CN114895240B - Robust node deployment and selection method in TDOA positioning - Google Patents
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Abstract
The invention discloses a robust node deployment and selection method in TDOA positioning, which comprises the following steps: constructing a multisource positioning network scene in which mobile nodes and fixed nodes coexist; calculating TOA value of the signal source relative to the sensor; calculating a TDOA-containing measurement of the signal source; calculating a confidence ellipse region of the signal source; determining a variance lower bound of an unbiased estimate of the spatial position of the signal source, i.e., a Kramer lower bound; calculating the weighted average worst caramerro lower bound of all sampling points in the signal source confidence region; constructing a robust node deployment optimization problem; calculating a weighted average worst caramerro lower bound determined by selecting a subset of K constituent sensors from the Z positioning nodes; constructing an optimization problem by taking the lowest Kelarmilo lower bound of the minimized weighted average as an objective function and a Boolean vector as a decision variable; and solving the optimization problem by using an improved iterative exchange greedy algorithm. The invention can improve the positioning precision and reduce the calculation complexity.
Description
Technical Field
The invention relates to the technical field of frequency spectrum monitoring, in particular to a robust node deployment and selection method in TDOA positioning.
Background
In the field of spectrum monitoring, passive positioning of signal sources is a technical means of directly correlating electromagnetic spectrum signals with their spatial locations. In spectrum monitoring, each monitoring node collects signal data and transmits the signal data back to a fusion processing center, the fusion processing center extracts position-related parameters from radiation signals, such as Time of arrival (TIME DIFFERENCE of arrival, TDOA), time of arrival (TOA), angle of arrival (Angle of arrival), and the like, and then, in combination with accurate spatial position information of each node, an equation set is constructed to solve the spatial position of a signal source. Among the above-mentioned various positioning parameters, the passive positioning system based on TDOA is widely used in the field of spectrum monitoring.
Under a passive positioning system based on TDOA parameters, the spatial geometrical configuration of each monitoring node relative to the signal source determines the spatial resolution of the signal source, and then has a larger influence on the positioning accuracy of the signal source, so that the optimization of the spatial position of each monitoring node is an effective means for improving the positioning accuracy of the signal source. For a deployed sensor positioning network, due to the characteristics of the sensors, all sensors in the network cannot be used for sensing a certain signal source, so that the sensor selection technology has been a hot spot for research in recent years.
In an actual wireless positioning scene, the position of a signal source cannot be known accurately, and the TDOA measurement error intensity is also unknown due to factors such as noise fluctuation of a receiving end and transmission distance. In existing solutions, the variance of TDOA measurement errors is typically normalized so as to ignore the effect [1]-[3] of the measurement errors on node deployment or node selection; on the other hand, due to the lack of signal source real location information, existing literature often replaces real CRLB with CRLB of signal source rough estimated locations, building node selection or deployment optimization problems [4]. However, either the TDOA measurement error normalization process, or CRLB of coarsely estimated locations as the optimization objective function, introduces uncertainty errors, which lead to a gradual deterioration of the positioning accuracy of the node deployment to the real signal source with increasing uncertainty errors.
Chinese patent CN 108051779B discloses a positioning node optimization method for TDOA, which is used to solve the technical problems of large energy consumption, high system complexity and low positioning accuracy when a large number of sensor nodes participate in positioning in the prior art. However, the above method has the following disadvantages: 1) The method fails to consider the influence of channel estimation errors and signal source rough estimation errors on positioning accuracy; 2) The method utilizes a convex optimization algorithm, the calculation complexity is too high, and the performance of a node selection algorithm cannot approach the optimal performance.
There is therefore a need for an optimization algorithm that takes into account uncertainty errors and that has a low computational complexity for node deployment and selection to obtain the best node deployment and the best subset of sensor locations.
[1].Meng W,Xie L,Xiao W.Optimal TDOA sensor-pair placement with uncertainty in source location[J].IEEE Transactions on Vehicular Technology,2016,65(11):9260-9271.
