Method and system for constructing source positioning efficient estimator based on hybrid measurement information

Abstract

The invention discloses a method and system for constructing a source positioning efficient estimator based on hybrid measurement information, and the method comprises the steps: constructing a hybrid information non-negative constraint least square framework based on an analysis sensor in a wireless sensor network; based on a hybrid information non-negative constraint least square framework, obtaining coarse suboptimal estimation; and completing the construction of an efficient estimator based on the coarse suboptimal estimation. According to the method, an original non-convex optimization problem is converted into a non-negative constraint least square framework through linear calculation. Obtaining a suboptimal estimator by using an index exchange process between an active set and a passive set in a linear solution mode; meanwhile, in order to reduce deviation caused by linearization and refine estimation obtained by linear solution, a deviation reduction method is adopted, and a weighting tool variable matrix which is in weak correlation with noise but in strong correlation with a data matrix is designed, so that the positioning precision is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of wireless positioning, and particularly to a method and system for constructing an efficient estimator for source localization based on hybrid measurement information. Background Art

[0002] Source localization in wireless sensor networks (WSNs) has attracted extensive attention in a wide range of applications such as intelligent transportation, mobile rescue, and national defense security. Spatially distributed sensor nodes with known positions can be used to locate the source through techniques such as received signal strength difference (RSSD), angle of arrival (AOA), time difference of arrival (TDOA), or a combination thereof. Among them, the methods based on TDOA and RSSD are more attractive. The method based on TDOA not only inherits the advantages of the technique based on time of arrival (TOA), but also eliminates the need for time synchronization. Similarly, the method based on RSSD not only retains the advantages of the technique based on received signal strength (RSS), but also avoids errors caused by changes in transmission power and reduces communication overhead.

[0003] Scholars have conducted research on some RSSD and TDOA measurement source localization schemes, which can be mainly divided into maximum likelihood (ML)- or least squares (LS)-based schemes. Although ML-based solutions can be asymptotically unbiased and efficient, they usually have high computational complexity due to the iterative nature of the algorithm. In addition, a reasonable initial solution is required to ensure its convergence to the global optimal solution. To overcome these drawbacks, some scholars have studied LS-based methods, which transform the original non-linear problem into a non-negative constrained LS framework problem based on a linearization process. However, this method usually introduces a certain bias, thereby degrading the localization performance.

[0004] To improve performance, although some hybrid positioning techniques, including RSS-TOA, RSS-TDOA, RSSD-TOA, RSSD-TDOA, etc., have attracted great attention. However, due to the need for strict clock synchronization, hybrid RSS and TOA methods are usually difficult to implement. For RSS-TDOA-based positioning, researchers use multi-resolution search of the dichotomy algorithm to simultaneously estimate the position and transmission direction. Scholars have also introduced balance parameters to obtain a generalized trust region problem and obtained the final solution through iteration. Among these solutions, the hybrid RSSD method has received much less attention in the literature, especially RSSD-TDOA measurements. A hybrid geolocation method has been studied to improve the estimation accuracy. A linear WLS estimator has been proposed to improve the accuracy of source-free source localization. However, these LS-based positioning methods usually approximately convert the corresponding non-linear problem into a linear problem. Due to the correlation between the data matrix and the noise vector, this will produce bias, which may cause significant estimation errors. Summary of the Invention

[0005] To solve the technical problems in the above background, the present invention starts from the direction of improving ML, and proposes a method to effectively reduce bias to construct an estimator in a wireless sensor network, using hybrid TDOA-RSSD measurement information to reduce bias and improve positioning accuracy.

[0006] To achieve the above object, the present invention provides a method for constructing an efficient estimator for source localization based on hybrid measurement information, and the steps include:

[0007] Based on the analysis sensors in the wireless sensor network, construct a non-negative constrained least squares framework for hybrid information;

[0008] Based on the non-negative constrained least squares framework for hybrid information, obtain a rough sub-optimal estimate;

[0009] Based on the rough sub-optimal estimate, complete the construction of the efficient estimator.

