阅读说明：本技术 一种信号载波频率先验误差存在下单平台多普勒两阶段闭式定位方法 (Single-platform Doppler two-stage closed positioning method in presence of signal carrier frequency prior error ) 是由 王鼎 尹洁昕 唐涛 杨宾 郑娜娥 聂福全 张莉 王成 张龙 岳嘉颖 于 2021-08-13 设计创作，主要内容包括：本发明公开一种信号载波频率先验误差存在下单平台多普勒两阶段闭式定位方法,首先利用单平台进行直线运动,获得辐射源的FOA观测量,包含多普勒信息；然后利用三角形正弦定理构建第1阶段线性观测方程；接着利用一阶误差分析方法获得该线性观测方程中的误差统计特性,确定最优加权矩阵,得到第1阶段辐射源位置估计值；将该估计值代入原始FOA观测方程中,通过代数变换获得第2阶段线性观测方程；随后利用一阶误差分析方法获得第2阶段线性观测方程中的误差统计特性,确定最优加权矩阵,得到第2阶段辐射源位置估计值,即定位结果。相比于已有单平台多普勒定位方法,本发明不仅能抑制信号载波频率先验误差的影响,还能获得渐近统计最优的定位精度。(The invention discloses a single-platform Doppler two-stage closed positioning method in the presence of signal carrier frequency prior errors, which comprises the steps of firstly utilizing a single platform to perform linear motion to obtain FOA observed quantity of a radiation source, wherein the FOA observed quantity contains Doppler information; then, constructing a stage 1 linear observation equation by utilizing a triangular sine theorem; then, obtaining error statistical characteristics in the linear observation equation by using a first-order error analysis method, determining an optimal weighting matrix, and obtaining a radiation source position estimation value in the 1 st stage; substituting the estimated value into an original FOA observation equation, and obtaining a 2 nd stage linear observation equation through algebraic transformation; and then, obtaining the error statistical characteristics in the 2 nd-stage linear observation equation by using a first-order error analysis method, determining an optimal weighting matrix, and obtaining the 2 nd-stage radiation source position estimation value, namely a positioning result. Compared with the existing single-platform Doppler positioning method, the method can not only inhibit the influence of the prior error of the signal carrier frequency, but also obtain the positioning precision with the optimal asymptotic statistics.)

1. A single-platform Doppler two-stage closed positioning method under the condition of signal carrier frequency prior error is characterized by comprising the following steps:

step 1: a single moving observation platform is used for positioning a static radiation source in space, the moving track of the platform consists of M straight line segments, and N is used together in the process of driving the mth straight line track_mObtaining FOA observations in a short time slot The FOA observation quantity of the single motion observation platform in the nth short time slot of the mth straight track is represented;

step 2: using FOA observationsAnd carrier frequency prior valueComputing a set of vectorsAnd vector setAngle therebetweenWherein u ═ x^(u)y^(u)z^(u)]^TRepresenting a radiation source position vector;a position vector representing the nth short time slot of the single motion observation platform in the mth straight track;a velocity vector representing the nth short time slot of the single motion observation platform in the mth straight track;

and step 3: sequentially utilizing FOA observed quantity in each linear trackObservation matrix constructed based on triangular sine theoremAnd observation vector

And 4, step 4: respectively will observe the matrixAnd observation vectorMerging to form high-dimensional observation matrixAnd high dimensional observation vector

And 5: calculating the initial value of the position of the radiation sourceAnd useComputing matricesAnd

step 6: computing an error covariance matrixDetermining an optimal weighting matrix, and obtaining the estimated value of the position of the radiation source in the 1 st stage by using the optimal weighting matrix

And 7: aiming at each linear track in sequence, the estimated value of the position of the radiation source in the 1 st stage is utilizedConstructing an observation matrixAnd observation vector

And 8: respectively will observe the matrixAnd observation vectorMerging to form high-dimensional observation matrixAnd high dimensional observation vector

And step 9: using estimation of radiation source position in stage 1Computing matricesAnd

step 10: computing an error covariance matrixDetermining an optimal weighting matrix, and obtaining the estimated value of the position of the radiation source in the 2 nd stage by using the optimal weighting matrixAnd will beAs a final positioning result.

