CN105487072A - Method and system of joint location based on T2/R time difference and Doppler shift - Google Patents

Abstract

The present invention discloses a method and system of joint location based on T2/R time difference and Doppler shift. The method comprises the following steps: S1, selecting two shortwave broadcasting stations with different signal frequencies as launch stations, obtaining their emission frequencies and coordinate positions, and calculating the big circle distances of the ground between the launch stations and an accepting station; S2, calculating the time difference data and Doppler shift data between a direct wave and a scattered wave according to the signal frequencies and the big circle distances of the ground; S3, jointing the obtained time difference data and the Doppler shift data to obtain an estimating equation of a target state, and obtaining a convergence result through calculation according to batch algorithms, namely the position and the flight speed of a flying target. Only two broadcasting stations are needed to be taken as sources of radiation to locate a moving aerial target, so that the aspects of the position precision and the speed precision are greatly improved for the targets in a uniform motion and a variable motion.

Description

Based on T2Method and system for joint positioning of time difference and Doppler frequency shift of/R

Technical Field

The invention relates to the field of signal processing, in particular to a T-based signal processing method²The method and system for joint positioning of time difference of/R and Doppler frequency shift.

Background

The target positioning has very important practical significance in the military field, the mobile communication field, the medical field, the civil field and the like. The passive positioning technology is an important direction for future development, because the system does not actively transmit signals, and only depends on receiving electromagnetic signals reflected by a positioned target to determine the spatial position of the target.

In recent years, in passive positioning systems, a target is generally positioned based on a direction of arrival (DOA), a time of arrival (TOA), a time difference of arrival (TDOA), a doppler frequency, a signal strength (RSSI), and various joint methods. Because the time difference is only relevant to the target position, the positioning equation is simple, and the position positioning precision is higher than the arrival angle of the incoming wave direction of the target, so the time difference positioning is mostly adopted. However, generally, the system mostly needs 3 or more transmitting stations, and for a randomly moving object, the time difference is not in great relation with the motion state, so that the estimation of the object motion speed by using the time difference positioning system has ambiguity. The method is based on double transmitting stations, proposed in liwanchun 2005, and is used for positioning a target by using time difference information, the speed positioning accuracy and the result are not evaluated separately, and when the target moves at a constant speed for a long time (N is 20). The Doppler frequency shift is closely related to the motion state, so that the target speed can be well estimated, and the positioning of the position and speed information of the target is performed by only adopting the Doppler frequency shift proposed in Shaozun 2011, so that when the number of the transmitting stations reaches 4, the position positioning accuracy is remarkably improved, and the target is assumed to move at a constant speed within 30 s. However, in practice the target is not generally constant or remains constant for a considerable period of time. Therefore, it is more practical to consider the goal of the variable speed motion.

Disclosure of Invention

The invention aims to solve the technical problem of providing a T-based passive positioning system which only needs two transmitting stations and can accurately position a target in variable-speed motion and is based on the fact that only the state of uniform-speed motion is considered in a passive positioning system in the prior art and the number of the required transmitting stations is excessive²The method and system for joint positioning of time difference of/R and Doppler frequency shift.

The technical scheme adopted by the invention for solving the technical problems is as follows:

the invention provides a T-based²The method for joint positioning of the time difference of the/R and the Doppler frequency shift comprises the following steps:

s1, selecting two short-wave broadcasting stations with different signal frequencies as transmitting stations, acquiring the transmitting frequencies and coordinate positions of the short-wave broadcasting stations, and calculating the ground great circle distance between the transmitting stations and the receiving stations according to the coordinate positions;

s2, calculating time difference data and Doppler frequency shift data between direct waves and scattered waves by using a time difference measuring method according to the signal frequency and the ground great circle distance, wherein the direct waves are signals of a transmitting station directly received by a receiving station, and the scattered waves are signals reflected to the receiving station after the transmitted signals irradiate an air flying target;

and S3, combining the obtained time difference data and the Doppler frequency shift data to obtain a target state estimation equation, and calculating by a batch processing algorithm to obtain a convergence result, namely the position and the flying speed of the flying target.

