CN104883733A - Cooperative localization method of combining exterior penalty function method and Powell algorithm - Google Patents

Abstract

The present invention provides a cooperative localization method of combining an exterior penalty function method and a Powell algorithm. In a wireless sensing network, absolute coordinates can be obtained by utilizing the relative coordinates and by the coordinate system conversion, so that a problem can be solved by the known relative coordinates. According to the present invention, supposing that all distances among nodes can be measured by a time of arrival (TOA) method, and a relative position problem namely, the cooperative localization, among the nodes can be solved by establishing a nonlinear programming method. In a nonlinear programming problem, a programming problem with a constraint condition is resolved into the programming problem without constraint by utilizing an exterior penalty, and then the optimal solution problem of each node in the cooperative localization is solved by utilizing the Powell algorithm. By a simulation experiment, even on the condition that a ranging value is very large, the precision of the relative coordinates among the nodes also can be guaranteed, the initial coordinate influence is not obvious, the more is the number of the nodes, the stronger is the connectivity, and the final optimization precision is higher.

Description

A kind of colocated method that exterior penalty function method is combined with Powell algorithm

Technical field

The present invention relates to a kind of Nonlinear Programming Algorithm, namely extrapunitiveness method and Powell (Bao Weier) combination algorithm namely obtain the optimum coordinates solution meeting euclidean distance between node pair relation by the minimum problem solving function, and namely the problem efficiently solved without architecture only need know that internodal distance value just can calculate the relative coordinate of node.

Background technology

Colocated system has huge using value and market potential, is generally used for the region cannot disposing base station, and provides the service of position-based information for it, such as outdoor personnel tracking and merge the positioning precision etc. improving building periphery with GPS.TOA (Time of arrival, time arrive) distance-finding method has higher range accuracy, is distance-finding method conventional in current many object locating systems, have compared with GPS that equipment is small and exquisite, cost less, precision high.Nonlinear programming problem is the advantageous methods solving optimal solution problem, utilize extrapunitiveness method and Powell (Bao Weier) combination algorithm can solve without the colocated problem under base station case by structure target function and constraints, and precision is high, efficiency is fast, initial coordinate impact is less.

Summary of the invention

The technical problem to be solved in the present invention is, in positioning field, when the Location-Unknown of all nodes, only need the internodal distance value recorded by TOA, then the colocated method that this exterior penalty function method of proposition is combined with Powell algorithm is utilized, extrapunitiveness method is utilized to be combined the optimization problem solved in colocated with Powell by structure target function and constraints, the method can improve positioning precision, its method is simply effective, the feature such as have high accuracy, low amount of calculation, overhead is little, efficiency is fast.

For solving the problems of the technologies described above, the present invention proposes a kind of colocated method that exterior penalty function method is combined with Powell algorithm, comprises step:

(1) random arrangement node in TOA ranging region, when all node location the unknowns, the target function solving optimal solution is configured to by the distance measurement value between node, range error is gone out according to range error model assessment, bound for objective function is constructed by range error, make the minimum finding target function in the scope of constraints, as the optimal solution of the elements of a fix;

(2) by exterior penalty function method, target function and constraints are converted into unconfined planning problem, using calling Powell algorithm as input parameter ask the minimum of target function and corresponding elements of a fix result as output without constrained objective function, initial coordinate, distance measurement value after conversion;

(3) judge whether coordinate result meets the condition of convergence of exterior penalty function method, stop exterior penalty function iterated conditional if meet, export and optimize coordinate result; If do not meet, repeat step (2).

Further, the initial coordinate of step (1) interior joint is OriginalAxis=[(x ₁, y ₁), (x ₂, y ₂) ... (x _n, y _n)], wherein n is node number;

Target function $F={\mathrm{\Σ}}_{i=1}^n{\mathrm{\Σ}}_{j=i+1}^m{(\sqrt{{(x_i-x_j)}^2+{(y_i-y_j)}^2}-\mathrm{Dis}\tan {\mathrm{ce}}_{\mathrm{ij}})}^2$ Wherein x, y representation node coordinate, the distance between Distance representation node.

Further, the exterior penalty function method principle in described step (2) is: $P_{\mathrm{ij}}=\left\{\begin{array}{c}1,G_{\mathrm{ij}}>0\\ 0,G_{\mathrm{ij}}\≤0\end{array}\right.;$ Without constrained objective function be then $F^{\′}=F+{\mathrm{\Σ}}_{i=1}^n{\mathrm{\Σ}}_{j=i+1}^m{P}_{\mathrm{ij}}*G_{\mathrm{ij}}.$

Further, describedly determine that elements of a fix result comprises following two steps:

A) utilize advance and retreat method to determine the scope of the region of search, the gained region of search;

B) determine the region of search by advance and retreat method, recycling Fibonacci method determines step-size in search; The coordinate of unknown position node is tried to achieve eventually through Powel l algorithm.

