CN105242238A - Wireless network positioning technology based on particle auxiliary random search - Google Patents
Wireless network positioning technology based on particle auxiliary random search Download PDFInfo
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Abstract
The invention discloses a wireless network positioning technology based on particle auxiliary random search, and is used for performing optimization processing on a positioning general objective function which is established after the positioned targets receive receiving signal energy parameters from all reference nodes and coordinate position parameters thereof, correlated to the position of the positioned targets and used for positioning location of the positioned targets so that positioning precision can be enhanced. Particle search can be prevented from being trapped in a local optimal solution. When initial coverage range of search particles does not cover a global optimal solution, the global optimal solution can still be found. When statistical information of the system is known, uncertainty of a reference signal or prior information of the system parameters can be included; meanwhile, the credibility of the search particles and detection particles is equivalent to probability measure, and the found global optimal solution is the mean square error minimal solution in the statistical sense. High-noise interference and distortion of a non-linear observation function can be resisted by using importance sampling particles so that the search technology is enabled to be more robust. The wireless network positioning technology based on the particle auxiliary random search is suitable for optimization of a non-convex non-concave objective function under any criteria.
Description
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 in wireless positioning.
Background
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 translated 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, and the like. However, due to the existence of non-ideal system factors (such as nonlinearity of system function, gaussian/non-gaussian environmental noise, uncertainty of reference variable, etc.), the target function is usually non-convex and non-concave, even has no closed expression, which brings serious difficulty to signal estimation and makes it difficult to find a globally optimal signal estimation.
Around the optimization problem of the non-convex and non-concave functions, a great deal of research work is carried out at home and abroad, and a lot of research results are obtained.
First, in 2000 and 2002, m.arulamaram et al in the documents "atom specific filter for on-line linear, non-gaussian bayesian, signaling processing, ieee transformation, 2002,50.2: 174-. The method can simplify the non-linear function of the system function, and then the approximation error can make the method diverge when the system has non-Gaussian interference or the system function is seriously non-linear.
Secondly, for the processing of non-gaussian probability density functions in complex objective functions, the c.taylor team in 2006 document "simultaneousization, calibrmation, and, as a-hocsensory network," proceedings software 5, international correlation information on networks, acm,2006 proposes to approximate non-gaussian probability density functions in the objective functions by using a laplacian approximation method, so that the optimization of the objective functions becomes simpler. Similarly, the method using the Laplace approximation was also proposed by KarlFriston team in the document "VariationnatrienopropriationNeuro-image," ELSEVIER, vol.34, No.1,2006, pp.220-234 in 2010 and was summarized and analyzed. In 2002, m.arulampaam et al, in the document "attribute on particle filters for on line linear/non-gaussian bayesian analysis," signal processing, ieee transaction, 2002,50.2: 174-. In 2011, the document "Anewapproachthostanenssochlelation RSSmeasurementWirelesssensingworks", 10.5(2011): 1389-.
In addition, in the optimization problem of the objective function induced by the statistical information, there is no closed expression problem for the objective function caused by the uncertainty of the reference variable, and in 2009, m.vemula et al propose a method for adopting importance in the document "SensorSelf-localization with beacon position uncertainty," signaling processing.vol.89, No.6,2009, pp.1144-1154, so that the integral in the complex objective function is converted into a simple and easily-processed finite term sum. Similarly, another idea is provided for the problem that the target function has no closed expression, variation inference is carried out, the complex posterior probability target function is approximated by utilizing a group of mutually independent and virtual probability distributions, and the expression of the optimal approximation of the target function is found by minimizing the singularity between the joint distribution of the virtual probability distributions and the target probability density function, so that the complex target function is decomposed into several independent and easily-processed virtual probability distributions. For example, in 2008, d.g. tzikas et al, the document "the variational approximation for bayesian inference," ieee signaling processing magazine, vol.25, No.6,2008, pp.131-146, proposed a method for solving the bayesian inference problem under the complex posterior probability density function by using the variational bayesian. Similarly, the principles and methods of variable inference are systematically summarized and analyzed in the 2012 article "ATutoralon variational Bayesian interference," artificial IntelligneReviewVol.38, No.2,2012, pp.85-95, by C.W.Fox et al.