[2].Yang B,Scheuing J.Cramer-Rao bound and optimum sensor array for source localization from time differences of arrival[A].Proceedings of the IEEE International Conference on Acoustics,Speech and Signal Processing[C].Philadelphia,Pennsylvania,USA:IEEE,2005.IV-961-IV-964
[3].Yang B,Scheuing J.A theoretical analysis of 2D sensor arrays for TDOA based localization[A].Proceedings of the IEEE International Conference on Acoustics,Speech and Signal Processing[C].Toulouse,France:IEEE:2006.IV-901-IV-904.
[4].Dai Z,Wang G,Chen H.Sensor selection for TDOA-based source localization using angle and range information[J].IEEE Transactions on Aerospace and Electronic Systems,2021,57(4):2597-2604.
Disclosure of Invention
In order to solve the problems, the invention provides a solving method of the robust node deployment and selection problem when the uncertain region of the signal source and the uncertain region of the TDOA measurement error exist, which improves the positioning accuracy and reduces the calculation complexity.
The technical scheme adopted by the invention is as follows:
a robust node deployment and selection method in TDOA positioning comprises the following steps:
step one: constructing a multisource positioning network scene in which mobile nodes and fixed nodes coexist, wherein the multisource positioning network scene comprises M fixed nodes, N mobile nodes and U electromagnetic radiation signal sources;
Step two: taking a signal source u k as an example, calculating TOA values, namely arrival time, of the signal source u k relative to a sensor, and adding Gaussian measurement errors to obtain equivalent TOA measurement values of all positioning nodes Wherein n i,k is zero-mean Gaussian variable, variance isDefining n k＝{n1,n2,…,nZ, its covariance matrix
Step three: selecting reference nodes to obtain a measured value of the signal source u k, wherein the measured value comprises TDOA (time difference of arrival) and the covariance matrix of the TDOA measured error vector xi k of the signal source u k of all the nodes is Q k;
step four: obtaining rough estimation result of signal source according to positioning result of additional measurement time Covariance matrix of concomitantly generated positioning errorsUnder the additive Gaussian measurement model, byAnd (3) withObtaining confidence elliptical region of signal source u k The equivalent TOA measurement errors when the fixed node and the mobile node are measured are uniformly distributed in the field of the true value, namely
Step five: determining a variance lower bound of an unbiased estimate of the spatial position of the signal source u k, i.e., a caramet lower bound CRLB, based on the existing TDOA location model; considering that the variance of the measurement error is maximized when a group of nodes measure TDOA, the lower Clamamaro bound of the positioning network for any signal source will reach the maximum value, namely the worst lower Clamamaro bound W-CRLB; randomly sampling in the confidence region in the fourth step, and carrying out average operation on the worst Kramer lower bound W-CRLB of all sampling points to serve as a mathematical representation for measuring the positioning accuracy of the confidence region, namely an average worst Kramer lower bound WA-CRLB;
Step six: simulating robust mathematical representation of the positioning accuracy of two signal sources in the step five, sampling according to Gaussian distribution in a confidence region, roughly estimating sampling points closer to the position, and calculating a weighted average worst Clamamolo lower bound WAW-CRLB of all sampling points in the confidence region of the signal source u k, wherein the weight is larger;
Step seven: in the sixth step, when all Z positioning nodes are obtained and all used for measuring WAW-CRLB of a single signal source u k, the average value of a plurality of signal sources WAW-CRLB is used as an objective function of node deployment facing multi-source positioning, namely The constraint condition is that all the motorized nodes are located in the deployment areaIn, constructing a robust node deployment optimization problem;
Step eight: defining a Z dimension Boolean vector b= (b 1,b2,…,bZ)T,bi = {0,1}, if b i = 1, indicating that the ith sensor node is selected, otherwise not selected;
step nine: constructing an optimization problem P by taking WAW-CRLB in the minimization step eight as an objective function and a Boolean vector b as a decision variable;
Step ten: and solving the optimization problem P by using an improved iterative exchange greedy algorithm MISG, calculating a global optimal solution of the objective function, and outputting a sensor node subset corresponding to the Boolean vector b at the moment.