2. The method of claim 1The single-platform Doppler two-stage closed positioning method under the condition of signal carrier frequency prior error is characterized in that in the step 1, FOA observed quantityThe expression of (a) is:

in the formula of_mnRepresenting a gaussian observation error; c represents the propagation speed of the radiation source signal; f. of₀Representing the carrier frequency of the radiation source signal, a priori of whichThe error of the prior is contained, and the corresponding expression is as follows:

where ξ represents the gaussian prior error.

3. The single-stage Doppler two-stage closed positioning method in the presence of signal carrier frequency prior error as claimed in claim 2, wherein in the step 2, the vector group is calculated as followsAnd vector setAngle therebetween

4. The single-platform Doppler two-stage closed positioning method according to claim 1, wherein in step 3, the observation matrix is used for estimating the Doppler spread spectrum in the presence of the prior error of the signal carrier frequencyAnd observation vectorThe corresponding calculation formula is:

5. the single-platform Doppler two-stage closed positioning method in the presence of signal carrier frequency prior error according to claim 1 or 4, characterized in that in the step 4, the high-dimensional observation matrixAnd high dimensional observation vectorThe corresponding expression is:

6. the single-stage Doppler two-stage closed positioning method according to claim 5, wherein the single-stage Doppler two-stage closed positioning method is performed in the presence of signal carrier frequency prior error, and is characterized in thatIn step 5, the initial value of the radiation source position is calculated as follows

Then useComputing matricesAndthe corresponding calculation formula is:

in the formula

Wherein

Wherein

WhereinRepresents N_m×N_mOrder unit matrixColumn 1 in (1);represents N_m×N_mOrder unit matrixThe nth column of (1);represents (N)_m-1)×(N_m-1) order identity matrixColumn n-1 of (1);to representAn order all-zero matrix;to representAn all zero matrix of order.

7. The single-stage Doppler two-stage closed positioning method in the presence of signal carrier frequency prior errors as claimed in claim 1, wherein in step 6, the error covariance matrix is calculated according to the following formula

Wherein E represents an FOA observation error covariance matrix;variance, σ, representing the prior error of the carrier frequency_fIndicating a priori error of carrier frequencyStandard deviation;

the stage 1 radiation source position estimate is then calculated as follows

8. The single-platform Doppler two-stage closed positioning method in the presence of signal carrier frequency prior error according to claim 1, wherein in the step 7, the observation matrix is constructed as followsAnd observation vector

9. The single-platform Doppler two-stage closed positioning method in the presence of signal carrier frequency prior error according to claim 1, wherein in the step 9, the matrix is calculated according to the following formulaAnd

in the formula

Wherein

10. The single-stage doppler two-stage closed positioning method according to claim 9, wherein in step 10, the error covariance matrix is calculated according to the following formula

Then, the estimated position of the radiation source in the 2 nd stage is obtained according to the following formula

(Vector)Namely the final positioning result.

Technical Field

The invention belongs to the technical field of radiation source positioning, and particularly relates to a single-platform Doppler two-stage closed positioning method in the presence of signal carrier frequency prior errors.

Background

As is well known, radiation source positioning technology plays an important role in many industrial and electronic information fields, such as target monitoring, navigation telemetry, seismic surveying, radio astronomy, emergency assistance, safety management, etc. The positioning (i.e. position parameter estimation) of the radiation source can be completed by using active equipment such as radar, laser, sonar and the like, which is called as an active positioning technology and has the advantages of all weather, high precision and the like. However, the active positioning system usually needs to be implemented by transmitting a high-power electromagnetic signal, so that the position of the active positioning system is easily exposed and easily found by the other party, and the active positioning system 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.

