阅读说明：本技术 一种考虑地球曲率的双基站三维无源定位方法 (Double-base-station three-dimensional passive positioning method considering earth curvature ) 是由 郭云飞 袁继成 薛安克 彭冬亮 左燕 于 2019-08-30 设计创作，主要内容包括：本发明公开了一种考虑地球曲率的双基站三维无源定位方法。本发明首先在考虑地球曲率的情况下,建立目标和外辐射源在地心地固坐标系下(ECEF)的运动方程,然后根据量测得到的双基站距离和角度信息建立似然函数,通过遗传算法求解出该似然函数的极值,将其作为目标的初始运动状态。此外考虑到遗传算法计算的时间随着数据量的增加而增加,本发明为了兼顾实时性和准确性的要求,只选取前十五个时刻的测量值来建立似然函数,在遗传算法求出似然函数的解得到目标的初始状态后,后面时刻使用概率数据关联算法(PDA)结合扩展卡尔曼滤波(EKF)进行目标状态的预测和更新。(The invention discloses a double-base-station three-dimensional passive positioning method considering the curvature of the earth. According to the method, firstly, under the condition of considering the curvature of the earth, a motion equation of a target and an external radiation source under an earth-centered earth-fixed coordinate system (ECEF) is established, then a likelihood function is established according to measured double-base-station distance and angle information, an extreme value of the likelihood function is solved through a genetic algorithm, and the extreme value is used as an initial motion state of the target. In addition, considering that the calculation time of the genetic algorithm is increased along with the increase of the data volume, in order to meet the requirements of real-time performance and accuracy, the invention only selects the measured values of the first fifteen moments to establish the likelihood function, and after the genetic algorithm calculates the solution of the likelihood function to obtain the initial state of the target, the probability data association algorithm (PDA) is used in combination with the Extended Kalman Filter (EKF) to predict and update the state of the target at the later moment.)

1. A double-base-station three-dimensional passive positioning method considering the curvature of the earth specifically comprises the following steps:

step 1: firstly, establishing a motion state of a target in a geocentric coordinate system ECEF, namely:

wherein x is_t,y_t,z_tThe motion states of the target at X, Y and Z positions in the ECEF coordinate system, X₀,y₀,z₀Is the initial position of the target in ECEF, v is the velocity of the target motion, δ is the angle of the north pole clockwise to the velocity direction, T_iThe sampling interval is represented, and,establishing the motion state of the external radiation source in the same way;

step 2: assuming that the target, the radiation source and the receiving station are both approximately in uniform linear motion, the obtained clutter measurement value is:

wherein h is_k(i) The measurement is noise-free;

wherein r is_k(i) For a double base station distance, theta_k(i) Is the azimuth angle of the echo path relative to the direct wave path, | | | · | | | is the Euclidean norm, X_k＝[X_k,Y_k,Z_k]^T，X_t,k＝[X_t,k,Y_t,k,Z_t,k]^T，X_r,k＝[0,0,0]^T，v_k～N(0,R_k)，σ_r,kMeasuring error, σ, for distance differences_θ,kFor azimuthal measurement error, wherein X_k,Y_k,Z_kFor the position of the target in the ECEF coordinate system at time k, X_t,k,Y_t,k,Z_t,kThe position of the external radiation source in an ECEF coordinate system at the moment k; clutter gamma_k(i) Assuming uniform distribution in a measurement space, wherein the number of the uniform distribution is subjected to Poisson distribution with clutter density of lambda;

and step 3: the distance r of the double base stations is obtained according to the measurement_k(i) And azimuth angle theta_k(i) Target is established every timeThe likelihood function of the moment is:

wherein, P_DIs the detection probability of the target, λ is the density of clutter, m^*(i) Number of measurements, σ, of targets and clutter_rMeasuring error, σ, for distance differences_θFor azimuthal measurement error, z_rj(i) For measured distance differences, z_βj(i) Is the measured azimuth angle;

as the time consumption of the genetic algorithm is increased along with the increase of the data quantity, only the measurement data of the first fifteen frames are selected to establish a likelihood function for the requirement of real-time property;

then the entire likelihood function is:

the initial state of the target is thus:thus, the problem is converted into a minimum value solution for solving the likelihood function, wherein n is the selected frame number;

step 4, solving a minimum value by using a genetic algorithm according to the likelihood function established in the step 3;

step 5, taking the result obtained in the step 4 as the initial state of the target, then using the target motion equation under the ECEF coordinate system established above to calculate the position of the target on X, Y and Z at the fifteenth moment, taking the position as the initial value of filtering, and then adopting a probability data association algorithm PDA to predict and update the target state at the sixteenth moment;

step 5.1: establishing a state transition matrix according to a motion equation of the target in an ECEF coordinate system:

state variable X ═[x y z v σ sinσ cosσ 1]^TThe state of the PDA is thus predicted to be:

X_k+1|k＝F_k+1X_k|k

the covariance prediction is:

