Hybrid RSS / AOA-based Wireless Sensor Network Localization Method with Unknown Transmission Power

Abstract

The present invention discloses a positioning method for a wireless sensor network based on hybrid RSS / AOA with unknown transmission power. Based on the RSS measurement model, the AOA azimuth measurement model, and the AOA elevation angle measurement model, an original non-convex objective optimization problem is constructed according to the least squares criterion; the semi-definite relaxation technique and the second-order cone relaxation technique are used to relax the variables or constraint conditions in the equivalent description after introducing variables in the original non-convex objective optimization problem constructed according to the least squares criterion, so as to obtain the final convex objective optimization problem; the hybrid semi-definite / second-order cone programming technique is used to solve the final convex objective optimization problem, and the position and transmission power of the target node are jointly estimated; the advantage is that it can ensure that the optimization of unknown variables can obtain the global optimal solution and is not affected by local convergence, thereby effectively improving the positioning accuracy and effectively suppressing the influence of measurement noise errors.

Description

Technical Field

[0001] The present invention relates to a wireless sensor network positioning technology, and in particular to a wireless sensor network positioning method based on hybrid RSS (Received Signal Strength) / AOA (Angle of Arrival) with unknown transmission power. Background Art

[0002] In recent years, indoor positioning applications using wireless sensor networks (WSNs) have been widely studied. A wireless sensor network composed of a large number of stationary or mobile sensors realizes data collection, processing, and transmission functions. Positioning technology is a supporting technology for wireless sensor network technology, that is, the position of a target node (unknown node, i.e., a sensor with unknown position) is determined by using the position of anchor nodes (known nodes, i.e., sensors with known positions) through measurement values.

[0003] Existing distance-related wireless sensor network positioning methods can be divided into positioning methods based on time of arrival (TOA), time difference of arrival (TDOA), angle of arrival (AOA), received signal strength (RSS), and their hybrids. Among them, the hybrid-based wireless sensor network positioning method can extract more effective information from the wireless sensor network, thereby improving the positioning accuracy. Currently, a variety of wireless sensor network positioning methods based on hybrid RSS / AOA have been proposed. A weighted least squares method (WLS) proposed by K. Yu, which obtains a closed-form analytical solution to the positioning problem, but the positioning accuracy of this method drops sharply under large noise power; Tomic S transforms the positioning problem into a generalized trust region subproblem (GTRS) framework and solves the non-convex problem by the bisection method. This method has a lower complexity, but the positioning performance of this method is poor. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a wireless sensor network positioning method based on hybrid RSS / AOA with unknown transmission power, which realizes positioning when the transmission power of the target node is unknown and has high positioning accuracy.

[0005] The technical solution adopted by the present invention to solve the above technical problem is as follows: A wireless sensor network positioning method based on hybrid RSS / AOA with unknown transmission power, characterized by comprising the following steps:

[0006] Step 1: Deploy a target node with an unknown position and N anchor nodes with known positions inside the wireless sensor network, and set the transmission power of the target node to be unknown; and establish a three-dimensional coordinate system inside the wireless sensor network as a reference coordinate system, record the position of the target node in the reference coordinate system as x, and record the position of the i-th anchor node in the reference coordinate system as a i; where N is a positive integer, representing the number of anchor nodes deployed in the wireless sensor network, N≥3, 1≤i≤N;