Further, the method for acquiring the transmitting frequency and the coordinate position of the short-wave broadcasting station in step S1 of the present invention comprises:

two transmitting stations are selected from a short-wave full-frequency-band radio frequency division list released by the international telecommunication union, the transmitting stations cannot be located on the same coordinate position with a receiving station, and two short-wave broadcast signals adopt an AM (amplitude modulation) mode and are short-wave signals with different frequencies.

Further, step S2 of the present invention specifically includes the following steps:

s21, extracting direct wave signals, wherein the direct waves are transmitting station signals directly received by a receiving station;

s22, extracting scattered wave signals, wherein the signals are signals which are reflected to a receiving station after the signals transmitted by the transmitting station irradiate the maneuvering target in the air;

s23, obtaining time difference information between the continuous k times of direct waves and scattered waves by using a time difference estimation method;

and S24, obtaining Doppler frequency shift information between the continuous k times of direct waves and scattered waves by using a Doppler frequency shift estimation algorithm.

Further, step S3 of the present invention specifically includes the following steps:

s31, calculating a Jacobi matrix of the time difference measurement equation to the target initial state vector;

s32, calculating a Jacobi matrix of the Doppler frequency shift measurement equation to the target initial state vector;

s33, performing joint processing on the calculation results of the step S31 and the step S32, namely combining the two obtained matrixes to obtain a target state estimation equation, wherein the formula is as follows:

$H_k\left(X_0\right)=\frac{\∂h\left(X\right)}{\∂X_0}=\[\begin{array}{cc}\frac{\∂T_{jk}}{\∂X_0}& \frac{\∂F_{jk}}{\∂X_0}\end{array}\],k=1,2,...N$

wherein,a Jacobi matrix representing the equation of time difference measurement versus the target initial state vector,a Jacobi matrix representing the Doppler shift measurement equation to the target initial state vector;

and S34, solving the problem by using a batch processing algorithm, and finally obtaining the position information and the speed information of the maneuvering target when the algorithm converges.

Further, the method for calculating the target initial state vector in step S31 of the present invention is:

X₀＝[[x₀y₀v_xv_y]]^T

wherein, X₀Is a target initial state vector, (x)₀,y₀) Is the target initial position, (v)_x,v_y) Components of the target velocity in the x, y axes, [. degree]^TIs a transpose operation on a matrix;

at the kth time, the constant speed of the target is (v)_x,v_y) Then, the target position is known:

x_k＝x₀+kΔtv_x；

y_k＝y₀+kΔtv_y；

where Δ t is the sampling interval time.

Further, in step S31 of the present invention, the equation of the time difference measurement is:

${\mathrm{\τ}}_{jk}=\frac{1}{c}\[r_{jk}+r_{0k}-R_{trj}\],(k=0,1,2,...,N),(j=1,2)$

wherein, tau_jkRepresenting the time difference obtained k times by the jth transmitting station, c the speed of light, r_jk,r_0k,R_trjRespectively representing the distance between a transmitting station j and a target, the distance between the target and a receiving station and the distance between the transmitting station j and the receiving station;

the first transmitting station is located at (x)_T1,y_T1) The second transmitting station is located at (x)_T2,y_T2) The receiving station is located at (x)_R,y_R) And has:

$r_{jk+i}=\sqrt{({\left(x_k-x_{jT}\right)}^2+{\left(y_k-y_{Tj}\right)}^2)}$

$r_{0k+i}=\sqrt{({\left(x_k-x_R\right)}^2+{\left(y_k-y_R\right)}^2)}$

$R_{trj}=\sqrt{({\left(x_R-x_{Tj}\right)}^2+{\left(y_R-y_{Tj}\right)}^2)}$

where k is 0,1,2, …, N.

Further, in step S32 of the present invention, the doppler shift measurement equation is:

$f_{jk}=\frac{f_j}{c}.\left(-\frac{\left(\left(x_k-x_{Tj}\right)v_x+\left(y_k-y_{Tj}\right)v_y\right)}{\sqrt{{\left(x_k-x_{Tj}\right)}^2+{\left(y_k-y_{Tj}\right)}^2}}-\frac{\left(\left(x_k-x_R\right)v_x+\left(y_k-y_R\right)v_y\right)}{\sqrt{{\left(x_k-x_R\right)}^2+{\left(y_k-y_R\right)}^2}}\right)$

f_jindicating the frequency at which the jth transmitting station transmits signals.

