A wireless positioning method based on biased RSS measurement

Abstract

A wireless positioning method based on biased RSS measurement, which uses biased RSS measurements collected by all anchor nodes to construct a high-dimensional space convex hull, so that the unknown parameter vector containing the target point position and sensor bias falls into the convex hull as much as possible, and the vertices of the convex hull are used as virtual points. Secondly, a constrained least squares estimation problem is established based on the obtained virtual points, and the convex combination coefficients are solved. Finally, the estimation of the unknown parameter vector is represented by the convex combination of the corresponding virtual points, and the target position estimation and sensor bias estimation are obtained. The positioning accuracy of this method under the condition of biased RSS measurement is significantly better than that of existing positioning methods that do not consider bias.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of wireless sensor network positioning technology, and particularly relates to a wireless positioning method based on biased RSS measurement. BACKGROUND

[0002] Wireless positioning technology is generally based on some physical measurement between target point and anchor node, such as angle of arrival, time of arrival, time difference of arrival and received signal strength (RSS). Among them, the wireless positioning method based on RSS measurement is widely used in many fields due to its low cost and easy implementation. In particular, it overcomes some shortcomings of satellite navigation positioning method, such as in indoor environment such as underground parking lot, satellite signal becomes weak or disappears, resulting in that the positioning system cannot work. The RSS positioning method uses sensors of different anchor nodes to collect RSS measurements about the target node, and on the basis of a certain measurement model (such as lognormal shadowing model), combined with the position measurement of anchor nodes, uses relevant positioning algorithm to estimate the target position.

[0003] Most of the existing RSS positioning methods assume that the measurement error only comes from random noise, and assumes zero mean Gaussian distribution. These methods include traditional maximum likelihood estimation, least squares estimation and other nonlinear methods, also including linear and convex optimization methods. However, these methods are only suitable for unbiased measurement model, that is, the above assumption of zero mean Gaussian noise. In practice, the sensor may collect RSS measurements with certain system bias, and the value may even be greater than the random noise. At this time, if the traditional positioning algorithm is used to process the biased RSS measurement, the positioning accuracy will be difficult to guarantee. The sources of sensor system bias include: (1) environmental error, that is, caused by the working environment of the sensor not being the standard state when calibrated, such as humidity, temperature change over time; (2) installation error, that is, caused by incorrect installation or placement of the sensor; (3) other errors, that is, caused by unexpected damage and other fault factors during use of the sensor. The RSS measurement equation with system bias is a nonlinear and non-convex function about the target position. If the bias is ignored in positioning, especially when multiple sensors in the sensor network have bias at the same time, it will have a great impact on the final positioning accuracy. Based on the above background, the positioning method based on biased RSS measurement has important significance for solving the bias of sensor collected RSS measurement and improving the positioning accuracy. SUMMARY

[0004] In order to overcome the defects of the existing RSS positioning technology, the purpose of the present application is to provide a wireless positioning method based on biased RSS measurement, a convex combination-based biased RSS positioning method, so that good positioning accuracy can be achieved even if there is bias in the sensor measurement.

[0005] In order to achieve the above purpose, the technical scheme of the present application is:

[0006] A wireless positioning method based on biased RSS measurement, comprising the following steps:

[0007] Step 1: based on the biased RSS measurement model and the biased RSS measurements collected by all anchor nodes in the scene at different times , different positions , different positions , different positions , a convex hull is constructed, and the vertices of the convex hull are called virtual points :

[0008] Specifically:

[0009] The biased RSS measurement model is:

[0010] (1)

[0011] Wherein, is the RSS measurement collected by the i-th anchor node at time , is the reference power, is the sensor bias of the i-th anchor node, is the path loss factor, is the distance between the position of the i-th anchor node at time and the position of the target point, is the measurement noise, which is assumed to be a zero-mean Gaussian random variable with variance , , , , , , , , , , , ,

[0012] Let , the following quadratic constraint quadratic programming problem is established

[0013] (2)

[0014] Wherein, ; solve the quadratic constraint quadratic programming problem shown in formula (2) to obtain the solution of . . Expand around in high-dimensional space to generate a convex hull, that is

