CN106842121B - Robust position location method based on reaching time-difference in sighting distance and non line of sight hybird environment - Google Patents
Robust position location method based on reaching time-difference in sighting distance and non line of sight hybird environment Download PDFInfo
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- 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
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Abstract
The invention discloses the robust position location methods based on reaching time-difference in sighting distance and non line of sight hybird environment, it separately handles the range difference measurement model under view distance environment and the range difference measurement model under nlos environment, establish the robust least square problem under worst case, the reference path being directed under nlos environment again simultaneously is sighting distance and common path is non line of sight and reference path is non line of sight and common path is two kinds of specific constraints of situations design of sighting distance, it realizes concrete condition concrete analysis, takes full advantage of the status information in path；Its disequilibrium problem for the range difference measurement model treatment under the range difference measurement model treatment and nlos environment under view distance environment, difference based on positioning accuracy under sighting distance and nlos environment devises an effective weight, robust least square problem under worst case is adjusted to weighted least-squares problem, so that the effect of los path is not fully exerted, so that positioning accuracy is further improved.
Description
Technical Field
The invention relates to a target positioning technology, in particular to a robust positioning method based on arrival time difference in a mixed environment of line-of-sight and non-line-of-sight.
Background
Target location technology plays an important role in many applications, for example, it has been widely used in the fields of military reconnaissance, emergency rescue, environmental monitoring, target navigation, remote control, etc. In recent years, with the rapid development of wireless sensors and mobile applications, a high-precision target positioning algorithm is urgently needed to meet the positioning requirement, and a wide application prospect is provided for the research of the high-precision target positioning algorithm. Therefore, the research of the high-precision target positioning method has very important significance.
In the conventional target location method, a Time of Arrival (TOA) based method is mainly used. In a typical wireless location environment (as shown in fig. 1), the basic principle of the time-of-arrival-based approach is: a target source transmits signals, the signals reach a plurality of sensors after passing through a complex channel, and the sensors calculate the time of the signals from the target source to the sensors so as to obtain a measured value of the distance from the target source to the sensors; although the time-of-arrival-based method can achieve target positioning well, it requires high-precision synchronization between the target source and the sensor in the measurement process. Unlike time of Arrival based methods, time difference of Arrival (TDOA) methods determine the location of a target source by detecting the time difference of Arrival of a signal at two sensors, rather than using the absolute time of Arrival; the time synchronization requirement is well reduced by the method based on the time difference of arrival. However, whether the method based on the arrival time or the method based on the arrival time difference is adopted, a straight-line propagation path of the signal from the target source to the sensor may be blocked, as shown in fig. 1, the blocked path in the signal transmission process is called a non line-of-sight (NLOS) path, and an error caused by the non-line-of-sight propagation of the signal is called a non-line-of-sight error. Since the influence of non-line-of-sight propagation of signals on the positioning accuracy is usually much larger than that of measurement noise, for example, in an actual cellular mobile communication system, the non-line-of-sight error can be as high as 0.589 km, and the measurement noise is only tens of meters, so that the suppression of the influence of non-line-of-sight error on the positioning accuracy is a key point for improving the positioning accuracy of the wireless network.
There are many existing target positioning methods for suppressing non-line-of-sight errors based on time difference of arrival, and the following two methods are more mainstream. The first method comprises the following steps: the target positioning is realized according to the accurate statistical information of the non-line-of-sight error and the measurement noise, however, the accurate statistical information of the non-line-of-sight error is very difficult to obtain, so that the method is difficult to be widely applied in reality. The second method comprises the following steps: the method only uses the upper bound of the non-line-of-sight error to uniformly perform robust semi-positive definite relaxation or second-order cone processing on all paths (including line-of-sight paths and non-line-of-sight paths) to realize target positioning, but the method completely ignores the state information of the paths, thereby seriously reducing the positioning performance and degrading the positioning accuracy.
Disclosure of Invention
The invention aims to solve the technical problem of providing a stable positioning method based on arrival time difference in a mixed environment of line-of-sight and non-line-of-sight, which makes full use of state information of a path and realizes high-precision positioning.