Further, in the first step, M fixed nodes are deployed, and the positions of the M fixed nodes cannot be adjusted; n mobile nodes are undeployed, the positions of the N mobile nodes can be adjusted, and the mobile nodes can only be deployed in the areaAnd (3) inner part.
Further, in step three, the measured value of the signal source u k including TDOA, i.e. the time difference of arrival, includes a measurement error, and follows gaussian distribution.
Further, in step four, confidence elliptical regionsIs centered atThe direction of the major axis and the minor axis is defined byIs determined by the eigenvectors of (a), the lengths of the major and minor axes are determined byIs determined by the characteristic value of the (c).
Further, in step five, the lower bound of cladoceramWherein the method comprises the steps ofIs the derivative of the TDOA true value with respect to the signal source location, characterizing the spatial resolution of the positioning node with respect to the signal source u k, Q k is the covariance matrix of the TDOA measurement error in step three.
Further, in step seven, the robust node deployment optimization problem is constructed as follows:
Wherein s Ⅱ represents the mobile node spatial position; aiming at the optimization problem According to the genetic algorithm, the decision variable s Ⅱ is regarded as an "individual", R is regarded as the fitness of the "individual", the constraint condition is regarded as the existence area of the "individual", and the optimal solution of the problem is obtained through a limited number of iterations.
Further, in step nine, an optimization problem P constructed with the WAW-CRLB in the minimization step eight as the objective function and the Boolean vector b as the decision variable is as follows:
s.t.C1:1Tb＝K，
Constraint C1 indicates that K sensor nodes are selected, C2 indicates the value of each dimension of the Boolean vector, and C3 indicates that all sampling points are within the confidence region.
Further, step ten comprises the sub-steps of:
Firstly, initializing, namely generating a random boolean vector b {0}, satisfying the requirement of b 0 =k, wherein the corresponding sensor subset is S sel,{0}, and the method is used for estimating the rough signal source position, generating the weight of WAW-CRLB, and calculating the initial global optimal solution CRLB waw,sel,{0}(uk of the target; a judgment index delta= -1, and iteration times N I = 0;
when the judgment index delta <0, selecting one sensor node from the selected sensor node subset and the unselected sensor node subset respectively, and exchanging to obtain a temporary Boolean vector The corresponding objective function value isWherein i=1, 2, …, K; j=1, 2, …, Z-K, coSeed arrangement combinations, respectively calculate thisThe objective function values corresponding to the seed combination are found out, the minimum value is used as a local optimal solution, the local optimal solution is compared with the global optimal solution of the previous generation, if the local optimal solution is smaller, the global optimal solution is updated, and the iteration number is increased by one; otherwise, the global optimal solution is unchanged, the judgment index delta=1 is output, and the sensor node subset corresponding to the Boolean vector at the moment is output.
The invention has the beneficial effects that: aiming at the problems of node deployment and node selection in a time difference positioning scene, an uncertain region of a signal source and an uncertain region of a TDOA measurement error are taken into consideration, and a reliable node deployment and selection scheme is obtained on the basis, so that the positioning precision can be improved, and meanwhile, the calculation complexity is reduced.
Drawings
FIG. 1 is a schematic diagram of multi-source positioning in which stationary and mobile positioning nodes coexist.
Fig. 2 is a diagram of multi-source average positioning accuracy variation in different node deployment modes.
Fig. 3 is a graph of the positioning accuracy of a single signal source in different node deployment modes.
FIG. 4 is a CRLB comparison of different algorithms.
Detailed Description
Specific embodiments of the present invention will now be described in order to provide a clearer understanding of the technical features, objects and effects of the present invention. It should be understood that the particular embodiments described herein are illustrative only and are not intended to limit the invention, i.e., the embodiments described are merely some, but not all, of the embodiments of the invention. All other embodiments, which can be made by a person skilled in the art without making any inventive effort, are intended to be within the scope of the present invention.
