An RSS positioning method with uncertain anchor node positions

Abstract

A RSS positioning method for uncertain anchor node positions is disclosed. First, the method performs an equivalent transformation on the original RSS measurement model for uncertain anchor node positions to obtain a new model. Second, a maximum likelihood estimation problem for target position estimation is established based on the new model. Third, mathematical methods such as convex relaxation and approximation are used to transform the non-convex maximum likelihood estimation problem into a convex semi-definite programming problem. Finally, the obtained semi-definite programming problem is solved using the interior point method to obtain the target position estimate, i.e., the final positioning result. The results of the present invention show that under the condition of uncertain anchor node positions, the positioning accuracy of this method is significantly higher than that of some existing positioning methods.

Description

Technical Field

[0001] The present invention relates to the technical field of wireless sensor network positioning, and in particular to a wireless RSS positioning method with uncertain anchor node positions. Background Art

[0002] Positioning technology based on wireless sensor networks is widely used in many fields, such as target tracking, emergency rescue, and intelligent transportation. In particular, wireless positioning technology offers numerous advantages over traditional satellite positioning technology in indoor environments. For example, in underground spaces, weakened or absent satellite signals can cause positioning systems to fail. However, wireless positioning technology does not rely on satellite signals and can function normally using the system's own wireless signals. Wireless positioning methods can be categorized by the type of wireless signal measurement used, including signal arrival angle positioning, signal arrival time positioning, signal arrival time difference positioning, and received signal strength (RSS) positioning. Among these different positioning methods, RSS-based positioning methods have garnered particular attention. This is because RSS measurements are easy to obtain, and the corresponding positioning systems are relatively inexpensive and simple to implement.

[0003] In existing RSS positioning methods, RSS measurements and anchor node locations constitute the two data sources of the positioning system. It is generally assumed that only RSS measurements contain noise, while the anchor node locations are precisely known. Based on this assumption, positioning methods can be categorized into nonlinear, linear, and optimization methods, depending on the different estimation problems and solution methods for the target location. However, in reality, anchor node locations are also obtained through GPS or other positioning methods, inevitably subject to certain errors or uncertainties. Anchor nodes play a key role in target positioning, acting as base stations. Uncertainty in their locations significantly impacts the accuracy of positioning results. Therefore, this uncertainty in anchor node locations, like RSS measurement noise, cannot be ignored. To this end, in related positioning technologies, anchor node location uncertainty is modeled as a zero-mean Gaussian random variable, resulting in some corresponding positioning methods. Clearly, in this modeling approach, the magnitude of anchor node location uncertainty can be unbounded, due to the characteristics of Gaussian random variables. However, in practice, location uncertainty or error is often a deterministic, non-random quantity and will not be infinite. Furthermore, in some cases, people have prior information about the error, such as its magnitude. Existing positioning technologies lack methods for addressing non-random anchor node position uncertainty. Given this background, research on RSS positioning methods for anchor node position uncertainty, particularly modeling methods and solutions for positioning problems under non-random uncertainty, is crucial for addressing the problem of low positioning accuracy caused by inaccurate anchor node positions. Summary of the Invention

[0004] In order to solve the problem of anchor node position uncertainty in existing RSS positioning, the purpose of the present invention is to provide an RSS positioning method with uncertain anchor node positions, so that even when the anchor node positions are uncertain, the positioning result can still achieve good accuracy.

[0005] In order to achieve the above object, the technical solution of the present invention is:

[0006] An RSS positioning method for an uncertain anchor node position includes the following steps:

[0007] Step 1: Perform equivalent transformation on the original RSS measurement model with uncertain anchor node positions to obtain a new model;

[0008] Assume that there are n anchor nodes and 1 target point in a wireless sensor network, based on the following RSS measurement model with uncertain anchor node locations:

[0009]