[0007] Step 2: The signals transmitted by the target node in the wireless sensor network are received by each anchor node. The signals received by the anchor nodes are described by the RSS measurement model as follows: The signals received by the anchor nodes are described by the AOA azimuth measurement model as follows: The signals received by the anchor nodes are described by the AOA elevation measurement model as follows: where L i represents the path loss value of the signal transmitted by the target node and received by the i-th anchor node on the transmission path. L i also represents the intensity measurement value of the signal transmitted by the target node and received by the i-th anchor node. L0 represents the reference path loss value of the signal transmitted by the target node at the reference distance d0. d0 represents the reference distance. γ represents the path loss factor, γ∈[2.2,2.8]. The symbol "||||" represents the modulus of the vector. ||x - a i || represents the true distance between the target node and the i-th anchor node. n i represents the intensity measurement noise of the signal transmitted by the target node and received by the i-th anchor node. n i follows a Gaussian distribution with a mean of 0 and a variance of . φ i represents the azimuth measurement value of the signal transmitted by the target node and received by the i-th anchor node. m i represents the azimuth measurement noise of the signal transmitted by the target node and received by the i-th anchor node. m i follows a Gaussian distribution with a mean of 0 and a variance of . represents the elevation measurement value of the signal transmitted by the target node and received by the i-th anchor node. v i represents the elevation measurement noise of the signal transmitted by the target node and received by the i-th anchor node. v i follows a Gaussian distribution with a mean of 0 and a variance of . x1 represents the first component of x, i.e., the component on the X-axis. x2 represents the second component of x, i.e., the component on the Y-axis. x3 represents the third component of x, i.e., the component on the Z-axis. a i1 represents the first component of a i , i.e., the component on the X-axis. a i2 represents the second component of a i , i.e., the component on the Y-axis. a i3 represents the third component of a i , i.e., the component on the Z-axis;

[0008] Step 3: Perform equation transformation on and perform a first-order Taylor expansion on the noise term to obtain an approximate expression for the noise term where

[0009] Similarly, perform equation transformation on and perform a first-order Taylor expansion on the noise term to obtain an approximate expression for the noise term ξ i ≈ c i (x - a i ), 1 ≤ i ≤ N; where ξ i = m i (cos(φ i )(x1 - a i1 ) + sin(φ i )(x2 - a i2 ))), c i = [-sin(φ i ), cos(φ i ), 0] T , and the superscript "T" represents the transpose of a vector;

[0010] Perform equation transformation on and perform a first-order Taylor expansion on the noise term to obtain an approximate expression for the noise term where k = [0, 0, 1] T .

[0011] Step 4: Based on Step 3, construct the original non-convex objective optimization problem according to the least squares criterion, described as: where min() is the function to take the minimum value;

[0012] Step 5: Introduce variables h, f, g, l, d, t into the description of the original non-convex objective optimization problem to equivalently describe the original non-convex objective optimization problem as:

[0013] where s.t. means "subject to...", h i represents the i-th component of variable h, d i represents the i-th component of variable d, f i represents the i-th component of variable f, l i represents the i-th component of variable l, g i represents the i-th component of variable g;

[0014] Step 6: Define variable z = x T x, η 2 = τ; then use the semi-definite relaxation technique to relax z = x T x to Using the second-order cone relaxation technique, relax η 2 = τ to Using the second-order cone relaxation technique, relax d i = ||x - a i || to d i ≥ ||x - a i ||; where, I3 represents the 3-order identity matrix, represents the matrix is a positive semi-definite matrix;

[0015] Step 7: According to and d i ≥ ||x - a i ||, obtain the final convex objective optimization problem, described as:

[0016] Step 8: Use the mixed semi-definite programming / second-order cone programming technique to solve the final convex objective optimization problem, and obtain the estimated values of x and L0 respectively.

[0017] In the said Step 8, use the CVX toolbox in the MATLAB simulation to solve the final convex objective optimization problem.

[0018] Compared with the prior art, the advantages of the present invention are as follows:

[0019] 1) The method of the present invention takes into account the hardware defects of the sensor during use. As the usage time changes and the power energy of the sensor is consumed, the transmission power of the target node is unstable. Therefore, the transmission power of the target node is regarded as an unknown variable, that is, positioning is performed when the transmission power of the target node is unknown.

[0020] 2) The method of the present invention uses the semi-definite relaxation and second-order cone relaxation techniques to relax the variables or constraint conditions in the equivalent description of the original non-convex objective optimization problem constructed according to the least squares criterion after introducing variables, and then obtains the final convex objective optimization problem, jointly estimating the position and transmission power of the target node, ensuring that the optimization of the unknown variables can obtain the global optimal solution and is not affected by local convergence, thereby effectively improving the positioning accuracy and effectively suppressing the influence of measurement noise errors.

