CN113945888A - Interval passive positioning method and system based on TDOA - Google Patents
Interval passive positioning method and system based on TDOA Download PDFInfo
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Abstract
The invention discloses an interval passive positioning method based on Time Difference Of Arrival (TDOA), which comprises the following steps: the method comprises the steps that two TDOA measured values generated between three observation stations in an observation station group and a radiation source are compartmentalized to obtain two TDOA measured intervals; uniformly dividing the position interval of the prior radiation source into a plurality of parts to form a plurality of cutting lines; selecting a reference observation station to solve a TDOA equation for the cutting lines, and finding discrete intersection points of each TDOA measurement interval on each cutting line; drawing an external rectangle which is an approaching area between the time difference lines according to the discrete intersection points on each cutting line; overlapping operation is carried out on all external rectangles measured in the TDOA interval, and external rectangles are constructed in the intersected areas; and taking the circumscribed rectangle as a new prior radiation source position interval, continuously reducing the position interval through iterative operation until the area size of the circumscribed rectangle is converged to obtain a source position estimation interval, taking the area as algorithm reliability, and taking the midpoint as a positioning result. The invention has the advantages of high positioning precision, good robustness and being beneficial to multi-system fusion.
Description
Technical Field
The invention relates to the technical field of passive positioning, in particular to a TDOA-based interval passive positioning method and system.
Background
Under the existing environment, for example, in scenes such as radar positioning, sound source positioning and the like, when a non-cooperative radiation source needs to be positioned, data transmission cooperation between the radiation source and an observation station is lacked, which brings great difficulty to positioning. Currently, passive positioning is mostly based on AOA (Angle Of Arrival), TDOA, FDOA (Frequency Difference Of Arrival) and their joint positioning. Like the passive positioning method based on TDOA, the distance difference or the time difference between the radiation source and different observation stations can be obtained only by cooperation among a plurality of observation stations without the distance between the radiation source and the observation stations, so that a corresponding TDOA equation is established, and the estimation result of the radiation source is finally obtained by solving. However, in an actual positioning scenario, due to a certain noise interference existing when measuring TDOA, a measurement error is generated, and in addition, the nonlinearity problem existing in the TDOA equation itself increases the difficulty for the passive positioning problem.
Through the scheme that the solution is carried out by Taylor series expansion and least square matching, the positioning accuracy is improved by reducing the measurement error, and a certain noise problem is solved, but the solution is possibly trapped in local optimization due to initial position limitation, so that a non-convex problem is generated. At present, the non-convexity problem is well solved by a scheme of converting the non-convexity problem into a semi-definite programming problem and a scheme of converting a non-convex target function into two convex functions with accurate difference through a convex relaxation technology. However, the above scheme is complex and limited by the problem of location initialization.
Another existing mainstream scheme for passive positioning is a TSWLS (Two-step Weighted Least Squares) method, which is improved for many years to continuously overcome the problems of positioning accuracy, noise influence, symbol blurring, and the like, and a positioning result approaching CRLB (Cramer-Rao Lower Bound) can be obtained by the method. However, the scheme has certain requirements on the number of observation stations, and the smaller the number of observation stations is, the poorer the positioning accuracy is.
The passive positioning solutions described above are based on numerical calculations, and the resulting position estimation result is also a numerical solution. Although there is a certain positioning accuracy, it cannot provide a basis for the reliability of the positioning result.
Disclosure of Invention
The technical problem to be solved by the invention is to provide a TDOA-based interval passive positioning scheme, which combines an interval analysis method, a bisection method and an iteration method on the basis of a basic TDOA positioning principle, solves the problems that the existing passive positioning scheme has limited noise adaptation capability and cannot ensure the reliability of a numerical value positioning result and the like, is favorable for multi-system fusion, has high positioning result precision and good robustness, can ensure the reliability of the positioning result, and has low equipment complexity and high environment containment degree.
