CN105353351A - Improved positioning method based on multi-beacon arrival time differences - Google Patents

Abstract

The invention discloses an improved positioning method based on multi-beacon arrival time differences. The method specifically comprises the steps of: (1) obtaining position information of a sensor in a multi-beacon arrival time difference positioning scene; (2) taking a target position and distances between a plurality of beacons and the target as unknown quantities, deriving a corresponding pseudo-linear equation group according to a non-linear measuring equation group of the multi-beacon arrival time differences; (3) according to a weighted least square algorithm, estimating the target position and the distances between the plurality of beacons and the target; and (4) according to the coupling relation between the target position and the distances between the plurality of beacons and the target, updating the estimation of the target position. According to the invention, the precision of the linear closed passive target positioning aimed at multi-beacon arrival time differences is improved. The plurality of beacons and the coupling relation between the target position and the distances between the plurality of beacons and the target are utilized to increase the positioning information amount and improve the positioning precision.

Description

A kind of based on multi-beacon difference time of arrival modified localization method

Technical field

The present invention relates to a kind of new type of passive object localization method based on difference time of arrival, particularly relate to a kind of based on multi-beacon difference time of arrival modified localization method.

Background technology

The mistiming arriving sensor based on passive target effectively can determine target location, and it is that passive target detection system measures one of gordian technique of target location.Its ultimate principle is by carrying out rational space layout to multiple sensor, analyzes with the signal that receiving target sends, and calculates target determined by each sensor azimuth-range relative to the mistiming of beaconing nodes.Be after obtaining target and arriving the mistiming data of different sensors based on difference object localization method the name of the game time of arrival, obtain target location by asking for one group of nonlinear equation, there is very large challenge.

A kind of method that tradition solves this Nonlinear System of Equations carries out linearization by Taylor series expansion method in local neighborhood, and solved by iterative manner.The defect of the method is the initial position estimation that arithmetic accuracy depends on target, and its convergence of separating can not be guaranteed, the calculated amount of this algorithm (compared to closed algorithm) bigger than normal simultaneously.Relative to iterative algorithm, another kind of algorithm is closed algorithm.By Nonlinear System of Equations being converted into the pseudo-linear equation of a class band measuring error, and utilize Minimum Mean Squared Error estimation, least square scheduling algorithm makes positioning error reach minimum.It is Chan algorithm that such algorithm typically represents, and this algorithm has that algorithm calculated amount is little, without the need to iterative computation, the advantage such as simply accurate, but the method exists the shortcoming of location ambiguity, namely exists bilingual or may without what separate by Chan Algorithm for Solving Nonlinear System of Equations.

Find through correlative study, the ambiguity of Chan algorithm solution can solve by the following method: (1) increases the supplementarys such as Bearing, energy, Doppler frequency difference; (2) quantity of sensor in space is increased; (3) methods such as the beacon number of positioning system are increased.Wherein the third method can not only eliminate the ambiguity of Chan algorithm solution, and can also improve target location accuracy, and therefore these class methods are of great significance the task performance tool improving positioning using TDOA system.

Summary of the invention

The object of the invention is to for the deficiencies in the prior art, provide a kind of based on multi-beacon difference time of arrival modified localization method.

In order to realize above-mentioned object, the present invention takes following technical scheme: a kind of based on multi-beacon difference time of arrival modified localization method, comprises the following steps:

Step (1) obtains the positional information of sensor from the scene of multi-beacon difference time of arrival location;

Step (2) regards target location and the distance between multiple beacon and target as unknown quantity, according to the corresponding pseudo-system of linear equations of nonlinear measure equations group derivation of multi-beacon difference time of arrival;

Step (3) according to weighted least square algorithm, estimating target position and the distance between multiple beacon and target;

Step (4), according to the coupled relation of the spacing of target location and multiple beacon, target, is estimated to upgrade to target location.