[0021] 3) The method of the present invention mainly uses the RSS measurement model and takes the AOA measurement model as an auxiliary for positioning, effectively improving the positioning accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 is the overall implementation block diagram of the method of the present invention;

[0023] Figure 2 Scenario diagram for hybrid RSS / AOA positioning;

[0024] Figure 3 Schematic diagram of the positioning performance of the method of the present invention, the existing weighted least squares method, and the existing generalized trust region subproblem method varying with the magnitude of the signal reception strength measurement noise when the number N of anchor nodes deployed in the wireless sensor network is 6, and the standard deviations of the azimuth measurement noise and the elevation measurement noise are both 5 deg;

[0025] Figure 4 Schematic diagram of the positioning performance of the method of the present invention, the existing weighted least squares method, and the existing generalized trust region subproblem method varying with the magnitude of the azimuth measurement noise when the number N of anchor nodes deployed in the wireless sensor network is 6, the standard deviation of the strength measurement noise is 6 dB, and the standard deviation of the elevation measurement noise is 5 deg;

[0026] Figure 5 Schematic diagram of the positioning performance of the method of the present invention, the existing weighted least squares method, and the existing generalized trust region subproblem method varying with the magnitude of the elevation measurement noise when the number N of anchor nodes deployed in the wireless sensor network is 6, the standard deviation of the strength measurement noise is 6 dB, and the standard deviation of the direction angle measurement noise is 5 deg;

[0027] Figure 6 Schematic diagram of the positioning performance of the method of the present invention, the existing weighted least squares method, and the existing generalized trust region subproblem method varying with the number of anchor nodes deployed in the wireless sensor network when the standard deviation of the strength measurement noise is 6 dB, and the standard deviations of the azimuth measurement noise and the elevation measurement noise are both 5 deg. Detailed implementation manners

[0028] The present invention will be further described in detail below in conjunction with the embodiments with reference to the drawings.

[0029] A wireless sensor network positioning method based on hybrid RSS / AOA with unknown transmission power proposed by the present invention has an overall implementation block diagram as shown in Figure 1 and includes the following steps:

[0030] Step 1: Deploy a target node with an unknown position and N anchor nodes with known positions in the wireless sensor network, and set the transmission power of the target node to be unknown; and establish a three-dimensional coordinate system in the wireless sensor network as a reference coordinate system, record the position of the target node in the reference coordinate system as x, and record the position of the i-th anchor node in the reference coordinate system as a i ; where N is a positive integer, N represents the number of anchor nodes deployed in the wireless sensor network, N≥3, and in this embodiment, N = 6, 1≤i≤N.

[0031] Step 2: The signals transmitted by the target node within the wireless sensor network are received by each anchor node. The signals received by the anchor nodes are described using the RSS measurement model as follows: The signals received by the anchor nodes are described using the AOA azimuth measurement model as follows: The signals received by the anchor nodes are described using the AOA elevation measurement model as follows: where, L i represents the path loss value of the signal transmitted by the target node and received by the i-th anchor node on the transmission path. L i also represents the intensity measurement value of the signal transmitted by the target node and received by the i-th anchor node. L0 represents the reference path loss value of the signal transmitted by the target node at the reference distance d0, that is, the transmission power of the target node. L0 is unknown. d0 represents the reference distance, which is the distance at a certain point on the transmission path of the signal transmitted by the target node. γ represents the path loss factor, γ ∈ [2.2, 2.8]. The symbol "||||" represents the modulus of the vector. ||x - a i || represents the true distance between the target node and the i-th anchor node. n i represents the intensity measurement noise of the signal transmitted by the target node and received by the i-th anchor node. n i obeys a Gaussian distribution with a mean of 0 and a variance of , which is given during simulation. φ i represents the azimuth measurement value of the signal transmitted by the target node and received by the i-th anchor node. m i represents the azimuth measurement noise of the signal transmitted by the target node and received by the i-th anchor node. m i obeys a Gaussian distribution with a mean of 0 and a variance of , which is given during simulation. In simulation, represents the elevation measurement value of the signal transmitted by the target node and received by the i-th anchor node. v i represents the elevation measurement noise of the signal transmitted by the target node and received by the i-th anchor node. v i obeys a Gaussian distribution with a mean of 0 and a variance of , which is given during simulation. x1 represents the first component of x, i.e., the component on the X-axis. x2 represents the second component of x, i.e., the component on the Y-axis. x3 represents the third component of x, i.e., the component on the Z-axis. a i1 represents the first component of a i on the X-axis. a i2 represents the second component of a i on the Y-axis. ai3 Denote a i The third component of, i.e., the component on the Z-axis.

