An Ocean Sensor Network Node Localization Method Based on Efficient Particle Filter

Abstract

The present invention relates to a method for positioning nodes in an ocean sensor network using efficient particle filtering. The method includes: 1) obtaining a first state vector of the posterior probability mean at time k-1; 2) establishing a state model of a nonlinear system; 3) obtaining an observation model of the nonlinear system; 4) propagating particles and calculating the state vector at the next time according to the particle vector at time k-1; 5) obtaining an observation value and calculating weights; 6) determining whether degeneracy occurs. If not, the weights are used to calculate the position expectation. Otherwise, step 7) is executed; 7) modifying particles with small weights; 8) performing improved residual resampling and normalizing the weights; 9) using the weights in step 8) to calculate the position expectation to achieve node positioning. Compared with the prior art, the present invention has advantages such as balancing the relationship between positioning accuracy and efficiency.

Description

Technical Field

[0001] The present invention relates to the field of node positioning in ocean wireless sensor networks, and in particular to a method for positioning nodes in an ocean sensor network with efficient particle filtering. Background Art

[0002] As one of the key technologies in the fields of ocean ecological environment monitoring, ocean disaster warning, and deep-sea exploration, Ocean Sensor Networks (OSNs) have important research significance and good application prospects. In OSNs, node positioning technology is an essential key link. Through node positioning, corresponding location information can be obtained, providing an important basis for the analysis and decision-making after collecting data. However, the ocean environment is complex and changeable, and its high dynamics and uncertainty pose severe challenges to node positioning technology. Currently, the positioning technology mainly adopts the particle filter positioning method. Although the positioning method based on particle filter can well handle the non-linear positioning problem in a high-dynamic and uncertain environment, the existing positioning method based on particle filter cannot well balance the relationship between positioning accuracy and positioning efficiency. Specifically, when the number of particles is sufficient, the positioning algorithm based on particle filter can have better positioning accuracy, but its positioning efficiency is greatly reduced. A large number of particles occupy a large amount of computing resources and consume the energy of the nodes. And the nodes deployed on the ocean are often not easy to charge and replace. Once the energy is insufficient, the lifespan of the entire OSNs network will be shortened, seriously affecting the performance of OSNs ocean monitoring. Summary of the Invention

[0003] The purpose of the present invention is to provide a method for positioning nodes in an ocean sensor network with efficient particle filtering that balances positioning accuracy and efficiency to overcome the defects of the above-mentioned existing technologies.

[0004] The purpose of the present invention can be achieved by the following technical solutions:

[0005] A method for positioning nodes in an ocean sensor network with efficient particle filtering includes the following steps:

[0006] S1. According to the motion characteristics of the velocity field in the sea area, considering the interaction force between the tidal field and the residual field, establish a state model of the non-linear system;

[0007] S2. Based on the signal strength attenuation model, model the signal strength received by each node in the ocean sensor network to obtain an observation model of the non-linear system;

[0008] S3. Obtain the first state vector of the posterior probability mean at the (k - 1)th moment Calculate the second state vector at the kth moment The state vector of the ith particle at the (k - 1)th moment It is represented by the first state vector, and then the state vector of the i-th particle at time k at the first state vector is Taylor-expanded to calculate the second particle state vectors of all particles approximated to the first-order Taylor series terms at time k. Then, the multi-dimensional Richardson extrapolation method is used to perform a two-step Taylor expansion on the second particle state vectors to obtain the third particle state vectors of all particles approximated to the second-order Taylor series terms at time k;

[0009] S4. Based on the normalized weights at time k - 1, the normalized weights at time k are calculated in a recursive manner, and the normalization is achieved based on the observation values obtained from the observation model;

[0010] S5. Determine whether the particles are degenerate based on the number of effective particles. If so, execute S6; if not, then use the normalized weights at time k and the current particle set as the result weights and the result particle set, and execute S8;

[0011] S6. Resampling is performed, and then the entire particle set is divided into a small-weight particle set and a large-weight particle set according to the weight threshold. The state vectors and weights of the particles in the large-weight particle set remain unchanged, the state vectors of the particles in the small-weight particle set are modified, and then the weights of the small-weight particles are modified and normalized to obtain the modified particles. The weights of the modified and normalized small-weight particles are used as the result weights;

[0012] S7. Residual resampling is performed according to the modified particles to obtain a replicated particle set, and the replicated particle set is used as the result particle set;

[0013] S8. Combining the result particle set and the result weights, calculate the posterior probability distribution of the unknown node at time k, and calculate the expected value of the position according to the obtained posterior probability distribution to obtain the estimated position of the unknown node at time k.