In order to solve the above problem, the present invention provides a TDOA-based ranging passive location method, which includes the following steps:
s1, selecting three of the four observation stations, constructing an observation station group by using the three observation stations, and determining two TDOA measurement intervals generated between the three observation stations and a source in the observation station group according to a UBB theory;
s2, determining a prior radiation source position interval according to prior knowledge in a two-dimensional coordinate, and uniformly dividing the prior radiation source position interval into a plurality of parts on one coordinate axis to form a plurality of cutting lines;
s3, selecting one observation station from the three observation stations in the observation station group as a reference observation station, solving a TDOA equation for the cutting lines through a bisection method, respectively bringing an upper bound value and a lower bound value of a TDOA measurement interval into the TDOA equation to obtain approximate solutions corresponding to the upper bound and the lower bound, and finding discrete intersection points of each TDOA measurement interval on each cutting line;
s4, drawing an external rectangle which is an approaching area between the time difference lines according to the discrete intersection points on each cutting line;
s5, performing overlapping operation on the circumscribed rectangles measured in all TDOA intervals, and constructing the circumscribed rectangles in the intersected areas, wherein the circumscribed rectangles are the results of one-time iterative computation;
and S6, taking the constructed circumscribed rectangle as a new prior radiation source position interval, repeating the steps S2-S5, continuously reducing the position interval through iterative operation until the area size of the circumscribed rectangle is converged, taking the obtained interval result as a source position estimation interval, taking the area as the algorithm reliability, and taking the middle point as a positioning result.
As a further improvement of the invention, the method also comprises the following steps:
s7, replacing three of the four observation stations, reconstructing an observation station group, determining two TDOA measurement intervals generated between the three observation stations in the observation station group and a source according to the theory UBB, and executing the steps S2-S6 to obtain a new source position estimation interval;
s8, taking the intersection of the source position estimation intervals obtained by the two observation station groups to obtain a final source position estimation interval, taking the area as the algorithm reliability, and taking the midpoint as the positioning result.
As a further improvement of the present invention, the number of the observation stations is four, and two different observation station groups are formed by selecting three observation stations in the four observation stations each time.
As a further development of the invention, the two TDOA measurement intervals are as follows:
[ri1]∈ri1°+[-3σ,3σ],i＝2,3
wherein r isi1The is the TDOA measurement, and σ is the standard deviation.
As a further improvement of the present invention, the TDOA equation is:
ri1°＝ri-r1,i＝2,3
wherein r is1,r2,r3Representing the distance of the radiation source to three observation stations, respectively.
As a further improvement of the invention, the discrete point set of the TDOA is as follows:
[xkj,ykj]
wherein, k is 1, 2.., m-1; j is 1, 2; j ═ 1 represents the solution corresponding to the lower bound of the TDOA measurement interval; j-2 represents a solution corresponding to the upper bound of the TDOA measurement interval;
the time difference line interval approximation area is as follows:
{[xk],[yk]}＝{[min(xk1,xk2,x(k+1)1,x(k+1)2),max(xk1,xk2,x(k+1)1,x(k+1)2)],[min(yk1,yk2,y(k+1)1,y(k+1)2),max(yk1,yk2,y(k+1)1,y(k+1)2)]},k＝1,...,m-1
wherein m is the number of cutting lines.
As a further improvement of the present invention, the intersection is taken from the approximation area between the two moveout lines generated by the two TDOA measurement intervals, as follows:
constructing a circumscribed rectangle for the intersected area as follows:
{[X°],[Y°]}＝{[min(Xk),max(Xk)],[min(Yk),max(Yk)]},k＝1,...,m-1
the invention also provides a TDOA-based compartmentalized passive location system comprising:
the observation station group construction module is used for constructing an observation station group by using three observation stations selected from the four observation stations;
the TDOA measurement interval construction module is used for constructing an observation station group by using the three observation stations, and determining two TDOA measurement intervals generated between the three observation stations and a source in the observation station group according to the UBB theory;
the cutting line construction module is used for determining a prior radiation source position interval according to prior knowledge under a two-dimensional coordinate, and uniformly dividing the prior radiation source position interval into a plurality of parts on one coordinate axis to form a plurality of cutting lines;
the TDOA equation solving module is used for selecting one observation station from three observation stations in the observation station group as a reference observation station, solving the TDOA equation for the cutting line through a bisection method, respectively bringing an upper bound value and a lower bound value of a TDOA measuring interval into the TDOA equation, obtaining approximate solutions corresponding to the upper bound and the lower bound, and finding discrete intersection points of each TDOA measuring interval on each cutting line;
the time difference line interval approximation region acquisition module is used for drawing an external rectangle which is a time difference line interval approximation region according to the discrete intersection points on the cutting lines;
the external rectangle construction module is used for performing overlapping operation on external rectangles measured in all TDOA intervals and constructing external rectangles on the intersected areas, namely a primary iterative computation result;
and the iterative operation module is used for taking the constructed external rectangle as a new prior radiation source position interval, continuously reducing the position interval through iterative operation until the area size of the external rectangle is converged, taking the obtained interval result as a source position estimation interval, taking the area as algorithm reliability, and taking the midpoint as a positioning result.
