CN110275133B - Non-common-view pulse signal passive positioning method based on virtual arrival time difference - Google Patents

Non-common-view pulse signal passive positioning method based on virtual arrival time difference Download PDF

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CN110275133B
CN110275133B CN201910567061.9A CN201910567061A CN110275133B CN 110275133 B CN110275133 B CN 110275133B CN 201910567061 A CN201910567061 A CN 201910567061A CN 110275133 B CN110275133 B CN 110275133B
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黄振
张尚煜
冯雪峰
何加智
石磊
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Tsinghua University
Shenzhen Research Institute Tsinghua University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
    • G01S5/02—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using radio waves
    • G01S5/06—Position of source determined by co-ordinating a plurality of position lines defined by path-difference measurements

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Abstract

The invention relates to a non-common-view pulse signal passive positioning method based on virtual arrival time difference, which comprises the following steps: receiving pulse signals continuously emitted by a radiation source u by using M observation platforms with the same time reference, detecting the rising edge of the received pulse signals at each observation platform, and estimating to obtain a time of arrival (TOA); simultaneously acquiring the position information of each platform corresponding to each arrival time; carrying out plane transformation on the received TOA sequence to obtain a two-dimensional image; the TOA sequence emitted by the same radiation source can form a continuous curve, and due to the non-common condition, part of points of the curve in the image are lost; fitting a curve in the two-dimensional image to obtain a curve parameter; estimating to obtain the coordinates of the lost points, and restoring the TOA of the lost pulse according to the coordinates of the lost points; estimating to obtain a virtual arrival time difference according to the TOA of the lost pulse; the virtual arrival time difference and the arrival time difference are jointly used for positioning, and the radiation source position is obtained through calculation by adopting a method for solving a nonlinear equation.

