formula of (2) is as follows:

in the formula

1_M×1Representing an mx 1 order all-1 vector;represents an identity matrix I of 5 × 5 order₅The 5 th column vector;representing a vector2 nd to 4 th elementsThe constructed column vector.

Further, in the step 15, an M × (M-1) order matrix is calculatedAnd Mx 3 Mth order matrixAnd to the matrixSingular value decomposition is carried out to obtain:

in the formulaRepresents an M (M-1) order column orthogonal matrix;represents an orthogonal matrix of order (M-1) × (M-1);representing an (M-1) × (M-1) order diagonal matrix whose diagonal elements are matricesThe singular value of (a).

Further, in the step 16, based on the mean square error matrix MSE in the step 9^(a)Calculating an optimal weighting matrix of order (4M-1) × (4M-1)The corresponding calculation formula is:

in the formula E_tRepresenting a target source range difference observation error covariance matrix;

then using the optimal weighting matrixCalculating the (3M +4) × (3M +4) order matrixAnd (3M +4) × 1 order vectorThe corresponding calculation formula is:

in the formula O_4×3MRepresenting a 4 x 3M order all-zero matrix; o is_3M×4Representing a 3 mx 4 order all-zero matrix; o is_3M×(M-1)Represents a 3 Mx (M-1) order all-zero matrix; o is_(M-1)×3MRepresenting an (M-1). times.3M order all-zero matrix.

Further, in the step 17, a matrix Λ of (3M +4) × (3M +4) order is constructed^(b)As shown in the following formula:

in the formula I₃Representing a 3 × 3 order identity matrix; o is_3(M-1)×1Represents a 3(M-1) × 1 order all-zero matrix; o is_1×3(M-1)Represents an all-zero matrix of order 1 × 3 (M-1); o is_{3(M-1)×3(M-1)}Represents a 3(M-1) × 3(M-1) order all-zero matrix;

then to the matrixThe characteristic value decomposition is carried out to obtain:

in the formulaIs a matrix made up of eigenvectors;whereinThe eigenvalues are represented and arranged in descending order of absolute value from large to small, only the first 4 eigenvalues are non-zero eigenvalues, and the rest are zero eigenvalues.

Further, in the step 18, a (3M +4) × 1 order vector is calculated using the eigenvalue decomposition result in the step 17Andthe corresponding calculation formula is:

then calculates the scalar quantityThe corresponding calculation formula is:

in the formula

WhereinRepresenting a vectorThe jth element in (a).

Further, in the step 19, the solution is solved by using Newton's method toFor the root of a univariate 6 th order polynomial of the coefficients, the corresponding polynomial equation can be expressed as:

let the root of the polynomial equation beAnd selects the real root using the following criteria

In the formulaE_tRepresenting a target source range difference observation error covariance matrix;

andrespectively indicate the utilization of the jth rootThe obtained position vector of the m-th sensor and the position vector of the target source are calculated according to the following formula:

wherein I₃Representing a 3 × 3 order identity matrix; o is_3×(3M+1)Represents a 3 × (3M +1) order all-zero matrix; o is_3×4Representing a 3 × 4 order all-zero matrix;representing an M × M order identity matrix I_MThe m-th column vector of (1).

Further, in the step 20, the root selected in the step 19 is utilizedComputing iterative resultsAndthe corresponding calculation formula is:

in the formula O_4×4Representing a 4 x 4 order all-zero matrix; i is₄Representing a 4 × 4 order identity matrix;

if it isThen obtaining the estimation result of the target source position vector in the stage bAnd the estimation of the sensor position vector in phase bOtherwise, the iteration index k: ═ k +1 is updated, and the process goes to step 14.