[0014] Furthermore, the two-step Taylor expansion is specifically as follows:

[0015] The second particle state vectors are Taylor-expanded at and then is Taylor-expanded at where Δu i is the corresponding gradient, α k-1 is the state noise, and F is the state equation.

[0016] Furthermore, the expression for the normalized weights at time k is:

[0017]

[0018] where is the weight of the i-th particle at time k, and ∝ represents the proportional symbol, is the weight of the i-th particle at the (k - 1) moment after normalization, represents the posterior distribution of the i-th particle at the k moment, z k represents the observed value at the k moment, represents the state of the i-th particle at the k moment;

[0019] The expression for the weight of the i-th particle at the (k - 1) moment after normalization is:

[0020]

[0021] where, is the weight of the i-th particle at the (k - 1) moment after normalization, N represents the number of particles, is the weight of the i-th particle at the (k - 1) moment.

[0022] Furthermore, the expression for the particle set divided into two categories is:

[0023]

[0024] where, is the third particle state vector of the i-th particle at the k moment, S l is the set of particles with small weights, S h is the set of particles with large weights, is the modified weight of the i-th particle at the k moment, W thres is the weight threshold.

[0025] Furthermore, the steps for determining the weight threshold are:

[0026] Sort all the sampled particles in ascending order according to their weights, store the sorted particles in a set. Assume the weight of the r-th particle as the weight threshold, obtain the expression for the weight difference between the set of particles with small weights and the set of particles with large weights, calculate the weight difference from the first particle in the set. When the weight difference is greater than 0, determine the serial number r of the particle at this time to obtain the weight threshold.

[0027] Furthermore, the method of linear interpolation is used to modify the state vectors of the particles in the set of particles with small weights. The modified state vectors of the particles in the set of particles with small weights are:

[0028]

[0029] where, is the modified state vector of the particle in the set of particles with small weights, represents the set of particles with small weights S l is the state vector of the s-th particle to be modified in the set of particles with small weights S represents the set of particles with large weights S hThe state vector of the j-th particle in denotes the set S of particles with small weights l The weight of the s-th particle with small weight in denotes the set S of particles with large weights h The weight of the j-th particle with large weight in, s = 1, 2,..., N l and j = 1, 2,..., N h , N l and N h respectively denote the set S l and S h The number of particles in

[0030] Furthermore, the weight of the modified particle with small weight is:

[0031]

[0032] where denotes the set S of particles with small weights l The weight of the s-th particle with small weight at the (k - 1)th moment in denotes the set S of particles with small weights l The weight of the s-th particle with small weight at the k-th moment in is the state vector of the particle in the modified set S of particles with small weights, z k denotes the observed value at the k-th moment, denotes the posterior distribution corresponding to the particle in the modified set S of particles with small weights.

[0033] Furthermore, in S7, when copying the particle set, deterministic selection and random selection are performed. When , where is the total number of times the i-th particle is selected in the first-step deterministic selection and the second-step random selection. For the i-th particle to be copied, Δh 1 denotes the maximum deviation value. The Δh of the i-th particle to be copied 1 is less than half of the minimum of the average state vector difference between the i-th particle to be copied and all other particles to be copied.

[0034] Furthermore, when copying the particle set, calculate the deviation value between the new particle state vector generated according to the state vector of the third particle and the state vector of the third particle . The expression of the deviation value is:

[0035]

[0036] where γ i is the parameter for adjusting the dispersion degree of the i-th particle to be resampled, Let \(n_i\) be the total number of times the \(i\)-th particle is selected during the first-step deterministic selection and the second-step random selection, \(g\) be the corresponding selection times index, and \(p\) be the number of times of being selected.

[0037] Further, when the particle set degenerates, after executing S6 and S7, the expression of the expected value of the position is:

[0038]

[0039] where \(E(u k |z_1: k )\) is the expected value of the position, \(u k \) is the state of the target to be located, \(z 1:k \) represents the observed values corresponding to the times from 1 to \(k\), \) is the particle set obtained by replication, \(N\) is the number of particles, \) is the modified normalized particle weight, \(p(u k |z 1:k )\) is the posterior probability distribution of the unknown node.

