CN105572636A - Underwater acoustic sensor network positioning method adapted to mobility - Google Patents

Abstract

The invention discloses an underwater acoustic sensor network positioning method adapted to the mobility. The positioning method belongs to the positioning algorithm field of the underwater acoustic sensor network, and is characterized in that the inherent mobility of nodes is adapted to effectively and the positioning precision is improved. According to the positioning method, a mathematical model is established to calculate positioning errors generated by different reference node sets, a reference node set with the minimal positioning error is selected as the optimal reference node set, another mathematic model is established, the reference message probability of all the different reference nodes received in a prescribed period of a positioned node is maximized to optimize reference message emission time of the different reference nodes, and the positioning precision is improved.

Description

Underwater acoustic sensor network positioning method adaptive to mobility

Technical Field

The invention belongs to the field of positioning algorithms of underwater acoustic sensor networks, and is characterized in that the method can better adapt to the inherent mobility of nodes and improve the positioning accuracy. According to the positioning method, the positioning errors generated by different reference node sets are calculated by establishing a mathematical model, the optimal reference node set with the minimum positioning error is selected, then the mathematical model is established, the reference message transmitting time of different reference nodes is optimized by utilizing the probability that the maximum positioned node receives the reference messages of all the different reference nodes in a specified time period, and the positioning precision is improved.

Background

The underwater acoustic sensor network is an underwater monitoring network system formed by sensor nodes with acoustic communication and computing capabilities, is deployed in underwater environments such as the ocean and has wide application prospects in the aspects of pollution monitoring of the underwater environments, underwater biological sample collection, natural disaster prevention, auxiliary navigation and the like. In many practical applications, data has practical significance only by combining with geographical position information, so that a positioning technology is an important foundation and support technology of an underwater acoustic sensor network and is very important for design and application of the underwater acoustic sensor network.

A node positioning method which is suitable for the characteristics of the underwater acoustic sensor network, high in energy efficiency, simple, accurate and expandable is researched and designed, and is the key point of the research of the underwater acoustic sensor network. The evaluation criteria of the quality of the positioning method generally include positioning accuracy (average positioning error), anchor node deployment proportion, network average connectivity, network scale, energy, calculation overhead and the like, wherein the positioning accuracy is the most important evaluation criterion for measuring the performance of the positioning method.

In the process of positioning the node positions of the underwater acoustic sensor network, the range of positioning errors generated by selecting different reference node sets is different. Assuming that the positioning error ranges of each length are the same and are represented by an ellipse, the actual positioning error range is the overlapping area of the positioning error ranges of three lengths at the node to be positioned (as shown in fig. 1), and it can be seen that the error range in 101 (example 1) is larger than 102 (example 2) due to the difference of the selection of the reference nodes. The invention provides a method for selecting the most suitable reference node set so as to improve the positioning accuracy.

Due to the long transmission distance and propagation delay in the underwater acoustic sensor network, the positioning accuracy is affected by the movement of the positioned node while waiting for receiving the reference message of the reference node. In the underwater acoustic sensor network, the positioning accuracy is directly affected by the movement of the positioned node within the time gap of receiving the reference message from the first reference node to the last reference node (as shown in fig. 2). Ideally, the located node would like to be able to receive the reference packets of all reference nodes simultaneously to reduce the impact of node mobility. The invention provides the method for optimizing the transmitting time of the reference message transmitted by the reference node so as to improve the positioning precision.

Disclosure of Invention

The purpose of the invention is as follows:

in the underwater acoustic sensor network, the positioning accuracy is the most important evaluation criterion for measuring the performance of the positioning method, and the inherent mobility of the node influences the positioning accuracy and further influences the performance of the positioning method.

The positioning accuracy and performance of the positioning method in the underwater acoustic sensor network are improved by selecting the reference node set suitable for the inherent mobility of the nodes and optimizing the reference message transmitting time of different reference nodes.

The technical scheme of the invention is as follows:

in the underwater acoustic sensor network, for the node to be positioned, there are various selection schemes of the reference node set, and the range of positioning errors generated by selecting different reference node sets is different (as shown in fig. 1), and since the underwater acoustic sensor node is expensive, the number of nodes in the underwater acoustic sensor network is usually not large.

The invention provides a positioning method for finding an optimal reference node set by traversing all possible reference node sets and comparing error ranges of different reference node sets, and provides a mathematical modeling scheme to reduce positioning errors and improve positioning accuracy.

The invention provides a method for optimizing reference message transmitting time of different reference nodes by utilizing the probability of maximizing the reference message of all different reference nodes received by a positioned node in a specified time period, and provides a mathematical modeling scheme to reduce the influence of inherent mobility of the node in a time gap from the time when the positioned node receives the reference message of a first reference node to the time when the positioned node receives the reference message of a last reference node, thereby providing positioning accuracy.

The invention has the beneficial effects that:

in the underwater acoustic sensor network, the positioning accuracy is the most important evaluation criterion for measuring the performance of the positioning method, and various influence factors of the positioning accuracy are provided, such as inherent mobility of an underwater node, selection of a reference node and the like.