P_k+1|k＝F_k+1P_kF_k+1+Q_k+1

Q_k+1is a process noise matrix, P_kThe covariance of the target at time k;

step 5.2: suppose that at time k +1 the sensor receives m_k+1An effective measurementAn effective measurement is one falling into the correlation tracking gate omega_k+1Internal measurements, i.e. the following conditions are fulfilled:

wherein the content of the first and second substances,for the target predictive measure, the expression is:

g is a tracking gate parameter, innovation S_k+1The expression of (A) is shown below;

step 5.3: the target state update and covariance update in the PDA are:

S_k+1＝HP_k+1|kH^T+R_k

X_k+1＝X_k+1|k+W_k+1v_k+1

wherein the content of the first and second substances,

wherein, X_k|k+1＝[x_k|k+1,y_k|k+1,z_k|k+1]，X_t,k|k+1＝[x_t,k|k+1,y_t,k|k+1,z_t,k|k+1]

Wherein W_k+1For filter gain, H is the Jacobian matrix, meaning that the measurement is linearized, I is the identity matrix,for the j-th valid measurement at time k +1The probability of association derived from the target is,the probability that no measurement originates from the target at time k + 1;

wherein the content of the first and second substances,

P_Grepresenting a threshold for tracking the door;

updated X_k+1Is the estimated state of the target.

Technical Field

The invention belongs to the field of radar data processing, and particularly relates to a double-base-station three-dimensional passive positioning method considering the curvature of the earth.

Background

Passive co-location system (PCL) laserA third-party signal transmitting station (frequency modulation broadcast, mobile phone base station and the like) is used as an external radiation source/opportunity irradiation source, and signal coherent processing is carried out on direct waves of the external radiation source and echoes reflected/scattered by a target, so that passive positioning of the target is realized. The system has low cost, strong anti-interference capability and good stealth/anti-stealth effect, is an important means for air defense early warning and has important strategic significance for military defense and airspace safety. A schematic diagram of a dual base station system can be seen in FIG. 1 of the drawings, wherein Tx denotes an external radiation source, Rx denotes a receiving station, Ox denotes an object, and d denotes a target_ORDenotes the distance between Ox and Rx, and will be referred to as | | | X in the following description_k-X_r,kI represents; d_OTDenotes the distance between Ox and Tx, and is expressed by | | | X in the following description_k-X_t,kI represents; d_RTThe distance between Rx and Tx is expressed by | | X in the following description_t,k-X_r,kAnd | l represents. Rx consists of a monitor antenna that receives the signal transmitted by Tx and reflected by Ox, and a reference antenna that receives the direct signal transmitted by Tx. By comparing the echo signal with the direct signal, passive positioning of Ox is achieved.

The target has a certain height in a real three-dimensional scene, however, the PCL system cannot measure pitch angle information from the target, so that the measured value does not contain information about the height, and further the target tracking accuracy of various filtering algorithms is reduced. Therefore, it is important to effectively estimate the three-dimensional state including the target height according to the conventional measurement values (azimuth angle, range difference, etc.). A Save team of China space group provides a target height estimation method based on radar local tracks, a nonlinear model about the target height is established through local track estimation of a plurality of base stations, and the target height is finally estimated by using unscented Kalman filtering. Aiming at the problem, the Liu Wei team of the university of Western An electronic technology provides a solution: and deducing a fusion center updating equation according to the measurement equation, and replacing the measured value of the updating equation by the local information of each base station, thereby realizing the target three-dimensional state estimation.

None of the above methods takes into account the effect of earth curvature on the three-dimensional tracking of the target. In fact at high altitudes, a curved earth becomes significant due to the extension of the horizon. The earth cannot be considered to be flat, and in this case, the influence of the curvature of the earth on the target altitude estimation needs to be considered. The error caused by neglecting the curvature of the earth can be seen in fig. 2 of the attached drawings of the specification, wherein R is the radius of the earth, h' is the height measured by a radar, h is the real height of the target when the curvature is considered, and deltah is the height error when the curvature is neglected. .

Disclosure of Invention

Aiming at the defects of the prior art, the invention provides a double-base-station three-dimensional passive positioning method considering the curvature of the earth.

The method comprises the following specific steps:

step 1, firstly, establishing the motion states of the target and the external radiation source in an earth-centered earth-fixed coordinate system (ECEF) coordinate system.

And 2, establishing a likelihood function according to the angle and distance information measured by the double base stations.

And 3, solving the established likelihood function by using a genetic algorithm, wherein the obtained extreme value is the initial state of the target.

And 4, performing prediction updating by using the PDA and an Extended Kalman Filter (EKF) according to the extreme value obtained in the step 3 as an initial state, and further obtaining the motion state of the target at each moment.

The invention has the beneficial effects that:

1. the influence of the curvature of the earth is considered in the three-dimensional passive positioning of the target, the target is closer to a real scene, and the target positioning and tracking precision is improved.