The technical scheme adopted by the invention for solving the technical problems is as follows: a robust positioning method based on arrival time difference in a mixed environment of line-of-sight and non-line-of-sight is characterized by comprising the following steps:
① a plane coordinate system or a space coordinate system is established as a reference coordinate system for the wireless network in the mixed environment of sight distance and non-sight distance, an unknown target source and N +1 sensors exist in the wireless network, one sensor is selected as a reference sensor, the other sensors are non-reference sensors, the coordinate position of the target source in the reference coordinate system is marked as x, and the coordinate position of the reference sensor in the reference coordinate system is marked as s0Sequentially corresponding the coordinate positions of the N non-reference sensors in the reference coordinate system as s1,s2,...,sN(ii) a Defining a path through which a measuring signal is transmitted from a target source to a reference sensor for receiving as a reference path, wherein the path state of the reference path is known, and recording the time t elapsed for the measuring signal to transmit on the reference path0(ii) a Defining a path through which a measuring signal is sent from a target source to each non-reference sensor for receiving as a common path, defining a path through which the measuring signal is sent from the target source to an ith non-reference sensor for receiving as an ith common path, wherein the path state of each common pathIt is known that the time elapsed for the measurement signal to travel on the ith ordinary path is denoted as ti(ii) a Then calculating the distance difference between the transmission of the measurement signal on each common path and the transmission of the measurement signal on the reference path, and recording the distance difference between the transmission of the measurement signal on the ith common path and the transmission of the measurement signal on the reference path as di，di＝c(ti-t0) (ii) a Then constructing a sight distance set phi with an initial value of an empty setlAnd a non-line-of-sight set phi with an initial value of null setnIn the measurement of the arrival time difference, all the ordinary paths under the condition that the reference path and the ordinary path through which the measurement signal passes are both the line-of-sight paths are found out, and the serial numbers of the non-reference sensors corresponding to the ordinary paths are assigned to the line-of-sight set philRather than a set of viewing distances phin＝{1,2,…,N}-Φl(ii) a Wherein N is more than or equal to 3, s1Representing the coordinate position, s, of the 1 st non-reference sensor in the reference coordinate system2Representing the coordinate position, s, of the 2 nd non-reference sensor in the reference coordinate systemNRepresenting the coordinate position of the Nth non-reference sensor in a reference coordinate system, wherein i is more than or equal to 1 and less than or equal to N, and c is the light speed;
② A model of the distance difference between the normal path and the reference path is created, and is expressed as di＝ri-r0+ni+ei,i∈ΦnWherein r isi＝||x-si||，r0＝||x-s0| | |, the symbol "| | | |" is the Euclidean norm symbol, siRepresenting the coordinate position of the ith non-reference sensor in a reference coordinate system, niRepresenting the difference between the measurement noise on the ith normal path and the measurement noise on the reference path, eiRepresents the difference between the non-line-of-sight error on the ith normal path and the non-line-of-sight error on the reference path, | ni|＜＜eiThe symbol "|" is an absolute value symbol; then to di＝ri-r0+ni+ei,i∈ΦnPerforming form conversion to obtaini∈ΦnWherein(s)0-si)TIs s is0-siTransposing;
and establishing a measurement model of the distance difference between the transmission of the measurement signal on the common path and the transmission of the measurement signal on the reference path in a line-of-sight environment, wherein the measurement model is represented as follows: di＝ri-r0+ni,i∈Φl(ii) a Then to di＝ri-r0+ni,i∈ΦlPerforming form conversion to obtainWherein(s)i-s0)TIs s isi-s0Transposing;
③ are in accordance withi∈ΦnAndthe positioning problem in the mixed environment of line-of-sight and non-line-of-sight is described as follows by adopting a robust least square method under the worst condition:
where min { } is a minimum function, max () is a maximum function, and y ═ x { }T,r0,r1,...,rN]TThe term "[ 2 ]]"is a vector representing a symbol, xTIs the transpose of x, [ x ]T,r0,r1,...,rN]TIs [ x ]T,r0,r1,...,rN]Is transferred, r1＝||x-s1||，rN＝||x-sNI, "s.t." means "constrained to", fl,i(x,r0) And fn,i(x,ri,ei) Are all the intermediate variables of the series of the Chinese characters,
then will be converted by simple conversion
To be converted intoWherein the symbol "|" is an absolute value symbol;
then, according to the triangle inequality, determiningWhere ρ isiDenotes eiUpper limit of (e), 0. ltoreq. ei≤ρi，h(ei) Is the intermediate variable(s) of the variable,
then will beTo be converted into
Then will be
Andandin combination with the above-mentioned materials,
to obtain Wherein, gn,i(x,ri) Is an intermediate variable;
④ are in accordance withInAndis unbalanced inIn which weight is added
A weighted least squares problem is obtained, described as:
⑤ based on the knowledge of the path stateA non-convex localization problem is obtained, described as:
wherein, w0Values representing non-line-of-sight errors on the reference path, wiA value representing a non-line-of-sight error on the ith ordinary path;
⑥ introduction of auxiliary variables gamma, tau in non-convex positioning problems1,τ2,…,τi,…,τN,η1,η2,…,ηi,…,ηNThe equivalent non-convex positioning problem after introducing the auxiliary variable is obtained, and is described as follows:
wherein,is s isiThe transpose of (a) is performed,is s is0Transposing;
⑦ adopting second-order cone relaxation to introduce | | x-s in the non-convex positioning problem after auxiliary variablei||＝riRelaxation to | | x-si||≤ri、||x-s0||＝r0Relaxation to | | x-s0||≤r0、Is relaxed toIs relaxed to||x||2Relaxing | | | x | | | non-woven phosphor2Less than or equal to gamma, and g is added to meet the requirement of convex problemn,i(x,ri) Is unfolded into
The second order cone programming problem is obtained and is described as:
⑧ solving the second-order cone programming problem by using an interior point method to obtain a global optimal solution of y, and then recording y as y #*Substituting y ═ xT,r0,r1,...,rN]TAnd obtaining an optimal solution of x, and marking the optimal solution as x, wherein x is a final positioning value of the coordinate position of the target source in the reference coordinate system.