Further, the specific method for using the batch processing algorithm in step S34 of the present invention is as follows:

let the true value of the target parameter be X₀The parameter estimation value isThe measurement equation can be written in the general form:

Z＝h(X)+n

n is noise, and is added to X₀And performing Taylor series expansion, and selecting only one item of the series sequence, then:

$Z=h\left(X_0\right)+H(\hat{X}-X_0)+n$

$H_k\left(X_0\right)=\frac{\∂h\left(X\right)}{\∂X_0}=\[\begin{array}{cc}\frac{\∂T_{jk}}{\∂X_0}& \frac{\∂F_{jk}}{\∂X_0}\end{array}\],k=1,2,...N$

the above formula is aboutThe linear equation of (a) can be processed by a linear least squares method, and then:

$\hat{X}=X_0+{\left(H^T{S}_k^{-1}H\right)}^{-1}{H}^T{S}_k^{-1}(Z-h(X_0\left)\right)$

whereinAs an initial value of a successive approximation method converging on the optimum estimation value;

according to the Gauss-Newton method, the following results were obtained:

${\hat{X}}_{n+1}={\hat{X}}_n-m{\left(H^T{S}_k^{-1}H\right)}^{-1}{H}^T{S}_k^{-1}(Z-h({\hat{X}}_n\left)\right)$

whereinIn order to be the latest estimate value,is the nth iteration estimation value, m is a convergence factor, and takes a value approximate to 1;

when in useThe algorithm is considered to be converged, and the final result is the target position information and the speed information。

The invention provides a T-based²The time difference of/R and Doppler frequency shift joint positioning system comprises:

the frequency and distance acquisition unit is used for selecting two short-wave broadcasting stations with different signal frequencies as transmitting stations, acquiring the transmitting frequencies and the coordinate positions of the short-wave broadcasting stations, and calculating the ground great circle distance between the transmitting stations and the receiving stations according to the coordinate information;

the time difference and Doppler frequency shift data calculation unit is used for calculating time difference data and Doppler frequency shift data between direct waves and scattered waves according to the signal frequency and the ground great circle distance by using a time difference measuring method, wherein the direct waves are signals of a transmitting station directly received by a receiving station, and the scattered waves are signals reflected to the receiving station after the transmitted signals irradiate an air flying target;

and the combined positioning unit is used for calculating and obtaining the position and the flying speed of the flying target according to the obtained time difference data and Doppler frequency shift data combined positioning.

The invention has the following beneficial effects: based on T of the invention²The time difference of the/R and Doppler frequency shift combined positioning method can position a moving aerial target by only needing two broadcasting stations as radiation sources; by adopting time difference information between direct waves and scattered waves, the number of transmitting stations is reduced, and the rapid establishment of a short-wave radar system is facilitated; and the time difference information and the Doppler frequency shift information are adopted, so that the position precision and the speed precision of the target which moves at a constant speed and a variable speed are greatly improved.

Drawings

The invention will be further described with reference to the accompanying drawings and examples, in which:

FIG. 1 is a T-based representation of an embodiment of the present invention²Flow of/R time difference and Doppler frequency shift combined positioning methodA flow chart;

FIG. 2 is a T-based representation of an embodiment of the present invention²A flow chart of a concrete implementation method of the joint positioning method of the time difference of the/R and the Doppler frequency shift;

FIG. 3 is a T-based representation of an embodiment of the present invention²A joint positioning schematic diagram of a time difference/R and Doppler frequency shift joint positioning method;

FIG. 4 is a T-based representation of an embodiment of the present invention²A functional block diagram of a/R time difference and Doppler frequency shift joint positioning system;

in the figure, 401-frequency and distance acquisition unit, 402-time difference and doppler shift data calculation unit. 403-joint positioning unit.

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

As shown in FIG. 1, the embodiment of the invention is based on T²The method for joint positioning of the time difference of the/R and the Doppler frequency shift comprises the following steps:

s1, selecting two short-wave broadcasting stations with different signal frequencies as transmitting stations, acquiring the transmitting frequencies and coordinate positions of the short-wave broadcasting stations, and calculating the ground great circle distance between the transmitting stations and the receiving stations according to the coordinate positions;

s2, calculating time difference data and Doppler frequency shift data between direct waves and scattered waves by using a time difference measuring method according to the signal frequency and the ground great circle distance, wherein the direct waves are signals of a transmitting station directly received by a receiving station, and the scattered waves are signals reflected to the receiving station after the transmitted signals irradiate an air flying target;

and S3, calculating the position and the flying speed of the flying target according to the obtained time difference data and Doppler frequency shift data in a combined positioning mode.