Furthermore, for the Non-convex and Non-concave problem of the target function, in the document "received signal strong-based wireless localization within a system of Non-collaborative and Non-collaborative positioning," vehicle technology, ieee transformation vol.59, No.3,2010, pp.1307-1318 by o.wentao et al in 2010, a method of applying semi-positive optimization is proposed for the cooperative and Non-cooperative positioning problem to relax the Non-convex and Non-concave target function into a convex function. Kulkarni et al, 2011 in "particle swarm optimization Wireless-sensornetworks," Systems, Man, and cybernetics, PartC, applied and reviews, IEEETransactionson,41.2(2011): 262-. Similarly, the document "RSS-based localization for wireless sensing Networks and communications systems", Networks & digital signal processing (csndsp) "by t.stoyanova et al in 2014 adopts a similar idea, however, since its local search for particles only depends on the historical trajectories of the particles it searches for, when the initial distribution of the particles does not cover the global optimum, its algorithm can only converge to the local optimum of the initial coverage, rather than the global optimum.
Comprehensively analyzing the research results of the optimization and parameter estimation problems of the complex non-convex and non-concave objective function at present at home and abroad, and a large number of results can be used for reference at present; however, most of the current research results only aim at a certain problem under a specific condition, the influence of system nonlinearity, reference uncertainty, non-gaussian interference and the like on the optimization problem is not comprehensively solved, and a systematic and reliable framework for solving the problem is not provided so as to hopefully search a global optimal solution and provide optimal estimation of a target variable, thereby improving the positioning accuracy and reliability.
Disclosure of Invention
In view of the above shortcomings in the prior art, the present invention aims to adopt a random search concept based on particle assistance in wireless positioning, and proposes a framework for finding a global optimal solution of a complex non-convex and non-concave objective function, so as to improve positioning accuracy and robustness.
The technical scheme adopted by the invention for solving the technical problems is as follows:
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, is used for positioning the position of the positioned target and is related to 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 variable; 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 particles for each search particle
Calculating the reputation degree of each search particle by using the proposed particle equipped by each search particle;
after the reputation degrees of all the search particles are obtained, finding the search particle with the highest reputation degree from all the search particles, and determining 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 particles
For each probe particle, a set of proposed particles
Calculating the reputation of each probe particle using the proposed particle with which each probe particle is equipped
After calculating the credibility of all the detection particles of each search particle, determining the detection particle with the highest credibility in the detection particle set of each search particle, and determining the local optimal update direction of each search particle according to the detection particle set
(5) Updating each search particle according to the obtained global optimal updating direction and local optimal updating direction;
according to the steps (3) - (5), continuously iterating each search particle in the way of finding global optimum + finding local optimum- > searching particle update until all the search particles are converged
(6) Finally, determining an estimate of the target parameter 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.
The difference between the algorithm of the present invention and the conventional algorithm is that compared with the prior art scheme shown in fig. 8:
(1) the algorithm of the invention introduces the proposal particles on the determination method of the global optimum updating direction of the search particles to resist the influence of external interference on the algorithm, so that the algorithm is more stable
(2) The algorithm of the invention introduces the detection particles and the proposal 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 capability.
(3) In the parameter estimation method, the algorithm adopts an estimation method based on the minimum mean square error principle, so that the estimation error of the algorithm is smaller than that of the original traditional algorithm.
In summary, the beneficial effects of the present invention are mainly expressed in the following four aspects.
(1) The global optimal solution and the optimal solution of the adjacent area are comprehensively considered in the iterative updating of the search particles, so that the particle search can be prevented from being trapped in the local optimal solution; in particular, when the initial coverage of the search particle does not cover the global optimal solution, the technology can still find the global optimal solution.