The obtaining process of θ in step ④ is:
④ _1, introducing an intermediate variable pi,j，i∈Φn,j∈ΦlWherein, the symbolsIn order to define a symbol or symbols,rj＝||x-sj||，njrepresenting the difference between the measurement noise on the jth ordinary path and the measurement noise on the reference path, njObedience mean is 0 and variance isGaussian distribution of(s)jRepresenting the coordinate position of the jth non-reference sensor in the reference coordinate system;
④ _2, according to di＝ri-r0+ni+ei,i∈ΦnAnd | niI is a very small value, consider di-ri≈-r0+ei,i∈Φn；
④ _3, according toAnd di-ri≈-r0+ei,i∈ΦnTo obtain
④ _4, according toAnd pi,jAt ei＝-ρiThen get the maximum value to get pi,jThe upper bound of (a) is,
④ _5, according toAnd 0 < r0≤α0And | nj|≤3σjObtaining pi,jIs marked asWherein, α0Representing the maximum distance the target source can take to the reference sensor;
④ _6, orderThen according toAndto obtain finally
Said step ⑤And w0The determination process of 0 is as follows: according to the conclusion that the measurement noise is far less than the non-line-of-sight error under the general condition, if the ith normal path is the non-line-of-sight path, namely wi> 0 and the reference path is the line of sight path, w00, then ei＝wi-w0＝wi》|niL, |; then according to ei＝wi-w0＝wi》|niI and di＝ri-r0+ni+ei,i∈ΦnTo obtain di+r0≥ri(ii) a Then to di+r0≥riAre simultaneously squared and spread, and combined with ri＝||x-siI and r0＝||x-s0| | obtaining constraint conditionsYet furtherWill be provided withIs described as
Said step ⑤And wiThe determination process of 0 is as follows: according to the conclusion that the measurement noise is far less than the non-line-of-sight error under the general condition, if the ith ordinary path is a line-of-sight path, wi0 and the reference path is a non-line-of-sight path, w0> 0, then ei＝wi-w0＝-w0《-|niL, |; then according to ei＝wi-w0＝-w0《-|niI and di＝ri-r0+ni+ei,i∈ΦnTo obtain ri-di≥r0(ii) a Then to ri-di≥r0Are simultaneously squared and spread, and combined with ri＝||x-siI and r0＝||x-s0| | obtaining constraint conditions
Will be still further
Is described as
And wi＝0。
Compared with the prior art, the invention has the advantages that:
1) the method separately processes the distance difference measurement model in the line-of-sight environment and the distance difference measurement model in the non-line-of-sight environment, establishes the problem of robust least square in the worst case, and simultaneously designs specific constraints aiming at two cases that the reference path in the non-line-of-sight environment is the line-of-sight and the common path is the non-line-of-sight and the common path is the line-of-sight, realizes specific analysis of specific cases, and fully utilizes the state information of the path.
2) Aiming at the problem of unbalance of the distance difference measurement model processing method in the line-of-sight environment and the distance difference measurement model processing method in the non-line-of-sight environment, the method designs an effective weight based on the difference of positioning accuracy in the line-of-sight environment and the non-line-of-sight environment, and adjusts the original robust least square problem in the worst case into the robust weighted least square problem in the worst case, so that the function of a line-of-sight path is fully exerted, and the positioning accuracy is further improved.