Radiation source localization can also be achieved using target (active) radiated or (passive) 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 platform 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-platform passive positioning system and a multi-platform passive positioning system according to the number of observation platforms, wherein the single-platform passive positioning system has the advantages of high flexibility, strong maneuverability, simple system, no need of communication and synchronization between the platforms and the like, and the patent mainly relates to a single-platform passive positioning system.

In a single-platform positioning system, the frequency of arrival (FOA) is a type of frequently used observation, which includes Doppler information, by which the radiation source can be positioned (Amar A, Weiss A J. localization of narrowband radio emission based on Doppler frequency shift [ J ]. IEEE Transactions on Signal Processing,2008,56(11): 5500.) (strict navigation, Yayayayakuan. Low-orbit single-satellite frequency measurement positioning technique and its accuracy analysis [ J ]. computer engineering, 2012,38(18):6-10.) (Yacaoxin. Single-satellite Doppler passive positioning algorithm and error analysis [ J ]. electronic measurement technique, 2017,40(2): 59-63.). Due to the non-linear nature of the FOA observations, iterations are typically required to obtain a localization result. However, the iterative method requires setting an initial value, and is prone to problems such as iterative divergence and local convergence. On the other hand, signal carrier frequency information is also needed for positioning by using FOA observation, but in a non-cooperative communication scene, the signal carrier frequency is also obtained through observation, wherein an a priori error exists, and the error can deteriorate the positioning performance.

Disclosure of Invention

The invention provides a single-platform Doppler two-stage closed positioning method in the presence of a priori error of a signal carrier frequency aiming at the problems of iterative divergence and local convergence in a single-platform positioning system and the problem of influence on positioning performance due to the prior error.

In order to achieve the purpose, the single-platform Doppler two-stage closed positioning method under the condition that the signal carrier frequency prior error exists comprises the steps of firstly utilizing a single motion observation platform to carry out linear motion, and utilizing a plurality of short time slots to obtain FOA observed quantity of a radiation source in the process of running each linear track, wherein the FOA observed quantity contains Doppler information. And then constructing a stage 1 linear observation equation by utilizing a triangular sine theorem. And then, based on the statistical characteristic of the FOA observation error and the statistical characteristic of the signal carrier frequency prior error, obtaining the error statistical characteristic in the linear observation equation by using a first-order error analysis method, and further determining an optimal weighting matrix, thereby obtaining the radiation source position estimation value in the 1 st stage. The theory proves that the estimated value of the 1 st stage does not have asymptotic statistical optimality, so the estimated value is substituted into the original FOA observation equation, and the linear observation equation of the 2 nd stage is obtained through certain algebraic transformation. And then, based on the statistical property of the estimated value in the 1 st stage, the statistical property of the FOA observation error and the statistical property of the signal carrier frequency prior error, obtaining the error statistical property in the linear observation equation in the 2 nd stage by using a first-order error analysis method, and further determining an optimal weighting matrix, thereby obtaining the estimated value of the radiation source position in the 2 nd stage, wherein the estimated value is the final positioning result. The invention specifically adopts the following technical scheme:

step 1: a single moving observation platform is used for positioning a static radiation source in space, the moving track of the platform consists of M straight line segments, and N is used together in the process of driving the mth straight line track_mObtaining FOA observations in a short time slotThe FOA observation quantity of the single motion observation platform in the nth short time slot of the mth straight track is represented;

step 2: using FOA observationsAnd carrier frequency prior valueComputing a set of vectorsAnd toMeasuring groupAngle therebetweenWherein u ═ x^(u) y^(u)z^(u)]^TRepresenting a radiation source position vector;a position vector representing the nth short time slot of the single motion observation platform in the mth straight track;a velocity vector representing the nth short time slot of the single motion observation platform in the mth straight track;

and step 3: sequentially utilizing FOA observed quantity in each linear trackObservation matrix constructed based on triangular sine theoremAnd observation vector