In another embodiment of the invention, as shown in fig. 2, the method comprises the steps of:

(1) receiving a short wave signal;

the existing short-wave broadcasting station is used as an external radiation source signal.

(2) Screening short wave broadcasting station

And obtaining the frequency of a short-wave broadcasting station and the site of a transmitting station according to a short-wave full-band radio frequency division list released by the international telecommunication union, and selecting any two of the frequency and the site. However, the transmitting station and the receiving station cannot be located at the same coordinate position, and the two short-wave broadcast signals adopt an AM modulation mode and are short-wave signals with different frequencies.

(3) Calculating the great circle distance between the ground between the two receiving and transmitting stations;

the ground great circle distance between the transmitting station and the receiving station is calculated by utilizing the longitude and latitude of the transmitting station of the short wave broadcasting station.

(4) Calculating time difference and Doppler frequency shift information;

under the condition of known signal frequency and large circular distance between the ground surfaces of receiving stations of the transmitting station, a direct wave signal is extracted, and the direct wave is a transmitting station signal directly received by the receiving station. And (4) extracting a scattered wave signal, wherein the signal is a signal which is reflected to a receiving station after a signal transmitted by a transmitting station irradiates a maneuvering target in the air. And then, obtaining time difference information between the continuous secondary direct wave and the scattered wave by using a time difference estimation calculation method, and obtaining Doppler frequency shift information between the continuous secondary direct wave and the scattered wave by using a Doppler frequency shift estimation algorithm.

(5) Performing combined positioning;

and obtaining the position and the flying speed of the flying target by joint positioning of the time difference and the Doppler frequency shift.

As shown in fig. 3, the specific steps of joint positioning are:

(5.1) calculating a Jacobi matrix of the time difference measurement equation to the target initial state vector;

assume the target initial state vector is X₀：

X₀＝[[x₀y₀v_xv_y]]^T

Wherein (x)₀,y₀) Is the target initial position, (v)_x,v_y) Representing the components of the target velocity in the x, y axes. [. the]^TRepresenting a transpose operation on a matrix.

At the kth time, the constant speed of the target is (v)_x,v_y) Then, the target position is known:

x_k＝x₀+kΔtv_x；

y_k＝y₀+kΔtv_y；

where Δ t represents the sampling interval time.

The equation for the time difference measurement is:

${\mathrm{\τ}}_{jk}=\frac{1}{c}\[r_{jk}+r_{0k}-R_{trj}\],(k=0,1,2,...,N),(j=1,2)$

wherein tau is_jkRepresenting the time difference obtained k times by the jth transmitting station, c the speed of light, r_jk,r_0k,R_trjRespectively representing the distance between the transmitting station j and the target, the distance between the target and the receiving station and the distance between the transmitting station j and the receiving station.

Wherein the first transmitting station is located at (x)_T1,y_T1) The second transmitting station is located at (x)_T2,y_T2) The receiving station is located at (x)_R,y_R)。

$r_{jk+i}=\sqrt{({\left(x_k-x_{jT}\right)}^2+{\left(y_k-y_{Tj}\right)}^2)}$

$r_{0k+i}=\sqrt{({\left(x_k-x_R\right)}^2+{\left(y_k-y_R\right)}^2)},(k=0,1,2,...,N)$

$R_{trj}=\sqrt{({\left(x_R-x_{Tj}\right)}^2+{\left(y_R-y_{Tj}\right)}^2)}$

The Jacobi matrix from which the equation for time difference measurement is derived is:

$\frac{\∂{\mathrm{\τ}}_{jk}}{\∂X_0}={\left[\begin{array}{cccc}\frac{\∂{\mathrm{\τ}}_{jk}}{\∂x_0}& \frac{\∂{\mathrm{\τ}}_{jk}}{\∂y_0}& \frac{\∂{\mathrm{\τ}}_{jk}}{\∂v_x}& \frac{\∂{\mathrm{\τ}}_{jk}}{\∂v_y}\end{array}\right]}^T$

wherein,

$\frac{\∂{\mathrm{\τ}}_{jk}}{\∂x_0}=\frac{1}{c}(\frac{x_k-x_{Tj}}{r_{jk}}+\frac{x_k-x_R}{r_{0k}})$