[0015] (3)

[0016] The vertex is called virtual point ;

[0017] Step 2: after obtaining the virtual point , solve the following constrained least squares problem:

[0018] (4)

[0019] Wherein, , Indicates the distance function, is called convex combination coefficient; is the optimal combination coefficient;

[0020] Step 3: combine the virtual point obtained in step 1 and the optimal combination coefficient obtained in step 2 to obtain the final estimate of the unknown parameter , that is, the target position estimate is

[0021] (5)

[0022] At the same time, the sensor bias estimate of each anchor node is

[0023] (6)

[0024] Through the position estimate of the target and the bias estimate of each sensor, the wireless positioning method of the biased RSS is realized.

[0025] The present application has the beneficial effects:

[0026] The present application designs a positioning method based on convex combination for the problem that the sensor collection measurement may produce system bias in wireless RSS positioning, effectively solves the problem that most of the existing RSS positioning methods cannot handle sensor bias. By constructing convex hull and virtual point, and using convex combination of virtual point to estimate the target point position, the original non-convex maximum likelihood estimation problem in target positioning is converted into a convex optimization problem, which can be effectively solved. Compared with the existing RSS positioning method without considering sensor bias, the positioning accuracy is obviously improved. DETAILED DESCRIPTION

[0027] Figure 1This is a flowchart illustrating a wireless positioning method based on biased RSS measurement according to the present invention.

[0028] Figure 2 This is a schematic diagram of a scenario where the method of this invention is used for target localization experiments.

[0029] Figure 3 It is in accordance with the method of the present invention , The true value of the sensor deviation at the three anchor nodes is , , noise level The figure shows a comparison of the RMSE performance and theoretical lower bound CRLB of the invented method with existing methods under different measurement and acquisition conditions.

[0030] Figure 4 It is in accordance with the method of the present invention , The true value of the deviation of the three anchor node sensors is , , Number of signal measurements The figure shows a comparison of the RMSE performance of the invented method with that of existing methods and the theoretical lower bound CRLB under different noise levels. Detailed Implementation

[0031] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0032] Figure 1 The flowchart of a wireless positioning method based on biased RSS measurement according to the present invention shows that the method first constructs a convex hull using biased RSS measurement to obtain virtual points; then calculates the convex combination coefficients using the virtual points; and finally uses the convex combination of the corresponding virtual points to obtain the position estimate, thereby achieving the positioning of the target.

[0033] The RSS measurement model used:

[0034] (1)

[0035] in, For the first Each anchor node at time The collected RSS measurements of the target point, For reference power, It is the first Sensor deviation at each anchor node For path loss factor, It is the first Each anchor node at time the position of the target point the distance between the target point position , is the measurement noise, assumed to be a zero-mean Gaussian random variable with variance . , , are known, and are unknown to be estimated. Let the vector of estimated parameters be .

[0036] Therefore, the specific steps of the present application are:

[0037] Step 1: Use each RSS measurement collected by the anchor nodes and its own position to construct a ring-shaped region so that the target point falls into it with a certain probability, i.e.

[0038] (2)

[0039] where , determines the width of the ring-shaped region. The target point will fall in the intersection of all ring-shaped regions with the maximum probability, i.e. .

[0040] For formula (2), a first-order Taylor expansion is used to approximate as the following convex constraint

[0041] (3)

[0042] where . In order to get a sufficiently small convex hull so that the target falls into it, the following quadratic constraint quadratic programming problem is established

[0043] (4)

[0044] where minimizing the objective function in formula (4) will make the convex hull as small as possible, and the first two constraint conditions of formula (4) can guarantee that the target point is in each sub-ring-shaped region, i.e. in their intersection, and the third constraint condition is an auxiliary variable introduced and relaxed. Since formula (4) is a convex optimization problem, its solution is easy to obtain. And is a point, which can be regarded as the limit case of the convex hull. Obviously, the target point is most likely to be located in the region near this point. Therefore, expanding can obtain a convex hull , which represents the size of the convex hull. The vertices of this convex hull​ as a virtual point.

