CN105242238A - Wireless network positioning technology based on particle auxiliary random search - Google Patents

Abstract

The invention discloses a wireless network positioning technology based on particle-assisted random search, which is used for the position related to the position of the positioned target established after receiving received signal energy parameters and coordinate position parameters from various reference nodes for the positioned target , and optimize the overall positioning objective function used to locate its own position, so as to improve the positioning accuracy. The invention can prevent the particle search from falling into the local optimal solution, and when the initial coverage of the search particles does not cover the global optimal solution, the global optimal solution can still be found. When the statistical information of the system is known, the uncertainty of the reference signal or the prior information of the system parameters can be included; at the same time, the credibility of the search particle and the detection particle is equivalent to the probability measure, and the global optimal solution found is Statistical mean square error minimum solution. The use of importance sampling particles can resist strong noise interference and distortion of nonlinear observation function, which makes the search technique more robust. Suitable for optimization of non-convex and non-concave objective functions under any criterion.

Description

A Wireless Network Location Technology Based on Particle-Assisted Random Search

technical field

The invention relates to wireless network positioning, in particular to an optimization method of a non-convex and non-concave objective function under nonlinear non-Gaussian conditions in wireless positioning.

Background technique

The optimization of non-convex and non-concave objective functions is a very important and open problem in the fields of wireless network positioning, statistical signal processing, wireless mobile communication, computer science and even basic mathematics. In the field of signal and communication applications, many problems can be transformed into parameter estimation and optimization problems, such as signal detection, time-varying channel estimation, frequency offset estimation, sparse signal reconstruction, adaptive filtering, decoding, wireless positioning and tracking Wait. However, due to the existence of non-ideal system factors (such as nonlinearity of system functions, Gaussian/non-Gaussian environmental noise, uncertainty of reference variables, etc.), the objective function is usually non-convex and non-concave, and even has no closed expression, which It brings serious difficulties to signal estimation, and it is difficult to find the globally optimal signal estimation.

Focusing on the optimization of non-convex and non-concave functions, a lot of research work has been carried out at home and abroad, and many research results have been obtained.

First of all, aiming at the nonlinear problem of the observation system, in 2000 and 2002, M. Arulampalam et al. respectively in the literature "Atutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking." Signal Processing, IEEE Transactions, 2002, 50.2:174-188 and the literature "Comparison of the particle In "Proc.Spie.Vol.4048.2000, the system summarizes a linearization method based on the first-order Taylor expansion for nonlinear system equations, and then estimates/filters the target variable according to the principle of the linear Gaussian filter system. . This method can simplify the nonlinear function of the system function, and then when the system has non-Gaussian interference or the system function is seriously nonlinear, the approximation error will make the method diverge.

Secondly, for the processing of non-Gaussian probability density functions in complex objective functions, the C.Taylor team proposed a method using Laplace approximation in the 2006 document "Simultaneous localization, calibration, and tracking inanad-hocsensor network." Proceeding of the 5th international conference on Information processing in sensor networks. ACM, 2006 To approximate the non-Gaussian probability density function in the objective function, making the optimization of the objective function easier. Similarly, in 2010, the Karl Friston team also proposed a method using Laplace approximation in the document "Variational free energy and the Laplace approximationNeuro-Image." ELSEVIER, vol.34, no.1, 2006, pp.220-234, and performed a Summary and analysis. In addition, in 2002, M. Arulampalam et al. in the literature "Atutorialonparticlefiltersforonlinenonlinear/non-GaussianBayesiantracking." SignalProcessing, IEEETransactionson, 2002, 50.2: 174-188 in view of the problem that the objective function has no closed expression, proposed the method of adopting the importance , which is used to approximate the non-Gaussian probability density function of the interference noise, and approximate the objective function. Domestic Wang Gang and others proposed a method based on tasteless transformation in the 2011 document "Anew approach to sensor node localization using RSS measurements in wireless sensor networks." IEEE Transactions on Wireless Communications, 10.5 (2011): 1389-1395, using a set of Sigma point sets to the first-order non-Gaussian probability density function and the second-order center distance to simplify the representation of complex objective functions.