$\frac{\∂{\mathrm{\τ}}_{jk}}{\∂y_0}=\frac{1}{c}(\frac{y_k-y_{Tj}}{r_{jk}}+\frac{y_k-y_R}{r_{0k}})$

$\frac{\∂{\mathrm{\τ}}_{jk}}{\∂v_x}=\frac{1}{c}(\frac{(x_k-x_{Tj})k\mathrm{\Δ}t}{r_{jk}}+\frac{(x_k-x_R)k\mathrm{\Δ}t}{r_{0k}})$

$\frac{\∂{\mathrm{\τ}}_{jk}}{\∂v_y}=\frac{1}{c}(\frac{(y_k-y_{Tj})k\mathrm{\Δ}t}{r_{jk}}+\frac{(y_k-y_R)k\mathrm{\Δ}t}{r_{0k}})$

(5.2) calculating a Jacobi matrix of the Doppler frequency shift measurement equation to the target original state vector; the doppler shift measurement equation is:

$f_{jk}=\frac{f_j}{c}\·(-\frac{\left(\right(x_k-x_{Tj})v_x+(y_k-y_{Tj}\left)v_y\right)}{\sqrt{{(x_k-x_{Tj})}^2+{(y_k-y_{Tj})}^2}}-\frac{\left(\right(x_k-x_R)v_x+(y_k-y_R\left)v_y\right)}{\sqrt{{(x_k-x_R)}^2+{(y_k-y_R)}^2}})$

f_jindicating the frequency at which the jth transmitting station transmits signals.

The Jacobi matrix for obtaining the doppler shift measurement equation is:

$\frac{\∂f_{jk}}{\∂X_0}={\left[\begin{array}{cccc}\frac{\∂f_{jk}}{\∂x_0}& \frac{\∂f_{jk}}{\∂y_0}& \frac{\∂f_{jk}}{\∂v_x}& \frac{\∂f_{jk}}{\∂v_y}\end{array}\right]}^T$

wherein,

$\frac{\∂f_{jk}}{\∂x_0}=\frac{f_j}{c}\left(\begin{array}{c}\frac{(y_k-y_{Tj})\left(\right(y_k-y_{Tj})v_x-(x_k-x_{Tj}\left)v_y\right)}{r_{jk}^3}\\ +\frac{(y_k-y_R)\left(\right(y_k-y_R)v_x-(x_k-x_R\left)v_y\right)}{r_{0k}^3}\end{array}\right)$

$\frac{\∂f_{jk}}{\∂y_0}=\frac{f_j}{c}\left(\begin{array}{c}\frac{(x_k-x_{Tj})\left(\right(x_k-x_{Tj})v_y-(y_k-y_{Tj}\left)v_x\right)}{r_{jk}^3}\\ +\frac{(x_k-x_R)\left(\right(x_k-x_R)v_y-(y_k-y_R\left)v_x\right)}{r_{0k}^3}\end{array}\right)$

$\frac{\∂f_{jk}}{\∂v_x}=\frac{f_j}{c}\left(\begin{array}{c}\frac{r_{jk}^2(x_k-x_{Tj})+(y_k-y_{Tj})k\mathrm{\Δ}t\left(\right(y_k-y_{Tj})v_x-(x_k-x_{Tj})v_y)}{r_{jk}^3}\\ +\frac{r_{0k}^2(x_k-x_R)+(y_k-y_R)k\mathrm{\Δ}t\left(\right(y_k-y_R)v_x-(x_k-x_R)v_y)}{r_{0k}^3}\end{array}\right)$

$\frac{\∂f_{jk}}{\∂v_y}=\frac{f_j}{c}\left(\begin{array}{c}\frac{r_{jk}^2(y_k-y_{Tj})+(x_k-x_{Tj})k\mathrm{\Δ}t\left(\right(x_k-x_{Tj})v_y-(y_k-y_{Tj})v_x)}{r_{jk}^3}\\ +\frac{r_{0k}^2{y}_k+(x_k-x_R)k\mathrm{\Δ}t\left(\right(x_k-x_R)v_y-(y_k-y_R)v_x)}{r_{0k}^3}\end{array}\right)$