And 4, step 4: respectively will observe the matrixAnd observation vectorMerging to form high-dimensional observation matrixAnd high dimensional observation vector

And 5: calculating the initial value of the position of the radiation sourceAnd useComputing matricesAnd

step 6: computing an error covariance matrixDetermining an optimal weighting matrix, and obtaining the estimated value of the position of the radiation source in the 1 st stage by using the optimal weighting matrix

And 7: aiming at each linear track in sequence, the estimated value of the position of the radiation source in the 1 st stage is utilizedConstructing an observation matrixAnd observation vector

And 8: respectively will observe the matrixAnd observation vectorMerging to form high-dimensional observation matrixAnd high dimensional observation vector

And step 9: using estimation of radiation source position in stage 1Computing matricesAnd

step 10: computing an error covariance matrixDetermining an optimal weighting matrix, and obtaining the estimated value of the position of the radiation source in the 2 nd stage by using the optimal weighting matrixAnd will beAs a final positioning result.

Further, in step 1, the FOA observation amountThe expression of (a) is:

in the formula of_mnRepresenting a gaussian observation error; c represents the propagation speed of the radiation source signal; f. of₀Representing the carrier frequency of the radiation source signal, a priori of whichThe error of the prior is contained, and the corresponding expression is as follows:

where ξ represents the gaussian prior error.

Further, in the step 2, the vector group is calculated as followsAnd vector setAngle therebetween

Further, in the step 3, the matrix is observedAnd observation vectorThe corresponding calculation formula is:

further, in step 4, a high-dimensional observation matrixAnd high dimensional observation vectorThe corresponding expression is:

further, in the step 5, the initial value of the position of the radiation source is calculated as follows

Then useComputing matricesAndthe corresponding calculation formula is:

in the formula

Wherein

Wherein

WhereinRepresents N_m×N_mOrder unit matrixColumn 1 in (1);represents N_m×N_mOrder unit matrixThe nth column of (1);represents (N)_m-1)×(N_m-1) order identity matrixColumn n-1 of (1);to representAn order all-zero matrix;to representAn all zero matrix of order.

Further, in step 6, the error covariance matrix is calculated according to the following formula

Wherein E represents an FOA observation error covariance matrix;variance, σ, representing the prior error of the carrier frequency_fStandard deviation representing the prior error of the carrier frequency;

the stage 1 radiation source position estimate is then calculated as follows

Further, in step 7, an observation matrix is constructed as followsAnd observation vector

Further, in step 8, a high-dimensional observation matrixAnd high dimensional observation vectorThe corresponding expression is:

further, in step 9, the matrix is calculated according to the following formulaAnd

in the formula

Wherein

Further, in the step 10, the error covariance matrix is calculated according to the following formula

Then, the estimated position of the radiation source in the 2 nd stage is obtained according to the following formula

(Vector)Namely the final positioning result.

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

the invention discloses a single-platform Doppler two-stage closed positioning method under the condition of a single-motion observation platform passive positioning scene, aiming at an FOA observation equation, two groups of linear observation equations are sequentially constructed, corresponding closed solutions are respectively obtained, and high-precision positioning of a radiation source is realized through two-stage calculation. Compared with the existing single-platform Doppler positioning method, the method provided by the invention can inhibit the influence of the prior error of the signal carrier frequency, and can obtain the positioning precision with the optimal asymptotic statistics.