[0040] Compared with the prior art, the present invention has the following beneficial effects:

[0041] Based on the mean value of the previous moment during the particle propagation process, the present invention combines the Taylor series expansion and applies the multi-dimensional Richardson extrapolation method to construct a high-precision particle state vector, which improves the efficiency while ensuring the accuracy. Subsequently, the linear interpolation method is used to modify the particles with small weights, and the dispersion parameter is introduced to improve the residual resampling method, obtaining a new particle replication method to calculate the posterior probability at the next moment and jointly estimate the position of the unknown node at the current moment. Compared with the existing particle filtering localization technology, the method of the present invention better balances the relationship between localization accuracy and efficiency, providing a feasible solution for the high-precision and high-energy-efficiency localization problem in a high-dynamic and uncertain marine environment. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 is the flowchart of the present invention;

[0043] Figure 2 is the improvement rate of the prediction step of the method of the present invention relative to the PF calculation time when the number of propagation times is 20;

[0044] Figure 3 is the improvement rate of the prediction step of the method of the present invention relative to the PF calculation time when the number of propagation times is 100;

[0045] Figure 4 is the influence of the dimension \(n\) of the state vector on the improvement rate of the calculation efficiency of the method of the present invention when the number of particles is 100;

[0046] Figure 5The influence of the dimension n of the state vector on the calculation efficiency improvement rate of the method of the present invention when the number of particles is 200;

[0047] Figure 6 Positioning error diagrams of different algorithms in the X-axis direction;

[0048] Figure 7 Positioning error diagrams of different algorithms in the X-axis direction;

[0049] Figure 8 Diagrams showing the variation of the processing time of two algorithms with the number of particles. Detailed implementation manners

[0050] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. This embodiment is implemented on the premise of the technical solution of the present invention, and detailed implementation manners and specific operation processes are given, but the protection scope of the present invention is not limited to the following embodiments.

[0051] Embodiment 1:

[0052] The present invention proposes a method for positioning nodes in an ocean sensor network with efficient particle filtering. The flowchart of the method is as Figure 1 shown.

[0053] The method proposed by the present invention includes the following steps:

[0054] 1) Obtain the first state vector of the posterior probability mean at time k - 1;

[0055] 2) According to the motion characteristics of the velocity field in the sea area, considering the interaction forces of the tidal field and the residual field, establish a state model of the nonlinear system;

[0056] 3) Based on the signal strength attenuation model, model the signal strength received by each node in the ocean sensor network to obtain an observation model of the nonlinear system;

[0057] 4) Propagate particles and calculate the state vector at the next moment according to the particle vector at time k - 1

[0058] 5) Obtain the observed value and calculate the weight;

[0059] 6) Determine whether degeneracy occurs. If not, use the weight to calculate the position expectation. Otherwise, execute 7);

[0060] 7) Modify the particles with small weights;

[0061] 8) Perform improved residual resampling and normalize the weights;

[0062] 9) Use the weights in 8) to calculate the position expectation and achieve node positioning.

[0063] 2), considering that most current OSNs are applied in offshore areas where the water flow velocity is relatively gentle, and in specific cases, the movement of nodes in the OSNs in the water flow is not completely random. Therefore, by utilizing its inherent temporal and spatial correlations, a movement model of the nodes is established, assuming that the velocity field of the node movement environment is formed by the superposition of a tidal field and a residual current field. The tidal field oscillates uniformly in one direction, while the residual current field is an infinite sequence that rotates alternately clockwise and counterclockwise. The coordinate system of the sea surface nodes is established with the X-axis and Y-axis perpendicular to the coast and along the coast respectively. This movement model is expressed as follows:

[0064]

[0065] In the formula, V x and V y respectively represent the velocities of the nodes in the OSNs in the X-axis and Y-axis directions; λ is the ratio of the tidal range to the diameter of the residual vortex; v represents the corresponding velocity; k1, k2, k3 are constant terms, and their values are related to environmental factors such as tides, salinity, and temperature, and these parameters will change depending on the node deployment in different sea areas; k4 and k5 are random parameters of the Gaussian distribution.

[0066] Combined with the movement model of formula (1), the state equation of the nodes of the nonlinear dynamic system, that is, the state model, is established, and the movement equation is rewritten as a differential movement equation, expressed as:

[0067]

[0068] In the formula, represents the state of the node; and respectively represent the process noises in the X-axis and Y-axis directions, and The values of both follow a normal distribution with a mean of 0 and a standard deviation of Q.

[0069] 3), considering the special environment of the ocean and the requirement of low cost, based on the characteristics of the signal strength attenuation model (RSSI) such as not requiring complex hardware and having low communication costs. Therefore, the ranging method based on RSSI is adopted for the positioning of OSNs nodes, and the signal reception power of the unknown node at time k and the signal transmission power of the anchor node at time k are used to estimate the distance between the unknown node and the anchor node at the current moment. Among them, the RSSI received by the unknown node at time k can be represented by the log-normal shadow model:

[0070]

[0071] In the formula, and respectively represent the RSSI value received by the node at time k and the transmission power of the anchor node; d0 is the reference distance, usually set to 1m; PL(d0) represents the RSSI loss value at a distance of d0; d represents the distance between the unknown node and the anchor node at time k; θ represents the path loss exponent (PLE), which is determined by the signal propagation environment.