[0010] Preferably, the method for constructing the non-negative constrained least squares framework for hybrid information includes:

[0011] Perform maximum likelihood estimation positioning on the hybrid signal data received by the analysis sensors in the wireless sensor network;

[0012] Based on the maximum likelihood estimation positioning, construct the non-negative constrained least squares framework for hybrid information.

[0013] Preferably, the method for obtaining the rough sub-optimal estimate includes: performing linear solution on the non-negative constrained least squares framework for hybrid information to obtain the rough sub-optimal estimate.

[0014] Preferably, the method for constructing the efficient estimator includes: optimizing the rough sub-optimal estimate by using a bias reduction method, and using a weighted instrumental variable matrix that is weakly correlated with noise but strongly correlated with the data matrix to obtain an optimal solution, thereby completing the construction of the efficient estimator.

[0015] The present invention also provides a system for constructing an efficient estimator for source localization based on hybrid measurement information. The system is used to implement the above method and includes: a construction module, a solution module, and an optimization module.

[0016] The construction module is used to construct a hybrid information non-negativity constrained least squares framework based on the analysis sensors in the wireless sensor network.

[0017] The solution module is used to obtain a rough sub-optimal estimate based on the hybrid information non-negativity constrained least squares framework.

[0018] The optimization module is used to complete the construction of the efficient estimator based on the rough sub-optimal estimate.

[0019] Preferably, the working process of the construction module includes:

[0020] Performing maximum likelihood estimation localization on the signal data received by the analysis sensors in the wireless sensor network;

[0021] Based on the maximum likelihood estimation localization, constructing the hybrid information non-negativity constrained least squares framework.

[0022] Preferably, the working process of the solution module includes: performing linear solution on the hybrid information non-negativity constrained least squares framework to obtain the rough sub-optimal estimate.

[0023] Preferably, the working process of the optimization module includes: optimizing the rough sub-optimal estimate by using a bias reduction method, and using a weighted instrumental variable matrix that is weakly correlated with noise but strongly correlated with the data matrix to obtain an optimal solution, thereby completing the construction of the efficient estimator.

[0024] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0025] Through linearized calculation, the present invention transforms the original non-convex optimization problem into a non-negativity constrained least squares framework. By using a linear solution method, a sub-optimal estimator is obtained through the index exchange process between the active set and the passive set; at the same time, in order to reduce the bias caused by linearization and refine the estimate obtained by linear solution, a bias reduction method is adopted, and a weighted instrumental variable matrix that is weakly correlated with noise but strongly correlated with the data matrix is designed to improve the positioning accuracy. Description of the Drawings

[0026] To more clearly illustrate the technical solution of the present invention, the accompanying drawings required for use in the embodiments will be briefly introduced below. Obviously, the accompanying drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other accompanying drawings can also be obtained based on these drawings.

[0027] Figure 1 It is a schematic diagram of the method flow of the present invention;

[0028] Figure 2 It is a schematic diagram of sensor deployment in the control experiment of the embodiment of the present invention;

[0029] Figure 3 It is a schematic diagram of the relationship between the RMSE and CRLB of source position estimation and the path loss exponent in the control experiment of the embodiment of the present invention;

[0030] Figure 4 It is a schematic diagram of the cumulative distribution function of the source position estimation error in the control experiment of the embodiment of the present invention. Specific Embodiments

[0031] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, rather than all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present invention.

[0032] To make the above objects, features, and advantages of the present invention more obvious and understandable, the present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0033] Embodiment 1

[0034] As Figure 1 shown, it is a schematic diagram of the method flow of the present invention, and the steps include:

[0035] S1. Based on the analysis sensors in the wireless sensor network, construct a hybrid information non - negative constrained least - squares framework.

[0036] This embodiment is actually an improvement of the position estimator in the existing wireless sensor network, and further optimization is carried out on the existing method. Currently, the methods used for position estimation in the sensing network can be mainly divided into the maximum likelihood (ML) - based or least squares (LS) - based schemes; and this embodiment is based on the maximum likelihood (ML) method for improvement.

