A RSSD positioning method in a Gaussian mixed noise environment

Abstract

The application relates to an RSSD positioning method in a Gaussian mixed noise environment, comprising the following steps: acquiring RSS measurement values collected by anchor nodes and calculating RSSD values; constructing a non-convex maximum likelihood problem based on RSSD and obtaining a diversified population based on reverse learning and a chaos graph; adopting an adaptive mutation strategy for global search, finally selecting an optimal individual through cross processing and abnormal value processing to serve as positioning information estimation of a target node. Compared with the prior art, the application constructs a non-convex maximum likelihood problem based on RSSD to avoid introducing additional errors due to approximation; obtains a feasible solution based on an improved differential evolution algorithm; combines reverse learning with a chaos graph to obtain a diversified population, thereby improving population quality; in addition, adaptive mutation based on two different sub-strategies is adopted to maintain balance between global exploration and convergence. Thus, the positioning problem of Gaussian mixed noise and unknown transmitting power can be effectively solved, and the positioning speed and precision are improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of wireless sensor positioning technology, and particularly relates to an RSSD positioning method in a Gaussian mixed noise environment. BACKGROUND

[0002] In applications such as environmental monitoring, military security and marine rescue, positioning in wireless sensor networks (WSN) is particularly important, mainly using spatially distributed sensors with known locations to obtain measurements, including received signal strength (RSS), received signal strength difference (RSSD), angle of arrival (AOA), time of arrival (TOA), time difference of arrival (TDOA) or a combination of these, to locate target nodes. However, TOA and TDOA-based positioning relies on precise clock synchronization, while AOA-based positioning relies on precise antenna arrays. In contrast, RSS and RSSD schemes are more attractive due to their low complexity and low cost.

[0003] Currently, most RSS-based estimation techniques require known transmit power (KTP), which is often unrealistic. Therefore, existing technologies propose the following solutions for the case of unknown transmit power:

[0004] One is a minimum-maximum strategy based on matrix decomposition, designed to provide good positioning accuracy;

[0005] One is a least squares relative error-based algorithm to improve positioning performance and use semi-definite relaxation to solve non-convex problems.

[0006] In addition, RSSD-based methods have the following advantages over RSS-based solutions: no KTP is required, and no coordination between anchors and targets is required. Some research proposes an extended total least squares method to handle blind channel positioning problems, another research develops a semi-definite programming-based estimator to improve the robustness of positioning, and in addition, some research proposes an RSSD convex relaxation method of the minimum mean square error semi-definite programming method to deal with sensor position errors.

[0007] In summary, the current positioning scheme using RSS and RSSD measurement values can have good positioning performance when only considering additive Gaussian white noise. However, this assumption does not hold in many cases, such as multiple heterogeneous sources or complex environmental factors. For this reason, some scholars have developed a robust recursive least squares method for non-Gaussian environments, and have proposed a robust fault-tolerant positioning technology for the case of faulty nodes. Although these methods perform well, they are based on certain approximations and require a suitable initial solution to ensure good positioning performance, and still cannot guarantee the speed and accuracy of positioning. SUMMARY

[0008] The purpose of the present application is to overcome the defects of the prior art and provide an RSSD positioning method in a Gaussian mixed noise environment. The method is based on RSSD measurement values and combines an improved differential evolution (IDE) algorithm to improve positioning accuracy and speed.

[0009] The purpose of the present application can be achieved by the following technical solution: an RSSD positioning method in a Gaussian mixed noise environment, comprising the following steps:

[0010] S1, obtaining RSS measurement values collected by anchor nodes and calculating RSSD values;

[0011] S2, constructing a non-convex maximum likelihood (ML) problem based on RSSD, and obtaining a diversified population based on backpropagation and chaotic maps;

[0012] S3, performing global search using an adaptive mutation strategy, and finally selecting an optimal individual as the positioning information estimate of the target node through cross processing and outlier processing.