[0072] Let This paper considers non-cooperative positioning, so the observation model of the non-linear dynamic system is:

[0073]

[0074] where, β k is the measurement noise at time k, and its value follows a Gaussian distribution with a mean of 0 and a standard deviation of R.

[0075] In (4), the present invention assumes that the state at time k-1 is known, predicts the state at time k according to the state equation, and combines the ranging model at time k to estimate the target position through an efficient particle filtering method. Traditional particle filtering calculates the state vectors of N particles at time k respectively through the state transition equation for the state vectors of N particles at time k-1. The method of the present invention, in the particle propagation stage, first calculates the state vector of the next moment based on the state vector of the mean of the posterior probability at time k-1

[0076]

[0077] The state vector of the i-th particle at time k-1 can be expressed using the mean of the posterior probability at time k-1 as:

[0078]

[0079] Then all the particle state vectors at time k can be approximately obtained using the Taylor expansion at as:

[0080]

[0081] To simplify equation (7), let Then equation (7) can be rewritten as:

[0082]

[0083] where the function F is:

[0084]

[0085] By using the Taylor expansion, it is avoided to calculate the state vectors of all particles at the next moment through numerical analysis. The state vectors of all sampled particles are approximated to the first-order Taylor series terms, and this approximation can be expressed as Δu i a function of, as shown in the following formula:

[0086]

[0087] According to Equation (8) and Equation (10), the state vectors of all particles approximated to the first-order Taylor series terms at time k can be obtained:

[0088]

[0089] However, the accuracy of the state vectors based on the first-order Taylor series expansion terms is not ideal, that is, the accuracy of Equation (11) is not ideal. In order to further improve the accuracy of the state vectors and improve the accuracy of the state vectors of all sampled particles at time k to the second-order Taylor series terms, the present invention uses the idea of multi-dimensional Richardson extrapolation method and uses the Taylor expansion in two steps. First, perform Taylor expansion from :

[0090]

[0091]

[0092] According to Equation (12) and Equation (13), we can obtain the following formula:

[0093]

[0094] In the formula, Therefore, the above formula can be rewritten as:

[0095]

[0096] We let:

[0097]

[0098] Then Equation (15) can be simplified to:

[0099]

[0100] Since:

[0101]

[0102] Therefore, Equation (17) can be approximately rewritten as:

[0103]

[0104] According to Equation (10) and Equation (18), we can obtain the following equation:

[0105]

[0106] Therefore, the state vector of the particle at time k can be approximated as:

[0107]

[0108] Subsequently,

[0109]

[0110] wherein is the Jacobian matrix of the function f at . By calculating the Jacobian matrix at each moment, the state vectors of all sampled particles can be obtained. Through the above analysis, the present invention uses the multi-dimensional Richardson extrapolation method, and only needs to calculate the state vector at the next moment through the state transition equation with the state vector of the posterior mean at the previous moment According to the obtained state vector, the state vectors of all sampled particles at this moment are obtained, and the accuracy of the second-order Taylor series term is maintained.

[0111] In 5), q(u 1:k |z 1:k ) is used as the importance probability density to represent the posterior distribution of the states at all past moments, where u 1:k ={u1, u2,..., u k}, and it is decomposed into:

[0112] q(u 1:k |z 1:k ) = q(u 1:k-1 |z 1:k-1 )q(u k |u 1:k-1 , z 1:k ) (22)

[0113] Subsequently, the recursive form of the posterior probability p(u 1:k |z 1:k ) of the states at all past moments can be deduced as:

[0114]

[0115] Taking q(u k |u k-1 , z k ) = p(u k |u k-1 ) as the sub-optimal case of q(·), the recursive equation of the weights of the sampled particles is:

[0116]

[0117] According to this method, at time k, each sampled particle (when k = 1, ), the weight of each sampled particle at time k can be calculated recursively according to the likelihood function and the normalized weight at time k - 1 as follows:

[0118]

[0119] where is the weight of the i-th particle after normalization:

[0120]

[0121] In 6), to determine whether particle filtering has particle degradation, the size of the effective number of particles is judged according to the dispersion of the weights of the sampled particles. The more dispersed the weights are, the greater the weight variance is, indicating that the weights of the current particle set are concentrated on a few particles, and the more serious the particle degradation is. Specifically, use N eff to represent the number of effective particles, that is

[0122]

[0123] If the obtained N eff is less than the set threshold, it is considered that there is a degradation problem, and the particles with small weights need to be modified.