1) According to the invention, the positioning error ranges of different reference node sets are compared by establishing a mathematical model, and the optimal reference node set with the minimum positioning error range is found, so that the positioning error can be effectively reduced, and the positioning precision and performance of the positioning method are improved.

2) According to the invention, the probability that the positioned node receives the reference messages of all different reference nodes within the specified time period is maximized by establishing a mathematical model so as to optimize the transmitting time of the reference messages of different reference nodes, so that the influence of the inherent mobility of the node can be effectively reduced, and the positioning accuracy is improved.

Drawings

FIG. 1 reference node set selection diagram

FIG. 2 schematic diagram of transmit time optimization

In fig. 1, 101 is example 1, 102 is example 2, 103 represents the positioning error range in example 1, 104 represents the positioning error range in example 2, 105 is a reference node legend, and 106 is a positioned node legend.

In fig. 2, 201 is example 1, 202 is example 2, 203 is a reference node legend, and 204 is a positioned node legend.

Detailed Description

The mathematical model scheme for determining the optimal reference node set by comparing the positioning error ranges of different reference node sets and the mathematical model scheme for optimizing the transmitting time of the reference messages of different reference nodes by maximizing the probability that the positioned node receives the reference messages of all different reference nodes within a specified time period are provided below, so that the influence of the inherent mobility of the nodes in the underwater acoustic sensor network is effectively reduced, and the positioning accuracy is improved.

The invention is not limited to the mathematical model scheme, and all the positioning method ideas of the invention, namely selecting the optimal reference node set by establishing the objective function of the positioning error range or optimizing the reference message transmitting time of different reference nodes by utilizing the objective function, are within the protection scope of the invention when the positioning method of the underwater acoustic sensor network is researched.

The specific implementation of the mathematical model scheme is described as follows:

a) and establishing a mathematical model, calculating the size of a positioning error range generated by different reference node sets, and selecting an optimal reference node set.

The positioning measurement method in the present scheme takes tdoa (timedifference of arrival) as an example, and calculates CRLB (Cramer-RaoLowerBound) of positioning error magnitudes of different reference node sets:

assume that the position vector of the located node is η ═ x_r，y_r]The position vector of the reference node is ξ_n＝[x_n，y_n]And n is a reference node index. For measuring the quantity of an objective functionDenotes,. DELTA.t_n1Represents the time difference, omega, between the reference message of the 1 st reference node and the reference message of the nth reference node and the node to be positioned_nRepresenting measurement noise, thenCan be expressed as a number of times,

equation (1-1) can be converted to a vector matrix form as follows:

to solve the nonlinear estimation problem of equation (1-2), an iterative least squares estimation method can be used, assuming that the estimate η is based on the i-th iterationⁱEstimate η at time i +1ⁱ⁺¹Can be updated as:

where R in equations (1-3) is the covariance matrix of ω, J is the Jacobian matrix, which is:

$J=\frac{\∂h(\mathrm{\η}\·\mathrm{\ξ})}{\∂\mathrm{\η}}{|}_{\mathrm{\η}={\mathrm{\η}}^i}---(1-4)$

j can be expanded to:

$J={\left(\begin{array}{cc}\frac{x_r-x_2}{d_2}-\frac{x_r}{d_1}& \frac{y_r-y_2}{d_2}-\frac{y_r}{d_1}\\ \frac{x_r-x_3}{d_3}-\frac{x_r}{d_1}& \frac{y_1-y_2}{d_2}-\frac{y_r}{d_1}\\ \·& \·\\ \·& \·\\ \·& \·\\ \frac{x_r-x_N}{d_N}-\frac{x_r}{d_1}& \frac{y_r-y_2}{d_2}-\frac{y_r}{d_1}\end{array}\right)}_{\mathrm{\η}={\mathrm{\η}}^i}---(1-5)$

wherein, $d_1=\sqrt{x_r^2+y_r^2+z_r^2},d_n=\sqrt{{(x_r-x_n)}^2+{(y_r-y_n)}^2+{(z_r-z_n)}^2}.$ after a sufficient number of iterations, a Mean Square Error (MSE) matrix may be found, as shown in equations (1-6):

E[(ηⁱ-η)^T(ηⁱ-η)]＝(J^TR^-1J)^-1(1-6)

assuming that r reference nodes are needed for each positioning and a total of s nodes are needed as reference nodes (if the positioning space is n-dimensional, n +1 reference nodes are needed), a total ofAnd (4) combination. For each combination, calculating the MSE of the positioning error of each positioned node and calculating the average value, and selecting the combination with the minimum average valueSelected as a set of reference nodes.

b) And establishing a mathematical model, and optimizing the reference message transmitting time of different reference nodes by maximizing the probability of receiving the reference messages of all different reference nodes by the positioned node in a specified time period.