(5.3) combining the two calculation results to obtain a target state estimation equation;

$H_k\left(X_0\right)=\frac{\∂h\left(X\right)}{\∂X_0}=\[\begin{array}{cc}\frac{\∂T_{jk}}{\∂X_0}& \frac{\∂F_{jk}}{\∂X_0}\end{array}\],k=1,2,...N$

i.e. the Jacobi matrix of the equation of time difference measurement with respect to the initial state vector of the target and the Jacobi matrix of the equation of doppler shift measurement with respect to the initial state vector of the target are combined.

And (5.4) obtaining position information and speed information of the maneuvering target by using Gauss-Newton batch processing algorithm.

Let the true value of the target parameter be X₀The parameter estimation value isThe measurement equation can be written in the general form:

$Z=h\left(X_0\right)+H(\hat{X}-X_0)+n$

$H_k\left(X_0\right)=\frac{\∂h\left(X\right)}{\∂X_0}=\[\begin{array}{cc}\frac{\∂T_{jk}}{\∂X_0}& \frac{\∂F_{jk}}{\∂X_0}\end{array}\],k=1,2,...N$

the above formula is aboutThe linear equation of (c), which can be processed by linear least squares, has:

$\hat{X}=X_0+{\left(H^T{S}_k^{-1}H\right)}^{-1}{H}^T{S}_k^{-1}(Z-h(X_0\left)\right)$

whereinAs an initial value of the successive approximation method converging on the optimum estimated value.

From the GN method, it is possible to obtain:

${\hat{X}}_{n+1}={\hat{X}}_n-m{\left(H^T{S}_k^{-1}H\right)}^{-1}{H}^T{S}_k^{-1}(Z-h({\hat{X}}_n\left)\right)$

whereinIn order to be the latest estimate value,is the estimated value of the nth iteration and m is the convergence factor, generally taking a value of approximately 1.

As shown in FIG. 4, the embodiment of the present invention is based on T²A time difference and Doppler shift joint positioning system of/R, which is used for realizing the T-based positioning system of the embodiment of the invention²The method for joint positioning of the time difference of the/R and the Doppler frequency shift comprises the following steps:

a frequency and distance acquiring unit 401, configured to select two short-wave broadcast stations with different signal frequencies as transmitting stations, acquire their transmitting frequencies and coordinate positions, and calculate a ground great circle distance between the transmitting station and the receiving station according to the coordinate information;

a time difference and doppler shift data calculation unit 402, configured to calculate time difference data and doppler shift data between a direct wave and a scattered wave according to the signal frequency and the ground great circle distance by using a time difference measurement method, where the direct wave is a signal of a transmitting station directly received by a receiving station, and the scattered wave is a signal reflected by the transmitting signal to the receiving station after the transmitting signal irradiates an airborne flying target;

and a joint positioning unit 403, configured to perform joint positioning according to the obtained time difference data and doppler shift data, and calculate a position and a flight speed of the flying target.

The invention can realize the positioning of the air maneuvering target by a method combining time difference and Doppler frequency shift by using the existing short wave broadcasting station as a radiation source on the basis of not establishing a transmitting station. Compared with other passive target positioning methods, the invention has the following characteristics:

(1) the invention uses the existing short-wave broadcasting station as a radiation source, and does not transmit signals by self, thereby having the advantages of long distance, hidden reception, difficult discovery by the outside and the like;

(2) different from the common positioning method using time difference information, the invention adopts the time difference information between direct waves and scattered waves instead of the time difference information between different transmitting stations and receiving stations, thereby reducing the number required by the transmitting stations and being beneficial to the rapid establishment of a short wave radar system;

(3) because the time difference information and the Doppler frequency shift information are simultaneously utilized, the position precision and the speed precision are greatly improved compared with other positioning systems which independently use time difference or Doppler frequency shift;

(4) since two measurement messages are used simultaneously and there are two transmitting stations, the system with four state parameters is always in a stable state. Therefore, the parameter estimation of the target position and speed information can be realized only in a short system accumulation time, and the method is very suitable for positioning a maneuvering target;

(5) because the invention adopts Gauss-Newton batch processing algorithm, the system positioning precision can effectively approach the CRLB boundary.