3) The method of the invention processes the weighted least square problem by using a second-order cone relaxation method and solves the problem by an interior point method, so that the global optimal solution of the problem can be ensured to be obtained, the influence of local convergence is effectively avoided, and the optimal estimated coordinate of the target source can be obtained.
Drawings
FIG. 1 is a schematic diagram of a typical wireless location environment;
FIG. 2 is a general flow diagram of the method of the present invention;
FIG. 3 is a diagram showing the variation of the positioning accuracy of the robust second-order cone programming (unknown path state), the robust semi-positive programming (unknown path state) and the method of the present invention with the measurement noise in the environment with non-line-of-sight, in which the number of non-line-of-sight paths is 3;
fig. 4 is a graph of the variation of the positioning accuracy of the robust second-order cone planning (unknown path state), the robust semi-positive planning (unknown path state) and the method of the present invention with the number of non-line-of-sight paths in an environment with non-line-of-sight, where σ is 0.3 m.
Detailed Description
The invention is described in further detail below with reference to the accompanying examples.
The present invention provides a robust positioning method based on arrival time difference in a mixed environment of line-of-sight and non-line-of-sight, the general flow diagram of which is shown in fig. 2, and the method comprises the following steps:
① a plane coordinate system or a space coordinate system is established as a reference coordinate system for the wireless network in the mixed environment of sight distance and non-sight distance, an unknown target source and N +1 sensors exist in the wireless network, one sensor is selected as a reference sensor, the other sensors are non-reference sensors, the coordinate position of the target source in the reference coordinate system is marked as x, and the coordinate position of the reference sensor in the reference coordinate system is marked as s0Sequentially corresponding the coordinate positions of the N non-reference sensors in the reference coordinate system as s1,s2,...,sN(ii) a Defining a path through which a measuring signal is transmitted from a target source to a reference sensor for receiving as a reference path, wherein the path state of the reference path is known, and recording the time t elapsed for the measuring signal to transmit on the reference path0(ii) a Defining a path through which a measuring signal is sent from a target source to each non-reference sensor for receiving as a common path, defining a path through which the measuring signal is sent from the target source to an ith non-reference sensor for receiving as an ith common path, wherein the path state of each common path is known, and recording the time t elapsed for the measuring signal to transmit on the ith common pathi(ii) a Then calculating the distance difference between the transmission of the measurement signal on each common path and the transmission of the measurement signal on the reference path, and recording the distance difference between the transmission of the measurement signal on the ith common path and the transmission of the measurement signal on the reference path as di，di＝c(ti-t0) (ii) a Then constructing a sight distance set phi with an initial value of an empty setlAnd a non-line-of-sight set phi with an initial value of null setnIn the measurement of the arrival time difference, all the ordinary paths under the condition that the reference path and the ordinary path through which the measurement signal passes are both the line-of-sight paths are found out, and the serial numbers of the non-reference sensors corresponding to the ordinary paths are assigned to the line-of-sight set philRather than a set of viewing distances phin＝{1,2,…,N}-Φl(ii) a Where N is not less than 3, in this embodiment, N is 5, s1Representing the coordinate position, s, of the 1 st non-reference sensor in the reference coordinate system2Representing the coordinate position, s, of the 2 nd non-reference sensor in the reference coordinate systemNAnd the coordinate position of the Nth non-reference sensor in the reference coordinate system is represented, i is more than or equal to 1 and less than or equal to N, and c is the speed of light.
② A model of the distance difference between the normal path and the reference path is created, and is expressed as di＝ri-r0+ni+ei,i∈ΦnWherein r isi＝||x-si||，r0＝||x-s0| | |, the symbol "| | | |" is the Euclidean norm symbol, siRepresenting the coordinate position of the ith non-reference sensor in a reference coordinate system, niRepresenting the difference between the measurement noise on the ith normal path and the measurement noise on the reference path, eiRepresents the difference between the non-line-of-sight error on the ith normal path and the non-line-of-sight error on the reference path, | ni|＜＜eiThe symbol "|" is an absolute value symbol; then to di＝ri-r0+ni+ei,i∈ΦnPerforming form conversion to obtainBy first subjecting d toi＝ri-r0+ni+ei,i∈ΦnR ini+eiMove to the left of the equation to obtain di-ri-ei＝-r0+niThen to di-ri-ei＝-r0+niBoth sides are squared simultaneously to obtainDue to the fact thatVery small and therefore subsequently neglectedAnd is substituted into ri＝||x-siI and r0＝||x-s0I can be obtained, where(s)0-si)TIs s is0-siThe transposing of (1).