[0124] In 7), although high - efficiency particle propagation is achieved by using the Taylor series expansion combined with Richardson extrapolation, the particles often still encounter the problem of impoverishment. Therefore, in the present invention, by changing the state vectors of the particles with small weights, the particles with small weights can obtain larger weights, thereby promoting the weights of the entire particle set to be more uniform. After resampling is required according to the preset threshold, before modifying the particles with small weights, the entire particle set is divided into a small - weight particle set and a large - weight particle set, and the particle set is divided into two categories according to the difference in the weights of the two sets:

[0125]

[0126] In the formula, the set S l and the set S h are respectively used to store all the particles with small weights and all the particles with large weights, W thres represents the weight threshold for dividing the particle set. To obtain this threshold, the N sampled particles are sorted in ascending order according to their weights, and the set is used to store the N particles:

[0127]

[0128] Wherein:

[0129]

[0130] If the weight of the r-th particle is used as the splitting weight, then the weight difference between the small-weight particle set and the large-weight particle set is:

[0131]

[0132] We start calculating E from the first particle in the set . When E r > 0, we use the weight of the r-th particle in the set r as the weight threshold for splitting. Wherein,

[0133]

[0134] In the formula, represents the weight of the r-th particle in the set . After dividing each particle into the large-weight particle set S h and the small-weight particle set S l , keep the state vector and weight of the particles in the large-weight particle set S h unchanged, and use the state vector and weight of the particles in the large-weight particle set S h to modify the state vector of the particles in the small-weight particle set S l . represents the state vector of the s-th particle to be modified in the small-weight particle set S l , represents the state vector of the j-th particle in the large-weight particle set S h . Then, the modified state vector of the s-th particle in the small-weight particle set is obtained by linear interpolation as:

[0135]

[0136] In the formula, represents the weight of the s-th small-weight particle in the small-weight particle set S l , represents the weight of the j-th large-weight particle in the large-weight particle set S h , s = 1, 2,..., N l and j = 1, 2,..., N h , N l and N h respectively represent the sets S l and S hThe number of medium particles. Each large-weight particle used to modify the small-weight particles is randomly selected from the set S of large-weight particles h and, according to the equation the weight of the modified small-weight particle is updated to:

[0137]

[0138] where represents the weight of the s-th small-weight particle in the set S of small-weight particles at time k - 1. When the state vectors and weights of all small-weight particles are updated, the new small-weight particles and all the large-weight particles in the set S l form N new particles and normalize the weights. h

[0139] 8), based on the modified particles, a residual resampling method for further proposing a new particle replication method is proposed. The new replicated particle set for the i-th particle to be replicated is generated by the following method

[0140]

[0141] where Δh g is the deviation value of the new particle state vector generated according to from and is:

[0142]

[0143] where γ i is used to adjust the dispersion degree of the i-th particle to be resampled. To make the resampled particles express as many regions as possible in the posterior distribution, the overlap between the states of the new resampled particles should be minimized as much as possible. According to equation (34), when for the i-th particle to be replicated, Δh 1 represents the maximum deviation value, and the Δh 1 of the i-th particle to be replicated should be less than half of the minimum average difference in state vectors between the i-th particle to be replicated and all other particles to be replicated. For the i-th particle to be replicated, γ i is:

[0144]

[0145] where represents the state vector of the i-th particle to be replicated more than 2 times among the selected resampled particles, represents the state vectors of all other selected resampled particles except the i-th particle. Inequality (36) can be rewritten as: ​

[0146]

[0147] In 9, according to the new particle set and combined with weights, the posterior probability distribution of the unknown node is further jointly estimated, that is

[0148]

[0149] In the formula is the modified normalized particle weight.

[0150] Finally, according to the obtained posterior probability distribution, the position of the target node is further estimated, that is

[0151]

[0152] In the formula, E(u k |z 1:k ) represents the expected value of the position.

[0153] To further verify the performance of the method proposed in the present invention in terms of positioning efficiency, the efficiency index of the improvement is represented by the calculation time percentage, that is

[0154]

[0155] In the formula, C HRT-PF represents the corresponding performance index of the improvement; T PF represents the calculation time of the original particle filter; T HE-PF represents the calculation time of the efficient particle filter proposed in the present invention.