[0010] Among them, P i,j is the RSS measurement collected by the j-th anchor node for the i-th time, P0 is the reference power, β is the path loss factor, x is the target point position to be estimated, y j is the unknown true position of the jth anchor node, d j It is y j The distance from x, z j is the uncertain anchor node position, and the error is ε j , and assume that the upper limit of its modulus is a j , n i,j For the measurement noise, assume it is a Gaussian random variable with zero mean and variance σ 2 ; P0, β, σ are all known; let X=[x,y1,y2,...,y n ] T is the parameter vector to be estimated;

[0011] The measurement model of formula (1) is equivalently converted into

[0012]

[0013] Step 2: Based on the new model, establish the maximum likelihood estimation problem for target position estimation;

[0014] Based on the model shown in formula (2), using the measurement {P i,j}Establish the maximum likelihood estimation problem with respect to the X-band constraint:

[0015]

[0016] in, k is the number of measurement sampling times;

[0017] Step 3: Use mathematical methods such as convex relaxation and approximation to transform the non-convex maximum likelihood estimation problem into a convex semi-definite programming problem;

[0018] The non-convex optimization problem shown in formula (3) is approximated as the following semi-positive programming problem:

[0019]

[0020] in, Z is an auxiliary variable;

[0021] Step 4: Use the interior point method to solve the convex optimization problem shown in formula (4) to obtain the optimization result about the target position x, that is, to obtain the target position estimate, and realize the RSS positioning method with uncertain anchor node position.

[0022] Beneficial effects of the present invention:

[0023] This paper addresses the problem of anchor node position uncertainty in wireless RSS positioning by designing a semidefinite programming method. This method effectively addresses the inability of existing RSS positioning methods to handle non-random anchor node position uncertainty. Through an equivalent transformation, the original RSS measurement model is transformed into a new model, thereby establishing a maximum likelihood estimation problem for the target position. Ultimately, the corresponding non-convex problem is transformed into a convex semidefinite programming problem, which can effectively solve and obtain the target position estimate. Compared with existing methods that do not consider anchor node position uncertainty, the positioning method of this paper achieves significantly higher accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 It is a flow chart of an RSS positioning method with uncertain anchor node position according to the present invention.

[0025] Figure 2 Schematic diagram of a scenario for a target positioning experiment using the method of the present invention.

[0026] Figure 3 According to the method of the present invention, P0 = -40dB, β = 3, the upper limit value of the anchor node position uncertainty range a j =2, the number of measurement acquisitions is 2 and the Monte Carlo experiment is repeated 200 times, and the comparison of the root-mean-square error (RMSE) of the invented method and the existing method with the change of the RSS measurement noise level is shown in the figure.

[0027] Figure 4 According to the method of the present invention, P0 = -40dB, β = 3, RSS noise level σ 2=2, RSS measurement acquisition is 2 and Monte Carlo experiment is performed 200 times, and the RMSE of the method of the present invention and the existing method changes with the uncertainty level of the anchor node position. DETAILED DESCRIPTION

[0028] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0029] like Figure 1 This is a flowchart of the RSS positioning method for anchor node position uncertainty. As can be seen, the method first performs an equivalent transformation on the original RSS measurement model to obtain a new model with uncertain anchor node positions. It then establishes a maximum likelihood estimation problem for target position estimation. Finally, this non-convex problem is transformed into a convex semidefinite programming problem and solved to obtain the positioning result.

[0030] The present invention specifically provides an RSS positioning method for an uncertain anchor node position, comprising the following steps:

[0031] Step 1: Assume that there are n anchor nodes and 1 target point in the wireless sensor network, based on the following RSS measurement model with uncertain anchor node locations:

[0032]

[0033] Among them, P i,j is the RSS measurement collected by the j-th anchor node for the i-th time, P0 is the reference power, β is the path loss factor, and y j is the unknown true position of the jth anchor node, d j It is y j The distance from the target point position x, z j is the uncertain anchor node position, and the error is ε j , and assume that the upper limit of its modulus is a j , n i,j is the RSS measurement noise, which is assumed to be a zero-mean Gaussian random variable with variance σ 2 P0, β, σ are all known. Let X=[x,x1,x2,...,x n ] T is the parameter vector to be estimated.