In described step (1), the positional information of described sensor refers to the planimetric coordinates of sensor, and may extend to three-dimensional coordinate; Suppose that positioning system is made up of N number of ordinary sensors and M reference sensor, wherein the n-th ordinary sensors is positioned at (x _n, y _n), n=1,2 ..., N, the position coordinates of m reference sensor is (x _b,m, y _b,m), m=1,2 ..., M.

Step (2) is specially, and hypothetical target position is (x _s, y _s), target is designated as d to the distance of the n-th ordinary sensors and m reference sensor _nand d _b,m; If the velocity of propagation of echo signal is c, echo signal is τ to the mistiming of the n-th ordinary sensors and m reference sensor _nm, wherein τ _nm=(d _n-d _b,m)/c; The range difference of the n-th ordinary sensors and m reference sensor is designated as d _nm, d _nm=d _n-d _b,m; By target location (x _s, y _s) and distance d between all beacons and target _{b, 1}, d _{b, 2}..., d _b,Mregarding unknown quantity as, through deriving, obtaining the pseudo-system of linear equations of multiple beacon difference time of arrival:

Φz-h＝δ，

$\mathrm{\Φ}=\left[\begin{array}{ccccc}{A}_1& r_1& 0& ...& 0\\ A_2& 0& r_2& ...& 0\\ .& .& .& .& .\\ .& .& .& .& .\\ .& .& .& .& .\\ A_M& 0& 0& ...& r_M\end{array}\right],h=\frac{1}{2}\left[\begin{array}{c}{u}_1\\ .\\ .\\ .\\ u_M\end{array}\right],$

Wherein

$A_m=\left[\begin{array}{cc}{x}_{b,m}-x_1& y_{b,1}-y_1\\ .& .\\ .& .\\ .& .\\ x_{b,m}-x_N& y_{b,1}-y_N\end{array}\right],r_m=\left[\begin{array}{c}{\tilde{d}}_{1m}\\ .\\ .\\ .\\ {\tilde{d}}_{Nm}\end{array}\right],u_m=\left[\begin{array}{c}{\tilde{d}}_{1m}^2-x_1^2-y_1^2+x_{b,m}^2+y_{b,m}^2\\ .\\ .\\ .\\ {\tilde{d}}_{Nm}^2-x_N^2-y_N^2+x_{b,m}^2+y_{b,m}^2\end{array}\right],$

Z=[x _s, y _s, d _{b, 1}..., d _b,M] ^tvector to be estimated, d _nm=d _n-d _b,mthe range difference of the n-th ordinary sensors and m reference sensor, ξ _nmobservation noise, δ=cB ξ+0.5c ²ξ ⊙ ξ, B=diag{d ₁..., d _n..., d ₁..., d _n, ξ=[ξ ₁₁..., ξ _n1..., ξ _1M..., ξ _nM] ^t.

Described step (3) is specially, and adopts weighted least square algorithm to estimate to unknown vector z; So have:

$\hat{z}={\left({\mathrm{\Φ}}^T{\mathrm{\Σ}}^{-1}\mathrm{\Φ}\right)}^{-1}{\mathrm{\Φ}}^T{\mathrm{\Σ}}^{-1}h,$

Wherein Σ=E [δ δ ^t]=c ²bQB, Q are the covariance matrixs of observation noise.

Described step (4) comprises following sub-step:

(A) under the condition that observational error is less, position estimated bias can be ignored, therefore be average be z, covariance matrix is stochastic variable; By the element representation in z be:

Z ₁=x _s+ e ₁, z ₂=y _s+ e ₂, z ₃=d _{b, 1}+ e ₃..., z _m+2=d _b,m+ e _m+2..., z _m+2=d _b,M+ e _m+2, wherein e ₁, e ₂e _m+2(m=1 ..., M) be evaluated error;

(B) by z ₁and z ₂deduct x respectively _{b, 1}..., x _b,Mand y _{b, 1}..., y _b,M, and work square, another one system of equations can be obtained:

Φ′z′-h′＝δ′

${\mathrm{\Φ}}^{\′}=\left[\begin{array}{cc}1& 0\\ 0& 1\\ 1& 1\end{array}\right],z^{\′}=\left[\begin{array}{c}{(x_s-x_{b,1}-x_{b,2}-...-x_{b,M})}^2\\ {(y_s-y_{b,1}-y_{b,2}-...-y_{b,M})}^2\end{array}\right],$

$h^{\′}=\left[\begin{array}{c}{(z_1-x_{b,1}-x_{b,2}-...-x_{b,M})}^2\\ {(z_2-y_{b,1}-y_{b,2}-...-y_{b,M})}^2\\ z_3^2+...+z_{M+2}^2-(M-1)(z_1^2+z_2^2)+K_b\end{array}\right],$

K _b＝2(x _b,1x _b,2+…+x _b,M-1x _b,M+y _b,1y _b,2+…+y _b,M-1y _b,M)，

$\begin{array}{c}{\mathrm{\δ}}^{\′}=\left[\begin{array}{c}-2(z_1-x_{b,1}-x_{b,2}-...-x_{b,M})e_1-e_1^2\\ -2(z_2-y_{b,1}-y_{b,2}-...-y_{b,M})e_2-e_2^2\\ (M-1)(2x_s{e}_1+2y_s{e}_2+e_1^2+e_2^2)-2d_{b,1}{e}_3-e_3^2-...-2d_{b,M}{e}_{M+2}-e_{M+2}^2\end{array}\right]\\ \≈2\left[\begin{array}{c}-(z_1-x_{b,1}-x_{b,2}-...-x_{b,M})e_1\\ -(z_2-x_{b,1}-x_{b,2}-...-x_{b,M})e_2\\ (M-1)(2x_s{e}_1+2y_s{e}_2)-2d_{b,1}{e}_3-...-2d_{b,M}{e}_{M+2}\end{array}\right];\end{array}$

(C) according to weighted least square algorithm, z ' estimated value can be obtained:

${\hat{z}}^{\′}={\left({\mathrm{\Φ}}^{\′T}{\mathrm{\Σ}}^{\′-1}{\mathrm{\Φ}}^{\′}\right)}^{-1}{\mathrm{\Φ}}^{\′T}{\mathrm{\Σ}}^{\′-1}{h}^{\′},$

Wherein ${\mathrm{\Σ}}^{\′}=E\[{\mathrm{\δ}}^{\′}{\mathrm{\δ}}^{\′T}\]=B^{\′}\mathrm{cov}\left(\hat{z}\right)B^{\′T},$

$B^{\′}=2\left[\begin{array}{ccccc}-(z_1-x_{b,1}-x_{b,2}-...-x_{b,M})& 0& 0& ...& 0\\ 0& -(z_2-y_{b,1}-y_{b,2}-...-y_{b,M})& 0& ...& 0\\ 2(M-1)z_1& 2(M-1)z_2& -z_3& ...& -z_{M+2}\end{array}\right];$

(D) (C) step acquired results is mapped to final target location to estimate:

$z_f=\sqrt{{\hat{z}}^{\′}}+{\left[\begin{array}{cc}{x}_{b,1}& y_{b,1}\end{array}\right]}^T+...+{\left[\begin{array}{cc}{x}_{b,M}& y_{b,M}\end{array}\right]}^T$

Or

$z_f=-\sqrt{{\hat{z}}^{\′}}+{\left[\begin{array}{cc}{x}_{b,1}& y_{b,1}\end{array}\right]}^T+...+{\left[\begin{array}{cc}{x}_{b,M}& y_{b,M}\end{array}\right]}^T.$

The invention has the beneficial effects as follows, the precision of the linear enclosed passive target location for multi-beacon difference time of arrival can be improved.Utilize the coupled relation of the spacing of multiple beacon and target location and multiple beacon and target, increase locating information amount, improve positioning precision.