[0032] Figure 2 Figure 2 shows the scenario diagram of hybrid RSS / AOA positioning.

[0033] Step 3: Perform equation transformation on and perform a first-order Taylor expansion on the noise term to obtain an approximate expression for the noise term where

[0034] Similarly, perform equation transformation on and perform a first-order Taylor expansion on the noise term to obtain an approximate expression for the noise term ξ i ≈c i (x - a i ), 1 ≤ i ≤ N; where ξ i = m i (cos(φ i )(x1 - a i1 ) + sin(φ i )(x2 - a i2 ))), c i = [-sin(φ i ), cos(φ i ), 0] T , and the superscript "T" represents the transpose of a vector.

[0035] Perform equation transformation on and perform a first-order Taylor expansion on the noise term to obtain an approximate expression for the noise term where k = [0, 0, 1] T .

[0036] Step 4: Based on Step 3, construct the original non-convex objective optimization problem according to the least square (LS) criterion, described as: where min() is the function to take the minimum value.

[0037] Step 5: Introduce variables h, f, g, l, d, t into the description of the original non-convex objective optimization problem to equivalently describe the original non-convex objective optimization problem as:

[0038] where s.t. means "subject to...", h i represents the i-th component of variable h, d i represents the i-th component of variable d, f i represents the i-th component of variable f, li represents the i-th component of variable l, g i represents the i-th component of variable g;

[0039] Step 6: Define variable z = x T x, η 2 = τ; then use the semidefinite relaxation technique (SDR) to relax z = x T x to Use the second-order cone relaxation technique (SOCR) to relax η 2 = τ to Use the second-order cone relaxation technique to relax d i = ||x - a i || to d i ≥ ||x - a i ||; where, I3 represents the 3-order identity matrix, represents the matrix is a positive semidefinite matrix.

[0040] Step 7: According to and d i ≥ ||x - a i ||, obtain the final convex objective optimization problem, described as:

[0041] Step 8: Use the hybrid semi-definite programming (SDP) / second-order cone programming (SOCP) technique to solve the final convex objective optimization problem, and obtain the respective estimated values of x and L0.

[0042] Here, in Step 8, the CVX toolbox is used in the MATLAB simulation to solve the final convex objective optimization problem.

[0043] To verify the effectiveness and feasibility of the method of the present invention, a simulation experiment is conducted on the method of the present invention.

[0044] In the wireless sensor network, a three-dimensional coordinate system is established as the reference coordinate system, and the positions of the anchor nodes and the target nodes are randomly distributed in a 30 m × 30 m × 30 m cube space.

[0045] In the simulation experiment, the root mean square error (RMSE) is used as the main performance index of the hybrid RSS / AOA-based wireless sensor network localization method with unknown transmit power, and its definition is: where, Mc represents the number of Monte Carlo experiments, 1 ≤ j ≤ Mc, x jDenote the actual position of the target node at the j-th Monte Carlo experiment, Denote the estimated position of the target node at the j-th Monte Carlo experiment.