Description

Non-common-view pulse signal passive positioning method based on virtual arrival time difference
Technical Field
The invention relates to the field of passive positioning, in particular to a non-common-view pulse signal passive positioning method based on virtual arrival time difference, aiming at a non-cooperative radiation source for transmitting pulse signals.
Background
The passive positioning means that the observation station is in a silent state, passively receives signals of the target radiation source, and positioning of the target radiation source is completed by receiving the signals. In practical application, due to the reasons of non-cooperation of targets, obstruction, different antenna direction directions and the like, signal loss can be caused, and an observation station cannot receive signals sent by all radiation sources, namely non-common-view. Whereas traditional observations, such as time difference of arrival, require that at least two platforms receive the same signal. Therefore, the non-common view causes a decrease in the conventional observation amount, resulting in a decrease in the positioning accuracy.
Disclosure of Invention
In view of the above problems, an object of the present invention is to provide a passive positioning method for non-common-view pulse signals based on virtual arrival time differences, which can effectively improve the positioning accuracy.
In order to achieve the purpose, the invention adopts the following technical scheme: a non-common-view pulse signal passive positioning method based on virtual arrival time difference comprises the following steps: 1) receiving pulse signals continuously emitted by a radiation source u by using M observation platforms with the same time reference, detecting the rising edge of the received pulse signals at each observation platform, and estimating to obtain a time of arrival (TOA); simultaneously acquiring the position information of each platform corresponding to each arrival time; 2) carrying out plane transformation on the received TOA sequence, wherein the width of the plane transformation is w, and obtaining a two-dimensional image; the TOA sequence emitted by the same radiation source can form a continuous curve, and due to the non-common condition, part of points of the curve in the image are lost; 3) fitting a curve in the two-dimensional image to obtain a curve parameter; 4) estimate the derived lossRestoring the TOA of the lost pulse according to the coordinates of the lost point; 5) from the TOA of the missing pulse, the virtual arrival time difference is estimated
Figure BDA0002109928330000011
6) By virtual arrival time differences
Figure BDA0002109928330000012
Positioning observation quantity can be obtained by combining the obtained time difference of arrival TDOA; the position of the observation platform corresponding to the TOA can be obtained by a self-positioning module of the observation platform, and the radiation source position can be obtained by resolving by adopting a method of solving a nonlinear equation in combination with the positioning observed quantity.
Further, in the step 4), after obtaining the coefficient of the curve fitting function, according to the cumulative plane transformation, wherein the X axis represents the observation window number and takes a value of a continuous positive integer, if a pulse is lost, the X coordinate of the midpoint of the curve is discontinuous, so that the corresponding point of the lost pulse in the cumulative plane transformation is estimated, and then the TOA of the lost pulse is obtained.
Further, TOA estimate of missing pulses
Figure BDA0002109928330000013
Comprises the following steps:
Figure BDA0002109928330000021
Figure BDA0002109928330000022
in the formula, f (x)m,i,αm) Representing a fitting function of the estimated curve. (ii) a x is the number ofm,iTransforming the abscissa of the corresponding point for the cumulative plane; alpha is alphamIs an estimation equation of the fitting coefficients.
Further, in the step 5), the virtual arrival time difference
Figure BDA0002109928330000023
Comprises the following steps:
Figure BDA0002109928330000024
wherein m is1≠m2，m1And m2Indicating the number of the two observation platforms receiving the ith pulse.
Due to the adoption of the technical scheme, the invention has the following advantages: aiming at the problem that a plurality of observation stations receive pulse signals of a radiation source, the positioning accuracy is reduced due to non-common vision, and a one-dimensional TOA sequence can be converted into a two-dimensional image by combining a plane transformation method according to the front-back constraint relation of the TOA sequence. The two-dimensional image has the characteristics that the ordinate corresponds to time and the value is continuous, and the abscissa corresponds to the number of the observation window and the value is a continuous positive integer. Therefore, the invention estimates the coordinates of the lost points in the curve by a curve fitting method, and effectively improves the positioning precision.
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FIG. 1 is a schematic overall flow diagram of the present invention;
FIG. 2 is a schematic view of the scenario of the present invention;
FIG. 3 is a schematic diagram of a transmit time series and an arrival time series of the present invention;
fig. 4 is a schematic diagram of a planar transformation of a transmit time series and an arrival time series of the present invention.
Detailed Description
The invention is described in detail below with reference to the figures and examples.
As shown in fig. 1, the present invention provides a non-common-view pulse signal passive positioning method based on virtual arrival time difference, which includes the following steps:
1) as shown in fig. 2, M observation platforms with the same time reference are used to receive pulse signals continuously emitted by a radiation source u, and the rising edge of the received pulse signal is detected at each observation platform to obtain a time sequence of arrival TOA by estimation; and simultaneously acquiring the position information of each platform corresponding to each arrival time.
As shown in FIG. 3, let TOT be the transmission time of the ith pulsei：
TOTi＝TOT0+i·PRI
Wherein, i is 1, 2, and N is the total number of transmitted pulses; TOT0PRI is the pulse repetition interval, which is the firing time of the initial pulse.
The arrival time t of the ith pulse received by the mth observation platformm，iComprises the following steps:
tm，i＝TOTi+Δtm，i＝TOT0+i·PRI+Δtm，i
wherein M is 1, 2, M; Δ tm，iThe propagation delay from the target to the observation station m for the ith pulse can be expressed as:
Figure BDA0002109928330000031
wherein c represents the speed of light, sm,iIndicating the position of the m-th observation platform when the i-th pulse is received. r ism,iDenotes the radiation sources u and sm,iThe distance between them. I | · | purple wind2Representing the two-norm of.
2) Carrying out plane transformation on the received TOA sequence, wherein the width of the plane transformation is w, and obtaining a two-dimensional image; the TOA sequence emitted by the same radiation source can form a continuous curve (as shown in fig. 4), and due to the non-common condition, the points of the curve part in the image are lost;
each TOA corresponds to a point (x, y) on the two-dimensional plane as:
x＝mod(tm，i，w)
y＝tm，i-wx；
3) fitting a curve in the two-dimensional image to obtain a curve parameter;
for the pulse received by the observation platform m, the arrival time is tm,iThe coordinates of the point corresponding to the cumulative planar transform are (x)m,i,ym,i) Assuming that the fitting function of the curve in the cumulative planar transform is f (x, α)m)，αmRepresenting the undetermined coefficients in the fitting function, then:
error of fit em,iComprises the following steps:
em,i＝ym,i-f(xm,i,αm)
error of fit em,iOf vector form emComprises the following steps:
em＝[em,1,em,2,...,em,N]T
the estimated equation for the fitting coefficient is:
Figure BDA0002109928330000032
wherein |2Representing a 2 norm. This is a least squares fitting method whose principle is to make the residuals em,iHas the smallest sum of squares, i.e.
Figure BDA0002109928330000033
The basis functions for fitting can be expressed as
f(xm,i,αm)＝f(xm,i,α1)+f(xm,i,α2)+…+f(xm,i,αK)
Where K is the number of basis functions.
In the present embodiment, a polynomial basis function is adopted, which can be expressed as
f(x,α0)＝α0
f(x,α1)＝α1x1
f(x,α2)＝α2x2
Figure BDA0002109928330000041
f(x,αK)＝αKxK-1
Wherein alpha ism＝[α0,α1,...,αK]。
Let ym＝Hmαm+emIn which H ism＝[1,x,x2,...,xK-1]。
Solving polynomial basis functions, namely linear least square problem, can obtain a fitting coefficient alphamIs composed of
Figure BDA0002109928330000042
4) Estimating to obtain the coordinates of the lost point, and then restoring the TOA of the lost pulse according to the coordinates of the lost point: after the coefficients of the curve fitting function are obtained, the X-axis represents the number of the observation window and takes the value of a continuous positive integer according to the cumulative plane transformation, and if pulse loss occurs, the X coordinate of the midpoint of the curve is discontinuous. Therefore, the corresponding point of the missing pulse in the cumulative plane transformation can be estimated, and the TOA of the missing pulse can be obtained.
TOA estimation of missing pulses
Figure BDA0002109928330000043
Comprises the following steps:
Figure BDA0002109928330000044
Figure BDA0002109928330000045
in the formula, f (x)m,i,αm) Representing a fitting function of the estimated curve.
5) From the TOA of the missing pulse, the virtual arrival time difference is estimated
Figure BDA0002109928330000046
Figure BDA0002109928330000047
Wherein m is1≠m2，m1And m2Indicating the number of the two observation platforms receiving the ith pulse.
6) By virtual arrival time differences
Figure BDA0002109928330000048
And combining the obtained arrival time difference TDOA to obtain a positioning observation quantity. The time difference of arrival can be expressed as
Figure BDA0002109928330000049
Wherein m is3≠m4，m3And m4Indicating the number of the two observation platforms receiving the ith pulse.
The self-positioning module of the observation platform can obtain the position of the observation platform corresponding to the TOA, and the observation quantity is positioned in combination
Figure BDA00021099283300000410
The radiation source position can be obtained by solving a nonlinear equation. After the virtual arrival time difference observed quantity is increased, the positioning precision can be effectively improved, especially under the condition that more pulses are lost.
The above embodiments are only for illustrating the present invention, and the steps may be changed, and on the basis of the technical solution of the present invention, the modification and equivalent changes of the individual steps according to the principle of the present invention should not be excluded from the protection scope of the present invention.