[0013] Further, the step S1 specifically obtains RSS measurement values of anchor nodes from a WSN with a dimension of M d , obtains a plurality of RSSD values by calculating the difference, and the WSN includes N anchor nodes with known positions and a target node with an unknown position: for the unknown target node, i=1,2,...,N, N>3 for the known anchor node positions, wherein (·) T is the transpose.

[0014] Further, the step S2 specifically includes the following steps:

[0015] S21, determine the received signal power of the anchor node according to the distance between the target node and the anchor node, and obtain the ML estimation expression of the target node in combination with the Gaussian mixture model;

[0016] S22, generate population individuals by using a logic diagram based on the chaotic variable, and obtain a reverse vector, thereby obtaining a diversified population.

[0017] Further, the specific process of step S21 is as follows:

[0018] The distance between the target node and the anchor node i is:

[0019]

[0020] The received signal power P at the anchor node i i is:

[0021]

[0022] Wherein, S0 is the path loss of the reference distance d0=1m, P t is the transmission power, and γ is the path loss index in the set range.

[0023] It is assumed that P i obeys the lognormal distribution, that is:

[0024]

[0025] Wherein, n i is a mixed noise composed of Gaussian noise and disturbance noise, and the mixed noise probability density function (PDF) is a Gaussian mixture model (GMM):

[0026] Ψ(n)=(1-ω)Ψ G (n)+ωΨ P (n)

[0027] Wherein, ω∈[0,1] is the pollution rate, Ψ G (n) and Ψ P (n) are independent random variables, which are Gaussian noise probability density function and disturbance noise probability density function respectively,

[0028] The RSSD between the i th and j th sensors is:

[0029]

[0030] Taking sensor j as the reference node, the matrix i,j = 1,2,...,N, i≠j of n ij The conditional PDF is expressed as:

[0031]

[0032] where, z = 1,...,N, maximizing the PDF in the above equation, the ML estimate of θ is:

[0033]

[0034] Taking sensor 1 as the reference node, the solution space is defined as

[0035]

[0036] where, d m and u m are the lower and upper limits, respectively.

[0037] Further, the probability density function of the Gaussian noise is The probability density function of the disturbance noise is

[0038] Further, the specific process of the step S22 is:

[0039] The chaotic variable is Logical diagram generation is used:

[0040] δ l+1,m = υδ l,m (1-δ l,m )

[0041] m = 1,...,M d

[0042] where, υ = 4, δ 1,m ∈(0,1), δ 1,m = 0, 0.25, 0.75, 1, L is the population size, and the population individual is:

[0043]

[0044] m = 1,...,M d

[0045] Further, the reverse vector is determined as:

[0046]

[0047] The initial population is taken as The first L values with the lowest fitness.

[0048] Further, the step S3 is specifically to perform global search by using an adaptive mutation strategy based on two different sub-strategies:

[0049] In the gth generation, a new population is created from the current population by using the AM strategy.

[0050] The adaptive control parameter is compared with a threshold value to select two different strategies, where f mean is the average objective function value of all individuals, and f best is the objective function value of the best individual.

[0051] Two sub-populations of equal size are created from the current population and subp1+subp2=L, and a new population is obtained by a first set of mutation operations and a second set of mutation operations.

[0052] Further, the calculation formula of the first set of mutation operations is specifically:

[0053]

[0054]

[0055] The calculation formula of the second set of mutation operations is specifically:

[0056]

[0057]

[0058] And,

[0059] o1,o2,o3,o4,o5∈{1,2,...,0.5L}

[0060] o1≠o2≠o3≠o4≠o5

[0061] Where R best is the best individual in the current population, and α∈[0,1] is a decay factor. When the first set of mutation operations is used to generate a mutant population, otherwise the second set of mutation operations is used to generate a mutant population.

[0062] Further, the specific process of the step S3 is as follows:

[0063] with the crossover probability p c cross the original population and the mutated population to generate a trial population its individuals are:

[0064]

[0065] For individuals outside the solution space S, adjust according to the following formula:

[0066]

[0067]

[0068]

[0069] m = 1,..., M d

[0070] wherein, and are the lower bound and the upper bound of the L individuals of the gth generation, respectively, is a uniform distribution in [0, 1];

[0071] Using the obtained minimum fitness threshold, select the (g+1)th generation individuals:

[0072]

[0073] After G generations, select the optimal individual in as the final target node positioning information estimate.