As a further improvement of the invention, the system also comprises the following modules:
the observation station group reconstruction computing module is used for replacing three of the four observation stations, reconstructing the observation station group, determining two TDOA measurement intervals generated between the three observation stations and a source in the observation station group according to the UBB theory, and executing the steps S2-S6 to obtain a new source position estimation interval;
and the final source position estimation interval calculation module is used for taking the intersection of the source position estimation intervals obtained by the two observation station groups to obtain a final source position estimation interval, taking the area as the algorithm reliability, and taking the middle point as the positioning result.
The invention has the beneficial effects that:
1. the method adopts the combination of interval analysis and TDOA to carry out passive positioning, the TDOA measurement error is converted into an interval range, the numerical values in the calculation process are subjected to interval calculation, and a source positioning result interval is finally obtained, the inclusion rate of the real position of a radiation source contained in the positioning result interval is more than 99%, and the positioning result interval has good reliability.
2. According to the invention, in a two-dimensional sensor network, a positioning result with certain accuracy can be obtained by only three observation stations, compared with the existing scheme, under the condition of four observation stations, the scheme reconstructs an observation station group for positioning by selecting three different observation stations, and performs overlapping calculation on a plurality of interval results, so that the obtained positioning result has higher accuracy and good robustness.
3. The invention is beneficial to multi-system fusion, can not only fuse the systems of the reconstructed observation station group, but also perform overlapping operation on the interval results of other positioning systems to obtain a fused positioning result, can avoid falling into local optimization, and can also be used as the reliability basis of other systems.
The foregoing description is only an overview of the technical solutions of the present invention, and in order to make the technical means of the present invention more clearly understood, the present invention may be implemented in accordance with the content of the description, and in order to make the above and other objects, features, and advantages of the present invention more clearly understood, the following preferred embodiments are described in detail with reference to the accompanying drawings.
Drawings
FIG. 1 is a flow chart of a TDOA-based compartmentalized passive location method in a preferred embodiment of the present invention;
FIG. 2 is a schematic diagram of TDOA-based compartmentalized passive location in a preferred embodiment of the present invention;
FIG. 3 is a schematic diagram of TDOA generation in a preferred embodiment of the present invention.
Detailed Description
The present invention is further described below in conjunction with the following figures and specific examples so that those skilled in the art may better understand the present invention and practice it, but the examples are not intended to limit the present invention.
As shown in fig. 1, the TDOA-based ranging passive location method in the preferred embodiment of the present invention includes the following steps:
s1, selecting three of the four observation stations, constructing an observation station group by using the three observation stations, and determining two TDOA measurement intervals generated between the three observation stations and a source in the observation station group according to a UBB theory;
specifically, according to UBB theory and the 3 σ error principle, two TDOA measurements will be generated from between three observers and the source
Compartmentalization to obtain TDOA measurement interval [ r21],[r31]. The specific compartmentalization operation is as follows: [ r ] ofi1]∈ri1°+[-3σ,3σ]I is 2, 3; wherein r isi1The is the TDOA measurement, and σ is the standard deviation.
S2, determining a prior radiation source position interval according to prior knowledge in a two-dimensional coordinate, and uniformly dividing the prior radiation source position interval into a plurality of parts on one coordinate axis to form a plurality of cutting lines;
in this embodiment, the prior radiation source location interval (initial location interval) is uniformly divided into m on the Y-axis, see fig. 2. In other embodiments, the a priori radiation source location interval may be chosen to be evenly divided in the X-axis.