In addition, in the optimization problem of the objective function induced by statistical information, there is no closed expression problem for the objective function caused by the uncertainty of the reference variable. In 2009, M. Vemula et al. in the literature "SensorSelf-localizationwithBeaconPositionUncertainty." Signal Processing. In vol.89, no.6, 2009, pp.1144-1154, the method of adopting importance is proposed, so that the integral in the complex objective function is transformed into a simple and easy-to-handle finite term sum. Also for the problem that the objective function has no closed expression, variational inference provides another way of thinking, which uses a set of independent, virtual probability distributions to approximate the complex posterior probability objective function, by minimizing the virtual probability distribution The singularity between the distribution and the target probability density function is used to find the expression of the best approximation of the target function, so that the complex target function is decomposed into several independent and easy-to-handle virtual probability distributions. For example, in 2008, D.G.Tzikas et al. proposed variational Bayesian to solve Bayesian under complex posterior probability density functions in the document "The Variational Approximation for Bayesian Inference," IEEE Signal Processing Magazine, Vol.25, No.6, 2008, pp. method of reasoning about the problem. Similarly, C.W.Fox et al systematically summarized and analyzed the principles and methods of variational inference in the 2012 document "ATutorialonVariationalBayesianInference," Artificial Intelligence Review Vol.38, No.2, 2012, pp.85-95.

Furthermore, for the non-convex and non-concave problem of the objective function, O. Wentao et al. in the 2010 document "Received Signal Strength-based Wireless Localization via Semi-definite Programming: Non-cooperative and Cooperative schemes." Vehicular Technology, IEEETransactionson.vol.59, no.3, 2010, pp In .1307-1318, for the cooperative and non-cooperative localization problem, a semi-positive definite optimization method is proposed to relax the non-convex and non-concave objective function into a convex function. In the 2011 document "Particles warm optimization in wireless-sensor networks: Abrief survey." Systems, Man, and Cybernetics, Part C: Applications and Reviews, IEEE Transactions, 41.2 (2011): 262-267, Kulkarni et al. adopted the idea of particle swarm optimization, using a set of random particles to search for the global optimum. Similarly, T. Stoyanova et al. adopted a similar idea in the 2014 document "RSS-based localization for wireless sensor network in practice." Proc. of 20149th International Symposium on Communication Systems, Networks & Digital Signal Processing (CSNDSP), 2014. However, since the local search of its search particles only depends on its search particle Therefore, when the initial distribution of search particles does not cover the global optimum, the algorithm can only converge to the local optimum of the initial coverage, not the global optimum.

A comprehensive analysis of the current research results around the optimization of complex non-convex and non-concave objective functions and parameter estimation problems at home and abroad, there are a lot of results that can be used for reference; however, most of the current research results are only for a certain problem in a specific situation Solve the influence of system nonlinearity, reference uncertainty, non-Gaussian interference, etc. on the optimization problem, and then did not propose a systematic and reliable framework for solving the problem, in order to expect to search for the global optimal solution, and give the target variable Optimal estimation, thereby improving positioning accuracy and reliability.

Contents of the invention

In view of the above deficiencies in the prior art, the purpose of the present invention is to adopt particle-assisted random search ideas in wireless positioning, and propose a framework for finding the global optimal solution of complex non-convex and non-concave objective functions, in order to improve positioning accuracy and robustness.