[0037] First, convert the ML positioning problem into a hybrid information nonnegative constrained least squares (HI-NCLS) framework. The purpose of this step is to transform the original non-convex optimization problem (i.e., the ML estimation problem) into a more easily solvable form. The specific methods include:

[0038] Suppose a two-dimensional wireless sensor network includes N anchor nodes with known positions and 1 target source with an unknown position. The position coordinates of the unknown target and the anchor nodes are represented as θ = [θ1, θ2] T and a i = [a i1 , a i2 T , i = 1, 2,..., N, N > 3, where (·) T is the transpose.

[0039] The received signal power at the i-th node can be defined as:

[0040]

[0041] where ||·|| represents the norm, P t is the transmission power, V0 represents the path loss with a reference distance of 1m, γ is the path loss exponent, and its distribution ranges from [1, 6].[[]END]

[0042] For the RSSD model, γ = 2 is considered a prior value, and the actual value depends on the environment. Based on the log-normal shadowing model, (1) can be expressed as: can be expressed as:

[0043] P i (dB) - V0(dB) = P t (dB) - 10γlog 10 (||θ - a i ||) + η i , (2)

[0044] where η i is the measurement noise, which can be modeled as Gaussian noise with a mean of 0 and a variance of , that is For convenience, generally set the distance between the target source and the i-th anchor node as:

[0045] r i = ||θ - a i || + ε i , (3)​

[0046] where ε i is the corresponding measurement noise, which can be modeled as Gaussian noise with mean 0 and variance , i.e., and it is assumed that

[0047] Generally, sensor 1 is taken as the reference sensor. The RSSD and TDOA measurement values between sensor 1 and i can be expressed as

[0048]

[0049]

[0050] where σ′ = 2σ 2 , c is the speed of light, P i1 = P i - P1, t i = t i - t1, and r i = ct i . Equation (5) can be rewritten as:

[0051] r i1 = ||θ - a i || - ||θ - a1|| + ε i1 , (6)

[0052] where r il = r i - r1, and δ′ = 2δ 2 .

[0053] Assuming independent RSSD and TDOA measurement data, for P = [P i1 T and r = [r i1 T , the conditional probability density function (PDF) of η i1 and ε i1 is:

[0054]

[0055] Maximizing the PDF equation (7) gives the ML estimate of θ as:

[0056]

[0057] ​​For the non-convex problem in (8), it is difficult to solve directly. Therefore, an alternative method is proposed based on the HI-NCLS framework. First, rewrite Equation (4) as:

[0058]

[0059] When the noise is small, the first-order Taylor series can be used to approximate the right side, and then square both sides to obtain

[0060]

[0061] Expanding both sides of Equation (10) gives:

[0062]

[0063] where and Then, rewrite (6) and square both sides to get:

[0064] (r i1 +||θ - a1||) 2 =(||θ - a i || + ε i1 ) 2 , (12)

[0065] Expanding both sides gives:

[0066]

[0067] Let and Combining (11) and (13), the problem in (8) can be expressed as:

[0068]

[0069] Let χ1 = ||θ - a1||, and φ = ||θ|| 2 be the variables to be estimated. Then the non-linear problem in Equation (8) can be transformed into a linear matrix form, with the constraint condition Then the HI-NCLS framework gives:

[0070]

[0071] where

[0072]

[0073] S2. Based on the hybrid information non-negative constrained least squares framework, obtain a rough sub-optimal estimate.

[0074] The (HI-NCLS) framework obtained through S1 (i.e., Equation 15) uses a linear solving method (LSM) to iteratively obtain a solution by adopting the active set method. Let be the column sum of ξ and the row index set of and Φ be subsets of, called the active set and the passive set respectively, and satisfy If there exists a vector that divides the values into as subsets and Φ, and then:

[0075]

[0076]

[0077] where j is the index of Φ. Then, the vector ξ j satisfies:

[0078]

[0079] and if it is a feasible solution to this problem, then:

[0080]

[0081] where ξ Φ is a 2(N - 1)×(t + 1) matrix and satisfies:

[0082]

[0083] The corresponding dual vector is and satisfies:

[0084]

[0085] When the above conditions are met, a feasible solution is obtained. The LSM implementation includes an outer loop and an inner loop. The outer loop solves (20), and then an index satisfying is moved from to Φ. For the inner loop, a new index α ∈ Φ can be obtained according to the following formula:

[0086]

[0087] Then, the solution is obtained by exchanging the feasible solution indices, thus obtaining a rough estimate.