[0074] Further, the optimal individual is specifically:

[0075]

[0076] Compared with the prior art, for the positioning problem of Gaussian mixed noise and unknown transmit power, the application utilizes RSSD measurement values and combines an improved differential evolution algorithm, first constructs a non-convex maximum likelihood (ML) problem based on RSSD, can effectively avoid introducing additional errors due to approximation, then obtains a feasible solution based on the improved differential evolution algorithm, adopts an opposition-based learning (OL) combined with a chaotic map (CM) mode, can obtain diversified populations, thereby improving the population quality. In addition, an adaptive mutation (AM) mode based on two different sub-strategies is adopted to ensure the balance between global exploration and convergence. Thus, the positioning accuracy can be effectively improved, and the positioning rapidity is also ensured. Attached Figure Description

[0077] Figure 1 This is a schematic diagram of the method flow of the present invention;

[0078] Figure 2 This is a schematic diagram illustrating the application process of the embodiment;

[0079] Figure 3a This is a two-dimensional fixed deployment effect diagram in the embodiment;

[0080] Figure 3b This is a diagram illustrating the effect of two-dimensional random deployment in the embodiment.

[0081] Figure 4a This is a schematic diagram showing the relationship between RMSE and CRLB and noise for different positioning methods under the fixed deployment scenario in the embodiment.

[0082] Figure 4b This is a schematic diagram showing the relationship between RMSE and CRLB and noise for different positioning methods under random deployment in the embodiment.

[0083] Figure 5a This is a schematic diagram of the cumulative distribution function (CDF) for different positioning methods under the fixed deployment scenario in the embodiment.

[0084] Figure 5b This is a schematic diagram of the cumulative distribution function (CDF) for different positioning methods under random deployment conditions in the embodiments. Detailed Implementation

[0085] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0086] Example

[0087] like Figure 1 As shown, an RSSD localization method in a Gaussian mixed noise environment includes the following steps:

[0088] S1. Obtain the RSS measurement value collected by the anchor node and calculate the RSSD value;

[0089] S2. Construct a non-convex maximum likelihood (ML) problem based on RSSD, and obtain a diverse population based on reverse learning and chaotic graphs;

[0090] S3. An adaptive mutation strategy is used for global search. Through crossover and outlier handling, the optimal individual is finally selected as the location information estimate of the target node.

[0091] The process of applying the above solution in this embodiment is as follows: Figure 2 As shown, it specifically includes:

[0092] I. For the case of Gaussian mixed noise environment without KTP, the non-convex RSSD-based localization problem is formulated as an ML problem and solved by a robust method OLAM-IDE.

[0093] It should be noted that currently a variety of population-based methods such as particle swarm optimization, differential evolution (DE), simulated annealing and genetic algorithm have been used to solve non-convex or nonlinear optimization problems. However, due to their randomness, the calculation time is very long. Among these methods, DE is more effective due to its convergence speed and robustness. Therefore, DE has been used to solve the WSN localization problem. For the case of unknown communication range and connection information, an improved DE scheme has been developed in existing research, such as an improved hybrid scheme based on glowworm algorithm and DE is proposed to estimate the passive target position using noisy TOA measurements, but it still cannot guarantee the accuracy and speed of localization at the same time. Therefore, the technical scheme proposes a robust method OLAM-IDE, which can improve the accuracy of localization solution for the case of Gaussian mixed noise environment without KTP.

[0094] II. Reverse learning and chaos map are combined to obtain a diversified population.

[0095] III. An adaptive mutation scheme based on two different sub-strategies is adopted to improve global search and convergence.

[0096] IV. Outliers are processed and optimal position estimates are selected.

[0097] Among them, step one is: considering a WSN with M d dimensions, including N known location anchor nodes and one unknown location target node. Let be the unknown location target node, let i=1,2,...,N,N>3 be the known anchor node position, where (·) T is the transpose.