[0034] According to formula (1), the true position of the anchor node can be expressed as:

[0035] y j =z j -ε j (2)

[0036] Therefore, the RSS measurement equation can be written as:

[0037]

[0038] Because, d j (x,z j -ε j )=d j (x+ε j ,z j ), formula (3) can be further written as

[0039]

[0040] Therefore, the RSS measurement model shown in formula (1) can be equivalently converted into the following new model:

[0041]

[0042] Step 2: Based on the model shown in formula (5) and the measurement noise being an independent Gaussian distribution, the target position estimation problem is established according to the maximum likelihood estimation criterion:

[0043]

[0044] in, k is the number of RSS measurement sampling times.

[0045] Step 3: According to

[0046] and The non-convex problem shown in formula (6) can be approximated as the following semi-positive programming problem:

[0047]

[0048] in, Z is an auxiliary variable.

[0049] Step 4: Use the interior point method to solve the semi-definite programming problem shown in formula (7) to obtain the target positioning result x, that is, the target position estimate, and implement the RSS positioning method with uncertain anchor node positions. This method is named SDP-NEW.

[0050] Figure 2 This diagram depicts a scenario for a target localization experiment using the present invention. Ten anchor nodes are randomly distributed within the area shown in the diagram. Each anchor node collects two RSS measurements of the target point. The RSS measurements collected by each anchor node are combined with the present invention's method to achieve target localization.

[0051] Figure 3 is Figure 2Schematic diagram of the positioning performance of the invented SDP-NEW method with the change of RSS measurement noise level in the scenario shown. Among them, the upper limit of the anchor node position uncertainty level a j It is fixed at 3. It can be seen that since the invented method takes this uncertainty into account, its positioning accuracy is significantly higher than that of the semi-definite programming method (denoted as SDP-R) and the optimal linear unbiased estimation method (denoted as BLUE-R) in the prior art that do not consider uncertainty.

[0052] Figure 4 is Figure 2 Schematic diagram of the positioning performance of the invented method in the scenario shown as the uncertainty level of the anchor node position changes. j is fixed to 2. It can also be seen that since the invented SDP-NEW method takes the uncertainty of the anchor node position into account, it has obvious performance advantages over the existing SDP-R and BLUE-R methods.

Claims

1. An RSS positioning method for uncertain anchor node positions, characterized in that: The following steps are involved: Step 1: Perform equivalent transformation on the original RSS measurement model with uncertain anchor node positions to obtain a new model; Step 2: Establish the maximum likelihood estimation problem for target position estimation based on the new model; Step 3: Use convex relaxation and approximate mathematical methods to transform the non-convex maximum likelihood estimation problem into a convex semi-definite programming problem; Step 4: Use the interior point method to solve the convex optimization problem shown in formula (4) to obtain the optimization result of the target position, that is, the target position estimate; The step 1 is specifically as follows: Assume that there are n anchor nodes and 1 target point in a wireless sensor network, based on the following RSS measurement model with uncertain anchor node locations: Among them, P i,j is the RSS measurement collected by the j-th anchor node for the i-th time, P0 is the reference power, β is the path loss factor, x is the target point position to be estimated, y j is the unknown true position of the jth anchor node, d j It is y j The distance from x, z j is the uncertain anchor node position, and the error is ε j , and assume that the upper limit of its modulus is a j , n i,j For the measurement noise, assume it is a Gaussian random variable with zero mean and variance σ 2 ; P0, β, σ are all known; let X=[x,y1,y2,...,y n ] T is the parameter vector to be estimated; The measurement model of formula (1) is equivalently converted to: The step 2 is specifically as follows: Based on the model shown in formula (2), using the measurement {P i,j }Establish the maximum likelihood estimation problem with X-band constraints in, k is the number of measurement sampling times; The step 3 is specifically as follows: The non-convex optimization problem shown in formula (3) is approximated as the following semi-positive programming problem in, Z is an auxiliary variable.

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