A weighted semi-positive definite programming positioning method based on received signal strength

Abstract

The present invention provides a weighted semi-positive definite programming positioning method based on received signal strength, which sets weights for different received signal strength data to further improve the positioning performance of the target node. Since the longer the signal propagation distance, the greater the measurement error of the received signal strength, the smaller the weight value of the received signal strength with a longer signal propagation distance. The technical solution provided by the present invention first introduces a two-dimensional environmental model, gives a semi-positive definite programming positioning method, and then proposes a weighted semi-positive definite programming positioning method and a weight setting method. The experimental simulation results provided by the present invention show that compared with the existing technical solutions, the weighted semi-positive definite programming positioning method provided by the present invention significantly improves the positioning accuracy.

Description

Technical Field

[0001] The present invention relates to the field of communication technology, and in particular to a weighted semi-positive definite programming positioning method based on received signal strength. Background Art

[0002] With the rapid development of chip technology, wireless communication technology, and micro-electromechanical systems, wireless sensors with diverse functions and excellent performance have been born. Wireless sensor nodes can not only sense the actual environmental characteristics, such as temperature and humidity, but also complete many functions such as data processing and signal transmission between nodes. Wireless sensor networks are composed of many wireless sensor nodes and have the characteristics of automatic networking and dynamic topology. Since the topology of wireless sensor networks is dynamic, obtaining the location of each wireless sensor node is the first and basic step in the practical application of wireless sensor networks.

[0003] Wireless sensor nodes in the network are divided into two categories according to whether the node location is known in advance: reference nodes and unknown location nodes. Reference nodes are relatively small in number in wireless sensor networks, and their location information is obtained in advance through additional methods, such as GPS devices or manual deployment. The coordinates of unknown location nodes cannot be known in advance, but since reference nodes can receive wireless signals transmitted by unknown location nodes, these unknown location nodes can be located through wireless node positioning technology. Unknown location nodes are objects that need to be located, also known as target nodes.

[0004] Existing wireless sensor target node positioning technologies are mainly divided into two categories: non-range-based target node positioning technology and range-based target node positioning technology. Non-range-based target node positioning technology does not need to estimate the distance between wireless sensor nodes, and mainly locates the target node through information such as the connectivity between nodes. The range-based target node positioning technology estimates the distance between nodes through information such as the signal fading size between nodes and the angle of the received signal source, and then estimates the coordinate value of the target node through wireless node positioning technology, which mainly includes methods based on received signal strength (RSSI), signal arrival time and signal arrival time difference. Among the range-based target node positioning technologies, the RSSI-based target node positioning technology not only has lower equipment overhead and communication overhead, but also has lower computational complexity, and can achieve satisfactory positioning accuracy. Therefore, the RSSI-based target node positioning technology is not only widely used in a variety of scenarios, but also has important theoretical research significance.

[0005] There are three main typical RSSI-based positioning methods, including trilateration, maximum likelihood estimation, and semi-definite programming estimation. Compared with the simplest positioning method, trilateration, the maximum likelihood estimation method, as a non-convex optimization positioning method, can effectively reduce the impact of noise. The semi-definite estimation method relaxes the constraints of the maximum likelihood estimation method, allowing the convex optimization method to be used, so it is the most practical in practice. However, the existing semi-definite programming positioning scheme does not take into account that in the actual signal propagation environment, the longer the signal propagation distance, the higher the RSSI volatility, and thus the greater the RSSI measurement error, which leads to a decrease in positioning performance. Summary of the invention

[0006] In order to solve the limitations and defects of the prior art, the present invention provides a weighted semi-positive definite programming positioning method based on received signal strength, comprising:

[0007] The expression of the received signal strength model of the i-th reference node receiving the j-th unknown position node is as follows:

[0008]

[0009] Among them, p ij (dB) =10log 10 p ij is the received signal strength p ij dB value, P j is the transmission signal strength of the unknown location node, d ij is the signal propagation distance between two nodes, α is the large-scale signal fading exponent, and the Gaussian random variable Used to characterize the effects of shadow fading and noise;