It will be understood that modifications and variations can be made by persons skilled in the art in light of the above teachings and all such modifications and variations are intended to be included within the scope of the invention as defined in the appended claims.

Claims (9)

1. Based on T²The method for joint positioning of time difference and Doppler frequency shift of/R is characterized by comprising the following steps:

s1, selecting two short-wave broadcasting stations with different signal frequencies as transmitting stations, acquiring the transmitting frequencies and coordinate positions of the short-wave broadcasting stations, and calculating the ground great circle distance between the transmitting stations and the receiving stations according to the coordinate positions;

s2, calculating time difference data and Doppler frequency shift data between direct waves and scattered waves by using a time difference measuring method according to the signal frequency and the ground great circle distance, wherein the direct waves are signals of a transmitting station directly received by a receiving station, and the scattered waves are signals reflected to the receiving station after the transmitted signals irradiate an air flying target;

and S3, combining the obtained time difference data and the Doppler frequency shift data to obtain a target state estimation equation, and calculating by a batch processing algorithm to obtain a convergence result, namely the position and the flying speed of the flying target.

2. The T-based of claim 1²The method for joint positioning of time difference and Doppler shift of/R is characterized in that the method for acquiring the transmitting frequency and the coordinate position of the short-wave broadcasting station in the step S1 comprises the following steps:

two transmitting stations are selected from a short-wave full-frequency-band radio frequency division list released by the international telecommunication union, the transmitting stations cannot be located on the same coordinate position with a receiving station, and two short-wave broadcast signals adopt an AM (amplitude modulation) mode and are short-wave signals with different frequencies.

3. The T-based of claim 1²The method for joint positioning of time difference and doppler shift of/R is characterized in that step S2 specifically includes the following steps:

s21, extracting direct wave signals, wherein the direct waves are transmitting station signals directly received by a receiving station;

s22, extracting scattered wave signals, wherein the signals are signals which are reflected to a receiving station after the signals transmitted by the transmitting station irradiate the maneuvering target in the air;

s23, obtaining time difference information between the continuous k times of direct waves and scattered waves by using a time difference estimation method;

and S24, obtaining Doppler frequency shift information between the continuous k times of direct waves and scattered waves by using a Doppler frequency shift estimation algorithm.

4. The T-based of claim 1²The method for joint positioning of time difference and doppler shift of/R is characterized in that step S3 specifically includes the following steps:

s31, calculating a Jacobi matrix of the time difference measurement equation to the target initial state vector;

s32, calculating a Jacobi matrix of the Doppler frequency shift measurement equation to the target initial state vector;

s33, performing joint processing on the calculation results of the step S31 and the step S32, namely combining the two obtained matrixes to obtain a target state estimation equation, wherein the formula is as follows:

$H_k\left(X_0\right)=\frac{\∂h\left(X\right)}{\∂X_0}=\[\begin{array}{cc}\frac{\∂T_{jk}}{\∂X_0}& \frac{\∂F_{jk}}{\∂X_0}\end{array}\],k=1,2,...N$

wherein,a Jacobi matrix representing the equation of time difference measurement versus the target initial state vector,a Jacobi matrix representing the Doppler shift measurement equation to the target initial state vector;

and S34, solving the problem by using a batch processing algorithm, and finally obtaining the position information and the speed information of the maneuvering target when the algorithm converges.

5. The T-based of claim 4²The method for joint positioning of time difference and Doppler shift of/R is characterized in that the calculation method of the target initial state vector in the step S31 is as follows:

X₀＝[x₀y₀v_xv_y]^T

wherein, X₀Is a target initial state vector, (x)₀,y₀) Is the target initial position, (v)_x,v_y) Components of the target velocity in the x, y axes, [. degree]^TIs a transpose operation on a matrix;

at the kth time, the constant speed of the target is (v)_x,v_y) Then, the target position is known:

x_k＝x₀+kΔtv_x；

y_k＝y₀+kΔtv_y；

where Δ t is the sampling interval time.