[0046] In the simulation experiment, the existing weighted least squares method and the existing generalized trust region subproblem method are selected as the comparison methods. The weighted least squares method is cited from K. Yu. 3-D localization error analysis in wireless networks[J]. IEEE Trans. Wirel. Commun., 2007, 6(10): 3473-3481. (3-D wireless network localization error analysis[J]. IEEE Transactions on Wireless Communications); the generalized trust region subproblem method is cited from S. Tomic, M. Beko, and R. Dinis. 3-D localization in wireless sensor networks using RSS and AOA measurements[J]. IEEE Transactions On Vehicular Technology, 2017, 66(4): 3197-3210. (3-D RSS and AOA localization in wireless sensor networks[J]. IEEE Transactions on Vehicular Technology).

[0047] 1) Test the variation of the positioning performance of the method of the present invention, the existing weighted least squares method, and the existing generalized trust region subproblem method with the magnitude of the signal reception strength measurement noise when the number of anchor nodes N = 6 deployed in the wireless sensor network, the standard deviation of the azimuth measurement noise and the standard deviation of the elevation measurement noise are both 5 deg, as Figure 3 shown.

[0048] 2) Test the variation of the positioning performance of the method of the present invention, the existing weighted least squares method, and the existing generalized trust region subproblem method with the magnitude of the azimuth measurement noise when the number of anchor nodes N = 6 deployed in the wireless sensor network, the standard deviation of the strength measurement noise is 6 dB, and the standard deviation of the elevation measurement noise is 5 deg, as Figure 4 shown.

[0049] 3) Test the variation of the positioning performance of the method of the present invention, the existing weighted least squares method, and the existing generalized trust region subproblem method with the magnitude of the elevation measurement noise when the number of anchor nodes N = 6 deployed in the wireless sensor network, the standard deviation of the strength measurement noise is 6 dB, and the standard deviation of the direction angle measurement noise is 5 deg, as Figure 5 shown.

[0050] FromFigure 3 , Figure 4 and Figure 5 It can be seen from [0000264], [0000265] and [0000266] that the method of the present invention has more accurate positioning accuracy and is closer to the Cramer-Rao lower bound within the range of variation of the standard deviation of the measurement noise considered in various cases. At the same time, it is observed that in general, as the standard deviation of the measurement noise increases, the positioning accuracy of all methods decreases. However, the method of the present invention is more stable under the influence of various measurement noises compared with the existing weighted least squares method.

[0051] 4) The variation of the positioning performance of the method of the present invention, the existing weighted least squares method and the existing generalized trust region subproblem method with the number of anchor nodes deployed in the wireless sensor network when the standard deviation of the test intensity measurement noise is 6 dB, and the standard deviations of the azimuth measurement noise and the elevation measurement noise are both 5 deg, as Figure 6 shown.

[0052] From Figure 6 it can be seen that the method of the present invention shows a downward trend as the number of anchor nodes increases. This is because as the number of anchor nodes increases, there is more information in the wireless sensor network for more accurate estimation. And in any scenario, the method of the present invention is closer to the Cramer-Rao bound compared with the existing methods. Moreover, as the number of anchor nodes increases, the gap in positioning accuracy between the existing methods and the method of the present invention increases, which shows the superior performance of the method of the present invention.

[0053] It can be seen from the above simulation results that the method of the present invention has good performance, can well meet the requirements of high-precision positioning, and can effectively suppress the influence of noise errors, which fully demonstrates the feasibility and effectiveness of the method of the present invention.