S3, selecting one observation station from the three observation stations in the observation station group as a reference observation station, solving a TDOA equation for the cutting lines through a bisection method, respectively bringing an upper bound value and a lower bound value of a TDOA measurement interval into the TDOA equation to obtain approximate solutions corresponding to the upper bound and the lower bound, and finding discrete intersection points of each TDOA measurement interval on each cutting line;
the TDOA equation is as follows:
ri1°＝ri-r1,i＝2,3
wherein r is1,r2,r3Representing the distance of the radiation source to three observation stations, respectively.
TDOA Generation Process As shown in FIG. 3, the positions of stations s1, s2, s3 are denoted as si＝[xi°,yi°]TWherein i is 1,2, 3. The position of the radiation source u is expressed as u ° - [ x °, y ° ]]T. The distance from the radiation source to the observation station is respectively
ri＝||u°-si°||,i＝1,2,3
Wherein | g | represents the euclidean distance.
Will observe the station s1As a reference station, the TDOA expression obtained between two other observers and the reference station is given:
ri1°＝ri-r1,i＝2,3
s4, drawing an external rectangle which is an approaching area between the time difference lines according to the discrete intersection points on each cutting line;
specifically, the discrete point set of the TDOA is:
[xkj,ykj]
wherein, k is 1, 2.., m-1; j is 1, 2; j ═ 1 represents the solution corresponding to the lower bound of the TDOA measurement interval; j-2 represents a solution corresponding to the upper bound of the TDOA measurement interval;
the time difference line interval approximation area is as follows:
{[xk],[yk]}＝{[min(xk1,xk2,x(k+1)1,x(k+1)2),max(xk1,xk2,x(k+1)1,x(k+1)2)],[min(yk1,yk2,y(k+1)1,y(k+1)2),max(yk1,yk2,y(k+1)1,y(k+1)2)]},k＝1,...,m-1
s5, performing overlapping operation on the circumscribed rectangles measured in all TDOA intervals, and constructing the circumscribed rectangles in the intersected areas, wherein the circumscribed rectangles are the results of one-time iterative computation;
specifically, the intersection of the approximation areas between the two moveout lines generated by the two TDOA measurement intervals is taken as follows:
and constructing a circumscribed rectangle for the intersected area in order to facilitate the next iterative operation. Constructing a circumscribed rectangle for the intersected area as follows:
{[X°],[Y°]}＝{[min(Xk),max(Xk)],[min(Yk),max(Yk)]},k＝1,...,m-1
so far, the position estimation result interval is an iteration position estimation result interval.
And S6, taking the constructed circumscribed rectangle as a new prior radiation source position interval, repeating the steps S2-S5, continuously reducing the position interval through iterative operation until the area size of the circumscribed rectangle is converged, taking the obtained interval result as a source position estimation interval, taking the area as the algorithm reliability, and taking the middle point as a positioning result.
To further increase the positioning accuracy, in some embodiments, the following steps are also included:
s7, replacing three of the four observation stations, reconstructing an observation station group, determining two TDOA measurement intervals generated between the three observation stations in the observation station group and a source according to the theory UBB, and executing the steps S2-S6 to obtain a new source position estimation interval;
s8, taking the intersection of the source position estimation intervals obtained by the two observation station groups to obtain a final source position estimation interval, taking the area as the algorithm reliability, and taking the midpoint as the positioning result;
specifically, the source position estimation intervals obtained by the two observation station groups are respectively
And
and (3) taking intersection to obtain:
optionally, the number of the observation stations is four, and two different observation station groups are formed by selecting three observation stations from the four observation stations each time.
The method adopts the combination of interval analysis and TDOA to carry out passive positioning, the TDOA measurement error is converted into an interval range, the numerical values in the calculation process are subjected to interval calculation, and a source positioning result interval is finally obtained, the inclusion rate of the real position of a radiation source contained in the positioning result interval is more than 99%, and the positioning result interval has good reliability.
According to the invention, in a two-dimensional sensor network, a positioning result with certain accuracy can be obtained by only three observation stations, compared with the existing scheme, under the condition of four observation stations, the scheme reconstructs an observation station group for positioning by selecting three different observation stations, and performs overlapping calculation on a plurality of interval results, so that the obtained positioning result has higher accuracy and good robustness.