[0045] Step 2: Based on the convex hull and the virtual point obtained in Step 1, according to the properties of the convex hull, we can get which can be expressed as a convex combination of the virtual point, i.e.

[0046] (5)

[0047] where is the virtual point obtained in Step 1, is an unknown convex combination coefficient and , is the number of virtual points.

[0048] At the same time, using the RSS measurements collected by the sensors of each anchor node at different times, we can get the maximum likelihood estimate of the target position and sensor bias as

[0049] (6)

[0050] Further, formula (6) can be written as

[0051] (7)

[0052] where .

[0053] According to formula (5), formula (7) is equivalent to

[0054] (8)

[0055] A mathematical theorem is introduced below.

[0056] Theorem: Suppose there is a point set which forms a convex hull, where , , . Let be the boundary sphere of with radius , and be a point outside the convex hull. Then, for any finite integer and all possible , the following limit holds

[0057] (9)

[0058] where is the measurement function defined in formula (7), .

[0059] From the above theorem, under the condition that the convex hull is small enough, formula (8) can be approximated as the following constrained least squares problem

[0060] (10)

[0061] wherein, , denotes a distance function, called convex combination coefficients; is an optimal combination coefficient; formula (4) is an approximate problem about the maximum likelihood estimation of , and is a convex optimization problem, and the corresponding optimal combination coefficient is obtained by solving.

[0062] Step 3: According to the virtual point obtained in step 1 and the combination coefficient obtained in step 2 and formula (5), the estimation of the unknown parameter vector can be expressed as , wherein, . Accordingly, the position estimation of the target is

[0063] (11)

[0064] The bias estimation of the sensor is

[0065] (12)

[0066] Through the position estimation of the target and the bias estimation of each sensor, the wireless positioning method of the biased RSS is realized, and the convex combination method of the biased RSS positioning is named as CCBRL.

[0067] Figure 2 A scene diagram of a target positioning experiment using the present application is described. Among them, three anchor nodes collect RSS measurements of the target point at different times through spatial motion, and realize target positioning in combination with the method of the present application.

[0068] Figure 3 is the positioning result performance using the Figure 2 scene and under different measurement collection times. It can be seen that no matter how many times the RSS measurements are collected, the CCRBL method of the present application has obviously higher positioning accuracy than the existing SDP-R method, and is close to the theoretical lower bound CRLB.

[0069] Figure 4 is the positioning result performance using the Figure 2 scene and under different noise levels. It can be seen that no matter how high or low the measurement noise level is, the CCRBL method of the present application has better positioning performance, effectively eliminating the influence of sensor bias on positioning accuracy.

Claims

1. A method of wireless positioning based on biased RSS measurements, characterized in that, The method comprises the following steps: Step 1: Based on the biased RSS measurement model and all scenarios Anchor nodes at different times Different positions The collected biased RSS measurements Construct a convex hull, and the vertices of the convex hull are called virtual points. : Step 2: Obtain the virtual point Afterwards, solve the following constrained least squares problem: （4） wherein, , denotes a distance function, are called convex combination coefficients; are optimal combination coefficients; Step 3: Combine the virtual point from Step 1 with the optimal combining coefficients from Step 2 to obtain the final estimate of the unknown parameter , i.e., the target position estimate is （5） At the same time, the anchor node sensor bias estimation is （6） Through the position estimation of the target and the bias estimation of each sensor, a biased RSS wireless positioning method is realized.

2. The wireless positioning method based on biased RSS measurement according to claim 1, wherein, The step 1 is specifically: The biased RSS measurement model is: （1） wherein, is the RSS measurement collected by the th anchor node at time , is the reference power, is the sensor bias of the th anchor node, is the path loss factor, is the distance between the position of the th anchor node at time and the target point position , is the measurement noise, assumed to be a zero-mean Gaussian random variable with variance , , , , , are known, and are unknown to be estimated. Let , establish the following quadratic constraint quadratic programming problem （2） where, solving the quadratic constraint quadratic programming problem shown in equation (2) to obtain the solution expanding around in the high-dimensional space to generate a convex hull, i.e.​ （3） The apex of which is called the virtual point .

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