Accompanying drawing explanation

Fig. 1 is the process flow diagram that the present invention is based on multi-beacon difference time of arrival modified localization method;

Fig. 2 is that acoustic target and microphone position demarcate schematic diagram;

Fig. 3 is that the different signal to noise ratio (S/N ratio) beacon that places an order compares result with two beacons-coupling objectives location estimation square error;

Fig. 4 is that place an order beacon, two beacon-couplings, two beacons-decoupling zero chorus source position of different signal to noise ratio (S/N ratio) estimate square error relatively result.

Embodiment:

Patent of the present invention uses the coupled relation realize target of the spacing of multi-beacon difference time of arrival and target location and multiple beacon and target to locate.Principle based on multi-beacon difference time of arrival modified localization method is: the sensor using multiple demarcation good obtains target and arrives ordinary sensors and reference sensor mistiming data.Regard target location and the distance between multiple beacon and target as unknown quantity, derive pseudo-system of linear equations and utilize weighted least square algorithm ask for target location estimate.Then utilize the coupled relation of the spacing of target location and multiple beacon and target, estimate to upgrade to target location.

Composition graphs 1, of the present inventionly comprises the following steps based on difference modified localization method multi-beacon time of arrival:

Step 1, obtain the positional information of sensor difference target localization scene from multi-beacon time of arrival, be specially: suppose that positioning system is made up of N number of ordinary sensors and M reference sensor, wherein the n-th ordinary sensors is positioned at (x _n, y _n), n=1,2 ..., N, the position coordinates of m reference sensor is (x _b,m, y _b,m), m=1,2 ..., M, the position of ordinary sensors and reference sensor can be demarcated in advance.

Step 2, regard target location and the distance between multiple beacon and target as unknown quantity, to derive corresponding pseudo-system of linear equations according to the nonlinear measure equations group of multi-beacon difference time of arrival.Be specially: hypothetical target position is (x _s, y _s), target is designated as d to the distance of the n-th ordinary sensors and m reference sensor _nand d _b,m.If the velocity of propagation of echo signal is c, echo signal is τ to the mistiming of the n-th ordinary sensors and m reference sensor _nm, wherein τ _nm=(d _n-d _b,m)/c.The range difference of the n-th ordinary sensors and m reference sensor is designated as d _nm, d _nm=d _n-d _b,m.By target location (x _s, y _s) and all beacons arrive the distance d of target _{b, 1}, d _{b, 2}..., d _b,Mregarding unknown quantity as, through deriving, obtaining the pseudo-system of linear equations of multiple beacon difference time of arrival:

Φz-h＝δ，

$\mathrm{\Φ}=\left[\begin{array}{ccccc}{A}_1& r_1& 0& ...& 0\\ A_2& 0& r_2& ...& 0\\ .& .& .& .& .\\ .& .& .& .& .\\ .& .& .& .& .\\ A_M& 0& 0& ...& r_M\end{array}\right],h=\frac{1}{2}\left[\begin{array}{c}{u}_1\\ .\\ .\\ .\\ u_M\end{array}\right],$

Wherein

$A_m=\left[\begin{array}{cc}{x}_{b,m}-x_1& y_{b,1}-y_1\\ .& .\\ .& .\\ .& .\\ x_{b,m}-x_N& y_{b,1}-y_N\end{array}\right],r_m=\left[\begin{array}{c}{\tilde{d}}_{1m}\\ .\\ .\\ .\\ {\tilde{d}}_{Nm}\end{array}\right],u_m=\left[\begin{array}{c}{\tilde{d}}_{1m}^2-x_1^2-y_1^2+x_{b,m}^2+y_{b,m}^2\\ .\\ .\\ .\\ {\tilde{d}}_{Nm}^2-x_N^2-y_N^2+x_{b,m}^2+y_{b,m}^2\end{array}\right],$

Z=[x _s, y _s, d _{b, 1}..., d _b,M] ^tvector to be estimated, ξ _nmobservation noise, δ=cB ξ+0.5c ²ξ ⊙ ξ, B=diag{d ₁..., d _n..., d ₁..., d _n, ξ=[ξ ₁₁..., ξ _n1..., ξ _1M..., ξ _nM] ^t.