(2) When the statistical information of the system is known, the search technique may incorporate a priori information of the uncertainty of the reference signal or the system parameters; meanwhile, the credit degrees of the search particles and the detection particles are equivalent to the logarithm of the probability measure, so that in this case, the global optimal solution found by the search technology is the minimum solution of the mean square error in the statistical sense.
(3) By the aid of the importance sampling particles, the search technology can resist strong noise interference, distortion of a nonlinear observation function and influence of uncertainty of a reference variable, so that the search technology and variable estimation are more robust.
(4) The search technique is applicable not only to non-convex and non-concave objective functions based on statistics, but also to optimization of non-convex and non-concave objective functions under any other criteria.
Drawings
FIG. 1 is a mathematical model suitable for implementing the techniques of the present invention.
FIG. 2 is a diagram of an objective function lnp (x | z) of the present technique.
FIG. 3 is a conceptual diagram illustrating the teachings of the present invention.
FIG. 4 is a flow chart illustrating an implementation of the present technique.
Fig. 5 is a positioning error in wireless positioning according to the present technology.
FIG. 6 is an iterative update trajectory of a search particle of the present technology.
FIG. 7 is an iterative update trajectory of search particles of a conventional particle swarm optimization algorithm.
FIG. 8 is a block diagram of prior art algorithm steps.
Detailed Description
In order to better understand the details of the present invention, the following further describes the steps of the present invention.
1. Extraction of positioning parameter and establishment of positioning objective function
First, a positioning target sends a positioning request to its surrounding nodes.
Then, network nodes around the positioned target detect the positioning request and respond (assuming that the number of nodes participating in the response is M, the nodes are referred to as reference nodes of the positioned target); at the same time, the energy of the radio wave signal of the positioning request sent by the positioned object is measured. The energy parameter is denoted as zi(in dBm), i is the reference node number.
Furthermore, each reference node transmits positioning parameters to the positioned target (or positioning processing center), including the radio wave energy z measured by the reference node and coming from the positioned targetiAnd the position coordinates of the positioning reference node itself (the position coordinate of the ith reference node is recorded as s)i)。
Then, the positioned target (or the positioning processing center) receives the received signal energy parameter z from each reference nodeiAnd its coordinate position parameter si。
Then, the positioned target (or the positioning processing center) is based on each positioning parameter z receivediAnd siEstablishing a positioning objective function g (x; z) related to the position of the positioned target (noted as x) for positioning its own positioni，si). Then, based on the positioning parameters from the M reference nodes, M objective functions g (x; z) can be obtained1，s1)，g(x；z2，s2)，……，g(x；zM，sM)。
Finally, according to the M objective functions, a total objective function is establishedWhereinRepresenting a running multiplication of M functions.
2. Initialization of random search particles
■ initialization of random search particles
Given an objective function f (x) (either statistical-based or non-statistical-based), it initially searches for a set of particlesCan be generated in two ways (where m denotes the search particle x)1Number of (m), NSIndicates the number of the searched particles, and the subscript 1 indicates that the particle set is the initial particle set, i.e. the iteration number k is 1):
if the prior statistical information p (x) of the target variable x is known, then the N can be generated according to its prior distribution p (x)SAn initial search particle
If the prior distribution p (x) of the target variable x is not known, the initial particles will be randomly generated uniformly within the defined domain.
3. Determining a global optimal update direction
■ particle reputation degree calculation
Given a set of search particles in a kth iterationSearching for particle xk(m) corresponding reputation degreeGiven by the following formula (where k denotes the iteration number):
wherein,representing search particle xk(m) the corresponding importance sample particle set (i.e., proposed particle set), xk(m; n) represents a search particle xk(m) the corresponding nth proposed particle, ωk(m; N) represents the weight corresponding to the proposed particle, N represents the number of the proposed particle, NMRepresenting the number of proposed particles; at the same time, search for particle xk(m) corresponding set of proposed particlesIs distributed according to the proposalIs randomly generated, where Θ represents the accuracy matrix of the proposed distribution. In addition, the first and second substrates are,representing from 1 to N according to the number NSAll variables/terms involved are summed.