Further, in described step (3), output condition is:

1. wherein F ₁for last iteration target function minimum, F ₂for current iteration target function minimum;

2. (X ₁-X ₂) ²≤ e ^-4wherein (X ₁for the coordinate vector that current iteration calculates, X ₂for the coordinate vector that last iteration calculates.

In the present invention, the distance supposing between node can be passed through TOA (Time Of Arrival, the time arrives method) and records.Internodal relative position problem is solved, i.e. co-positioned by the method setting up Non-Linear Programming.In nonlinear programming problem, utilize extrapunitiveness method that the planning problem of band Prescribed Properties is dissolved as unconfined planning problem, recycling Powell (Powell algorithm) solves the optimal solution problem of each node in co-positioned.Found by emulation experiment, even if when distance measurement value is very large, the precision of internodal relative coordinate also can be ensured, and initial coordinate impact and not obvious, node number is more, and connectedness is stronger, and final optimization precision is higher.

Accompanying drawing explanation

Fig. 1 is the flow chart of the colocated method that a kind of exterior penalty function method of the embodiment of the present invention is combined with Powell algorithm;

Fig. 2 is the true coordinate deployment diagram of embodiment of the present invention random distribution;

Fig. 3 is the coordinate deployment diagram that the embodiment of the present invention is calculated by the colocated method optimization that exterior penalty function method is combined with Powell algorithm;

Fig. 4 is embodiment of the present invention Powell (Bao Weier) algorithm flow chart;

Fig. 5 is the flow chart that the embodiment of the present invention utilizes the advance and retreat method determination region of search;

Fig. 6 is the flow chart that the embodiment of the present invention utilizes Fibonacci method determination step-size in search.

Embodiment

Below in conjunction with accompanying drawing, the present invention is described further:

See Fig. 1, the figure shows the colocated method that a kind of exterior penalty function method of the embodiment of the present invention is combined with Powell algorithm, specifically comprise step:

Step S101: when all need location node Location-Unknown, initial coordinate is OriginalAxis=[(x ₁, y ₁), (x ₂, y ₂) ... (x _n, y _n)].

Wherein n is node number.

Step S102: utilize internodal distance relation between two to construct objective function F,

Wherein $F={\mathrm{\Σ}}_{i=1}^n{\mathrm{\Σ}}_{j=i+1}^m{(\sqrt{{(x_i-x_j)}^2+{(y_i-y_j)}^2}-\mathrm{Dis}\tan {\mathrm{ce}}_{\mathrm{ij}})}^2$

Wherein x, y representation node coordinate, the distance between Distance representation node.

Then according to outdoor range error model, arrange range error E=ε, distance measurement value is larger than actual value under normal circumstances, and the scope being limited euclidean distance between node pair by range error can not exceed+ε, so carry out structure constraint condition by the scope of range error; Namely under line of sight conditions, produce average is 1.25, and variance is the range error of 0.5, and in non line of sight situation, produce average is 4.5, and variance is the range error of 0.5, by the random range error structure bound for objective function produced;

Wherein $G_{ij}=\sqrt{{\left(x_i-x_j\right)}^2+{\left(y_i-y_j\right)}^2}-{\mathrm{Distance}}_{ij}-\mathrm{\ϵ}$

Wherein x, y representation node coordinate, the distance between Distance representation node, ε represents range error.

Step S103: utilize exterior penalty function method that the target function of belt restraining is changed into the target function of not belt restraining,

Its exterior penalty function method principle is:

$P_{ij}=\left\{\begin{array}{cc}1,& G_{ij}>0\\ 0,& G_{ij}\≤0\end{array}\right.$

The then target function of not Problem with Some Constrained Conditions $F^{\′}=F+{\mathrm{\Σ}}_{i=1}^n{\mathrm{\Σ}}_{j=i+1}^m{P}_{ij}*G_{ij}.$

Step S104: utilize Powel l (Bao Weier) algorithm ask the minimum of the target function of not belt restraining and make to become minimizing coordinate figure, wherein Powel l (Bao Weier) calculates ratio juris and is divided into two steps to try to achieve with reference to the computational methods of λ in figure 4, Fig. 4:

1. utilize advance and retreat method to determine the scope of the region of search, the flow process of method of wherein retreating is as Fig. 5; Wherein a ₀=0, h=e ^-5, [a, the b] of gained is the region of search.