Drawings

FIG. 1 is a basic flowchart of a single-platform Doppler two-stage closed positioning method in the presence of a signal carrier frequency prior error according to an embodiment of the present invention;

FIG. 2 is a scatter plot of radiation source positioning results and an elliptical curve of positioning error (X-Y plane coordinates);

FIG. 3 is a scatter plot of radiation source positioning results and an elliptical curve of positioning error (Y-Z plane coordinates);

FIG. 4 shows the RMS error of an estimated source position as a function of the standard deviation σ_eThe variation curve of (d);

FIG. 5 shows the RMS error of an estimated source position as a function of the standard deviation σ_fThe 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 single-platform doppler two-stage closed positioning method in the presence of a signal carrier frequency prior error includes:

step 1: a single moving observation platform is used for positioning a static radiation source in space, the moving track of the platform consists of M straight line segments, and N is used together in the process of driving the mth straight line track_mObtaining FOA observations in a short time slotThe FOA observation quantity of the single motion observation platform in the nth short time slot of the mth straight track is represented;

step 2: using FOA observationsAnd carrier frequency prior valueComputing a set of vectorsAnd vector setAngle therebetween

And step 3: sequentially utilizing FOA observed quantity in each linear trackObservation matrix constructed based on triangular sine theoremAnd observation vector

And 4, step 4: respectively will observe the matrixAnd observation vectorMerging to form high-dimensional observation matrixAnd high dimensional observation vector

And 5: calculating the initial value of the position of the radiation sourceAnd useComputing matricesAnd

step 6: computing an error covariance matrixDetermining an optimal weighting matrix, and obtaining the estimated value of the position of the radiation source in the 1 st stage by using the optimal weighting matrix

And 7: aiming at each linear track in sequence, the estimated value of the position of the radiation source in the 1 st stage is utilizedConstructing an observation matrixAnd observation vector

And 8: respectively will observe the matrixAnd observation vectorMerging to form high-dimensional observation matrixAnd high dimensional observation vector

And step 9: using estimation of radiation source position in stage 1Computing matricesAnd

step 10: computing an error covariance matrixDetermining an optimal weighting matrix, and obtaining the estimated value of the position of the radiation source in the 2 nd stage by using the optimal weighting matrixAnd will beAs a final positioning result.

Further, in the step 1, a single moving observation platform is used for positioning the stationary radiation source in space, the moving track of the platform is composed of M straight line segments, and a total of N straight line segments are used in the process of driving the mth straight line track_mObtaining FOA observations in a short time slotThe corresponding expression is:

wherein u ═ x^(u) y^(u) z^(u)]^TRepresenting a radiation source position vector;presentation sheetThe position vector (known quantity) of the nth short time slot of the platform in the mth straight track;a velocity vector (known quantity) representing the nth short time slot of the single platform in the mth straight track; epsilon_mnRepresenting a gaussian observation error; c represents the propagation velocity (known quantity) of the radiation source signal; f. of₀Representing the carrier frequency of the radiation source signal, a priori of whichThe error of the prior is contained, and the corresponding expression is as follows:

where ξ represents the gaussian prior error.

Further, in the step 2, the FOA observation quantity is usedAnd carrier frequency prior valueComputing a set of vectorsAnd vector setAngle therebetweenThe corresponding calculation formula is:

further, in step 3, the FOA observation in each linear track is sequentially utilizedMeasurement ofObservation matrix constructed based on triangular sine theoremAnd observation vectorThe corresponding calculation formula is:

further, in the step 4, the observation matrixes are respectively usedAnd observation vectorMerging to form high-dimensional observation matrixAnd high dimensional observation vectorThe corresponding expression is:

further, in the step 5, an initial value of the radiation source position is calculatedThe corresponding calculation formula is:

then using the value to calculate a matrixAndthe corresponding calculation formula is:

in the formula

Wherein

Wherein

WhereinRepresents N_m×N_mOrder unit matrixColumn 1 in (1);represents N_m×N_mOrder unit matrixThe nth column of (1);represents (N)_m-1)×(N_m-1) order identity matrixColumn n-1 of (1);to representAn order all-zero matrix;to representAn all zero matrix of order.