The embodiment provides a robust node deployment and selection method in TDOA positioning, which comprises the following steps:
Step one: FIG. 1 is a schematic diagram of multi-source positioning in which stationary and mobile positioning nodes coexist, including M stationary nodes, N mobile nodes, and U electromagnetic radiation signal sources; the M fixed nodes are deployed, and the positions of the M fixed nodes cannot be adjusted; n mobile nodes are undeployed, the positions of the N mobile nodes can be adjusted, and Z positioning nodes are formed; in a two-dimensional cartesian coordinate system, the spatial position coordinates of all positioning nodes are s i＝(si,x,si,y)T, i=1, 2, …, m+n; a fixed set of positioning nodes and a motorized set of positioning nodes are defined as s Ⅰ＝{s1,s2,…,sM},sⅡ＝{sM+1,sM+2,…,sM+N, respectively. Motorized nodes can only be deployed in areas And (3) inner part. The real space position coordinates of the U signal sources are U k＝(uk,x,uk,y)T, k=1, 2, … and U;
Step two: taking the signal source u k as an example, the transmission time of the signal radiation to the positioning node s i, i.e. TOA is Wherein c is the propagation speed of electromagnetic waves, d i,k is the distance between the signal source u k and the sensor node s i; the actual measurement value has measurement errors, so the Gaussian measurement errors are added to the actual measurement value to obtain the equivalent TOA measurement value of each positioning nodeWherein n i,k is zero-mean Gaussian variable, variance isThe value of which is proportional to the distance between the signal source and the positioning node, i.eHere, theIs the reference variance of the equivalent TOA measurement corresponding to the reference distance d 0; defining n k＝{n1,n2,…,nZ, its covariance matrix
Step three: selecting a positioning node s 1 as a reference node, and measuring TDOA (time difference of arrival) values of a signal source u k relative to s i and s 1 Wherein t i1,k is the TDOA true value, t k＝{t21,k,t31,k,…,tZ1,k};ξi1,k＝ni,k-n1,k is the TDOA measurement error, ζ i1,k is the sum of two Gaussian variables, the obeying mean is zero, and the variance isGaussian distribution, the covariance matrix of the TDOA measurement error vector ζ k of all nodes for signal source u k is
Step four: obtaining rough estimation result of signal source according to positioning result of additional measurement timeCovariance matrix of concomitantly generated positioning errorsUnder the additive Gaussian measurement model, byAnd (3) withConfidence elliptical regions of the signal source u k can be obtainedThe center of the ellipse isThe directions of the major axis and the minor axis of the ellipse are defined byIs determined by the eigenvectors of (a), the lengths of the major and minor axes are determined byIs determined by the characteristic value of the (2); the equivalent TOA measurement errors when the fixed node and the mobile node are measured are uniformly distributed in the field of the true value, namely
Step five: based on the existing TDOA location model, determining a variance lower bound of an unbiased estimate of the spatial position of the signal source u k, i.e. a cladmerol lower bound (CRLB),Wherein the method comprises the steps ofIs the derivative of the TDOA true value with respect to the signal source position, characterizes the spatial resolution of the positioning node with respect to the signal source u k, and Q k is the covariance matrix of the TDOA measurement error in step three; taking into account that the variance of the measurement errors of a set of nodes when measuring TDOA reaches a maximum, i.e. the equivalent TOA measurement errors of the reference nodeIs (sigma i,k)2+σi,k, and equivalent TOA measurement error of another positioning nodeFor (at sigma i,k)2+σi,k, the positioning network will reach the maximum value for CRLB of any signal source, namely the worst CRLB (W-CRLB), randomly sampling in the confidence region in the fourth step, averaging the W-CRLB of all sampling points, and using the average calculation as the mathematical representation for measuring the positioning accuracy of the confidence region, whereinN s sampling points are randomly acquired, the occurrence probability of each sampling point is P (u p),p＝1,2,…,Ns, the average value of each sampling point W-CRLB, namely the average worst CRLB (WA-CRLB) of the confidence region is