As for the proposed particle xk(m; n) corresponding to the objective function f (x)k(m; n)) assuming that the original objective function f (x) is a logarithmic posterior probability density function lnp (x | z)i) Then its calculation can be specifically expressed as follows:
where we assume that the target variable exists a prioriDistribution p (x) and likelihood distribution p (z)i|x，si) Then, thenIndicate the proposed particle xk(m; n) values corresponding to the probability density functions under the prior distribution p (x) of the target variable, andis to propose particle xk(m; n) corresponds to likelihood probability density distribution p (z)i|x，si) The function value of (1). In addition, symbol siRepresents the ith uncertainty reference variable, and is setDenotes a reference variable siA corresponding set of proposed particles for approximating a prior distribution p(s) of an uncertainty reference variablei) (ii) a Where t represents the number of particles in the proposed set of particles, si(t) denotes the t-th proposed particle,representing their corresponding particle weights. In addition, ziRepresentative and reference variables siAnd the ith observation sample associated with the target variable x, and Ψ represents the total number of observation samples (it is assumed herein that one reference variable corresponds to one observation sample).
■ determining a global optimal update direction
Obtaining search particles and corresponding credit degrees thereofThen, the global best update direction is defined as the difference vector between the global best search particle and the current search particle:whereinRepresents the globally optimal search particle position, which is defined as the reputation of all search particlesThe largest one, i.e. search particleWherein the symbolsRepresents the variable x that selects the corresponding element max in a given set {. DEG }k(m) means.
4. Determining a locally optimal update direction
■ detecting particle generation
In the present invention, each random search particle xk(m) are all provided with a size NDSet of detected particles ofTo find the search particle xk(m) (where the superscript τ represents the number of the detected particles that are searching for the particle x)k(m) is generated uniformly at random according to the circumferential angle on a circle with the detection step length L as the radius, and the circle is as the center:
where rand (0, 2 π) represents a uniform distribution within (0, 2 π), and the symbol — represents the meaning of "left variable is generated according to the right probability density" (or left variable obeys the right distribution).
■ calculating the credibility of the detected particle
Obtaining a probe particleThen, its corresponding reputation degreeThe calculation is as follows:
wherein the setRepresenting detected particlesCorresponding set of proposed particles, n representing a proposed particleThe number of (a) is included,representing detected particlesThe n-th proposed particle of (1),presentation of proposed particlesWeight of (1), NMRepresenting the total number of proposed particles; whileIndicating its corresponding proposed distribution of the data,is the corresponding integrated variable;representing from 1 to N according to the number NSThe variables or terms involved are summed.
Meanwhile, if the objective function f (x) is assumed to be a logarithmic posterior probability density function lnp (x | z)i) Then it detects the particleCorresponding objective functionThe calculation is as follows:
wherein,indicate to propose the particleCorresponding to the value of the probability density function under the prior distribution p (x) of the target variableIs to propose particlesCorresponding to likelihood probability density distribution p (z)i|x，si) The function value of (1).
■ finding the local optimum update direction
Obtaining search particle xk(m) each of the detection particlesDegree of credit ofThen xk(m) the best update direction of the local region is defined as its best probe particle and current search particle xkDifference vector of (m):whereinRepresenting search particle xk(m) an optimum probe particle, which is defined as a search particle xk(m) goodness of credit in all detected particlesThe largest one of the detected particles, i.e.
Also, note that if the reputation of the current search particle is greater than the reputations of all the probe particles it is equipped with (i.e., if the reputation of the current search particle is greater than the reputations of all the probe particles it is equipped with) Then the search particle x is setk(m) the local optimal update direction is zeroVector (y)k(m) is 0, i.e. xk(m) the local best information will not be considered at the time of this iterative update, and only the global best information will be considered).