Claims

1. A positioning method for a wireless sensor network based on hybrid RSS / AOA with unknown transmission power, characterized in that Including the following steps: Step 1: Deploy a target node at an unknown location and N anchor nodes at known locations inside the wireless sensor network, and set the transmission power of the target node to be unknown; And establish a three-dimensional coordinate system within the wireless sensor network as the reference coordinate system. Denote the position of the target node in the reference coordinate system as x, and denote the position of the i-th anchor node in the reference coordinate system as a i ; where N is a positive integer, N represents the number of anchor nodes deployed within the wireless sensor network, N≥3, and 1≤i≤N; Step 2: The signal transmitted by the target node within the wireless sensor network is received by each anchor node. The received signal at the anchor node is described using the RSS measurement model as follows: The received signal at the anchor node is described using the AOA azimuth measurement model as follows: The received signal at the anchor node is described using the AOA elevation measurement model as follows: where RSS is the received signal strength, AOA is the angle of arrival, L i represents the path loss value of the signal transmitted by the target node and received by the i-th anchor node on the transmission path. L0 represents the reference path loss value of the signal transmitted by the target node at the reference distance d0. d0 represents the reference distance, γ represents the path loss factor, γ ∈ [2.2, 2.8]. The symbol "|| ||" represents the modulus of a vector. ||x - a i || represents the true distance between the target node and the i-th anchor node. n i represents the intensity measurement noise of the signal transmitted by the target node and received by the i-th anchor node. n i obeys a Gaussian distribution with a mean of 0 and a variance of . φ i represents the azimuth measurement value of the signal transmitted by the target node and received by the i-th anchor node. m i represents the azimuth measurement noise of the signal transmitted by the target node and received by the i-th anchor node. m i obeys a Gaussian distribution with a mean of 0 and a variance of . represents the elevation measurement value of the signal transmitted by the target node and received by the i-th anchor node. v i represents the elevation measurement noise of the signal transmitted by the target node and received by the i-th anchor node. v i obeys a Gaussian distribution with a mean of 0 and a variance of . x1 represents the first component of x, i.e., the component on the X-axis. x2 represents the second component of x, i.e., the component on the Y-axis. x3 represents the third component of x, i.e., the component on the Z-axis. a i1 represents the first component of a i , i.e., the component on the X-axis. a i2 represents the second component of a i , i.e., the component on the Y-axis. a i3 represents the third component of a i , i.e., the component on the Z-axis; Step 3: For perform equation transformation and perform first-order Taylor expansion on the noise term to obtain an approximate expression of the noise term where Similarly, for perform equation transformation and perform first-order Taylor expansion on the noise term to obtain the approximate expression ξ of the noise term i ≈c i (x - a i ), 1 ≤ i ≤ N; where ξ i = m i (cos(φ i )(x1 - a i1 ) + sin(φ i )(x2 - a i2 ))), c i = [-sin(φ i ), cos(φ i ), 0] T , the superscript "T" represents the transpose of the vector; For perform equation transformation and perform first-order Taylor expansion on the noise term to obtain an approximate expression for the noise term where k = [0, 0, 1] T ; Step 4: Based on Step 3, construct an original non-convex objective optimization problem according to the least squares criterion, which is described as: where min() is the function for taking the minimum value; Step 5: Introduce variables h, f, g, l, d, t into the description of the original non-convex objective optimization problem, so that the original non-convex objective optimization problem is equivalently described as: Among them, s.t. means "subject to...", h i represents the i-th component of the variable h, d i represents the i-th component of the variable d, f i represents the i-th component of the variable f, l i represents the i-th component of the variable l, g i represents the i-th component of the variable g; Step 6: Define the variable z = x T x, η 2 = τ; then use the semidefinite relaxation technique to relax z = x T x to Use the second-order cone relaxation technique to relax η 2 = τ to Use the second-order cone relaxation technique to relax d i = ||x - a i || to d i ≥ ||x - a i ||; where, I3 represents the 3rd order identity matrix, represents the matrix is a positive semidefinite matrix; Step 7: According to and d i ≥ ||x - a i ||, the final convex objective optimization problem is obtained and described as: Step 8: Use the hybrid semidefinite programming / second-order cone programming technique to solve the final convex objective optimization problem, and obtain the respective estimated values of x and L0.

2. The wireless sensor network positioning method based on hybrid RSS / AOA with unknown transmission power according to claim 1, characterized in that In Step 8 described above, use the CVX toolbox in MATLAB simulation to solve the final convex objective optimization problem.

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