Further, in the step 6, an error covariance matrix is calculatedThe corresponding calculation formula is:

wherein E represents an FOA observation error covariance matrix;variance, σ, representing the prior error of the carrier frequency_fRepresenting the standard deviation of the prior error of the carrier frequency. Then using the matrixDetermining an optimal weighting matrix asAnd obtaining the estimated value of the position of the radiation source in the 1 st stage by using the optimal weighting matrixThe corresponding calculation formula is:

further, in step 7, the estimated value of the radiation source position in the 1 st stage is used for each linear track in turnConstructing an observation matrixAnd observation vectorThe corresponding calculation formula is:

further, in the step 8, the observation matrixes are respectively setAnd observation vectorMerging to form high-dimensional observation matrixAnd high dimensional observation vectorThe corresponding expression is:

further, in the step 9, the estimated value of the position of the radiation source in the stage 1 is usedComputing matricesAndcorresponding calculation is disclosedThe formula is as follows:

in the formula

Wherein

Further, in the step 10, an error covariance matrix is calculatedThe corresponding calculation formula is:

then using the matrixDetermining an optimal weighting matrix asAnd obtaining the estimated value of the position of the radiation source in the 2 nd stage by using the optimal weighting matrixCorresponding toThe calculation formula is as follows:

(Vector)namely the final positioning result.

To verify the effect of the present invention, the following experiment was performed:

let the radiation source position vector be u [ -223 ]]^T(kilometer), the carrier frequency of the radiation signal is 500MHz, a single observation platform runs 4 straight tracks in total, 6 short time slots are utilized in each track to obtain FOA observed quantity, the position coordinates of the short time slots of the single observation platform in each straight track are shown in tables 1 to 4, and the speed of the single observation platform in each straight track is shown in table 5. The FOA observation error obeys zero mean value and variance(ii) a gaussian distribution of; the prior error of the signal carrier frequency is subjected to the mean value of zero and the variance ofOf a Gaussian distribution of where σ_eAnd σ_fAre all standard deviations.

TABLE 1 position coordinates (unit: kilometer) of 6 short time slots of a single observation platform in the 1 st straight-line track of travel

TABLE 2 position coordinates (units: kilometers) of 6 short time slots of a single observation platform in the 2 nd straight-line track of travel

TABLE 3 position coordinates (unit: kilometer) of 6 short time slots of single observation platform in the 3 rd straight-line track

TABLE 4 position coordinates (unit: kilometer) of 6 short time slots of single observation platform in the 4 th straight-line track

TABLE 5 speed of a single observation platform (units: kilometers per second) while traveling each straight track

First, the standard deviation σ is calculated_eAnd σ_fAre respectively set to sigma_e3 and σ_fFig. 2 shows a scatter diagram of the positioning result of the radiation source and an elliptic curve of the positioning error (X-Y plane coordinates); figure 3 shows a scatter plot of the radiation source positioning results versus an elliptical plot of the positioning error (Y-Z plane coordinates). As can be seen from fig. 2 and 3, the shape of the localization result scattergram of the localization method disclosed by the present invention is consistent with the positioning error ellipse shape, and the large probability corresponds to the large area ellipse, and the small probability corresponds to the small area ellipse, thereby verifying the validity of the method of the present invention.

The standard deviation σ is then calculated_fIs set to sigma_f5, and varying the standard deviation σ_eFigure 4 gives the root mean square error of the radiation source position estimate as a function of the standard deviation sigma_eThe variation curve of (d); the standard deviation sigma_eIs set to sigma_e3, and varying the standard deviation σ_fFigure 5 shows the root mean square error of the radiation source position estimate as a function of the standard deviation sigma_fThe change curve of (2). As can be seen from fig. 4 and 5: (1) the Doppler two-stage closed positioning method disclosed by the patent can achieve the Cramer-Rao bound for the root mean square error of the radiation source position estimation, thereby verifying the asymptotic statistical optimality of the new method; (2) the estimation accuracy of the Doppler two-stage closed positioning method disclosed by the patent is higher than that of the existing closed positioning method, and the advantages of the Doppler two-stage closed positioning method are more obvious along with the increase of FOA observation errors and carrier frequency prior errors, because the new method obtains the positioning accuracy which is asymptotically statistically optimal through two-stage processing.

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.