The technical solution adopted by the present invention to solve its technical problems is as follows:

A wireless network positioning technology based on particle-assisted random search, which is used to establish the position of the target after receiving the received signal energy parameters and its coordinate position parameters from each reference node, and is used to locate its own position and communicate with the positioned target. The total objective function of positioning related to the target position is optimized to improve the positioning accuracy and robustness, including the following sequential steps:

(1) First, the positioning system responds and establishes the positioning objective function:

The positioned target sends a positioning request;

The surrounding reference nodes respond and send positioning signals;

The positioning center extracts the positioning parameters and establishes the positioning target function;

(2) Then, generate a group of initial search particles, that is, the initialization of search particles:

Generate a group of search particles according to the prior distribution of the target variable; or randomly and uniformly generate search particles within the feasible domain of the target variable;

(3) Then, determine the global optimal update direction of each search particle:

Equip each search particle with a set of proposal particles

Use the proposed particles equipped with each search particle to calculate the credibility of each search particle;

After obtaining the reputation of all search particles, find the search particle with the highest reputation among all particles, so as to determine the global best update direction;

(4) Second, determine the local optimal update direction of each search particle:

Equip each search particle with a set of detector particles

Equip each probe particle with a set of proposed particles

Use the proposed particles equipped with each detection particle to calculate the credibility of each detection particle

After calculating the credibility of all the detection particles of each search particle, determine the detection particle with the highest credibility in the detection particle set of each search particle, and use this to determine the local optimal update direction of each search particle

(5) Furthermore, each search particle is updated according to the obtained global best update direction and local best update direction;

According to steps (3)-(5), continuously iterate on each search particle like this: find the global optimum + find the local optimum -> update the search particles until all the search particles converge

(6) Finally, determine the estimation of the target parameters according to the obtained converged search particles:

· Estimate the target variable according to the principle of the minimum estimated mean square error, and the output result is the position of the target being located.

The algorithm of the present invention is different from the traditional algorithm, compared with the prior art scheme shown in Figure 8:

(1) The algorithm of the present invention refers to the proposed particle in the determination method of the global optimal update direction of the search particle to counteract the influence of external interference on the algorithm, making the algorithm more stable

(2) The algorithm of the present invention refers to the detection particles and the proposed particles in the determination method of the local optimal update direction of the search particles, so that the algorithm not only has stable performance, but also has strong local search capabilities.

(3) On the parameter estimation method, the algorithm of the present invention adopts the estimation method of the least mean square error principle, so that its estimation error is smaller than that of the original traditional algorithm.

Generally speaking, the beneficial effects of the present invention are mainly manifested in the following four aspects.

(1) Since the global optimal solution and the optimal solution in the adjacent area are comprehensively considered in the iterative update of the search particles, it can prevent the particle search from falling into the local optimal solution; especially, when the initial coverage of the search particles does not cover When the global optimal solution is found, this technology can still find the global optimal solution.

(2) When the statistical information of the system is known, the search technology can incorporate the uncertainty of the reference signal or the prior information of the system parameters; at the same time, the credibility of the search particle and the detection particle is equivalent to the pair of probability measures. number, so in this case, the global optimal solution found by this search technique is the minimum mean square error solution in the statistical sense.

(3) With the assistance of importance sampling particles, this search technology can resist the influence of strong noise interference, distortion of nonlinear observation function, and uncertainty of reference variables, making the search technology and variable estimation more robust.

(4) This search technique is not only applicable to non-convex and non-concave objective functions based on statistics, but also suitable for the optimization of non-convex and non-concave objective functions under any other criteria.

Description of drawings

Figure 1 is a mathematical model suitable for implementing the technique of the present invention.

FIG. 2 is a schematic diagram of the objective function lnp(x|z) of the technology of the present invention.

Fig. 3 is a schematic diagram of the connotation of the technology of the present invention.

Fig. 4 is a schematic diagram of the implementation process of the technology of the present invention.

Fig. 5 is the positioning error of the technology of the present invention in wireless positioning.

Fig. 6 is the iterative update trajectory of the search particle in the technology of the present invention.

Fig. 7 is the iterative update trajectory of the search particles of the traditional particle swarm optimization algorithm.

Fig. 8 is a block diagram of algorithm steps in the prior art.

detailed description

In order to have a more detailed understanding of the details of the present invention, the details of the steps of the present invention will be further introduced below.

1. Extraction of positioning parameters and establishment of positioning target function

First, the target to be located sends a positioning request to its surrounding nodes.