Step 3, according to weighted least square algorithm, estimating target position and the distance between multiple beacon and target.Be specially: adopt weighted least square algorithm to estimate to unknown vector z.So have:

$\hat{z}={\left({\mathrm{\Φ}}^T{\mathrm{\Σ}}^{-1}\mathrm{\Φ}\right)}^{-1}{\mathrm{\Φ}}^T{\mathrm{\Σ}}^{-1}h,$

Wherein Σ=E [δ δ ^t]=c ²bQB, Q are the covariance matrixs of observation noise.

Step 4, according to the coupled relation between target location and the distance between multiple beacon and target, to target location estimate upgrade.Be specially:

(A) under the condition that observational error is less, position estimated bias can be ignored, therefore be average be z, covariance matrix is stochastic variable.By the element representation in z be:

Z ₁=x _s+ e ₁, z ₂=y _s+ e ₂, z ₃=d _{b, 1}+ e ₃..., z _m+2=d _b,m+ e _m+2..., z _m+2=d _b,M+ e _m+2, wherein e ₁, e ₂e _m+2(m=1 ..., M) be evaluated error.

(B) by z ₁and z ₂deduct x respectively _{b, 1}..., x _b,Mand y _{b, 1}..., y _b,M, and work square, another one system of equations can be obtained:

Φ′z′-h′＝δ′

${\mathrm{\Φ}}^{\′}=\left[\begin{array}{cc}1& 0\\ 0& 1\\ 1& 1\end{array}\right],z^{\′}=\left[\begin{array}{c}{(x_s-x_{b,1}-x_{b,2}-...-x_{b,M})}^2\\ {(y_s-y_{b,1}-y_{b,2}-...-y_{b,M})}^2\end{array}\right],$

$h^{\′}=\left[\begin{array}{c}{(z_1-x_{b,1}-x_{b,2}-...-x_{b,M})}^2\\ {(z_2-y_{b,1}-y_{b,2}-...-y_{b,M})}^2\\ z_3^2+...+z_{M+2}^2-(M-1)(z_1^2+z_2^2)+K_b\end{array}\right],$

K _b＝2(x _b,1x _b,2+…+x _b,M-1x _b,M+y _b,1y _b,2+…+y _b,M-1y _b,M)，

$\begin{array}{c}{\mathrm{\δ}}^{\′}=\left[\begin{array}{c}-2(z_1-x_{b,1}-x_{b,2}-...-x_{b,M})e_1-e_1^2\\ -2(z_2-y_{b,1}-y_{b,2}-...-y_{b,M})e_2-e_2^2\\ (M-1)(2x_s{e}_1+2y_s{e}_2+e_1^2+e_2^2)-2d_{b,1}{e}_3-e_3^2-...-2d_{b,M}{e}_{M+2}-e_{M+2}^2\end{array}\right]\\ \≈2\left[\begin{array}{c}-(z_1-x_{b,1}-x_{b,2}-...-x_{b,M})e_1\\ -(z_2-x_{b,1}-x_{b,2}-...-x_{b,M})e_2\\ (M-1)(2x_s{e}_1+2y_s{e}_2)-2d_{b,1}{e}_3-...-2d_{b,M}{e}_{M+2}\end{array}\right];\end{array}$

(C) according to weighted least square algorithm, z ' estimated value can be obtained:

${\hat{z}}^{\′}={\left({\mathrm{\Φ}}^{\′T}{\mathrm{\Σ}}^{\′-1}{\mathrm{\Φ}}^{\′}\right)}^{-1}{\mathrm{\Φ}}^{\′T}{\mathrm{\Σ}}^{\′-1}{h}^{\′},$

Wherein ${\mathrm{\Σ}}^{\′}=E\[{\mathrm{\δ}}^{\′}{\mathrm{\δ}}^{\′T}\]=B^{\′}\mathrm{cov}\left(\hat{z}\right)B^{\′T},$