Claims (1)

1. A non-common-view pulse signal passive positioning method based on virtual arrival time difference is characterized by comprising the following steps:
1) receiving pulse signals continuously emitted by a radiation source u by using M observation platforms with the same time reference, detecting the rising edge of the received pulse signals at each observation platform, and estimating to obtain a time of arrival (TOA); simultaneously acquiring the position information of each platform corresponding to each arrival time;
2) carrying out plane transformation on the received TOA sequence, wherein the width of the plane transformation is w, and obtaining a two-dimensional image; the TOA sequence emitted by the same radiation source can form a continuous curve, and due to the non-common condition, part of points of the curve in the image are lost;
3) fitting a curve in the two-dimensional image to obtain a curve parameter;
4) estimating to obtain the coordinates of the lost points, and then restoring the TOA of the lost pulse according to the coordinates of the lost points;
5) from the TOA of the missing pulse, the virtual arrival time difference is estimated
Figure FDA0002876262050000011
6) By virtual arrival time differences
Figure FDA0002876262050000012
Positioning observation quantity can be obtained by combining the obtained time difference of arrival TDOA; the position of the observation platform corresponding to the TOA can be obtained by a self-positioning module of the observation platform, and the radiation source position can be obtained by resolving by adopting a method of solving a nonlinear equation in combination with the positioning observed quantity;
in the step 4), after the coefficient of the curve fitting function is obtained, according to the cumulative plane transformation, wherein the X axis represents the number of the observation window and takes the value as a continuous positive integer, if the pulse is lost, the X coordinate of the middle point of the curve is discontinuous, so that the corresponding point of the lost pulse in the cumulative plane transformation is estimated, and the TOA of the lost pulse is further obtained;
TOA estimation of missing pulses
Figure FDA0002876262050000013
Comprises the following steps:
Figure FDA0002876262050000014
in the formula (I), the compound is shown in the specification,
Figure FDA0002876262050000015
a fitting function representing the estimated curve; x is the number ofm,iTransforming the abscissa of the corresponding point for the cumulative plane;
Figure FDA0002876262050000016
an estimation equation for the fitting coefficients;
in the step 5), the virtual arrival time difference
Figure FDA0002876262050000017
Comprises the following steps:
Figure FDA0002876262050000018
wherein m is1≠m2，m1And m2Indicating the number of the two observation platforms receiving the ith pulse.
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