And establishing a measurement model of the distance difference between the transmission of the measurement signal on the common path and the transmission of the measurement signal on the reference path in a line-of-sight environment (no non-line-of-sight error), wherein the measurement model is represented as follows: di＝ri-r0+ni,i∈Φl(ii) a Then to di＝ri-r0+ni,i∈ΦlPerforming form conversion to obtainBy first subjecting d toi＝ri-r0+ni，i∈ΦlR in0Move to the left of the equation to obtain di+r0＝ri+niThen to di+r0＝ri+niBoth sides are squared simultaneously to obtainDue to the fact thatVery small and therefore subsequently neglectedAnd is substituted into ri＝||x-siI and r0＝||x-s0I can be obtained, where(s)i-s0)TIs s isi-s0The transposing of (1).
③ are in accordance withAndthe positioning problem in the mixed environment of line-of-sight and non-line-of-sight is described as follows by adopting a robust least square method under the worst condition:
where min { } is a minimum function, max () is a maximum function, and y ═ x { }T,r0,r1,...,rN]TThe term "[ 2 ]]"is a vector representing a symbol, xT is a transposition of x, [ x ]T,r0,r1,...,rN]TIs [ x ]T,r0,r1,...,rN]Is transferred, r1＝||x-s1||，rN＝||x-sNI, "s.t." means "constrained to", fl,i(x,r0) And fn,i(x,ri,ei) Are all the intermediate variables of the series of the Chinese characters,
then will be converted by simple conversion
To be converted intoWherein the symbol "|" is an absolute value symbol.
Then, according to the triangle inequality, determiningWhere ρ isiDenotes eiUpper limit of (e), 0. ltoreq. ei≤ρiIn this example, take ρi6 m, h (e)i) Is the intermediate variable(s) of the variable,
then will beTo be converted into
Then will be
Andandin combination with the above-mentioned materials,
to obtain Wherein, gn,i(x,ri) Is composed ofAnd (4) a variable.
④ are in accordance withInAndis unbalanced inIn which weight is added
A weighted least squares problem is obtained, described as:
it is well known that the accuracy of line-of-sight measurements is much greater than the accuracy of non-line-of-sight measurements, and because of thisInAndthe imbalance of (2) and the visual range information play a very weak role, so a larger theta needs to be selected, so that the method of the present invention is more dependent on the visual range information, and based on this, the present invention proposes an acquisition process of theta, that is, in this specific embodiment, the acquisition process of theta in step ④ is:
④ _1, introducing an intermediate variable pi,j，Wherein, the symbolIn order to define a symbol or symbols,dj＝rj-r0+nj，rj＝||x-sj||，njrepresenting the difference between the measurement noise on the jth ordinary path and the measurement noise on the reference path, njObedience mean is 0 and variance isIs a Gaussian distribution of (a) in the present embodimentjThe value range of (a) is 0.1-0.8 m, for example, the value of sigmaj0.3 m, sjIndicating the coordinate position of the jth non-reference sensor in the reference coordinate system.
④ _2, according to di＝ri-r0+ni+ei,i∈ΦnAnd | niI is a very small value, consider di-ri≈-r0+ei,i∈Φn。
④ _3, according toAnd di-ri≈-r0+ei,i∈ΦnTo obtain
④ _4, according toAnd pi,jAt ei＝-ρiThen get the maximum value to get pi,jThe upper bound of (a) is,
④ _5, according toAnd 0 < r0≤α0And | nj|≤3σjObtaining pi,jIs marked asWherein, α0Representing the maximum distance the target source can take to the reference sensor, the fact that the extent of the scene during the localization process is known, α0Can be obtained by measurement, when njObedience mean is 0 and variance isThe probability of 99.74% is found by experiment in the case of the Gaussian distribution of (g) | nj|≤3σjThis is true.
④ _6, orderThen according toAndto obtain finally
⑤ based on a weighted least squares problem with known path statesA non-convex localization problem is obtained, described as:
wherein, w0Values representing non-line-of-sight errors on the reference path, wiA value representing a non-line-of-sight error on the ith ordinary path.