$B^{\′}=2\left[\begin{array}{ccccc}-(z_1-x_{b,1}-x_{b,2}-...-x_{b,M})& 0& 0& ...& 0\\ 0& -(z_2-y_{b,1}-y_{b,2}-...-y_{b,M})& 0& ...& 0\\ 2(M-1)z_1& 2(M-1)z_2& -z_3& ...& -z_{M+2}\end{array}\right].$

(D) (C) step acquired results is mapped to final target location to estimate:

$z_f=\sqrt{{\hat{z}}^{\′}}+{\left[\begin{array}{cc}{x}_{b,1}& y_{b,1}\end{array}\right]}^T+...+{\left[\begin{array}{cc}{x}_{b,M}& y_{b,M}\end{array}\right]}^T$

Or

$z_f=-\sqrt{{\hat{z}}^{\′}}+{\left[\begin{array}{cc}{x}_{b,1}& y_{b,1}\end{array}\right]}^T+...+{\left[\begin{array}{cc}{x}_{b,M}& y_{b,M}\end{array}\right]}^T.$

Below in conjunction with embodiment, the present invention will be further described in detail:

The invention of this positioning system participates in the single acoustic target in location for 4 common microphones, 2 reference microphones, and sound source is positioned at (200,150), realizes based on multi-beacon difference time of arrival modified target localization.Concrete steps are:

The first step, the coordinate demarcating 4 common microphones within the scope of 500 × 500 square metres is (200,300), (300,250), (100,350), (400,200), 2 positions with reference to microphone are (450,350), (450,50), as shown in Figure 2.

Second step, provides sound source and arrives common microphone and the time difference measurements value with reference to microphone, under sound propagation velocity rigid condition, be range difference under different signal to noise ratio (S/N ratio)s.Observation noise is zero-mean, variance is σ ²gaussian probability-density function, standard deviation sigma is taken as 0.07,0.11,0.18,0.28,0.45,0.71,1.12,1.78.Emulated data is substituted into weighted least square algorithm obtain target location estimated value under identical simulated conditions, do 1000 experiments, obtain estimated value averaged Square Error of Multivariate, as shown in Figure 3.

3rd step, utilizes second step acquired results, upgrades covariance matrix with h ' vector, acquired results is substituted into obtain estimated value.

4th step, according to the 3rd step acquired results, according to $z_f=\sqrt{{\hat{z}}^{\′}}+{\left[\begin{array}{cc}{x}_{b,1}& y_{b,1}\end{array}\right]}^T+{\left[\begin{array}{cc}{x}_{b,2}& y_{b,2}\end{array}\right]}^T$ Or $z_f=-\sqrt{{\hat{z}}^{\′}}+{\left[\begin{array}{cc}{x}_{b,1}& y_{b,1}\end{array}\right]}^T+{\left[\begin{array}{cc}{x}_{b,2}& y_{b,2}\end{array}\right]}^T$ Calculate final sound source position to estimate.Under identical simulated conditions, do 1000 experiments, obtain estimated value z _faveraged Square Error of Multivariate, as shown in Figure 4.

Can find out, second step can obtain better positioning precision than poor auditory localization time of arrival of single beacon based on the auditory localization of two beacon differences time of arrival, but does not utilize target location and two beacons to arrive the coupled relation of the distance of sound source.But after being through the 3rd step and the 4th step solution coupling processing, can obtain than positioning precision better before solution coupling.

Claims (5)

1., based on a multi-beacon difference time of arrival modified localization method, it is characterized in that, comprise the following steps:

Step (1) obtains the positional information of sensor from the scene of multi-beacon difference time of arrival location;

Step (2) regards target location and the distance between multiple beacon and target as unknown quantity, according to the corresponding pseudo-system of linear equations of nonlinear measure equations group derivation of multi-beacon difference time of arrival;

Step (3) according to weighted least square algorithm, estimating target position and the distance between multiple beacon and target;

Step (4), according to the coupled relation of the spacing of target location and multiple beacon, target, is estimated to upgrade to target location.