Assuming that 3 reference nodes are needed for determining the position of the node to be located, and the distances from the 3 reference nodes to all the nodes, the time required for transmitting the reference message is as follows:

$\mathrm{\τ}=\left(\begin{array}{cccc}{\mathrm{\τ}}_{11}& {\mathrm{\τ}}_{12}& \·\·\·& {\mathrm{\τ}}_{1N}\\ {\mathrm{\τ}}_{21}& {\mathrm{\τ}}_{22}& \·\·\·& {\mathrm{\τ}}_{2N}\\ {\mathrm{\τ}}_{31}& {\mathrm{\τ}}_{32}& \·\·\·& {\mathrm{\τ}}_{3N}\end{array}\right)---(1-7)$

suppose that the reference message transmission time point of 3 reference nodes is T ═ T₁，t₂，t₃]Then, the arrival time of the reference packet of the 3 reference nodes at each node is:

$\mathrm{\τ}=\left(\begin{array}{cccc}{t}_1+{\mathrm{\τ}}_{11}& t_1+{\mathrm{\τ}}_{12}& \·\·\·& t_1+{\mathrm{\τ}}_{1N}\\ t_2+{\mathrm{\τ}}_{21}& t_2+{\mathrm{\τ}}_{22}& \·\·\·& t_2+{\mathrm{\τ}}_{2N}\\ t_3+{\mathrm{\τ}}_{31}& t_3+{\mathrm{\τ}}_{32}& \·\·\·& t_2+{\mathrm{\τ}}_{3N}\end{array}\right)---(1-8)$

defining a binary variable θ_iComprises the following steps:

therefore, the aim of the optimization problem of the transmission time of different reference messages is to maximize the theta problem

$\mathrm{\θ}=\underset{T}{\max }\left({\mathrm{\Σ}}_{i=1}^N{\mathrm{\θ}}_i\right)---(1-9)$

Assuming that λ represents the time difference of 3 reference packets arriving at the node to be located, the following equations (1-10) can be obtained:

$\left\{\begin{array}{c}{\mathrm{\λ}}_{1i}=|t_1+{\mathrm{\τ}}_{1i}-t_2-{\mathrm{\τ}}_{2i}|\\ {\mathrm{\λ}}_{2i}=|t_1+{\mathrm{\τ}}_{1i}-t_3-{\mathrm{\τ}}_{3i}\\ {\mathrm{\λ}}_{3i}=|t_1+{\mathrm{\τ}}_{2i}-t_3-{\mathrm{\τ}}_{3i}|\end{array},|\right.---(1-10)$

since the transmission time must be positive, the following two constraints can be obtained from equations (1-9) and (1-10), such as equations (1-11) and (1-12):

$1,\left\{\begin{array}{c}{t}_1\≥0\\ t_2\≥0\\ t_3\≥0\end{array}\right.---(1-11)$

$2,{\mathrm{\θ}}_i\≤1-\frac{{\mathrm{\λ}}_{\mathrm{mi}}-\mathrm{\δ}}{M},m=\mathrm{1,2,3}---(1-12)$

where M in equations (1-12) is a large positive integer, it can be understood for equations (1-9), equations (1-10), equations (1-11), and equations (1-12): if all the reference messages are not received in the time period, the lambda is larger than,will be a small positive number, thenTherefore, to constrain the equations (1-11) and (1-12) to be true, θ must be 0, which is consistent with the condition that θ is defined as O.

Also, if all reference messages are received within a time period, thenIt will be a negative number which will,for positive, so to make the constraint equations (1-11) and (1-12) hold, θ can be 0 or 1, but because of doing the maximization process, θ tends to 1, also meets the condition that θ is defined as 1, so the constraint equations (1-11) and (1-12) prove to be correct and meaningful, and thus can be used as the constraint condition.

The optimization problem can be converted into a linear optimization problem by the method, and the linear optimization problem can be solved by a standard linear optimization algorithm such as Branch-and-Cut. The optimization problem determines the transmission time of each reference message, reduces the influence of mobility in the transmission process and can effectively improve the positioning accuracy.

Claims (4)

1. A method for positioning an underwater acoustic sensor network adaptive to mobility is characterized in that: the method for optimizing the reference message transmitting time of different reference nodes by utilizing the probability of maximizing the reference message of all different reference nodes received by the positioned node in the specified time period is provided, and the method can better adapt to the inherent mobility of the node and improve the positioning accuracy.

2. The invention provides a method for selecting an optimal reference node set with the minimum positioning error by calculating the positioning errors generated by different reference node sets according to the underwater acoustic sensor network positioning method adaptive to mobility in claim 1, which can better adapt to the inherent mobility of nodes and improve the positioning accuracy.

3. The underwater acoustic sensor network positioning method adapting to mobility according to claim 1, which provides a mathematical modeling scheme for optimizing reference packet transmission moments of different reference nodes, and the mathematical modeling scheme can acquire the reference packet transmission moments of different reference nodes, thereby reducing the influence of inherent mobility of the nodes and improving positioning accuracy.

4. The method for positioning an underwater acoustic sensor network adaptive to mobility according to claim 2, wherein a mathematical modeling scheme for selecting an optimal reference node set by calculating positioning errors generated by different reference node sets is provided, and the optimal reference node set can be obtained by the mathematical modeling scheme, so that the positioning accuracy is improved.