Then, the network nodes around the positioned target detect the positioning request and respond (assuming that the number of nodes participating in the response is M, these nodes are called the reference nodes of the positioned target); at the same time, measure the radio frequency of the positioning request sent by the positioned target wave signal energy. The energy parameter is denoted as z _i (unit is dBm), and i is the reference node number.

Furthermore, each reference node sends positioning parameters to the positioned target (or the positioning processing center), including the radio wave energy z _i measured by the reference node from the positioned target, and the location coordinates ( The location coordinates of the i-th reference node are denoted as s _i ).

Then, the positioned target (or the positioning processing center) receives received signal energy parameters z _i and its coordinate position parameters s _i from each reference node.

Then, the positioned target (or the positioning processing center) establishes a positioning objective function g related to the position of the positioned target (denoted as x) for locating its own position according to each received positioning parameter z _i and _si (x; z _i , s _i ). Then, according to the positioning parameters from M reference nodes, M objective functions g(x; z ₁ , s ₁ ), g(x; z ₂ , s ₂ ), ..., g(x; z _M , s _M ).

Finally, according to these M objective functions, the total objective function is established in Represents the multiplication of M functions.

2. Initialization of random search particles

■Initialization of random search particles

Given a (statistics-based or non-statistics-based) objective function f(x), its initial search particle set It can be generated in the following two ways (wherein, m represents the serial number of the search particle x ₁ (m), N _S represents the number of search particles, and the subscript 1 represents that the particle set is the initial particle set, that is, the iteration number k=1):

If the prior statistical information p(x) of the target variable x is known, then the N _S initial search particles can be generated according to its prior distribution p(x)

If the prior distribution p(x) of the target variable x is unknown, then the initial particles will be randomly and uniformly generated in the defined domain.

3. Determine the global best update direction

■ Particle reputation calculation

Given the set of search particles in the kth iteration process Search for the reputation corresponding to the particle x _k (m) is given by the following formula (where k represents the iteration number):

in, Indicates the importance sampling particle set (i.e. the proposed particle set) corresponding to the search particle x _k (m), x _k (m; n) represents the nth proposed particle corresponding to the search particle x _k (m), ω _k (m; n) represents the weight corresponding to the proposed particle, n represents the number of the proposed particle, N _M represents the number of proposed particles; at the same time, search for the proposed particle set corresponding to the particle x _k (m) is distributed as proposed to be randomly generated, where Θ represents the precision matrix of the proposed distribution. in addition, Indicates that all variables/items involved are summed according to the number n from 1 to _NS .

As for the calculation method of the objective function f(x _k (m; n)) corresponding to the proposed particle x _k (m; n), it is assumed that the original objective function f(x) is a logarithmic posterior probability density function lnp(x|z _i ), then its calculation method can be specifically expressed as follows:

Among them, we assume that the target variable has prior distribution p(x) and likelihood distribution p(z _i |x, s _i ), then It means that the proposed particle x _k (m; n) corresponds to the value of the probability density function under the prior distribution p(x) of the target variable, and It is the function value of the proposed particle x _k (m; n) corresponding to the likelihood probability density distribution p(z _i |x, s _i ). In addition, the symbol s _i represents the i-th uncertainty reference variable, and the set Indicates the proposed particle set corresponding to the reference variable s _i , which is used to approximate the prior distribution p( _si ) of the uncertain reference variable; where, t represents the number of the particle in the proposed particle set, and s _i (t) represents the t proposed particles, Indicates its corresponding particle weight. In addition, _zi represents the i-th observation sample related to the reference variable s _i and the target variable x, and Ψ represents the total number of observation samples (here it is assumed that one reference variable corresponds to one observation sample).

■ Determine the global best update direction

Get the search particle and its corresponding reputation Afterwards, the global optimal update direction is defined as the difference vector between the global optimal search particle and the current search particle: in Represents the globally optimal search particle position, which is defined as the reputation of all search particles The largest search particle, that is, where the symbol Indicates the meaning of selecting the variable x _k (m) with the largest corresponding element in the given set {·}.