[0088] S3. Based on the rough sub-optimal estimate, complete the construction of an efficient estimator.

[0089] Although the LSM can provide a closed - form estimate, the bias in the linearization process caused by noise affects the positioning performance. To mitigate the impact of the bias, a bias reduction method (BRM) is used to replace the original data matrix (DM) based on the instrumental variables matrix (IVM) to obtain a corrected estimate. Let:

[0090]

[0091] where Υ = [(ζ1) 2 ,(ζ2) 2 ,(ζ3) 2 ,ζ4] T , κ = [(θ1) 2 ,(θ2) 2 ,(Γ1) 2 ,(Γ2) 2 T , and:

[0092]

[0093] where χ = (χ1) 2 , Γ1 = θ1 - a 11 , Γ2 = θ2 - a 12 .

[0094] Then κ can be estimated as:

[0095]

[0096] and:

[0097]

[0098] The square root in (26) is not advisable, and in may increase the estimation error.

[0099] Therefore, for the problem in (15) can be re - defined as then

[0100]

[0101] where ξ = [ξ,0 2(N-1)×2 and B = [B;0 2×1 .

[0102] For ​Using the first-order Taylor series, when is close to we get:

[0103]

[0104] where

[0105]

[0106] Then, (27) can be rewritten as:

[0107]

[0108] Taking the partial derivative of (29) gives:

[0109]

[0110] Let Then:

[0111]

[0112] where C = ξ T ξ.

[0113] The matrix C is corrupted by noise, so there is a correlation between DM and the noise vector, leading to an additional bias. Therefore, C uses an IVMC IVM We can obtain:

[0114]

[0115] where ξ w = wξ,G w = wG.

[0116] Re-estimate μ i and r i1 , we get:

[0117]

[0118] and

[0119] Thus, the construction of the estimator is completed.

[0120] Example 2

[0121] To verify the superiority of the present invention, this example specifically selects a variety of methods for comparison, and the specific comparison methods are shown in Table 1.

[0122] Table 1

[0123] Method Description LLS Linear Least Squares WLS Weighted Least Squares SRWLS Square Root Weighted Least Squares IPM Interior Point Method BRLA The method of the present invention

[0124] For both LLS and WLS, they are LS-based methods. SRWLS utilizes the generalized trust region subproblem framework and uses a bisection process to estimate the target location. IPM reformulates the original problem using a logarithmic barrier function and iteratively obtains the estimate. The sensor deployment considers the target source located at (8, 26) and 9 anchor points. As Figure 2 shown, the positioning performance is evaluated using the root mean square error (RMSE), which is defined as where is the estimated value of the source location θ in the i-th trial, and M is the total number of trials. i

[0125] Figure 3 shows the relationship between the RMSE of the source location estimation of the related methods and the CRLB with the path loss exponent. These results indicate that when the noise variance increases from 3 dB to 5 dB, the change in TDOA accuracy is very small. This is because it does not consider the path loss exponent. In addition, the performance of other methods improves with the increase of the path loss exponent. Among these methods, BRLA provides the best estimate. For example, for γ = 3, (σ′) 2 = 3 dB and (δ′) 2 = 3 m, there is a difference of 1.42 m in the RMSE between BRLA and the CRLB, while the RMSE of BRLA RSSD is 1.78 m, SRWLS is 1.87 m, LSM is 2.31 m, IPM is 2.36 m, LLS is 2.43 m, and WLS is 5.42 m.

[0126] Figure 4 gives the cumulative distribution function (CDF) of the source location estimation error of the related methods, where γ = 4.5, N = 8, (σ′) 2 = 7 dm and (δ′) 2 = 7 m. As expected, the two-step BRLA with information fusion provides the best performance. For example, when the probability is 95%, for a noise variance of 7 dB, the BRLA error is 6.43 m. For the same noise variance, the corresponding errors of other methods are higher, especially 14.42 m for WLS.