[0098] Then the distance between the target node and the anchor node i is:

[0099]

[0100] The received signal power P i at node i is represented as:

[0101]

[0102] where S0 represents the path loss of the reference distance d0=1m, P tis the transmit power, and γ is the path loss exponent in the range [1, 6]. For the RSSD model, γ = 2 is considered as a priori value, and the actual value depends on the environment.

[0103] Assume P i Subject to lognormal distribution, equation (2) is rewritten as:

[0104]

[0105] where n i is the measurement noise composed of Gaussian noise with probability density function (PDF) and disturbance noise with probability density function ξ≥1. Then, the mixed noise PDF is a Gaussian mixture model (GMM):

[0106] Ψ(n)=(1-ω)Ψ G (n)+ωΨ P (n) (4)

[0107] where ω∈[0,1] is the pollution rate, Ψ G (n) and Ψ P (n) are independent random variables,

[0108] According to equation (3), the RSSD between the ith and jth sensors is:

[0109]

[0110] Taking sensor j as the reference node, the matrix i,j=1,2,...,N,i≠j of n ij is expressed as:

[0111]

[0112] where z=1,...,N.

[0113] Maximizing the PDF in equation (6), the ML estimate of θ is:

[0114]

[0115] Sensor 1 is considered as the reference node, and the solution space is defined as:

[0116]

[0117] where dm and u m are lower and upper limits, respectively.

[0118] Step two is specifically:

[0119] chaotic variable, using logic diagram generation

[0120] delta l+1，m = u delta l，m (1 - delta l，m ), m = 1, …, M d (9)

[0121] where u = 4, delta 1,m e (0, 1), delta 1,m = 0, 0.25, 0.75, 1, L is the population size. The population individuals are:

[0122]

[0123] Then, the reverse vector is:

[0124]

[0125] The initial population is taken from the first L values with the lowest fitness in

[0126] Step three is specifically:

[0127] In the gth generation, a new population is created from the current population by using the AM strategy. Considering the real source localization scenario, this avoids the shortcomings of a single operator, such as slow convergence and falling into local optimum. By comparing the adaptive control parameter with the threshold , two different strategies are selected, where f mean is the average objective function value of all individuals, and f best is the objective function value of the best individual. Two subpopulations and of equal size are created from the current population , subp1 + subp2 = L. The new population can be obtained by two sets of mutation operations:

[0128]

[0129]

[0130] and​

[0131]

[0132]

[0133] wherein R best is the best individual in the current population, and α∈[0,1] is a decay factor;

[0134] o1,o2,o3,o4,o5∈{1,2,...,0.5L}, o1≠o2≠o3≠o4≠o5.

[0135] When Equations (12a) and (12b) are used to generate the mutant population, otherwise equations (13a) and (13b) are used to generate the mutant population.

[0136] Step four is specifically:

[0137] The original population and the mutant population are crossed using a crossover probability ρ c ∈[0,1] to generate a trial population whose individuals are

[0138]

[0139] Boundary processing is performed, and individuals outside the solution space S are adjusted according to equation (15):

[0140]

[0141] wherein, m=1,...,M d are the lower and upper bounds of the gth generation of L individuals, respectively, is a uniform distribution in [0,1].

[0142] Finally, the minimum fitness threshold obtained is used to select the (g+1)th generation individuals:

[0143]

[0144] After G generations, the best individual is selected from as the final estimate:

[0145]

[0146] To verify the effectiveness of the technical solution, the present embodiment selects a plurality of different methods as shown in Table 1 for comparative experiments.

[0147] Table 1

[0148]

[0149]

[0150] For the ETLS-SDP method, the yalmip toolbox with SeDuMi solver is used, while for the ML-USR method, the lsqnonlin function with Levenberg-Marquardt algorithm and USR estimator is used as initial point instead of true position.