Step six: simulating the robust mathematical representation of the positioning accuracy of two signal sources in the fifth step, sampling according to Gaussian distribution in a confidence region, wherein the closer the sampling point is to the roughly estimated position, the larger the weight is, and in figure 1,For the spatially confidence region of the signal source u k, according toGenerating N s -1 sampling pointsSetting the weight of each sampling point asP=2, 3, …, N s, roughly estimating the signal source to be at the positionConsidered as the first sampling point, i.eAnd the weight w 1 is set to be 1, and then all sampling points in the confidence region are collected asThe expression of weighted average worst CRLB (WAW-CRLB) is Wherein wsum = i = 1Nswi is the sum of all weights;
Step seven: in the sixth step, when all Z positioning nodes are obtained and all used for measuring WAW-CRLB of a single signal source u k, the average value of a plurality of signal sources WAW-CRLB is used as an objective function for node deployment facing multi-source positioning, namely The constraint condition is that all the motorized nodes are located in the deployment areaIn summary, the robust node deployment optimization problem can be constructed as:
aiming at the optimization problem According to a genetic algorithm, the decision variable s Ⅱ is regarded as an individual, R is regarded as the fitness of the individual, the constraint condition is regarded as the existence area of the individual, and the optimal solution of the problem is obtained through limited iterations;
Step eight: on the basis of the optimized deployment wireless positioning network obtained in the first step to the seventh step, we further study the node selection optimization problem with resource constraint, namely selecting a sensor subset to participate in positioning, and realize the trade-off between positioning precision and resource consumption. Defining a Z-dimension Boolean vector b= (b 1,b2,…,bZ)T,bi = {0,1}, if b i = 1, then indicating that the ith sensor node is selected, otherwise not selected, the CRLB expression determined by selecting the K constituent sensor subsets from the Z positioning nodes is Wherein the method comprises the steps of The scalar α and Γ 0 are decomposed by Γ q in step two, i.e., Γ q＝αI+Γ0;Γt is the partial derivative of the TOA truth with respect to the actual signal source location, i.e
The weighted average worst klamerol lower bound (WAW-CRLB) of the selected subset of sensors is expressed asΓ t,p is the partial derivative of the TOA truth value with respect to the position of the p-th sample point, i.e
Step nine: the optimization problem is built by taking WAW-CRLB in the minimization step eight as an objective function and Boolean vector b as a decision variable as follows:
s.t.C1:1Tb＝K，
Constraint C1 indicates that K sensor nodes are selected, C2 indicates the value of each dimension of the Boolean vector, and C3 indicates that all sampling points are in a confidence region;
Step ten: solving a problem P by using an improved iterative exchange greedy algorithm (MISG), firstly initializing to generate a random Boolean vector b {0}, meeting the requirements of II b 0 =K, wherein the corresponding sensor subset is S sel,{0}, and the method is used for estimating the rough signal source position, generating the weight of WAW-CRLB and calculating the initial global optimal solution CRLB waw,sel,{0}(uk of the target; the judgment index delta= -1, and the iteration number N I =0. When the judgment index delta <0, selecting one sensor node from the selected sensor node subset and the unselected sensor node subset respectively, and exchanging to obtain a temporary Boolean vector The corresponding objective function value isWherein i=1, 2, …, K; j=1, 2, …, Z-K, coSeed arrangement combinations, respectively calculate thisThe objective function values corresponding to the seed combination are found out, the minimum value is used as a local optimal solution, the local optimal solution is compared with the global optimal solution of the previous generation, if the minimum value is small, the global optimal solution is updated, the iteration times are increased by one, and the algorithm is continued; otherwise, the global optimal solution is unchanged, the indication delta=1 is judged, the sensor node subset corresponding to the Boolean vector at the moment is output, and the algorithm is ended.
To verify the robustness of the node deployment method of this embodiment, two algorithms are adopted as a comparison: 1) Non-robust node deployment algorithm based on genetic algorithm: will beTo be regarded as the true position of the signal sourceIs constructed to be the variance of the true equivalent TOA measurement errorCRLB is an optimization problem of an objective function, and a genetic algorithm is adopted to obtain the position of the mobile node; 2) Random deployment algorithm: n mobile positioning nodes are randomly deployed in a deployment area.