[0156] Figure 2 and Figure 3 respectively show the relationship between the improvement rate of the calculation time of the present invention (IHE-PF) relative to the original particle filter (PF) in the prediction step and the number of particles N, the dimension n of the state vector, and the number of basic operations required to calculate the differential motion equation f when the number of particle propagation times L is 20 and 100 times respectively. It can be found from the figure that as the number of particles increases, the improvement rate of the calculation time of IHE-PF relative to PF will also increase rapidly, and the highest value of the improvement rate of its calculation time can be reached when the number of particles is small. Respectively from Figure 2 and Figure 3It can be seen from the comparison that as the number of particle propagation times L increases, the improvement rate of the calculation time of IHE-PF relative to PF will increase, and the upper limit of the improvement will also increase. At the same time, as the number of basic operations j required to calculate the differential motion equation f increases, the improvement rate of the calculation time of HE-PF relative to PF will increase, and the upper limit of the improvement will also increase. However, as the dimension n of the state vector increases, the improvement rate of the calculation time of IHE-PF relative to PF will decrease, and the upper limit of the improvement rate will also decrease. Through the above analysis, it can be concluded that without considering the dimension n of the state vector, the more complex the calculation, the higher the improvement rate of the calculation time of IHE-PF relative to PF, and the complexity determines the upper limit of the improvement efficiency.

[0157] However, according to equation (40), we find that the dimension n of the state vector has a cubic and quadratic influence on T HRT-PF and a linear influence on T PF . Therefore, when the dimension n of the state vector increases infinitely, the situation where the numerator is less than 0 will occur, that is, the calculation efficiency of the prediction step of IHE-PF is not better than that of PF. Figure 4 and Figure 5 respectively show the limitations of the dimension n of the state vector on the improvement rate of the calculation time of the prediction step of IHE-PF when the number of particles is 100 and 200. From Figure 4 and Figure 5 , it can be seen that as the number of particles N increases, the limitation of the dimension n of the state vector on the improvement rate of the calculation time of IHE-PF relative to the prediction step of PF remains unchanged. As the number of particle propagation times L or the number of basic operations j required to calculate the differential motion equation f increases, the limit value of the dimension n of the state vector that makes the calculation time of the prediction step of IHE-PF better than that of PF will also increase. The dimension n of the state vector directly determines whether the calculation time of HE-PF in the prediction step is better than that of PF. For the OSNs positioning problem, the dimension of the state vector in this paper is 2. Therefore, the prediction step of IHE-PF can maintain a high calculation efficiency relative to PF. Through the above analysis, according to the changes in the number of particle propagation times L, the number of particles N, and the number of basic operations j required to calculate the differential motion equation f, using HE-PF can increase the calculation time of the prediction step of traditional PF by more than 90%. Although the upper limit of its improvement rate is limited by the dimension n of the state vector, in the OSNs positioning problem, the number of state variables is usually 2 to 4, which is less than its limit number. Therefore, the calculation efficiency of the OSNs node positioning algorithm based on IHE-PF can be increased by more than 90% relative to PF, realizing real-time monitoring of the marine environment.

[0158] To further verify the performance of the method of the present invention in terms of positioning accuracy, a simulation experiment was conducted in MATLAB R2021b. Three anchor nodes were set, and the case of one node positioning was considered. The process noise standard deviation Q of the motion equation of the OSNs node was 4m, the measurement noise standard deviation R of the measurement equation was 2dB, and the number of particles N was 300. The original particle filter (PF), the method provided by the present invention (IHE-PF), and the unscented Kalman filter (UKF) algorithm were compared respectively. In addition, to further verify that the inventive method can improve a certain positioning accuracy in terms of resampling improvement, the Taylor series expansion and multi-dimensional Richardson extrapolation method provided by the present invention were adopted in the particle propagation stage of the original PF, but the original importance resampling method was applied to the resampling nodes. This method is abbreviated as HE-PF.

[0159] Figure 6 and Figure 7 respectively represent the positioning errors of the OSNs positioning algorithms based on PF, IHE-PF, and UKF in the X-axis and Y-axis directions within 60s. It can be seen from the figure that the method provided by the present invention, after the Taylor series expansion and multi-dimensional Richardson extrapolation method, and combined with the improved resampling method, has slightly lower positioning errors in the X-axis and Y-axis directions than the original PF, and is lower than the HE-PF positioning algorithm that only adopts the Taylor series expansion and multi-dimensional Richardson extrapolation method. The errors of the UKF algorithm in the X-axis and Y-axis directions are greater than those of the other three PF-based algorithms. It can be seen that combining the improved residual resampling can effectively improve the positioning accuracy.

[0160] To better compare the change in the processing time of IHE-PF with improved residual resampling relative to HE-PF in the real-time positioning process, the PF algorithm was not added for comparison in the simulation part. Figure 8 The change in the calculation time required for the OSNs positioning algorithms based on IHE-PF and HE-PF to complete one 60s real-time positioning was analyzed as the number of particles increased. From Figure 8 it can be seen that as the number of particles increases, the calculation times of HE-PF and IHE-PF to complete the 60s positioning process are not much different. When the number of particles reaches 2000, the processing time of IHE-PF is 25.66s, the processing time of HE-PF is 24.78s, and the processing time of the particle filter is 357.57s. Therefore, there is basically no change in the calculation time of IHE-PF with improved residual resampling and HE-PF in the real-time positioning process, but the positioning accuracy of the OSNs based on IHE-PF has been significantly improved.