In this embodiment, step ⑤And w0The determination process of 0 is as follows: according to the conclusion that the measurement noise is far less than the non-line-of-sight error under the general condition, if the ith normal path is the non-line-of-sight path, namely wi> 0 and the reference path is the line of sight path, w00, then ei＝wi-w0＝wi＞＞|niL, |; then according to ei＝wi-w0＝wi＞＞|niI and di＝ri-r0+ni+ei,i∈ΦnTo obtain di+r0≥ri(ii) a Then to di+r0≥riAre simultaneously squared and spread, and combined with ri＝||x-siI and r0＝||x-s0| | obtaining constraint conditionsWill be still furtherIs described asAnd w0＝0。
In this embodiment, step ⑤And wiThe determination process of 0 is as follows: according to the conclusion that the measurement noise is far less than the non-line-of-sight error under the general condition, if the ith ordinary path is a line-of-sight path, wi0 and the reference path is a non-line-of-sight path, w0> 0, then ei＝wi-w0＝-w0＜＜-|niL, |; then according to ei＝wi-w0＝-w0＜＜-|niI and di＝ri-r0+ni+ei,i∈ΦnTo obtain ri-di≥r0(ii) a Then to ri-di≥r0Are simultaneously squared and spread, and combined with ri＝||x-siI and r0＝||x-s0| | obtaining constraint conditionsWill be still furtherIs described asAnd wi＝0。
⑥ introduction of auxiliary variables gamma, tau in non-convex positioning problems1,τ2,…,τi,…,τN,η1,η2,…,ηi,…,ηNThe equivalent non-convex positioning problem after introducing the auxiliary variable is obtained, and is described as follows:
wherein,is s isiThe transpose of (a) is performed,is s is0The transposing of (1).
⑦ adopting second-order cone relaxation method to introduce auxiliary variable in non-convex positioning problem | | | x-si||＝riRelaxation to | | x-si||≤ri、|||x-s0|||＝r0Relaxation to | | | x-s0|||≤r0、Is relaxed toIs relaxed to||x|||2Relaxing | | | | x | | | | non-woven phosphor2Less than or equal to gamma, and g is added to meet the requirement of convex problemn,i(x,ri) Is unfolded into
The second order cone programming problem is obtained and is described as:
⑧ solving the second-order cone programming problem by using an interior point method to obtain a global optimal solution of y, and recording the global optimal solution as y*(ii) a Then y is*Substituting y ═ xT,r0,r1,...,rN]TIn (3), obtaining the optimal solution of x, which is marked as x*，x*The final positioning value of the coordinate position of the target source in the reference coordinate system.
The feasibility, the effectiveness and the positioning of the method are verified through simulationAnd (4) performance. Assuming that 6 sensors are used for measuring the performance of the method, 1 sensor is selected as a reference sensor and is arranged at the origin of a reference coordinate system, the other 5 sensors are uniformly distributed on a circle which takes the origin as the center of a circle and has the radius of 10 meters as non-reference sensors, and unknown target sources are randomly distributed in a circular area which takes the origin as the center of a circle and has the radius of 15 meters. The power (variance) of the measurement noise of all sensors is assumed to be the same, i.e. to beThe same upper bound of non-line-of-sight errors is rho0＝ρ1＝...＝ρ5ρ is 6 m. In the simulation of fig. 3 and 4, on the premise that the "robust second-order cone plan (unknown path state)" represents the unknown path state, the robust second-order cone relaxation algorithm based on least square is adopted; the robust semi-definite relaxation algorithm based on least square is carried out on the premise that the robust semi-definite plan (unknown path state) represents the unknown path state; the "method of the present invention" means a second-order cone relaxation algorithm based on weighted robust least squares under the condition of known path state and no error.
Fig. 3 shows the variation of the positioning accuracy of the robust second-order cone programming (unknown path state), the robust semi-positive programming (unknown path state) and the method of the present invention with the measurement noise in the environment with non-line-of-sight, in which the number of non-line-of-sight paths is 3. As can be seen from fig. 3, in the process of changing the power of the measurement noise from small to large, the positioning performance of the method of the present invention is always better than that of robust second-order cone planning (unknown path state) and robust semi-positive planning (unknown path state).
Fig. 4 shows the variation of the positioning accuracy of the robust second-order cone planning (unknown path state), the robust semi-positive planning (unknown path state) and the method of the present invention with the number of non-line-of-sight paths in an environment with non-line-of-sight, where σ is 0.3 m. As can be seen from fig. 4, under the condition of fewer non-line-of-sight paths, the positioning performance of the method of the present invention is always better than that of robust second-order cone planning (unknown path state) and robust semi-positive planning (unknown path state); only when the number of the non-line-of-sight paths is large, the robust second-order cone planning (unknown path state), the robust semi-positive planning (unknown path state) and the positioning performance of the method are close to each other, and on the whole, the method still has sufficient advantages in the aspect of positioning accuracy.