[0127] Example 3

[0128] This embodiment also provides a construction system for an efficient estimator of source localization based on hybrid measurement information, including: a construction module, a solution module, and an optimization module; the construction module is used to construct a hybrid information non-negative constrained least squares framework based on the analysis sensors in the wireless sensor network; the solution module is used to obtain a rough sub-optimal estimate based on the hybrid information non-negative constrained least squares framework; the optimization module is used to complete the construction of the efficient estimator based on the rough sub-optimal estimate.

[0129] Among them, the working process of the construction module includes: performing maximum likelihood estimation localization on the signal data received by the analysis sensors in the wireless sensor network; constructing a hybrid information non-negative constrained least squares framework based on the maximum likelihood estimation localization. The working process of the solution module includes: performing linear solution on the hybrid information non-negative constrained least squares framework to obtain a rough sub-optimal estimate. The working process of the optimization module includes: optimizing the rough sub-optimal estimate by using a bias reduction method, and using a weighted instrumental variable matrix that is weakly correlated with noise but strongly correlated with the data matrix to obtain an optimized solution, and completing the construction of the efficient estimator.

[0130] The embodiments described above are only descriptions of the preferred embodiments of the present invention, and do not limit the scope of the present invention. Without departing from the design spirit of the present invention, various deformations and improvements made by those of ordinary skill in the art to the technical solutions of the present invention shall fall within the protection scope determined by the claims of the present invention.

Claims

1. A method for constructing an efficient estimator for source localization based on hybrid measurement information, characterized in that the steps including: Construct a hybrid information non - negative constrained least - squares framework based on the analytical sensors in the wireless sensor network; Obtain a rough sub - optimal estimate based on the hybrid information non - negative constrained least - squares framework; Complete the construction of an efficient estimator based on the rough sub - optimal estimate.

2. The construction method of the efficient estimator for source localization based on hybrid measurement information according to claim 1, wherein The method for constructing the hybrid information non - negative constrained least - squares framework includes: Perform maximum likelihood estimation localization on the signal data received by the analytical sensors in the wireless sensor network; Construct the hybrid information non - negative constrained least - squares framework based on the maximum likelihood estimation localization.

3. The construction method of the efficient estimator for source localization based on hybrid measurement information according to claim 1, characterized in that, The method for obtaining the rough sub - optimal estimate includes: performing linear solution on the hybrid information non - negative constrained least - squares framework to obtain the rough sub - optimal estimate.

4. The construction method of the efficient estimator for source localization based on hybrid measurement information according to claim 1, characterized in that, The method for completing the construction of the efficient estimator includes: optimizing the rough sub - optimal estimate using a bias reduction method and using a weighted instrumental variable matrix that is weakly correlated with noise but strongly correlated with the data matrix to obtain the optimized solution, thereby completing the construction of the efficient estimator.

5. A system for constructing an efficient estimator for source localization based on hybrid measurement information, the system being used to implement the method according to any one of claims 1-4, characterized in that, including: A construction module, a solution module, and an optimization module; The construction module is used to construct a hybrid information non - negative constrained least - squares framework based on the analytical sensors in the wireless sensor network; The solution module is used to obtain a rough sub - optimal estimate based on the hybrid information non - negative constrained least - squares framework; The optimization module is used to complete the construction of an efficient estimator based on the rough sub - optimal estimate.

6. The construction system of the efficient estimator for source localization based on hybrid measurement information according to claim 5, wherein The working process of the construction module includes: Perform maximum likelihood estimation localization on the signal data received by the analytical sensors in the wireless sensor network; Construct the hybrid information non - negative constrained least - squares framework based on the maximum likelihood estimation localization.

7. The construction system of the efficient estimator for source localization based on hybrid measurement information according to claim 5, characterized in that, The working process of the solution module includes: performing linear solution on the hybrid information non - negative constrained least - squares framework to obtain the rough sub - optimal estimate.

8. The construction system of the efficient estimator for source localization based on hybrid measurement information according to claim 5, characterized in that, The working process of the optimization module includes: optimizing the rough sub - optimal estimate using a bias reduction method and using a weighted instrumental variable matrix that is weakly correlated with noise but strongly correlated with the data matrix to obtain the optimized solution, thereby completing the construction of the efficient estimator.

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