[0161] To further significantly compare the calculation time and positioning accuracy, the corresponding average values are taken for comparison. As shown in Table 1, during the 60s positioning process, the calculation time of the IHE-PF-based OSNs positioning algorithm is 71.5ms at each moment, the calculation time of the HE-PF positioning algorithm is 71.4ms, while that of PF is as high as 945ms. The mean absolute error of PF in the X-axis direction during the 60s real-time positioning process is 4.34m, the mean absolute error of HE-PF in the X-axis direction is 5.12m, and the mean absolute error of IHE-PF in the X-axis direction is 4.27m. The mean absolute error of PF in the Y-axis direction during the 60s real-time positioning process is 3.92m, the mean absolute error of HE-PF in the Y-axis direction is 4.76m, and the mean absolute error of IHE-PF in the Y-axis direction is 3.85m. Therefore, the mean absolute error of IHE-PF in the X-axis direction is improved by 0.85m relative to HE-PF and by 0.07m relative to PF. The mean absolute error of IHE-PF in the Y-axis direction is improved by 1.01m relative to HE-PF and by 0.17m relative to PF. Although the required calculation time of the UKF positioning algorithm is 8.5ms, its average error is 5.18m and 4.95m higher than that of IHE-PF in the X-axis and Y-axis directions respectively.

[0162] Table 1 Average positioning error and calculation time of PF, HE-PF and IHE-PF

[0163]

[0164] The IHE-PF-based OSNs positioning algorithm improves the calculation time by 92.4% relative to PF, and the positioning accuracy in the X-axis and Y-axis directions is improved by 1.6% and 4.3% respectively. Compared with HE-PF, the IHE-PF only increases the calculation time by 0.1ms, while the positioning accuracy in the X-axis and Y-axis directions is improved by 16% and 21% respectively. Although the calculation time of IHE-PF increases by 63ms compared with UKF, the positioning accuracy in the X-axis and Y-axis directions is improved by 54.8% and 56.9% respectively.

[0165] From the corresponding experiments, the method of the present invention significantly improves the calculation efficiency of the original PF, and at the same time maintains good positioning accuracy, providing a feasible high-efficiency calculation method for the particle filter positioning method of ocean sensor networks in high-dynamic and uncertain environments.

[0166] The preferred specific embodiments of the present invention have been described in detail above. It should be understood that those of ordinary skill in the art can make many modifications and variations based on the concept of the present invention without creative efforts. Therefore, all technical solutions that can be obtained by those skilled in the art in this technical field based on the concept of the present invention through logical analysis, reasoning, or limited experiments on the basis of the prior art shall fall within the protection scope determined by the claims.

Claims

1. An ocean sensor network node positioning method based on efficient particle filtering, characterized in that It includes the following steps: S1. Based on the motion characteristics of the velocity field in the sea area, considering the interaction force between the tidal field and the residual field, establish a state model of the nonlinear system; S2. Based on the signal strength attenuation model, model the signal strength received by each node in the marine sensor network to obtain an observation model of the nonlinear system; S3. Obtain the first state vector of the posterior probability mean at time k-1 Calculate the second state vector at time k Express the state vector of the i-th particle at time k-1 in terms of the first state vector, and then express the state vector of the i-th particle at time k Perform a Taylor expansion at the first state vector to calculate the second particle state vectors of all particles approximated to the first-order Taylor series terms at time k. Then, use the multi-dimensional Richardson extrapolation method to perform a two-step Taylor expansion on the second particle state vectors to obtain the third particle state vectors of all particles approximated to the second-order Taylor series terms at time k; S4. Based on the normalized weight at time k - 1, calculate the normalized weight at time k in a recursive manner, and the normalization is achieved based on the observation value obtained from the observation model; S5. Judge whether the particles degenerate based on the effective particle number. If so, execute S6. If not, use the normalized weight at time k and the particle set at this time as the result weight and the result particle set, and execute S8; S6. Conduct resampling, and then divide the entire particle set into a small - weight particle set and a large - weight particle set according to the weight threshold. Keep the state vectors and weights of the particles in the large - weight particle set unchanged, modify the state vectors of the particles in the small - weight particle set, and then modify and normalize the weights of the particles in the small - weight particle set to obtain the modified particles. Use the modified and normalized weights of the small - weight particles as the result weight; S7. Conduct residual resampling according to the modified particles to obtain a replicated particle set, and use the replicated particle set as the result particle set; S8. Combine the result particle set and the result weight, calculate the posterior probability distribution of the unknown node at time k, calculate the expected value of the position according to the obtained posterior probability distribution, and obtain the estimated position of the unknown node at time k.