4. Determine the local best update direction

■ Detection of particle generation

In the present invention, each random search particle x _k (m) is equipped with a set of detection particles whose size is N _D It is used to find the local optimal update direction of the search particle x _k (m) (the superscript τ represents the number of the detection particle), and these detection particles are centered on the search particle x _k (m) with a detection step length Randomly and uniformly generated according to the circumference angle on a circle with L as the radius:

Among them, rand(0, 2π) means a uniform distribution within (0, 2π), and the symbol ~ means "the variable on the left is generated according to the probability density on the right" (or the variable on the left obeys the distribution on the right).

■Calculation of credibility of detected particles

get probe particle After that, its corresponding reputation Calculated as:

collection of them Indicates the detected particle The corresponding proposed particle set, n represents the proposed particle number of Indicates the detected particle The nth proposed particle of , represents the proposed particle The weight of , N _M represents the total number of proposed particles; and Denotes its corresponding proposal distribution, is the corresponding integrated variable; Indicates that the variables or items involved are summed according to the number n from 1 to _NS .

At the same time, if the objective function f(x) is assumed to be a logarithmic posterior probability density function lnp(x|z _i ), then its detection particle Corresponding objective function Calculated as follows:

in, proposed particle Corresponding to the value of the probability density function under the prior distribution p(x) of the target variable, and proposed particle Corresponds to the function value of the likelihood probability density distribution p(z _i |x, s _i ).

■Find the local best update direction

get each probe particle of the search particle x _k (m) reputation Then the optimal update direction of the local area of x _k (m) is defined as the difference vector between its best detection particle and the current search particle x _k (m): in Represents the best detection particle of the search particle x _k (m), which is defined as the credibility of all detection particles of the search particle x _k (m) The largest detected particle, that is,

At the same time, it should be noted that if the credibility of the current search particle is greater than the credibility of all the detection particles it is equipped with (ie ), then set the local optimal update direction of the search particle x _k (m) as the zero vector (y _k (m) = 0, that is, x _k (m) will not consider the local optimal update direction in this iterative update best information, only consider the global best information).

5. Search particle updates

According to the above steps, the global optimal update direction of the search particle x _k (m) can be obtained and the local optimal update direction y _k (m), then the next-generation search particle x _k+1 (m) will be based on the original search particle x _k (m) plus the weighted calculation of these two update directions and items are updated iteratively:

Wherein, γ ₁ and γ ₂ represent the update step size, and γ ₁ , γ ₂ ≥0 and 0<γ ₁ +γ ₂ ≤1. All other search particles are iteratively updated according to the above formula.

According to steps 3 to 5, repeat (determine the global optimal update direction, determine the local optimal update direction, search particle update) until the search particle iteration converges.

6. Parameter estimation and positioning result output

The search particles in the random search technology are continuously updated according to the above iterative formula, and can finally converge to the global optimal point. Then, during the kth iteration of the search particles, or when the search particles finally converge, according to these search particles and their corresponding reputation Then the target variable x can be estimated.

There are two situations here that the present technique can take into account. Now introduce them separately and estimate the variables.

(1) Assume that the objective function f(x) is a function induced according to the statistical information of the system, such as the logarithmic likelihood function (such as lnp(z _i |x)) or the logarithmic posterior probability density function (such as lnp(x| z _i )), then, according to the minimum mean square error criterion, or the maximum likelihood probability/maximum posterior probability criterion, the following two estimates can be obtained for the distribution:

Among them, the function exp(·) represents an exponential function with the base e of the natural logarithm. In other words, the least mean square estimate of the target variable is the exponential function of all search particles x _k (m) in their credibility and the maximum likelihood/posteriori estimation is to find the search particle with the highest reputation as the estimation of the target variable.

(2) If the objective function is induced by non-statistical information, such as the reciprocal of the error norm etc., then, according to the minimum estimation error norm criterion, we can get:

Finally, the parameter estimation when the algorithm converges It is used as the final estimation of the algorithm of the present invention, that is, the positioning output of the wireless network positioning system—the position estimation of the positioned node.