6. The T-based of claim 5²The method for joint positioning of time difference and Doppler shift of/R is characterized in that the method for measuring time difference in step S31The process is as follows:

${\mathrm{\τ}}_{jk}=\frac{1}{c}\[r_{jk}+r_{0k}-R_{trj}\],(k=0,1,2,...,N),(j=1,2)$

wherein, tau_jkRepresenting the time difference obtained k times by the jth transmitting station, c the speed of light, r_jk,r_0k,R_trjRespectively representing the distance between a transmitting station j and a target, the distance between the target and a receiving station and the distance between the transmitting station j and the receiving station;

the first transmitting station is located at (x)_T1,y_T1) The second transmitting station is located at (x)_T2,y_T2) The receiving station is located at (x)_R,y_R) And has:

$r_{jk+i}=\sqrt{({(x_k-x_{jT})}^2+{(y_k-y_{Tj})}^2)}$

$r_{0k+i}=\sqrt{({(x_k-x_R)}^2+{(y_k-y_R)}^2)}$

$R_{trj}=\sqrt{({(x_R-x_{Tj})}^2+{(y_R-y_{Tj})}^2)}$

where k is 0,1,2, …, N.

7. The T-based of claim 4²The method for joint positioning of time difference and Doppler shift of/R is characterized in that in step S32, the Doppler shift measurement equation is as follows:

$f_{jk}=\frac{f_j}{c}\·(-\frac{\left(\right(x_k-x_{Tj})v_x+(y_k-y_{Tj}\left)v_y\right)}{\sqrt{{(x_k-x_{Tj})}^2+{(y_k-y_{Tj})}^2}}-\frac{\left(\right(x_k-x_R)v_x+(y_k-y_R\left)v_y\right)}{\sqrt{{(x_k-x_R)}^2+{(y_k-y_R)}^2}})$

f_jindicating the frequency at which the jth transmitting station transmits signals.

8. The T-based of claim 4²The method for joint positioning of time difference and doppler shift of/R is characterized in that the specific method of using batch processing algorithm in step S34 is as follows:

let the true value of the target parameter be X₀The parameter estimation value isThe measurement equation can be written in the general form:

Z＝h(X)+n

n is noise, and is added to X₀And performing Taylor series expansion, and selecting only one item of the series sequence, then:

$Z=h\left(X_0\right)+H(\hat{X}-X_0)+n$

$H_k\left(X_0\right)=\frac{\∂h\left(X\right)}{\∂X_0}=\[\begin{array}{cc}\frac{\∂T_{jk}}{\∂X_0}& \frac{\∂F_{jk}}{\∂X_0}\end{array}\],k=1,2,...N$

the above formula is aboutThe linear equation of (a) can be processed by a linear least squares method, and then:

$\hat{X}=X_0+{\left(H^T{S}_k^{-1}H\right)}^{-1}{H}^T{S}_k^{-1}(Z-h(X_0\left)\right)$

whereinAs an initial value of a successive approximation method converging on the optimum estimation value;

according to the Gauss-Newton method, the following results were obtained:

${\hat{X}}_{n+1}={\hat{X}}_n-m{\left(H^T{S}_k^{-1}H\right)}^{-1}{H}^T{S}_k^{-1}(Z-h({\hat{X}}_n\left)\right)$

whereinIn order to be the latest estimate value,is the nth iteration estimation value, m is a convergence factor, and takes a value approximate to 1;

when in useThe algorithm is considered to have converged, and the final result is the target position information and the speed information.

9. Based on T²the/R time difference and Doppler frequency shift joint positioning system is characterized by comprising:

the frequency and distance acquisition unit is used for selecting two short-wave broadcasting stations with different signal frequencies as transmitting stations, acquiring the transmitting frequencies and the coordinate positions of the short-wave broadcasting stations, and calculating the ground great circle distance between the transmitting stations and the receiving stations according to the coordinate information;

the time difference and Doppler frequency shift data calculation unit is used for calculating time difference data and Doppler frequency shift data between direct waves and scattered waves according to the signal frequency and the ground great circle distance by using a time difference measuring method, wherein the direct waves are signals of a transmitting station directly received by a receiving station, and the scattered waves are signals reflected to the receiving station after the transmitted signals irradiate an air flying target;

and the combined positioning unit is used for calculating and obtaining the position and the flying speed of the flying target according to the obtained time difference data and Doppler frequency shift data combined positioning.