[0010] Set the coordinate of the i-th reference node to x i =[a i ,b i ], where a i is the horizontal axis coordinate of the two-dimensional plane, b i is the vertical axis coordinate of the two-dimensional plane, i=1,2,…,I;

[0011] Set the coordinate vector of the target node to p j =[m j ,n j ], where m j is the horizontal axis coordinate of the two-dimensional plane, n j is the vertical axis coordinate of the two-dimensional plane, j = 1, 2, ···, J, and the coordinate matrix of the J unknown position nodes is The matrix size of the coordinate matrix is ​​2×J;

[0012] The distance d between the reference node and the unknown position node ij The expression is as follows:

[0013]

[0014] Among them, the column vector Only the element at position j is 1, and the elements at other positions are all 0. is the unit matrix, matrix Y = P T P is a symmetric positive definite matrix;

[0015] Make the following settings:

[0016]

[0017]

[0018]

[0019] According to expressions (3), (4) and (5), expression (2) is transformed into:

[0020]

[0021] According to the maximum a posteriori probability theory, the optimization formula for positioning the target is as follows:

[0022]

[0023] in, is the ratio of the median received signal strength to the signal transmission power of the unknown location node;

[0024] According to expression (7), the weighted semi-positive definite programming objective optimization formula is as follows:

[0025]

[0026] Among them, w ij is the weight coefficient;

[0027] set up is the variance of the N received signal strength data received by the i-th reference node from the j-th unknown node, is the variance of K signals Average value, g1 is the environmental threshold, when When confirming that the overall quality of the received signal strength data in the environment is qualified, When determining that some of the received signal strength data in the environment has measurement errors, the received signal strength data is deleted from the positioning target optimization formula.

[0028] Optionally, also include:

[0029] The expression for obtaining the discriminant feature is as follows:

[0030]

[0031] Among them, the constant μ is used to adjust the gap in the variance of the received signal strength in different propagation distance intervals;

[0032] Initialize all weights to 1, set g2 as the error threshold, and update the weight coefficient w when C ij > g2 ij is 0, and when C ij < g2, the weight coefficient w ij remains 1.

[0033] Optionally, The relational expression with g2 is as follows:

[0034]

[0035] Among them, γ1, γ2, and γ3 are parameters of the influence function curve.

[0036] Optionally, μ = 20, γ1 = 184, γ2 = -0.2757, γ3 = -83.71.

[0037] The present invention has the following beneficial effects:

[0038] The present invention provides a weighted semi - definite programming localization method based on the received signal strength, which sets weights for different received signal strength data to further improve the positioning performance of the target node. Since the measurement error of the received signal strength is larger when the signal propagation distance is farther, the weight value of the received signal strength with a farther signal propagation distance is smaller. The technical solution provided by the present invention first introduces a two - dimensional environment model, gives a semi - definite programming localization method, then proposes a weighted semi - definite programming localization method, and a weight setting method. The experimental simulation results provided by the present invention show that compared with the existing technical solutions, the weighted semi - definite programming localization method provided by the present invention significantly improves the positioning accuracy. Brief Description of the Drawings

[0039] Figure 1 It is a schematic diagram of the received signal strength system model provided in the first embodiment of the present invention.

[0040] Figure 2 It is the box - and - whisker plot of the median of the received signal strength in different distance intervals when σ 2 = 1 provided in the first embodiment of the present invention.

[0041] Figure 3 It is provided for different environmental parameters σ in the first embodiment of the present invention 2, Schematic diagram of the average positioning error of weighted and unweighted semi-positive definite programming methods.

[0042] Figure 4a σ provided in the first embodiment of the present invention 2 Box plot of relative positioning error of the semi-positive definite programming method when =1, J=150.

[0043] Figure 4b σ provided in the first embodiment of the present invention 2 Box plot of relative error of weighted semi-positive definite programming method when =1, J=150. DETAILED DESCRIPTION

[0044] In order to enable those skilled in the art to better understand the technical solution of the present invention, the weighted semi-positive definite programming positioning method based on received signal strength provided by the present invention is described in detail below with reference to the accompanying drawings.