2. determine the region of search [a, b] by advance and retreat method, recycling Fibonacci method determines step-size in search λ, and wherein the flow process of Fibonacci method is as Fig. 6, and wherein gained approximate solution r is then required λ.

Can in the hope of the coordinate of unknown position node eventually through Powell (Bao Weier) algorithm

Step S105: by the condition of convergence, that is:

3. wherein F ₁for last iteration target function minimum, F ₂for current iteration target function minimum

4. (X ₁-X ₂) ²≤ e ^-4wherein (X ₁for the coordinate vector that current iteration calculates, X ₂for the coordinate vector that last iteration calculates

When simultaneously meet 1. 2. time, optimize terminate, then this coordinate calculated is final optimization coordinate, forwards step S106 to.

If do not meet, the coordinate OptimizeAxis after upgrading is re-used the target function that extrapunitiveness method calculates not Problem with Some Constrained Conditions, then repeats step S104.

Eventually through embodiment, final optimum results is as Fig. 3, wherein can be for communication between internodal line representation node, the co-positioned problem without base station can well be solved as seen from the figure by the method for Non-Linear Programming, by contrasting with Fig. 2 physical location, can find to be combined with Powel l (Bao Weier) algorithm by extrapunitiveness method that to process this problem precision very high.

The present invention also can have other various embodiments; when not deviating from the present invention's spirit and essence thereof; those skilled in the art are when making various corresponding change and distortion according to the present invention, but these change accordingly and are out of shape the protection range that all should belong to the claim appended by the present invention.

Claims (5)

1. the colocated method that is combined with Powell algorithm of exterior penalty function method, is applied to the sensor network system without base station, it is characterized in that, comprise the following steps:

(1) random arrangement node in TOA ranging region, when all node location the unknowns, the target function solving optimal solution is configured to by the distance measurement value between node, range error is gone out according to range error model assessment, bound for objective function is constructed by range error, make the minimum finding target function in the scope of constraints, as the optimal solution of the elements of a fix;

(2) by exterior penalty function method, target function and constraints are converted into unconfined planning problem, using calling Powell algorithm as input parameter ask the minimum of target function and corresponding elements of a fix result as output without constrained objective function, initial coordinate, distance measurement value after conversion;

(3) judge whether coordinate result meets the condition of convergence of exterior penalty function method, stop exterior penalty function iterated conditional if meet, export and optimize coordinate result; If do not meet, repeat step (2).

2. colocated method according to claim 1, is characterized in that, the initial coordinate of step (1) interior joint is OriginalAxis=[(x ₁, y ₁), (x ₂, y ₂) ... (x _n, y _n)], wherein n is node number;

Target function $F={\mathrm{\Σ}}_{i=1}^n{\mathrm{\Σ}}_{j+i+1}^m{(\sqrt{{(x_i-x_j)}^2+{(y_i-y_j)}^2}-\mathrm{Dis}\tan {\mathrm{ce}}_{\mathrm{ij}})}^2$ Wherein x, y representation node coordinate, the distance between Distance representation node.

3. colocated method according to claim 2, is characterized in that, the exterior penalty function method principle in described step (2) is: $P_{\mathrm{ij}}=\left\{\begin{array}{cc}1,& G_{\mathrm{ij}}>0\\ 0,& G_{\mathrm{ij}}\≤0\end{array}\right.;$ Without constrained objective function be then $F^{\′}=F+{\mathrm{\Σ}}_{i=1}^n{\mathrm{\Σ}}_{j=i+1}^m{P}_{\mathrm{ij}}*G_{\mathrm{ij}}.$

4. colocated method according to claim 3, is characterized in that, describedly determines that elements of a fix result comprises following two steps:

A) utilize advance and retreat method to determine the scope of the region of search, the gained region of search;

B) determine the region of search by advance and retreat method, recycling Fibonacci method determines step-size in search; The coordinate of unknown position node is tried to achieve eventually through Powell algorithm.

5. colocated method according to claim 4, is characterized in that, in described step (3), output condition is:

1. wherein F ₁for last iteration target function minimum, F ₂for current iteration target function minimum;

2. (X ₁-X ₂) ²≤ e ^-4wherein (X ₁for the coordinate vector that current iteration calculates, X ₂for the coordinate vector that last iteration calculates.