2. The genetic algorithm is time-consuming to solve the problem, and the genetic algorithm and the PDA are combined to solve the time-consuming problem of the genetic algorithm, so that the real-time requirement is met.

Drawings

FIG. 1 is a schematic diagram of a dual base station PCL system;

FIG. 2 is a schematic diagram of errors generated by high estimation in target three-dimensional tracking when earth curvature is ignored;

FIG. 3 is a flow chart of the present invention.

Detailed Description

The invention provides a double-base-station three-dimensional passive positioning method considering the curvature of the earth by considering the influence of the curvature of the earth and aiming at a double-base-station external radiation source radar network. The specific flow chart of the invention can be seen in figure 3 of the attached drawings of the specification.

The method specifically comprises the following steps:

step 1: firstly, establishing a motion state of the target in an ECEF coordinate system, namely:

wherein x is_t,y_t,z_tThe motion states of the target at X, Y and Z positions in the ECEF coordinate system, X₀,y₀,z₀Is the initial position of the target in the ECEF coordinate system, v is the velocity of the target motion, δ is the angle of the north pole clockwise to the velocity direction, T_iThe sampling interval is represented, and,the motion state of the external radiation source is established in the same way.

Step 2: assuming that the target and the radiation source both move approximately in a straight line at a constant velocity and the receiving station is stationary, the resulting clutter measurement is:

wherein h is_k(i) The measurement is noise-free.

Wherein r is_k(i) For a double base station distance, theta_k(i) Is the azimuth angle of the echo path relative to the direct wave path, | | | · | | | is the Euclidean norm, X_k＝[X_k,Y_k,Z_k]^T，X_t,k＝[X_t,k,Y_t,k,Z_t,k]^T，X_r,k＝[0,0,0]^T，v_k～N(0,R_k)，σ_r,kMeasuring error, σ, for distance differences_θ,kFor azimuthal measurement error, wherein X_k,Y_k,Z_kFor the position of the target in the ECEF coordinate system at time k, X_t,k,Y_t,k,Z_t,kThe position of the external radiation source in the ECEF coordinate system is time k. Clutter gamma_k(i) The measurement space is assumed to be uniformly distributed, and the number of the measurement spaces is subjected to Poisson distribution with clutter density of lambda.

And step 3: the distance r of the double base stations is obtained according to the measurement_k(i) And azimuth angle theta_k(i) The likelihood function of each time of establishing the target is as follows:

wherein, P_DIs the detection probability of the target, λ is the density of clutter, m^*(i) Number of measurements, σ, of targets and clutter_rMeasuring error, σ, for distance differences_θFor azimuthal measurement error, z_rj(i) For measured distance differences, z_βj(i) Is the azimuth angle of the measurement.

Since the genetic algorithm increases the time consumption along with the increase of the data volume, only the measurement data of the first fifteen frames can be selected to establish the likelihood function for the requirement of real-time property.

Then the entire likelihood function is:

the initial state of the target is thus:the problem is then converted into a minimum solution for solving the likelihood function, where n is the choiceThe number of frames.

And 4, solving the minimum value by using a genetic algorithm according to the likelihood function established in the step 3.

And 5, taking the result obtained in the step 4 as an initial state of the target, then using the target motion equation under the ECEF coordinate system established above to obtain the position of the target on X, Y and Z at the fifteenth moment, taking the position as an initial value of filtering, and then adopting a probability data association algorithm PDA to predict and update the target state at the sixteenth moment.

Step 5.1: establishing a state transition matrix according to a motion equation of the target in an ECEF coordinate system:

the state variable is X ═ X yz v σ sin σ cos σ 1]^TThe state of the PDA is thus predicted to be:

X_k+1|k＝F_k+1X_k|k

the covariance prediction is:

P_k+1|k＝F_k+1P_kF_k+1+Q_k+1

Q_k+1is a process noise matrix, P_kThe covariance of the target at time k.

Step 5.2: suppose that at time k +1 the sensor receives m_k+1An effective measurementAn effective measurement is one falling into the correlation tracking gate omega_k+1Internal measurements, i.e. the following conditions are fulfilled:

wherein the content of the first and second substances,for the target predictive measure, the expression is:

g is a tracking gate parameter, innovation S_k+1The expression of (c) is shown below.

Step 5.3: the target state update and covariance update in the PDA are:

S_k+1＝HP_k+1|kH^T+R_k

X_k+1＝X_k+1|k+W_k+1v_k+1

wherein the content of the first and second substances,

wherein, X_k|k+1＝[x_k|k+1,y_k|k+1,z_k|k+1]，X_t,k|k+1＝[x_t,k|k+1,y_t,k|k+1,z_t,k|k+1]

Wherein W_k+1For filter gain, H is the Jacobian matrix, meaning that the measurement is linearizedAnd I is a unit matrix,for the j-th valid measurement at time k +1The probability of association derived from the target is,the probability that no measurement originates from the target at time k + 1.

Wherein the content of the first and second substances,

P_Gto track the threshold of the door.

Updated X_k+1Is the estimated state of the target.