[0151] The deployment scenarios of the present application, on the one hand, consider two-dimensional (2D) fixed deployment, with the target source located at (18, 22), as shown in Figure 3a , on the other hand, also consider random deployment, as shown in Figure 3b In this case, the coordinates of the target and anchor nodes will change under each trial. The deployment area is 100m x 50m, and the lower and upper bounds are u1 = 100, u2 = 50.

[0152] The variances of the Gaussian mixture noise are set to 4 and 1, i.e. Ψ G (η) ~ N(0, 1 2 ) and Ψ P (η) ~ N(0, 2 2 ).

[0153] Other parameters are L = 12, G = 50, I = 1000, α = 0.4 + (0.5-0.4) x rand(0, 1), ρ c = 0.6 + (0.7-0.6) x rand(0, 1), τ = 10 -5 . These parameters are determined from extensive preliminary experiments and take into account the values in the relevant literature.

[0154] In addition, the experiments also include the corresponding Cramer-Rao bound as a performance benchmark, and the root mean square error (RMSE) is taken as the positioning performance indicator, defined as where, is the estimated value of the target θ i in the i-th trial, and M c = 1000 is the number of Monte Carlo trials.

[0155] The target estimation RMSE of the OLAM-IDE algorithm and other algorithms proposed in the present application and the noise σ 2 is given in Figure 4a and 4b , where ω = 0.5, γ = 3.5 and N = 9, and the CRLB is also shown. As expected, the performance of the algorithm decreases with the increase of σ 2 . Figure 4a The RMSE and CRLB of the fixed sensor distribution are given with σ2 Relationship, Figure 4b Results for randomly deployed sensors are presented. These results show that ETLS-SDP, SRWLS, and LLS are more robust to this distribution compared to randomly deployed sensors, but they are still inferior to ML-based methods due to the LS approximation. Therefore, the method proposed in this invention provides the best performance. Figure 4b Among these methods, LLS has the highest RMSE, followed by ETLS-SDP. Since they are all based on least squares, their robustness to environmental conditions is worse than other algorithms. SRWLS improves performance by transforming the problem into a generalized trust domain subproblem, but it is still less efficient than ML-based methods. OLAM-IDE provides the lowest RMSE. For example, in σ... 2 At 5dB, for a fixed sensor distribution, the RMSE difference between this method and CRLB is 0.18m, while ETLS-SDP is 3.90m, SRWLS is 2.31m, LLS is 2.03m, ML-USR is 1.17m, and TLFA is 0.45m. For randomly deployed sensors, the corresponding results show an RMSE difference of 0.99m between the proposed method and CRLB, while LLS is 17.67m, SRWLS is 14.92m, ETLS-SDP is 14.47m, ML-USR is 6.46m, and TLFA is 2.13m.

[0156] Figure 5a and 5b The cumulative distribution function (CDF) of the target estimation error for different methods is given, where ω = 0.5, γ = 3.5, N = 9, and σ 2 =3.

[0157] For a fixed sensor distribution, when CDF = 96%, the error of OLAM-IDE is... The probability error is 1.26m, while other methods have larger probabilistic errors, including 1.52m for TLFA, 1.91m for ML-USR, 5.34m for LLS, 5.52m for SRWLS, and 8.79m for ETLS-SDP.

[0158] For randomly deployed sensors, OLAM-IDE has an error of 7.95m, while other methods have higher errors, including TLFA (9.61m), ML-USR (14.32m), LLS (42.91m), SRWLS (44.92m), and ETLS-SDP (51.90m).

[0159] In summary, the technical scheme is directed to a Gaussian mixed noise environment without KTP, formulates a positioning problem based on a non-convex RSSD as an ML problem, and solves it through a robust method OLAM-IDE. The technical scheme combines reverse learning and a chaos map to obtain a diversified population, and adopts an adaptive mutation scheme based on two different sub-strategies to improve global search and convergence. Thus, the positioning performance can be significantly improved in a mixed Gaussian noise environment.