Claims (3)
1. A robust positioning method based on arrival time difference in a mixed environment of line-of-sight and non-line-of-sight is characterized by comprising the following steps:
① a plane coordinate system or a space coordinate system is established as a reference coordinate system for a wireless network in a mixed environment of sight distance and non-sight distance, an unknown target source and N +1 sensors exist in the wireless network, one sensor is selected as a reference sensor, the other sensors are non-reference sensors, the coordinate position of the target source in the reference coordinate system is marked as x, and the reference sensor in the reference coordinate system is marked as xCoordinate position in (1) is noted as s0Sequentially corresponding the coordinate positions of the N non-reference sensors in the reference coordinate system as s1,s2,...,sN(ii) a Defining a path through which a measuring signal is transmitted from a target source to a reference sensor for receiving as a reference path, wherein the path state of the reference path is known, and recording the time t elapsed for the measuring signal to transmit on the reference path0(ii) a Defining a path through which a measuring signal is sent from a target source to each non-reference sensor for receiving as a common path, defining a path through which the measuring signal is sent from the target source to an ith non-reference sensor for receiving as an ith common path, wherein the path state of each common path is known, and recording the time t elapsed for the measuring signal to transmit on the ith common pathi(ii) a Then calculating the distance difference between the transmission of the measurement signal on each common path and the transmission of the measurement signal on the reference path, and recording the distance difference between the transmission of the measurement signal on the ith common path and the transmission of the measurement signal on the reference path as di，di＝c(ti-t0) (ii) a Then constructing a sight distance set phi with an initial value of an empty setlAnd a non-line-of-sight set phi with an initial value of null setnIn the measurement of the arrival time difference, all the ordinary paths under the condition that the reference path and the ordinary path through which the measurement signal passes are both the line-of-sight paths are found out, and the serial numbers of the non-reference sensors corresponding to the ordinary paths are assigned to the line-of-sight set philRather than a set of viewing distances phin＝{1,2,…,N}-Φl(ii) a Wherein N is more than or equal to 3, s1Representing the coordinate position, s, of the 1 st non-reference sensor in the reference coordinate system2Representing the coordinate position, s, of the 2 nd non-reference sensor in the reference coordinate systemNRepresenting the coordinate position of the Nth non-reference sensor in a reference coordinate system, wherein i is more than or equal to 1 and less than or equal to N, and c is the light speed;
② A model of the distance difference between the normal path and the reference path is created, and is expressed as di＝ri-r0+ni+ei,i∈ΦnWherein r isi＝||x-si||，r0＝||x-s0| | |, the symbol "| | | |" is the Euclidean norm symbol, siRepresenting the coordinate position of the ith non-reference sensor in a reference coordinate system, niRepresenting the difference between the measurement noise on the ith normal path and the measurement noise on the reference path, eiRepresents the difference between the non-line-of-sight error on the ith normal path and the non-line-of-sight error on the reference path, | ni|＜＜eiThe symbol "|" is an absolute value symbol; then to di＝ri-r0+ni+ei,i∈ΦnPerforming form conversion to obtainWherein(s)0-si)TIs s is0-siTransposing;
and establishing a measurement model of the distance difference between the transmission of the measurement signal on the common path and the transmission of the measurement signal on the reference path in a line-of-sight environment, wherein the measurement model is represented as follows: di＝ri-r0+ni,i∈Φl(ii) a Then to di＝ri-r0+ni,i∈ΦlPerforming form conversion to obtainWherein(s)i-s0)TIs s isi-s0Transposing;
③ are in accordance withAndthe positioning problem in the mixed environment of line-of-sight and non-line-of-sight is described as follows by adopting a robust least square method under the worst condition:
where min { } is a minimum function, max () is a maximum function, and y ═ x { }T,r0,r1,...,rN]TThe term "[ 2 ]]"is a vector representing a symbol, xTIs the transpose of x, [ x ]T,r0,r1,...,rN]TIs [ x ]T,r0,r1,...,rN]Is transferred, r1＝||x-s1||，rN＝||x-sNI, "s.t." means "constrained to", fl,i(x,r0) And fn,i(x,ri,ei) Are all the intermediate variables of the series of the Chinese characters,