5. Updating search particles
Obtaining search particle x according to the above stepsk(m) global optimal update directionAnd local optimal update direction yk(m), then the next generation of search particles xk+1(m) particles x will be searched for in the originalkAnd (m) adding the weighted summation terms of the two updating directions to perform iterative updating:
wherein, γ1And gamma2Representing the update step size with gamma1，γ2Not less than 0 and not more than 0 < gamma1+γ2Less than or equal to 1. All remaining search particles are iteratively updated according to the above equation.
And according to the steps 3 to 5, circularly repeating the steps (determining the global optimal updating direction, determining the local optimal updating direction and searching for particle updating) until the iteration of the searching particles is converged.
6. Parameter estimation and positioning result output
The search particles in the random search technology are continuously updated according to the iterative formula, and can finally converge to a global optimal point. Then, during the kth iteration of searching for particles, or when the searching particles eventually converge, the search particles and their corresponding reputations are based onThe target variable x can be estimated.
There are two cases where the present technology is contemplated. They are now introduced separately and subjected to variable estimation.
(1) Assume that the objective function f (x) is a system-based statistical-information-induced function, such as a log-likelihood function (e.g., lnp (z))i| x)) or a logarithmic posterior probability density function (e.g., lnp (x | z))i) Then, based on the minimum mean square error criterion, or the maximum likelihood probability/maximum a posteriori probability criterion, the distribution can yield the following two estimates:
wherein the function exp (·) represents an exponential function with a natural logarithmic base e as base. That is, the least mean square estimate of the target variable is all the search particles xk(m) an exponential function in its goodwillWeighted summation of the following; and the maximum likelihood/a posteriori estimation is the estimation of which search particle with the greatest reputation is found as the target variable.
(2) If the objective function is non-statistical, e.g. inverse of the error normEtc., then, according to the minimum estimation error norm criterion, one can derive:
finally, parameter estimation at algorithm convergenceAs a final estimate of the algorithm of the invention, i.e. the positioning of the wireless network positioning systemOutput- -location estimate of the located node.
Examples
The method of the present invention is further described with reference to the accompanying drawings and specific examples.
Firstly, a positioned target sends a positioning request; then the response of the positioning system is extracted to obtain a positioning parameter si(i.e., location of ith reference node) and zi(i.e., the received signal energy detected by the ith reference node).
Observation data z according to the law of attenuation of the energy of the radio waves in a wireless positioning systemiIt can be expressed as a target variable x (i.e. the position of the target node) and an ith reference variable siThrough a system nonlinear observation function h (x, s)i) And additive observation noise is added to the output of the action ofi：
zi＝h(x，si)+i.
In a wireless sensor network, the non-linear observation function of wireless positioning based on observed signal strength can be expressed as a logarithmic function:
h(x，si)＝φi-10ρlog10||x-si||2，
wherein phi isiWith ρ being a given known constant, | · | non calculation2Representing the two-norm of the vector.
Whereas in wireless positioning applications, the reference variable s is due to the presence of a positioning errori(i.e., the coordinates of the reference nodes) are typically inaccurate. Without loss of generality, it is assumed that it follows a gaussian distribution:wherein U isiIs siA gaussian distribution accuracy matrix of; simultaneously supposing that the target variable x has Gaussian prior distributionWhere u is its mean parameter, andis the corresponding accuracy matrix. In addition, it is assumed that additive observation noise follows a zero-mean Gaussian distribution, i.e.Wherein wiIs the observation accuracy. Assuming a total of Ψ observation data for the located target, and defining a new observation vectorWherein the symbolsRepresenting a transpose of a vector or matrix. Fig. 1 presents a mathematical model of the positioning system.
From these known statistics, an objective function lnp (x | z) of the log posterior probability density can be derived to maximize the objective function for estimation of the objective variables. In particular, based on the above statistical information, and assuming that the observations are independent of each other, the corresponding likelihood function can be described as:
wherein,indicating that all entries numbered i ∈ Ψ are multiply concatenated, and the notation ∈ indicates "belong".