Example

The method of the present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

First, the target to be positioned sends a positioning request; then the positioning system responds, and extracts the positioning parameters _si (that is, the position of the i-th reference node) and _zi (that is, the received signal energy detected by the i-th reference node) .

According to the attenuation law of radio wave energy in the wireless positioning system, the observation data z _i can be expressed as the target variable x (that is, the position of the target node) and the i-th reference variable s _i , through the system nonlinear observation function h(x, s The output of the action of _i ), and add the additive observation noise ε _i :

z _i = h(x, s _i )+ε _i .

In wireless sensor networks, the nonlinear observation function of wireless positioning based on observed signal strength can be expressed as a logarithmic function:

h(x, s _i )＝φ _i -10ρlog ₁₀ ||xs _i || ₂ ,

Among them, φ _i and ρ are given known constants, and ||·|| ₂ represents the two-norm of the vector.

However, in wireless positioning applications, due to the existence of positioning errors, the reference variable s _i (that is, the coordinates of the reference node) is usually inaccurate. Without loss of generality, assume it follows a Gaussian distribution: Where U _i is the Gaussian distribution accuracy matrix of s _i ; at the same time, it is assumed that the target variable x has a Gaussian prior distribution where u is its mean parameter, and is the corresponding precision matrix. In addition, it is assumed that the additive observation noise follows a Gaussian distribution with zero mean, namely where w _i is the observation precision. Assume that the target to be located has a total of Ψ observation data, and define a new observation vector where the symbol Represents the transpose of a vector or matrix. Figure 1 introduces the mathematical model corresponding to the positioning system.

According to these known statistical information, the objective function lnp(x|z) of the logarithmic posterior probability density can be obtained, so as to maximize the objective function to estimate the target variable. Specifically, according to the above statistical information, and assuming that the observations are independent of each other, the corresponding likelihood function can be described as:

in, Indicates to multiply all items numbered i∈Ψ, and the symbol ∈ means "belongs to".

Furthermore, the posterior probability density function corresponding to the target variable can be expressed as:

Among them, ∝ means "in direct proportion", |·| means to take the absolute value (for scalar).

However, due to the existence of the nonlinear observation function h(x, s _i ), the uncertainty of the reference variable s _i , and the interference of additive noise, the objective function lnp(x|z) is usually non-convex and non-concave , that is, there are multiple local optimal values, and the surface of the objective function is extremely rough and unstable, as shown in Figure 2. This brings difficulties to the search, optimization, and estimation of optimal variables.

According to the spirit of the technology of the present invention, in this embodiment, we will find the global optimal variable position by processing the non-convex and non-concave objective function lnp(x|z), so as to obtain the least mean square estimation, or maximum a posteriori estimation.

For convenience, the objective function lnp(x|z) is uniformly replaced by f(x) in the subsequent introduction. It should be noted that the present invention is not only applicable to objective functions based on statistical information (such as logarithmic posterior lnp(x|z), or logarithmic likelihood lnp(z|x), etc.), but also applicable to objective functions without statistical information The objective function where available, or an objective function related to the error norm, such as

Then, according to the connotation of the random search technology of the present invention, the specific implementation steps are as follows.

First, according to the prior distribution of the target variable generate a set of random search particles The parameter m represents the number of the search particle x _k (m), and N _S represents the number of search particles (here, since it is an initial search particle, its iteration number k is actually k=1).