then will be converted by simple conversion
s.t.||x-si||＝ri,i＝1,…,N
||x-s0||＝r0
To be converted intoWherein the symbol "|" is an absolute value symbol;
then, according to the triangle inequality, determining
，
Where ρ isiDenotes eiUpper limit of (e), 0. ltoreq. ei≤ρi，h(ei) Is the intermediate variable(s) of the variable,then will beTo be converted into
Then will beAndandin combination with the above-mentioned materials,
to obtain Wherein, gn,i(x,ri) Is an intermediate variable;
④ are in accordance withInAndis unbalanced inIn which weight is added
A weighted least squares problem is obtained, described as:
⑤ based on the knowledge of the path stateA non-convex localization problem is obtained, described as:
wherein, w0Values representing non-line-of-sight errors on the reference path, wiA value representing a non-line-of-sight error on the ith ordinary path;
⑥ introduction of auxiliary variables gamma, tau in non-convex positioning problems1,τ2,…,τi,…,τN,η1,η2,…,ηi,…,ηNThe equivalent non-convex positioning problem after introducing the auxiliary variable is obtained, and is described as follows:
||x-si||＝ri,i＝1,...,N
||x-s0||＝r0
||x||2＝γ
wherein,is s isiThe transpose of (a) is performed,is s is0Transposing;
⑦ adopting second-order cone relaxation to introduce | | x-s in the non-convex positioning problem after auxiliary variablei||＝riRelaxation to | | x-si||≤ri、||x-s0||＝r0Relaxation to | | x-s0||≤r0、Is relaxed toIs relaxed to||x||2Relaxing | | | x | | | non-woven phosphor2Less than or equal to gamma, and g is added to meet the requirement of convex problemn,i(x,ri) Is unfolded into
The second order cone programming problem is obtained and is described as:
||x-si||≤ri,i＝1,...,N
||x-s0||≤r0
⑧ two-step pair using interior point methodSolving the cone programming problem to obtain a global optimal solution of y, and recording the solution as y*(ii) a Then y is*Substituting y ═ xT,r0,r1,...,rN]TIn (3), obtaining the optimal solution of x, which is marked as x*，x*The final positioning value of the coordinate position of the target source in the reference coordinate system.
2. A robust positioning method based on arrival time difference in mixed line-of-sight and non-line-of-sight environment according to claim 1, wherein said step ④ is performed by the following steps:
④ _1, introducing an intermediate variable pi,j，Wherein, the symbolIn order to define a symbol or symbols,dj＝rj-r0+nj，rj＝||x-sj||，njrepresenting the difference between the measurement noise on the jth ordinary path and the measurement noise on the reference path, njObedience mean is 0 and variance isGaussian distribution of(s)jRepresenting the coordinate position of the jth non-reference sensor in the reference coordinate system;
④ _2, according to di＝ri-r0+ni+ei,i∈ΦnAnd | niI is a very small value, consider di-ri≈-r0+ei,i∈Φn；
④ _3, according toAnd di-ri≈-r0+ei,i∈ΦnTo obtain
④ _4, according toAnd pi,jAt ei＝-ρiThen get the maximum value to get pi,jThe upper bound of (a) is,
④ _5, according toAnd 0 < r0≤α0And | nj|≤3σjObtaining pi,jIs marked as Wherein, α0Representing the maximum distance the target source can take to the reference sensor;
④ _6, orderThen according toAndto obtain finally
3. A robust positioning method based on time difference of arrival in mixed line-of-sight and non-line-of-sight environment according to claim 1 or 2, wherein said step ⑤And w0The determination process of 0 is as follows: according to the conclusion that the measurement noise is far less than the non-line-of-sight error under the general condition, if the ith normal path is the non-line-of-sight path, namely wi> 0 and the reference path is the line of sight path, w00, then ei＝wi-w0＝wi＞＞|niL, |; then according to ei＝wi-w0＝wi＞＞|niI and di＝ri-r0+ni+ei,i∈ΦnTo obtain di+r0≥ri(ii) a Then to di+r0≥riAre simultaneously squared and spread, and combined with ri＝||x-siI and r0＝||x-s0| | obtaining constraint conditionsWill be still furtherIs described asAnd w0＝0；
Said step ⑤And wiThe determination process of 0 is as follows: according to the conclusion that the measurement noise is far less than the non-line-of-sight error under the general condition, if the ith ordinary path is a line-of-sight path, wi0 and the reference path is a non-line-of-sight path, w0> 0, then ei＝wi-w0＝-w0＜＜-|niL, |; then according to ei＝wi-w0＝-w0＜＜-|niI and di＝ri-r0+ni+ei,i∈ΦnTo obtain ri-di≥r0(ii) a Then to ri-di≥r0Are simultaneously squared and spread, and combined with ri＝||x-siI and r0＝||x-s0| | obtaining constraint conditionsWill be still furtherIs described asAnd wi＝0。
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