To verify the effect of the present invention, assume that the target source is located by using TDOA information (i.e. range difference information) obtained by 6 sensors in space, the position coordinates of the sensors are shown in table 1, the range difference observation error is subject to mean value of zero and covariance matrix ofOf a Gaussian distribution of where σ_tThe standard deviation of observation error of the range difference is represented. The position vector of the sensor can not be accurately obtained, only the prior value can be obtained, and the prior error obeys that the mean value is zero and the covariance matrix isOf a Gaussian distribution of where σ_sThe standard deviation of the prior error is indicated. In order to inhibit the influence of the prior error of the position of the sensor, 1 correction source is placed in a positioning area, the sensor can also obtain distance difference information about the correction sources, the distance difference observation error obeys mean value zero and covariance matrixA gaussian distribution of (a).

TABLE 1 sensor 3D position coordinate (unit: m)

Firstly, the position vector of the target source is set as u [ -6400-]^T(m) setting the correction source position vector to u_d＝[-5600 -6200 6500]^T(m) the standard deviation σ_tAnd σ_sAre respectively set to sigma_t1 and σ_s0.8, and comparing the weighted multi-dimensional scale positioning method disclosed in this patent with existing weighted multi-dimensional scale positioning methods, fig. 2 shows a target source positioning result scatter plot versus positioning error elliptic curve (X-Y plane coordinates), and fig. 3 shows a target source positioning result scatter plot versus positioning error elliptic curve (Y-Z plane coordinates). As can be seen from fig. 2 and 3, under the condition that the prior errors of the correction source and the sensor position coexist, the weighted multidimensional scaling positioning method disclosed by the patent has higher positioning accuracy than the existing weighted multidimensional scaling positioning method, and the elliptical area of the former is obviously smaller than that of the latter, which shows that the influence of the prior errors of the sensor position on the positioning accuracy of the target source can be effectively overcome by using the observed quantity of the correction source.

Then the target source location vector is set as u ═ 5200-]^T(m) setting the correction source position vector to u_d＝[4600 -4200 5500]^T(m) the standard deviation σ_sIs set to sigma_s0.8, change in standard deviation σ_tAnd comparing the weighted multi-dimensional scale positioning method disclosed in this patent with existing weighted multi-dimensional scale positioning methods, fig. 4 shows the root mean square error of the target source location vector estimate as a function of the standard deviation σ_tFigure 5 shows the estimated root mean square error of the sensor position vector as a function of the standard deviation sigma_tThe change curve of (2). Then, the target source position vector is set as u ═ 5200-]^T(m) setting the correction source position vector to u_d＝[4600 -4200 5500]^T(m) the standard deviation σ_tIs set to sigma_t1, change the standard deviation σ_sAnd comparing the weighted multi-dimensional scale positioning method disclosed in this patent with existing weighted multi-dimensional scale positioning methods, fig. 6 shows the root mean square error of the target source location vector estimate as a function of the standard deviation σ_sFigure 7 shows the estimated root mean square error of the sensor position vector as a function of the standard deviation sigma_sCurve of change of。

As can be seen from fig. 4 to 7: (1) the weighted multi-dimensional scale (TDOA) location method disclosed in this patent has higher location accuracy than the existing weighted multi-dimensional scale location method, and the difference in performance between the two is with the standard deviation σ_tDecreases with the standard deviation σ_sThe increase of the position of the target source is increased, which shows that the positioning accuracy of the target source can be improved by using the corrected source observation quantity, and the performance gain caused by the prior error of the position of the sensor is higher; (2) the weighted multi-dimensional scale (TDOA) positioning method disclosed by the patent can achieve the Clarithrome bound for the root mean square error of target source position vector estimation, and verifies the asymptotic statistical optimality of the method; (3) the weighted multi-dimensional scale (TDOA) location method disclosed by the patent can further improve the estimation accuracy of the sensor position vector, and the estimation root mean square error of the sensor position vector can also reach the Claritrol bound, which verifies the asymptotic statistical optimality of the method again.

The above shows only the preferred embodiments of the present invention, and it should be noted that it is obvious to those skilled in the art that various modifications and improvements can be made without departing from the principle of the present invention, and these modifications and improvements should also be considered as the protection scope of the present invention.