[0045] Embodiment 1

[0046] Figure 1 Schematic diagram of the received signal strength system model provided in the first embodiment of the present invention. The received signal strength (RSSI) signal propagation environment provided in this embodiment is as follows Figure 1 As shown in the figure. The wireless sensor network is deployed in a two-dimensional D×D square monitoring area, where I reference nodes and J unknown position nodes are randomly distributed. The unknown position nodes are marked as circles, which can move within the area and transmit wireless signals; the reference nodes are marked as five-pointed stars, which are fixed in position and can only receive wireless signals. The effective signal propagation distance of the jth unknown position node is defined as d j If the i-th reference node is within the coverage of the j-th unknown location node, the reference node only collects one RSSI sequence for the unknown location node, and the sequence contains a total of N RSSI values. Assume that in this two-dimensional propagation environment, the i-th reference node collects k RSSI values ​​from different unknown location nodes. i RSSI sequences, then I reference nodes collect K = k1 + k2 + ... + k I RSSI sequence.

[0047] In the actual wireless signal propagation environment, the RSSI value will be affected by a variety of channel characteristics, such as large-scale signal fading, shadow fading, and noise. Large-scale signal fading is caused by the diffusion of radio waves, and the signal fading value has a functional relationship with the signal propagation distance. The impact of shadow fading and noise on RSSI is usually modeled as a random variable that obeys a Gaussian distribution. In addition, in the actual signal propagation environment, as the wireless signal propagation distance increases, the variance of RSSI fluctuations will gradually increase, resulting in greater RSSI measurement errors.

[0048] Considering the above RSSI characteristics, this embodiment adopts a large-scale log-normal shadow path loss model. The RSSI model of the i-th reference node receiving the j-th unknown node is specifically as follows:

[0049]

[0050] where p ij (dB) =10log 10 p ij is the received signal strength p ij dB value. j is the transmission signal strength of the unknown location node, d ij is the signal propagation distance between two nodes, α is the large-scale signal fading exponent, and the Gaussian random variable Used to characterize the effects of shadow fading and noise.

[0051] From expression (1), we can see that the target node positioning accuracy and ε ij Highly relevant. Figure 2 The first embodiment of the present invention provides the 2 =1. Box plot of the median received signal strength in different distance intervals. Figure 2 For σ 2 =1, the median RSSI value at different distance intervals Box plot statistics are performed, and other detailed environmental parameters are shown in Table 2. Figure 2 The horizontal axis in represents the signal propagation distance interval, such as the horizontal axis 13 represents the signal propagation distance interval [12.5,13.5]. Figure 2 The vertical axis represents the RSSI value within the corresponding signal propagation distance range. Figure 2 Indicates the median RSSI As the signal propagation distance increases, its fluctuation becomes more severe, which is more likely to cause large measurement errors and lead to a decrease in positioning performance. Therefore, it is necessary to propose a more reasonable weighting scheme to improve the accuracy of wireless positioning.

[0052] In order to better describe the weighted semi-positive definite programming positioning solution, this embodiment first describes the semi-positive definite programming positioning solution. In this embodiment, the coordinates of the i-th reference node are defined as x i =[a i ,b i ], where a i and b i are the horizontal and vertical coordinates of the two-dimensional plane, i = 1, 2, ..., I. The coordinate vector of the target node is p j =[m j ,n j ], where m j and n j are the horizontal and vertical coordinates of the two-dimensional plane, respectively, j = 1, 2, ···, J. Then the coordinate matrix of the J unknown position nodes is The matrix size is 2×J. The distance d between the reference node and the unknown position node ij It is expressed as:

[0053]

[0054] Among them, the column vector Only the element at position j is 1, and the elements at other positions are all 0. is the unit matrix, matrix Y = P T P is a symmetric positive definite matrix.

[0055] This embodiment further defines as follows:

[0056]

[0057]

[0058]

[0059] Expression (2) can be converted to:

[0060]

[0061] After deducing the maximum a posteriori probability theory, the optimization formula for positioning the target is:

[0062]

[0063] in, It is the ratio of the median RSSI to the signal transmission power of the node at the unknown location.