Setting two uncertain factors to have the same change trend in simulation, equivalently normalizing uncertainty, changing the reference standard deviation of the equivalent TOA measured value in the second step from 0.002/c second to 0.02/c second with the increment of 0.002/c second, namely increasing the reference standard deviation of the equivalent ROA measured value from 0.002 meters to 0.02 meters, setting the reference distance d 0 to be only 1 meter, and setting the variance of the equivalent TOA measured errorIs set by the value of the uncertain interval parameter delta i,k Increment toDelta i,k increment of deltaAssume thatIn an uncertain intervalThe inner parts are uniformly distributed. In addition, let mobile node number n=3, and the number of sampling points is N s =20. Fig. 2 and 3 are graphs of average CRLB variation of the positioning network for multiple signal sources and CRLB variation of the positioning network for a single signal source for different mobile node deployments. It can be seen from the figure that in the presence of two uncertainties, the performance of the proposed robust node deployment algorithm is superior to that of a non-robust genetic algorithm, and to that of a random deployment algorithm that does not take into account the uncertainties.
In order to verify the superiority of the node selection method of the embodiment and more clearly show the gain of the method, a three-dimensional scene for TDOA positioning aiming at a single signal source is designed, and the positioning accuracy of the single signal source is used as a measurement index to respectively compare the performances of an improved greedy algorithm (MISG) with greedy algorithm (ISG), SDR (SDR), K-nearest method (KN) and exhaustive search method (ES) in solving the problem of the best positioned sensor subset. The latter four algorithms are labeled ISG (ISGwESP), SDRwESP, KNwESP and ESwESP, respectively, with estimated source position, with CRLB of the estimated source as the objective function. Fig. 4 shows the result of CRLB comparison of different algorithms, and it can be seen that the proposed MISG algorithm performs better than other algorithms, especially in the case of increased TDOA error intensity. The partial graph in fig. 4 shows the difference between ESwESP and MISG in that the ES algorithm is optimal for the case where the source is estimated rather than the actual source location.
The foregoing is merely a preferred embodiment of the invention, and it is to be understood that the invention is not limited to the form disclosed herein but is not to be construed as excluding other embodiments, but is capable of numerous other combinations, modifications and environments and is capable of modifications within the scope of the inventive concept, either as taught or as a matter of routine skill or knowledge in the relevant art. And that modifications and variations which do not depart from the spirit and scope of the invention are intended to be within the scope of the appended claims.
Claims (8)
1. A method for robust node deployment and selection in TDOA location, comprising the steps of:
step one: constructing a multisource positioning network scene in which mobile nodes and fixed nodes coexist, wherein the multisource positioning network scene comprises M fixed nodes, N mobile nodes and U electromagnetic radiation signal sources;
step two: for signal sources Calculating TOA value, namely arrival time, of the sensor relative to the sensor, and adding Gaussian measurement error to obtain equivalent TOA measurement values of all positioning nodesWhereinIs zero mean Gaussian variable, variance is; Definition of the definitionCovariance matrix of it；
Step three: selecting a reference node to obtain a signal sourceIncluding TDOA, i.e., the measured value of the time difference of arrival, then all nodes are for the source of the signalTDOA measurement error vector of (a)Covariance matrix of (2) is；
Step four: obtaining rough estimation result of signal source according to positioning result of additional measurement timeCovariance matrix of concomitant generated positioning errorUnder the additive Gaussian measurement model, byAnd (3) withObtaining the signal sourceConfidence elliptical region of (a); The equivalent TOA measurement errors when the fixed node and the mobile node are measured are uniformly distributed in the field of the true value, namely；
Step five: determining signal sources based on existing TDOA positioning modelsThe variance lower bound of the unbiased estimate of spatial position, i.e., the Kramer lower bound CRLB; considering that the variance of the measurement error is maximized when a group of nodes measure TDOA, the lower Clamamaro bound of the positioning network for any signal source will reach the maximum value, namely the worst lower Clamamaro bound W-CRLB; randomly sampling in the confidence region in the fourth step, and carrying out average operation on the worst Kramer lower bound W-CRLB of all sampling points to serve as a mathematical representation for measuring the positioning accuracy of the confidence region, namely an average worst Kramer lower bound WA-CRLB;
Step six: simulating robust mathematical representation of the positioning accuracy of two signal sources in the fifth step, sampling according to Gaussian distribution in a confidence region, and calculating the signal source with larger weight as the distance from a sampling point which is roughly estimated to be closer The weighted average worst clamamterol lower bound WAW-CRLB of all sampling points in the confidence region;
Step seven: in the sixth step, all Z positioning nodes are obtained and are all used for measuring a single signal source When WAW-CRLB is used, the average value of a plurality of signal sources WAW-CRLB is used as an objective function deployed for nodes facing multi-source positioning, namelyThe constraint condition is that all motorized nodes are located in the deployment areaIn, constructing a robust node deployment optimization problem;
Step eight: defining a Z-dimension Boolean vector If (3)Indicating that the ith sensor node is selected, otherwise, not selecting the ith sensor node; calculating WAW-CRLB determined by selecting K sensor subsets from the Z positioning nodes;
step nine: with WAW-CRLB in the minimization step eight as an objective function, boolean vector Constructing an optimization problem P for the decision variable;
step ten: solving the optimization problem P by using an improved iterative exchange greedy algorithm MISG, calculating a global optimal solution of the objective function, and outputting a Boolean vector at the moment A corresponding subset of sensor nodes.