2. a kind of based on multi-beacon difference time of arrival modified localization method according to claim 1, it is characterized in that: in described step (1), the positional information of described sensor refers to the planimetric coordinates of sensor, and may extend to three-dimensional coordinate; Suppose that positioning system is made up of N number of ordinary sensors and M reference sensor, wherein the n-th ordinary sensors is positioned at (x _n, y _n), n=1,2 ..., N, the position coordinates of m reference sensor is (x _b,m, y _b,m), m=1,2 ..., M.

3. a kind of based on multi-beacon difference time of arrival modified localization method according to claim 1, it is characterized in that: described step (2) is specially, hypothetical target position is (x _s, y _s), target is designated as d to the distance of the n-th ordinary sensors and m reference sensor _nand d _b,m; If the velocity of propagation of echo signal is c, echo signal is τ to the mistiming of the n-th ordinary sensors and m reference sensor _nm, wherein τ _nm=(d _n-d _b,m)/c; The range difference of the n-th ordinary sensors and m reference sensor is designated as d _nm, d _nm=d _n-d _b,m; By target location (x _s, y _s) and distance d between all beacons and target _{b, 1}, d _{b, 2}..., d _b,Mregarding unknown quantity as, through deriving, obtaining the pseudo-system of linear equations of multiple beacon difference time of arrival:

Φz-h＝δ，

$\mathrm{\Φ}=\left[\begin{array}{ccccc}{A}_1& r_1& 0& ...& 0\\ A_2& 0& r_2& ...& 0\\ \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}.\\ .\\ .\end{array}\\ A_M& 0& 0& ...& r_M\end{array}\right],$ $h=\frac{1}{2}\left[\begin{array}{c}{u}_1\\ .\\ .\\ .\\ u_M\end{array}\right],$

Wherein

$A_m=\left[\begin{array}{cc}{x}_{b,m}-x_1& y_{b,1}-y_1\\ \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}.\\ .\\ .\end{array}\\ x_{b,m}-x_N& y_{b,1}-y_N\end{array}\right],$ $r_m=\left[\begin{array}{c}{\tilde{d}}_{1m}\\ \begin{array}{c}.\\ .\\ .\end{array}\\ {\tilde{d}}_{Nm}\end{array}\right],$ $u_m=\left[\begin{array}{c}{\tilde{d}}_{1m}^2-x_1^2-y_1^2+x_{b,m}^2+y_{b,m}^2\\ .\\ .\\ .\\ {\tilde{d}}_{Nm}^2-x_N^2-y_N^2+x_{b,m}^2+y_{b,m}^2\end{array}\right],$

Z=[x _s, y _s, d _{b, 1}..., d _b,M] ^tvector to be estimated, d _nm=d _n-d _b,mthe range difference of the n-th ordinary sensors and m reference sensor, ξ _nmobservation noise, δ=cB ξ+0.5c ²ξ ⊙ ξ, B=diag{d ₁..., d _n..., d ₁..., d _n, ξ=[ξ ₁₁..., ξ _n1..., ξ _1M..., ξ _nM] ^t.

4. one according to claim 1 is based on multi-beacon difference time of arrival modified localization method, and it is characterized in that, described step (3) is specially, and adopts weighted least square algorithm to estimate to unknown vector z; So have:

$\hat{z}={\left({\mathrm{\Φ}}^T{\mathrm{\Σ}}^{-1}\mathrm{\Φ}\right)}^{-1}{\mathrm{\Φ}}^T{\mathrm{\Σ}}^{-1}h,$

Wherein Σ=E [δ δ ^t]=c ²bQB, Q are the covariance matrixs of observation noise.