[0064] Without considering the noise, the goal of solving expression (7) is to find a suitable Z that satisfies expression (6) and Y = X TX. However, the quadratic equality constraint causes the problem to be severely non-convex, and the coordinates of the unknown node cannot be solved by the convex optimization method. Therefore, the positioning solution relaxes the constraint condition of expression (7) and replaces the constraint condition Y = P T P is relaxed to Y ≥ P T P. The matrix inequality constraint Y ≥ P T P and Z ≥ 0 are equivalent. Therefore, the semi-positive programming positioning solution is:

[0065]

[0066] In order to solve the problem that the RSSI measurement error increases with the increase of signal propagation distance, this embodiment proposes a weighted semi-positive definite programming node positioning solution based on the semi-positive definite programming positioning solution. Since the RSSI has a strong volatility due to the large propagation distance, the median RSSI There is a large measurement error. The semi-positive definite programming node positioning solution is based on Get Beta ij Therefore, the positioning accuracy decreases. In the actual positioning process, although the reference node can measure RSSI, it cannot obtain the RSSI measurement error. Considering that the RSSI measurement error and RSSI variance are positively correlated, this embodiment uses RSSI variance to measure the RSSI measurement error.

[0067] Based on the above analysis, on the basis of the semi-positive definite programming positioning scheme, the weighted semi-positive definite programming objective optimization formula is proposed as follows:

[0068]

[0069] Among them, w ij is the weight coefficient. For parts i and j, when the variance of the related RSSI sequence is large, β ij The measurement error is large. ij is set to 0, ij Delete it from the target optimization formula to eliminate its impact on positioning performance. When all weight coefficients are 1, it means that the variance of all RSSI sequences is small and the RSSI measurement error is acceptable. At this time, the target optimization formula is equivalent to the semi-positive definite programming optimization expression (8).

[0070] Table 1 describes in detail the scheme of setting some weight values ​​to 0. The scheme mainly includes two parts: 1) measuring the overall quality of RSSI in the environment. 2) setting the corresponding weight coefficient based on RSSI variance.

[0071] Table 1 Weight setting scheme

[0072]

[0073] The first part of the scheme corresponds to the first three rows in Table 1. Analysis of the actual collected RSSI found that when the RSSI quality in the environment is high enough, the variance of the entire RSSI sequence is small, and the measurement error of the RSSI median (including the RSSI median with a longer signal propagation distance) is small. At this time, setting some weight values ​​to 0 will result in a decrease in the amount of RSSI data used to locate a target node, and the decrease in the amount of RSSI data may lead to a deterioration in positioning performance. Therefore, all weight coefficients are set to 1, so that all RSSI data is used to locate the target node. Based on the above reasons, this embodiment estimates the average RSSI measurement error based on the average variance of K RSSI sequences in the environment, thereby further measuring the quality of RSSI in the environment. Definition is the variance of the N RSSI data received by the i-th reference node from the j-th unknown node, is the variance of K signals This embodiment introduces the environmental threshold g1. When , the overall quality of RSSI data in the environment is considered to be high. Otherwise, some RSSI data in the environment have large measurement errors and should be deleted from the positioning target optimization formula. In the simulation parameters of the two-dimensional environment, σ 2 The higher the value, the lower the RSSI quality in the environment. 2 In this embodiment, the median RSSI value of the signal propagation distance is longer. and the theoretical value p ij When a large RSSI measurement error begins to appear in the environment, Set to threshold g1.

[0074] The purpose of the second part of the scheme is to set the RSSI weight coefficient with large error to 0, corresponding to rows 4 to 10 in Table 1. When the overall quality of RSSI data in the environment does not meet the requirements, the variance ε of some RSSI sequences can be determined. ij Too large, the weight coefficient w needs to be ij Set to 0. However, due to the large transmission distance, RSSI fluctuations are large and the amount of data in the RSSI sequence is limited, the RSSI variance estimate The volatility is strong and may be different from the true value of the variance ε ij The difference is large, so it cannot accurately measure the RSSI measurement error. 10 (·) function can further reduce The volatility of , produces more stable discriminant features, so the discriminant features proposed in this embodiment are as follows:

[0075]

[0076] Among them, μ is a constant that can adjust the difference in RSSI variance in different propagation distance intervals. Therefore, in order to more effectively determine the median RSSI within a certain propagation distance interval Whether there is a large measurement error, a larger μ is set in this embodiment.