2. The method for deployment and selection of robust nodes in TDOA location of claim 1 wherein in step one, M stationary nodes are deployed whose locations cannot be adjusted; n mobile nodes are undeployed, the positions of the N mobile nodes can be adjusted, and the mobile nodes can only be deployed in the areaAnd (3) inner part.
3. The method for deployment and selection of robust nodes in TDOA localization of claim 1, wherein in step three, the signal sourceThe measured values containing TDOA, i.e. the time difference of arrival, contain measurement errors, subject to gaussian distribution.
4. The method of claim 1, wherein in step four, confidence elliptical regionsIs centered atThe directions of the major axis and the minor axis are defined byIs determined by the eigenvectors of (a), the lengths of the major and minor axes are determined byIs determined by the characteristic value of the (c).
5. The method for deployment and selection of robust nodes in TDOA location of claim 1 wherein in step five, the lower bound CRLB @ of caramet)=WhereinIs the derivative of the TDOA true value with respect to the signal source location, characterizing the location node with respect to the signal sourceIs used for the spatial resolution of the (c) optical system,Is the covariance matrix of the TDOA measurement error in step three.
6. The method for deployment and selection of robust nodes in TDOA localization of claim 1, wherein in step seven, the robust node deployment optimization problem is constructed as:
Wherein, Representing the spatial position of the mobile node; aiming at the optimization problemBased on genetic algorithm, decision variables are determinedRegarding as "individual", R regarding as the fitness of "individual", and regarding the constraint condition as the existence area of "individual", obtaining the optimal solution of the problem through a limited number of iterations.
7. The method of claim 1, wherein in step nine, the boolean vector is used as an objective function to minimize the WAW-CRLB in step eightThe optimization problem P constructed for decision variables is as follows:
P：
s.t.C1:1Tb＝K，
C2：
C3：
Constraint C1 indicates that K sensor nodes are selected, C2 indicates the value of each dimension of the Boolean vector, and C3 indicates that all sampling points are within the confidence region.
8. A method of robust node deployment and selection in TDOA localization according to claim 1, wherein step ten comprises the sub-steps of:
First initialize to generate a random Boolean vector Satisfies the following conditionsThe corresponding sensor subset isFor estimating coarse source position, generating WAW-CRLB weights, and calculating initial global optimal solution of the target; Judgment indexNumber of iterations；
When judging the indexWhen the sensor nodes are selected from the selected sensor node subset and the unselected sensor node subset, a temporary Boolean vector is obtained after mutual exchangeThe corresponding objective function value isWhereinCo-mingling withSeed arrangement combinations, respectively calculate thisThe objective function values corresponding to the seed combination are found out, the minimum value is used as a local optimal solution, the local optimal solution is compared with the global optimal solution of the previous generation, if the local optimal solution is smaller, the global optimal solution is updated, and the iteration number is increased by one; otherwise, the global optimal solution is unchanged, and the index is judgedAnd outputting the sensor node subset corresponding to the Boolean vector at the moment.
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