Claims

1. A method for RSSD positioning in a Gaussian mixture noise environment, characterized in that, The method comprises the following steps: S1, acquiring RSS measurement values collected by anchor nodes and calculating RSSD values; S2, constructing a non-convex maximum likelihood problem based on RSSD, and obtaining a diversified population based on reverse learning and a chaos map; S3, performing global search by using an adaptive mutation strategy, and finally selecting an optimal individual as positioning information estimation of the target node through cross processing and outlier processing; Step S3 is specifically performing global search by using an adaptive mutation strategy based on two different sub-strategies: In the first generation, a new population is created from the current population using an AM strategy g ;​​ Adaptive control parameters are selected compared to a threshold to select two different strategies, where is the average objective function value of all individuals, is the objective function value of the best individual; from the current population creating two sub-populations of equal size and , , L for the population size, and then through the first set of mutation operations and the second set of mutation operations to obtain a new population ; The calculation formula of the first group of mutation operations is specifically: The calculation formula of the second group of mutation operations is specifically: And wherein, is the best individual in the current population, is a decay factor, when if then a first set of mutation operations is used to generate the mutated population, otherwise a second set of mutation operations is used to generate the mutated population. 2.The RSSD positioning method in a Gaussian mixture noise environment according to claim 1, wherein, The step S1 is specifically to obtain RSS measurement values of anchor nodes from a WSN with dimensions of A plurality of RSSD values are obtained by calculating the difference. The WSN includes Anchor nodes with known positions and a target node with an unknown position: The target node with an unknown position, , The anchor node position is known, wherein is the transpose. 3.The RSSD positioning method in a Gaussian mixture noise environment according to claim 2, characterized in that, The step S2 specifically comprises the following steps: S21, determining the received signal power of the anchor nodes according to the distance between the target node and the anchor nodes, and obtaining the ML estimation expression of the target node in combination with a Gaussian mixture model; S22, generating population individuals by using a logic map based on a chaos variable, and obtaining a reverse vector, thereby obtaining a diversified population.

4. The RSSD positioning method in a Gaussian mixture noise environment according to claim 3, characterized in that, The specific process of the step S21 is: The distance between the target node and the anchor node i is: is: Anchornode i received signal power at the access point is: wherein, is a reference distance m is a path loss, is a transmit power, is a path loss exponent within a set range; Setting Submits to a lognormal distribution, i.e. there is: wherein, is a mixed noise composed of a Gaussian noise and a disturbance noise, and a probability density function (PDF) of the mixed noise is a Gaussian mixture model: wherein, is the pollution rate, and are independent random variables, respectively a Gaussian noise probability density function and a perturbation noise probability density function, ; No. i The and the first j The RSSD between the sensors is: With the sensor j as the reference node, the matrix , of the conditional PDF is expressed as: where, , , , maximizing the PDF in the above equation, we get the ML estimate of as Taking sensor 1 as a reference node, the solution space is defined as wherein and are the lower and upper limits, respectively.

5. The RSSD positioning method in a Gaussian mixture noise environment according to claim 4, characterized in that, The probability density function of the Gaussian noise is , and the probability density function of the perturbation noise is , .

6. The RSSD positioning method in a Gaussian mixture noise environment according to claim 4, characterized in that, The specific process of the step S22 is: The chaotic variable is generated using a logic diagram: wherein , , , L is the population size, the population individuals are: Further determining the reverse vector is: initial population then take the first L values with the lowest fitness.

7. The RSSD positioning method in a Gaussian mixture noise environment according to claim 1, characterized in that, The specific process of cross processing, outlier processing and final selection of the optimal individual in the step S3 is: Using crossover probabilities Crossover is performed on the original and mutated populations to generate trial populations whose individuals are: for individuals outside the solution space is adjusted according to the following formula: in, and They are the first g generation L The lower and upper bounds of an individual. The distribution is uniformly distributed in [0,1]. Using the resulting minimum fitness threshold, select the individuals with fitness values above the threshold for generation (1 g +1). ， In subsequent generations, the optimal individual is selected as the final target node positioning information estimate. 8.The RSSD positioning method in a Gaussian mixture noise environment according to claim 7, wherein, The optimal individual is specifically: 。

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