Then, calculate the credibility of each search particle x _k (m) according to the following formula

in, Indicates the proposed particle set corresponding to the search particle x _k (m), the parameter n represents the number of the proposed particle, x _k (m; n) represents the nth proposed particle, ω _k (m; n) represents the proposed particle x _k ( The weights corresponding to m; n); and the proposed particle set is generated from the Gaussian proposal distribution centered on the current search particle x _k (m) where Θ represents the precision matrix of the proposed distribution. In addition, the objective function f(x _k (m; n)) corresponding to each proposed particle is calculated according to the following formula:

h(x _k (m; n), s _i (t)) = φ _i -10ρlog ₁₀ || x _k (m; n) - s _i (t)|| ₂ ,

in, Indicates the set of proposed particles corresponding to the reference variable s _i , which is used to approximate the prior distribution of the uncertain reference variable Here, the parameter t represents the number of the proposed particle s _i (t), Indicates the weight of the proposed particle s _i (t). At the same time, in the above formula, det( ) means to find the determinant of the matrix, Represents the transpose of a vector or matrix. In addition, in this embodiment, the target variable x has prior distribution p(x) and likelihood distribution p(z _i |x, s _i ), then It means that the proposed particle x _k (m; n) corresponds to the value of the probability density function under the prior distribution p(x) of the target variable, and It is the function value of the proposed particle x _k (m; n) corresponding to the likelihood probability density distribution p(z _i |x, s _i ).

Furthermore, according to the obtained credibility of all search particles x _k (m) To determine the global optimal update direction of each search particle. The global best update direction for each search particle x _k (m) Defined as the global best search particle The difference vector with the search particle x _k (m), namely Among them, the global optimal search particle Defined as the search particle with the highest reputation among all search particles:

Second, for each search particle x _k (m) is equipped with a set of detection particles Among them, the superscript τ represents the detection particle , N _D represents the number of detected particles. Specifically, the probe particle of search particle x _k (m) It is randomly and uniformly generated according to the circumference angle on a circle centered on the current search particle x _k (m) and with the detection step length L as the radius, namely:

Then, for each detected particle credibility of:

in, Indicates the detected particle The corresponding set of proposed particles, the parameter n represents the proposed particle number of Indicates the detected particle The nth proposed particle of , Indicates the weight of proposed particles, N _M indicates the number of detected particles; detected particles The corresponding proposed particle set is based on the current detected particle Gaussian proposal distribution centered on randomly generated, where Θ represents the precision matrix of the proposed distribution, namely:

In addition, each proposed particle Corresponding objective function Calculate according to the following formula:

in, Indicates the set of proposed particles corresponding to the reference variable s _i , which is used to approximate the prior distribution of the uncertain reference variable Here, the parameter t represents the number of the proposed particle s _i (t), Indicates the weight of the proposed particle s _i (t). In addition, in this embodiment, the target variable x has prior distribution p(x) and likelihood distribution p(z _i |x, s _i ), then represents the proposed particle Corresponding to the value of the probability density function under the prior distribution p(x) of the target variable, and proposed particle Corresponding to the function value of the likelihood probability density distribution p(z _i |x, s _i ).

Furthermore, according to the obtained credibility of these detection particles, find the detection particle with the highest credibility,

The best update direction for the local area of the search particle x _k (m) can be obtained. The local optimal update direction of the search particle x _k (m) is defined as its optimal detection particle The difference vector with the current search particle x _k (m):

Finally, according to the global best update direction and local best update direction obtained above, the final update direction of the search particle is the weighted average of the local best and the best of the whole play, namely:

Wherein, γ ₁ and γ ₂ represent the update step size, and γ ₁ , γ ₂ ≥0 and 0<γ ₁ +γ ₂ ≤1.

Repeatedly, all search particles are iterated continuously (determine the global best update direction, determine the local best update direction, and then search particle update), until convergence or reach the maximum number of iterations.

Correspondingly, during each iteration of searching for particles, the target variable is estimated simultaneously. According to the minimum mean square criterion or the maximum a posteriori criterion, there are two estimation methods:

Among them, the least mean square estimation (the first estimator in the above formula) in the embodiment of the present technology is the optimal estimation in the statistical sense.

Figure 3 and Figure 4 respectively provide a simple schematic diagram of the technical connotation and a schematic diagram of the implementation process. Its technical connotation and implementation process are consistent with the foregoing description, and more concisely reflect the spirit of the technology of the present invention.