Furthermore, the posterior probability density function corresponding to the target variable can be expressed as:
where ∈ indicates "proportional rate", and | · | indicates taking an absolute value (for scalar quantity).
However, due to the non-linear observation function h (x, s)i) Presence of, reference variable siThe objective function lnp (xz) is typically non-convex or non-concave, i.e., there are multiple local optima, and the objective function surface is extremely rough and not flat, as shown in fig. 2. This presents difficulties in the search, optimization, and estimation of the optimal variables.
In accordance with the spirit of the present technique, in this embodiment, we will find the global optimal variable position by processing the non-convex and non-concave objective function lnp (x | z), resulting in a least mean square estimate, or a maximum a posteriori estimate, of the objective variable.
For convenience, the objective function lnp (x | z) is uniformly replaced with f (x) in the following description. It should be noted that the present invention is applicable not only to an objective function based on statistical information (such as logarithm posterior lnp (x | z), or log likelihood lnp (z | x)), but also to an objective function in which no statistical information is available, or an objective function related to an error norm, such as
Then the specific implementation steps are as follows, in accordance with the teachings of the random search technique of the present invention.
First, according to the prior distribution of the target variableGenerating a set of random search particlesWhere the parameter m represents the search particle xkNumber of (m), NSThe number of search particles is shown (since this is the initial search particle, the iteration number k is actually k 1).
Then, each search particle x is calculated as followsk(m) degree of credit
Wherein,representing search particle xk(m) a corresponding set of proposed particles, the parameter n representing the number of proposed particles, xk(m; n) denotes the nth proposed particle, ωk(m; n) represents the proposed particle xk(m; n) corresponding weights; and the proposed set of particles is generated by searching for particle x at the current timek(m) -centered Gaussian proposed distributionWhere Θ represents the accuracy matrix of the proposed distribution. In addition, each proposed particle corresponds to an objective function f (x)k(m; n)) is calculated according to the following formula:
h(xk(m；n)，si(t))＝φi-10ρlog10||xk(m；n)-si(t)||2，
wherein,denotes a reference variable siA corresponding set of proposed particles for approximating the prior distribution of the uncertainty reference variableHere, the parameter t represents the proposed particle si(ii) the number of (t),representing proposed particles si(t) weight. Also in the above equation, det (-) denotes the determinant of the matrix,representing a transpose of a vector or matrix. In addition, in this embodiment, there are a prior distribution p (x) and a likelihood distribution p (z) for the target variable xi|x，si) Then, thenIndicate the proposed particle xk(m; n) values corresponding to the probability density functions under the prior distribution p (x) of the target variable, andis to propose particle xk(m; n) corresponds to a likelihood probability density distribution p (z)i|x，si) The function value of (1).
Further, all the search particles x obtained are used as the basisk(m) degree of creditTo determine individual search particlesThe global best update direction. Each search particle xk(m) global optimal update directionDefined as a globally optimal search particleAnd the search particle xk(m) a difference vector, i.e.Wherein the global best search particleDefined as the search particle with the highest reputation among all search particles:
next, for each search particle xk(m) providing a set of probe particlesWherein the superscript τ represents the detection particleNumber of (2), NDIndicating the number of detected particles. Specifically, particle x is searchedk(m) detecting particlesIs searching for particle x at the presentk(m) is generated uniformly at random according to the circumferential angle on a circle with the detection step length L as the radius, namely:
then, each detected particle is calculatedThe reputation degree of (c):
wherein,representing detected particlesCorresponding set of proposed particles, parameter n representing a proposed particleThe number of (a) is included,representing detected particlesThe n-th proposed particle of (1),weight, N, representing proposed particlesMRepresenting the number of detected particles; detecting particlesThe corresponding proposed particle set is based on the current detected particleCentered gaussian proposed distributionRandomly generated, where Θ represents the accuracy matrix of the proposed distribution, i.e.:
in addition, each proposed particleCorresponding objective functionCalculated according to the following formula:
wherein,denotes a reference variable siA corresponding set of proposed particles for approximating the prior distribution of the uncertainty reference variableHere, the parameter t represents the proposed particle si(ii) the number of (t),representing proposed particles si(t) weight. In addition, in this embodiment, there are a prior distribution p (x) and a likelihood distribution p (z) for the target variable xi|x，si) Then, thenPresentation of proposed particlesCorresponding to the value of the probability density function under the prior distribution p (x) of the target variableIs to propose particlesCorresponding to likelihood probability density distribution p (z)i|x，si) The function value of (1).