The invention is beneficial to multi-system fusion, can not only fuse the systems of the reconstructed observation station group, but also perform overlapping operation on the interval results of other positioning systems to obtain a fused positioning result, can avoid falling into local optimization, and can also be used as the reliability basis of other systems.
The preferred embodiment of the invention also discloses a TDOA-based interval passive positioning system, which comprises the following modules:
the observation station group construction module is used for constructing an observation station group by using three observation stations selected from the four observation stations;
the TDOA measurement interval construction module is used for constructing an observation station group by using the three observation stations, and determining two TDOA measurement intervals generated between the three observation stations and a source in the observation station group according to the UBB theory;
the cutting line construction module is used for determining a prior radiation source position interval according to prior knowledge under a two-dimensional coordinate, and uniformly dividing the prior radiation source position interval into a plurality of parts on one coordinate axis to form a plurality of cutting lines;
the TDOA equation solving module is used for selecting one observation station from three observation stations in the observation station group as a reference observation station, solving the TDOA equation for the cutting line through a bisection method, respectively bringing an upper bound value and a lower bound value of a TDOA measuring interval into the TDOA equation, obtaining approximate solutions corresponding to the upper bound and the lower bound, and finding discrete intersection points of each TDOA measuring interval on each cutting line;
the time difference line interval approximation region acquisition module is used for drawing an external rectangle which is a time difference line interval approximation region according to the discrete intersection points on the cutting lines;
the external rectangle construction module is used for performing overlapping operation on external rectangles measured in all TDOA intervals and constructing external rectangles on the intersected areas, namely a primary iterative computation result;
and the iterative operation module is used for taking the constructed external rectangle as a new prior radiation source position interval, continuously reducing the position interval through iterative operation until the area size of the external rectangle is converged, taking the obtained interval result as a source position estimation interval, taking the area as algorithm reliability, and taking the midpoint as a positioning result.
Optionally, the following modules are further included:
the observation station group reconstruction computing module is used for replacing three of the four observation stations, reconstructing the observation station group, determining two TDOA measurement intervals generated between the three observation stations and a source in the observation station group according to the UBB theory, and executing the steps S2-S6 to obtain a new source position estimation interval;
and the final source position estimation interval calculation module is used for taking the intersection of the source position estimation intervals obtained by the two observation station groups to obtain a final source position estimation interval, taking the area as the algorithm reliability, and taking the middle point as the positioning result.
The calculation steps involved in the system module are the same as those in the above method embodiments, and are not described herein again.
The above embodiments are merely preferred embodiments for fully illustrating the present invention, and the scope of the present invention is not limited thereto. The equivalent substitution or change made by the technical personnel in the technical field on the basis of the invention is all within the protection scope of the invention. The protection scope of the invention is subject to the claims.
Claims (9)
1. A TDOA-based ranging passive positioning method is characterized by comprising the following steps:
s1, selecting three observation stations from the four observation stations, constructing an observation station group by using the three observation stations, and determining two TDOA measurement intervals generated between the three observation stations and a source in the observation station group according to UBB (Unknown But bounded) theory;
s2, determining a prior radiation source position interval according to prior knowledge in a two-dimensional coordinate, and uniformly dividing the prior radiation source position interval into a plurality of parts on one coordinate axis to form a plurality of cutting lines;
s3, selecting one observation station from the three observation stations in the observation station group as a reference observation station, solving a TDOA equation for the cutting lines through a bisection method, respectively bringing an upper bound value and a lower bound value of a TDOA measurement interval into the TDOA equation to obtain approximate solutions corresponding to the upper bound and the lower bound, and finding discrete intersection points of each TDOA measurement interval on each cutting line;
s4, drawing an external rectangle which is an approaching area between the time difference lines according to the discrete intersection points on each cutting line;
s5, performing overlapping operation on the circumscribed rectangles measured in all TDOA intervals, and constructing the circumscribed rectangles in the intersected areas, wherein the circumscribed rectangles are the results of one-time iterative computation;
and S6, taking the constructed circumscribed rectangle as a new prior radiation source position interval, repeating the steps S2-S5, continuously reducing the position interval through iterative operation until the area size of the circumscribed rectangle is converged, taking the obtained interval result as a source position estimation interval, taking the area as the algorithm reliability, and taking the middle point as a positioning result.