[0077] Based on the proposed discriminant features, this embodiment first initializes all weights to 1, then introduces the error threshold g2, and calculates the error threshold g2 according to the error threshold g2 and C ij Update the weight coefficient w ij is 0. When C ij When it is greater than the error threshold g2, β ij is unreliable, w ij is updated to 0, otherwise w ij Keep it at 1. Set the threshold g2 to the RSSI with large error C ij Based on the actual collected data, the statistical results show that the error threshold g2 and It shows a negative exponential corresponding relationship, so this embodiment proposes The relationship expression with g2 is as follows:

[0078]

[0079] Among them, γ1, γ2, and γ3 are parameters that affect the function curve. Based on the exponential function curve fitting method, the specific parameter settings are shown in Table 2.

[0080] In order to verify the positioning performance of the weighted semi-positive definite programming positioning scheme proposed in this embodiment, this embodiment provides relevant experimental simulations to compare the proposed scheme and the semi-positive definite programming positioning scheme based on the first-order Taylor expansion. This embodiment estimates the coordinates of the unknown position nodes based on the SDPT3 solver of the CVX front end in the MATLAB platform. The relevant simulation parameters are shown in Table 2, and the average positioning error of J reference nodes is calculated to evaluate the positioning performance of different schemes.

[0081] Table 2 Simulation parameters

[0082]

[0083] Figure 3 The first embodiment of the present invention provides different environmental parameters σ 2 , Schematic diagram of the average positioning error of weighted and unweighted semi-positive definite programming methods. Figure 3 The results for different environmental parameters σ are given. 2 , the average positioning error of the weighted scheme and the unweighted scheme based on the first-order Taylor expansion. The results show that when the number of reference nodes I and the environmental parameter σ 2The weighted semi-positive definite programming positioning solution provided in this embodiment has a higher positioning accuracy than the unweighted solution. 2 When σ remains unchanged, as the number of reference nodes increases, the positioning error of the unweighted positioning scheme remains basically unchanged. This is because, as the number of reference nodes increases, the number of reference nodes with longer and shorter signal propagation distances will increase simultaneously within the communication range of the unknown node. Although the increase in the number of reference nodes theoretically improves positioning performance, the unweighted positioning scheme does not delete RSSI data with longer signal propagation distances. These RSSI data with larger errors lead to a decrease in wireless positioning performance. Therefore, the positioning performance of the unweighted positioning scheme does not change significantly. The weighted semi-positive definite programming positioning scheme provided in this embodiment has a significant difference in σ. 2 When the number of reference nodes is unchanged, the average positioning error gradually decreases, indicating that the weighted semi-positive definite programming positioning solution provided in this embodiment can effectively delete RSSI with large measurement errors, thereby improving the accuracy of wireless positioning.

[0084] Figure 4a σ provided in the first embodiment of the present invention 2 Box plot of relative positioning error of the semi-positive definite programming method when =1, J=150. Figure 4b σ provided in the first embodiment of the present invention 2 =1, J = 150. In order to analyze the positioning error under different transmission and reception distances, Figure 4 shows the relative positioning error box plot of the weighted semi-positive definite programming positioning scheme and the unweighted positioning scheme. In this simulation environment, σ 2 =1 and I = 150. Define the average signal propagation distance of the jth unknown location node is the average distance from the unknown location node to the reference node within the communication range. Since different unknown location nodes have different average signal propagation distances The relative positioning error is used to evaluate the positioning accuracy. The relative positioning error of the jth unknown position node is the absolute positioning error of the node divided by In FIG4 , the horizontal axis represents the average signal propagation distance interval, such as the horizontal axis 25 represents the interval [24.5, 25.5], and the vertical axis represents the relative positioning error. Figure 4a The relative localization error distribution of the unweighted localization scheme is shown. Figure 4a It shows that the relative positioning error of the unweighted positioning scheme remains basically unchanged as the average signal propagation distance increases. Figure 4b The relative positioning error box plot of the weighted semi-positive definite programming positioning solution. Compared with the unweighted positioning solution, the weighted semi-positive definite programming positioning solution basically has better positioning performance in each distance interval.