2. An efficient particle filter-based node localization method for ocean sensor networks according to claim 1, characterized in that The specific two - step Taylor expansion is as follows: Perform a Taylor expansion on the second particle state vector at , and then perform a Taylor expansion on at , where Δu i is the corresponding gradient, α k-1 is the state noise, and F is the state equation.

3. An ocean sensor network node positioning method based on an efficient particle filter according to claim 1, characterized in that The expression of the normalized weight at time k is: Among them, is the weight of the i-th particle at time k, and ∝ represents the proportional symbol. is the normalized weight of the i-th particle at time k-1. represents the posterior distribution of the i-th particle at time k, and z k represents the observation value at time k. represents the third particle state vector of the i-th particle at time k. The expression of the weight of the i - th particle at time k - 1 is: Among them, is the weight of the i-th particle at the (k - 1)-th moment after normalization, N represents the number of particles, is the weight of the i-th particle at the (k - 1)-th moment.

4. An ocean sensor network node positioning method based on an efficient particle filter according to claim 1, characterized in that The expression of the particle set divided into two categories is: Among them, is the third particle state vector of the i-th particle at time k, S l is the set of particles with small weights, S h is the set of particles with large weights, is the modified weight of the i-th particle at time k, W thres is the weight threshold.

5. An efficient particle filter-based node localization method for ocean sensor networks according to claim 4, characterized in that, The determination steps of the weight threshold are as follows: Sort all the sampled particles in ascending order according to the weight, store the sorted particles in a set. Assume that the weight of the r - th particle is used as the weight threshold, obtain the expression of the weight difference between the small - weight particle set and the large - weight particle set, calculate the weight difference from the first particle in the set. When the weight difference is greater than 0, determine the serial number r of the particle at this time to obtain the weight threshold.

6. An efficient particle filter-based node localization method for ocean sensor networks according to claim 5, characterized in that, The method of linear interpolation is used to modify the state vectors of the particles in the small - weight particle set. The modified state vector of the particle in the small - weight particle set is: Among them, is the state vector of the particles in the modified small-weight particle set, representing the small-weight particle set S l the state vector of the s-th particle to be modified in it, representing the state vector of the j-th particle in the large-weight particle set S h where j = 1, 2,..., N representing the small-weight particle set S l the weight of the s-th small-weight particle in it, representing the large-weight particle set S h the weight of the j-th large-weight particle in it, s = 1, 2,..., N l and j = 1, 2,..., N h , N l and N h respectively represent the number of particles in the sets S l and S h respectively.

7. An ocean sensor network node positioning method based on efficient particle filtering according to claim 5, characterized in that, The weight of the modified small - weight particle is: Among them, represents the weight of the s-th small-weight particle in the small-weight particle set S l at the (k - 1)-th moment, represents the weight of the s-th small-weight particle in the small-weight particle set S l at the k-th moment, is the state vector of the particles in the modified small-weight particle set, z k represents the observed value at the k-th moment, represents the posterior distribution corresponding to the particles in the modified small-weight particle set.

8. An efficient particle filtering-based node localization method for ocean sensor networks according to claim 1, characterized in that, In S7, when copying a particle set, deterministic selection and random selection are performed. When , where is the total number of times the i-th particle is selected in the first-step deterministic selection and the second-step random selection. For the i-th particle to be copied, Δh 1 represents the maximum deviation value. The Δh 1 of the i-th particle to be copied is less than half of the minimum of the average state vector differences between the i-th particle to be copied and all other particles to be copied.

9. An ocean sensor network node positioning method based on efficient particle filtering according to claim 8, characterized in that, Calculating according to the third particle state vector when replicating a particle set The deviation value between the newly generated particle state vector and the third particle state vector is as follows. The expression for the deviation value is: Among them, γ i is a parameter for adjusting the dispersion degree of the i-th particle that needs to be resampled, is the total number of times the i-th particle is selected in the first-step deterministic selection and the second-step random selection process, g is the corresponding selection times index, and p is the number of times of being selected.

10. An ocean sensor network node positioning method based on an efficient particle filter according to claim 1, characterized in that, When the particle set degenerates, after executing S6 and S7, the expression of the expected value of the position is: where \(E(u k |z_1: k )\) is the expected value of the position, \(u k \) is the state of the target to be located, \(z 1:k \) represents the observed values corresponding to the time instants from \(1\) to \(k\), \) is the particle set obtained by replication, \(N\) is the number of particles, \) is the modified normalized particle weight, \(p(u k |z 1:k )\) is the posterior probability distribution of the unknown node.

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