In order to verify the implementation performance of the particle-assisted random search technology of the present invention in this case, we consider to simulate and verify its positioning performance in wireless sensor network positioning according to the relevant parameters in Table 1 below.

Table 1 Simulation parameters under the condition of fixed frequency offset

Note: The symbol I represents the identity matrix under the same matrix dimension.

The corresponding collaborative positioning accuracy is shown in Figure 5. It can be seen from the figure that since its novel search strategy can resist the distortion of the nonlinear system function and the uncertainty of the reference variable, the technology of the present invention can make the search particles quickly converge to the global optimum; thereby improving the approximation efficiency of the search particles to the objective function , through its optimal estimator, the variable estimation with smaller error than the traditional particle swarm optimization algorithm (PSO) and the estimation algorithm based on importance (ISP) is obtained.

In order to verify the search capability of the technology of the present invention, this implementation case deliberately tests a special scenario - the situation when the initial search particles do not cover the global optimal solution. Therefore, for the initial search particle, we artificially introduce a large offset so that it does not cover the global optimum as follows:

Figure 6 and Figure 7 show the search capabilities of the technology of the present invention and the traditional PSO technology respectively. It can be seen from the figure that since the local search strategy of the traditional PSO algorithm only depends on the historical trajectory of the search particles, when the initial distribution of the search particles does not cover the global optimum, the search particles can only converge within the initial distribution range The local optimum can not be searched for the global optimum. However, because the technology of the present invention adopts a local search strategy based on detection particle assistance, it can search for the global optimum.

Those of ordinary skill in the art clearly understand and understand that the above examples of the method of the present invention are only used to illustrate the method of the present invention, and are not intended to limit the method of the present invention. While the invention has been effectively described by way of example for the guidance of those of ordinary skill in the art, there are many variations of the invention without departing from the spirit of the invention. Without departing from the spirit and essence of the method of the present invention, those skilled in the art can make various corresponding changes or deformations according to the method of the present invention, but these corresponding changes or deformations all belong to the claims of the method of the present invention protected range.

Claims (1)

1. A wireless network positioning technology based on particle-assisted random search is used for optimizing a positioning total objective function which is established after a positioned target receives a received signal energy parameter and a coordinate position parameter thereof from each reference node and is related to the position of the positioned target and used for positioning the position of the positioned target, so as to improve the positioning accuracy and the robustness, and comprises the following steps of sequentially executing:

(1) first, the positioning system responds and establishes a positioning objective function:

sending a positioning request by the positioned target;

its surrounding reference nodes respond and send positioning signals;

extracting positioning parameters by the positioning center and establishing a positioning target function;

(2) then, a set of initial search particles is generated, i.e. the initialization of the search particles:

generating a set of search particles according to the prior distribution of the target variables (i.e. the coordinate variables of the located target); or randomly and uniformly generating search particles within the feasible definition domain range of the target variable;

(3) then, the global best update direction for each search particle is determined:

prepare a set of proposed particle sets for each search particle

Calculating the reputation degree of each search particle by using the proposed particle set equipped by each search particle;

according to the obtained credibility of all the search particles, finding the search particle with the highest credibility in all the particles so as to determine the global optimal updating direction;

(4) secondly, the local best update direction of each search particle is determined:

equipping each search particle with a set of probe particle sets

Set of proposed particle sets for each probe particle

Calculating the reputation of each probe particle using the set of proposed particles with which each probe particle is equipped

After the credibility of all the detection particles is obtained through calculation, the detection particle with the maximum credibility in the detection particle set of each search particle is determined, and the local optimal update direction of each search particle is determined according to the detection particle set

(5) Updating each search particle according to the obtained global optimal updating direction and local optimal updating direction;

repeating the steps (3) - (5), and continuously iterating each search particle in a way of finding global optimum + finding local optimum- > searching particle update until all the search particles are converged

(6) Finally, an estimate of the target variable is determined from the obtained converged search particles:

and estimating the target variable according to the principle of minimum estimation mean square error, wherein the output result is the position of the located target.