2. The TDOA-based compartmentalized passive location method as recited in claim 1, further comprising the steps of:
s7, replacing three of the four observation stations, reconstructing an observation station group, determining two TDOA measurement intervals generated between the three observation stations in the observation station group and a source according to the theory UBB, and executing the steps S2-S6 to obtain a new source position estimation interval;
s8, taking the intersection of the source position estimation intervals obtained by the two observation station groups to obtain a final source position estimation interval, taking the area as the algorithm reliability, and taking the midpoint as the positioning result.
3. The TDOA-based compartmentalized passive location method of claim 2, wherein said number of observation stations is four, and wherein two different groups of observation stations are formed in succession by selecting three observation stations at a time among the four observation stations.
4. The TDOA-based compartmentalized passive location method of claim 1, wherein said two TDOA measurement intervals are as follows:
[ri1]∈ri1 o+[-3σ,3σ],i＝2,3
wherein,
for TDOA measurements, σ is the standard deviation.
5. The TDOA-based compartmentalized passive location method as recited in claim 4, wherein said TDOA equation is:
rio o＝ri-r1,i＝2,3
wherein r is1,r2,r3Representing the distance of the radiation source to three observation stations, respectively.
6. The TDOA-based compartmentalized passive location method as recited in claim 5, wherein said TDOA's discrete point set is:
[xkj,ykj]
wherein, k is 1, 2.., m-1; j is 1, 2; j ═ 1 represents the solution corresponding to the lower bound of the TDOA measurement interval; j-2 represents a solution corresponding to the upper bound of the TDOA measurement interval;
the time difference line interval approximation area is as follows:
wherein m is the number of cutting lines.
7. The TDOA-based compartmentalized passive location method of claim 6, wherein said intersecting the two moveout line inter-regional approximation areas generated by two TDOA measurement zones is as follows:
constructing a circumscribed rectangle for the intersected area as follows:
{[Xo],[Yo]}＝{[min(Xk),max(Xk)],[min(Yk),max(Yk)]},k＝1,...,m-1
8. the TDOA-based ranging passive location system is characterized by comprising the following components:
the observation station group construction module is used for constructing an observation station group by using three observation stations selected from the four observation stations;
the TDOA measurement interval construction module is used for constructing an observation station group by using the three observation stations, and determining two TDOA measurement intervals generated between the three observation stations and a source in the observation station group according to the UBB theory;
the cutting line construction module is used for determining a prior radiation source position interval according to prior knowledge under a two-dimensional coordinate, and uniformly dividing the prior radiation source position interval into a plurality of parts on one coordinate axis to form a plurality of cutting lines;
the TDOA equation solving module is used for selecting one observation station from three observation stations in the observation station group as a reference observation station, solving the TDOA equation for the cutting line through a bisection method, respectively bringing an upper bound value and a lower bound value of a TDOA measuring interval into the TDOA equation, obtaining approximate solutions corresponding to the upper bound and the lower bound, and finding discrete intersection points of each TDOA measuring interval on each cutting line;
the time difference line interval approximation region acquisition module is used for drawing an external rectangle which is a time difference line interval approximation region according to the discrete intersection points on the cutting lines;
the external rectangle construction module is used for performing overlapping operation on external rectangles measured in all TDOA intervals and constructing external rectangles on the intersected areas, namely a primary iterative computation result;
and the iterative operation module is used for taking the constructed external rectangle as a new prior radiation source position interval, continuously reducing the position interval through iterative operation until the area size of the external rectangle is converged, taking the obtained interval result as a source position estimation interval, taking the area as algorithm reliability, and taking the midpoint as a positioning result.
9. The TDOA-based compartmentalized passive location system of claim 8, further comprising the following modules:
the observation station group reconstruction computing module is used for replacing three of the four observation stations, reconstructing the observation station group, determining two TDOA measurement intervals generated between the three observation stations and a source in the observation station group according to the UBB theory, and executing the steps S2-S6 to obtain a new source position estimation interval;
and the final source position estimation interval calculation module is used for taking the intersection of the source position estimation intervals obtained by the two observation station groups to obtain a final source position estimation interval, taking the area as the algorithm reliability, and taking the middle point as the positioning result.
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