[0085] The present embodiment provides a weighted semi-positive definite programming positioning method based on received signal strength, which sets weights for different received signal strength data to further improve the positioning performance of the target node. Since the longer the signal propagation distance, the greater the measurement error of the received signal strength, the smaller the weight value of the received signal strength with a longer signal propagation distance. The technical solution provided by the present embodiment first introduces a two-dimensional environmental model, gives a semi-positive definite programming positioning method, and then proposes a weighted semi-positive definite programming positioning method and a weight setting method. The experimental simulation results provided by the present embodiment show that compared with the existing technical solutions, the weighted semi-positive definite programming positioning method provided by the present embodiment significantly improves the positioning accuracy.

[0086] It is to be understood that the above embodiments are merely exemplary embodiments used to illustrate the principles of the present invention, but the present invention is not limited thereto. For those of ordinary skill in the art, various modifications and improvements can be made without departing from the spirit and essence of the present invention, and these modifications and improvements are also considered to be within the scope of protection of the present invention.

Claims

1. A weighted semi-positive definite programming positioning method based on received signal strength, characterized in that: include: The expression of the received signal strength model of the i-th reference node receiving the j-th unknown position node is as follows: Among them, p ij (dB) =10log 10 p ij is the received signal strength p ij dB value, P j is the transmission signal strength of the unknown location node, d ij is the signal propagation distance between two nodes, α is the large-scale signal fading exponent, and the Gaussian random variable Used to characterize the effects of shadow fading and noise; Set the coordinate of the i-th reference node to x i =[a i ,b i ], where a i is the horizontal axis coordinate of the two-dimensional plane, b i is the vertical axis coordinate of the two-dimensional plane, i=1,2,…,I; Set the coordinate vector of the target node to p j =[m j ,n j ], where m j is the horizontal axis coordinate of the two-dimensional plane, n j is the vertical axis coordinate of the two-dimensional plane, j = 1, 2, ···, J, and the coordinate matrix of the J unknown position nodes is The matrix size of the coordinate matrix is ​​2×J; The distance d between the reference node and the unknown position node ij The expression is as follows: Among them, the column vector Only the element at position j is 1, and the elements at other positions are all 0. is the unit matrix, matrix Y = P T P is a symmetric positive definite matrix; Make the following settings: According to expressions (3), (4) and (5), expression (2) is transformed into: According to the maximum a posteriori probability theory, the optimization formula for positioning the target is as follows: in, is the ratio of the median received signal strength to the signal transmission power of the unknown location node; According to expression (7), the weighted semi-positive definite programming objective optimization formula is as follows: Among them, w ij is the weight coefficient; set up is the variance of the N received signal strength data received by the i-th reference node from the j-th unknown node, is the variance of K signals Average value, g1 is the environmental threshold, when When confirming that the overall quality of the received signal strength data in the environment is qualified, When determining that some of the received signal strength data in the environment has measurement errors, the received signal strength data is deleted from the positioning target optimization formula.

2. The weighted semi-positive definite programming positioning method based on received signal strength according to claim 1, characterized in that: Also includes: The expression for obtaining the discriminant features is as follows: Among them, the constant μ is used to adjust the difference in the variance of the received signal strength in different propagation distance intervals; Initialize all weights to 1, set g2 as the error threshold, and update the weight coefficient w ij to 0 when C ij > g2, and keep the weight coefficient w ij as 1 when C ij < g2.

3. The weighted semi-positive definite programming positioning method based on received signal strength according to claim 2, characterized in that: The relationship expression with g2 is as follows: Among them, γ1, γ2, and γ3 are parameters that affect the function curve.

4. The weighted semi-positive definite programming positioning method based on received signal strength according to claim 3 is characterized in that: μ=20, γ1=184, γ2=-0.2757, γ3=-83.71.

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