Further, based on the obtained degrees of reputation of the probe particles, the probe particle having the greatest degree of reputation is found,
the search particle x can be obtainedk(m) optimal update direction of the local area. Searching for particle xkLocal optimization of (m)The update direction is defined as the best detected particle for itWith the current search particle xkDifference vector of (m):
finally, according to the global optimal update direction and the local optimal update direction obtained above, the final update direction of the search particle is the weighted average of the local optimal and the global optimal, that is:
wherein, γ1And gamma2Representing the update step size with gamma1，γ2Not less than 0 and not more than 0 < gamma1+γ2≤1。
The loop is repeated, and all the search particles are continuously iterated (global optimal update direction is determined, local optimal update direction is determined, and then particle update is searched) until convergence or the maximum iteration number is reached.
Accordingly, the target variable is simultaneously estimated during each iteration of searching for particles. According to the least mean square criterion, or the maximum a posteriori criterion, there can be two estimation methods, respectively:
the least mean square estimation (the first estimator in the above equation) in the present embodiment is a statistically optimal estimation.
Fig. 3 and 4 respectively show a simple schematic diagram and an implementation flow schematic diagram of the technical content. The technical content and the implementation flow are consistent with the above description, and the spirit of the technology of the invention is reflected more concisely.
To verify the performance of the particle-assisted random search based technique of the present invention in this case, we consider the simulation verification of the positioning performance in wireless sensor network positioning according to the relevant parameters in table 1 below.
TABLE 1 simulation parameters under fixed frequency offset conditions
Note: where symbol I represents the unit matrix in the same matrix dimension.
The corresponding co-location accuracy is shown in fig. 5. As can be seen from the figure, the novel search strategy can resist the distortion of the nonlinear system function and the uncertainty of the reference variable, so that the search particles can be quickly converged to the global optimum by the technology of the invention; therefore, the approximate efficiency of the search particles to the target function is improved, and variable estimation with smaller error is obtained through the optimal estimator compared with the traditional Particle Swarm Optimization (PSO) algorithm and the estimation algorithm (ISP) adopted based on the importance.
To verify the search capabilities of the present technique, the present embodiment purposely tests a special scenario- -the situation when the initial search particle does not cover the global optimal solution. Therefore, for the initial search particle, we artificially introduce a large offset such that it does not cover the global optimum as follows:
fig. 6 and 7 show the search capabilities of the inventive technique and the conventional PSO technique, respectively. As can be seen from the figure, since the local search strategy of the conventional PSO algorithm only depends on the historical track of the search particle, when the initial distribution of the search particle does not cover the global optimum, the search particle can only converge to the local optimum within the initial distribution range, but cannot search the global optimum. The technology of the invention adopts a local search strategy based on the assistance of the detection particles, so that the global optimum can be searched.
It will be clear and understood by those of ordinary skill in the art that the above examples of the method of the present invention are illustrative only and not intended to be limiting. While the present invention has been described effectively by way of examples for guidance to those of ordinary skill in the art, numerous variations of the invention exist without departing from the spirit of the invention. Various corresponding changes or modifications can be made by those skilled in the art without departing from the spirit and substance of the method of the present invention, and these corresponding changes or modifications are within the scope of the claims of the method of the present invention.
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.
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