5. a kind of based on multi-beacon difference time of arrival modified localization method according to claim 1, it is characterized in that, described step (4) comprises following sub-step:

(A) under the condition that observational error is less, position estimated bias can be ignored, therefore be average be z, covariance matrix is stochastic variable; By the element representation in z be:

Z ₁=x _s+ e ₁, z ₂=y _s+ e ₂, z ₃=d _{b, 1}+ e ₃..., z _m+2=d _b,m+ e _m+2..., z _m+2=d _b,M+ e _m+2, wherein e ₁, e ₂e _m+2(m=1 ..., M) be evaluated error;

(B) by z ₁and z ₂deduct x respectively _{b, 1}..., x _b,Mand y _{b, 1}..., y _b,M, and work square, another one system of equations can be obtained:

Φ′z′-h′＝δ′

${\mathrm{\Φ}}^{\′}=\left[\begin{array}{cc}1& 0\\ 0& 1\\ 1& 1\end{array}\right],$ $z^{\′}=\left[\begin{array}{c}{(x_s-x_{b,1}-x_{b,2}-...-x_{b,M})}^2\\ {(y_s-y_{b,1}-y_{b,2}-...-y_{b,M})}^2\end{array}\right],$

$h^{\′}=\left[\begin{array}{c}{(z_1-x_{b,1}-x_{b,2}-...-x_{b,M})}^2\\ {(z_2-y_{b,1}-y_{b,2}-...-y_{b,M})}^2\\ z_3^2+...+z_{M+2}^2-(M-1)(z_1^2+z_2^2)+K_b\end{array}\right],$

K _b＝2(x _b,1x _b,2+...+x _b,M-1x _b,M+y _b,1y _b,2+...+y _b,M-1y _b,M)，

$\begin{array}{c}{\mathrm{\δ}}^{\′}=\left[\begin{array}{c}-2\left(z_1-x_{b,1}-x_{b,2}-...-x_{b,M}\right)e_1-e_1^2\\ -2\left(z_2-y_{b,1}-y_{b,2}-...-y_{b,M}\right)e_2-e_2^2\\ \left(M-1\right)\left(2x_s{e}_1+2y_s{e}_2+e_1^2+e_2^2\right)-2d_{b,1}{e}_3-e_3^2-...-2d_{b,M}{e}_{M+2}-e_{M+2}^2\end{array}\right]\\ \≈2\left[\begin{array}{c}-\left(z_1-x_{b,1}-x_{b,2}-...-x_{b,M}\right)e_1\\ -\left(z_2-y_{b,1}-y_{b,2}-...-y_{b,M}\right)e_2\\ \left(M-1\right)\left(2x_s{e}_1+2y_s{e}_2\right)-2d_{b,1}{e}_3-...-2d_{b,M}{e}_{M+2}\end{array}\right];\end{array}$

(C) according to weighted least square algorithm, z ' estimated value can be obtained:

${\hat{z}}^{\′}={\left({\mathrm{\Φ}}^{\′T}{\mathrm{\Σ}}^{\′-1}{\mathrm{\Φ}}^{\′}\right)}^{-1}{\mathrm{\Φ}}^{\′T}{\mathrm{\Σ}}^{\′-1}{h}^{\′},$

Wherein ${\mathrm{\Σ}}^{\′}=E\[{\mathrm{\δ}}^{\′}{\mathrm{\δ}}^{\′T}\]=B^{\′}\mathrm{cov}\left(\hat{z}\right)B^{\′T},$

$B^{\′}=2\left[\begin{array}{ccccc}-(z_1-x_{b,1}-x_{b,2}-...-x_{b,M})& 0& 0& ...& 0\\ 0& -(z_2-y_{b,1}-y_{b,2}-...-y_{b,M})& 0& ...& 0\\ 2(M-1)z_1& 2(M-1)z_2& -z_3& ...& -z_{M+2}\end{array}\right];$

(D) (C) step acquired results is mapped to final target location to estimate:

$z_f=\sqrt{{\hat{z}}^{\′}}+{\left[\begin{array}{cc}{x}_{b,1}& y_{b,1}\end{array}\right]}^T+...+{\left[\begin{array}{cc}{x}_{b,M}& y_{b,M}\end{array}\right]}^T$

Or

$z_f=-\sqrt{{\hat{z}}^{\′}}+{\left[\begin{array}{cc}{x}_{b,1}& y_{b,1}\end{array}\right]}^T+...+{\left[\begin{array}{cc}{x}_{b,M}& y_{b,M}\end{array}\right]}^T.$