CN115906413B - Dirichlet process hybrid model node self-positioning method - Google Patents
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Abstract
The invention provides a Dirichlet process mixed model node self-positioning method based on importance sampling, which takes node position coordinates as time variables, builds a sensor node self-positioning model by combining the Dirichlet process mixed model on the basis, and simultaneously directly samples a node position posterior probability density function in a Gibbs iteration process to obtain node positions; by utilizing an importance sampling principle in a Monte Carlo sampling approximation method, a suggested distribution of posterior probability distribution of a target node is found, the sampling difficulty of the posterior probability distribution is simplified, and the positioning accuracy performance of the sensor network node is improved. The invention solves the problem that in practice, the sensor network measures the influence of multipath interference, so that the sensor can adaptively adjust the interference information of underwater multipath; a new node self-positioning model is constructed, so that the actual situation is effectively fitted, the difficulty in sampling the node position state is reduced, and the self-positioning precision of the sensor network is improved.
Description
Technical Field
The invention relates to the field of underwater acoustic networks, in particular to a self-positioning method of an underwater acoustic network, which relates to a statistical signal processing and non-parameterized Bayesian theory and performs high-precision node self-positioning under the conditions of underwater complex multipath environment and sensor network node drift.
Background
Scientific researches on the aspects of marine construction and development of the underwater acoustic sensor, tracking, positioning, fusion and the like are based on a high-performance underwater acoustic sensor network, and the importance of the underwater acoustic network is increasingly prominent. The self-positioning of the sensor nodes in the underwater acoustic sensor network is a foundation for realizing various functions of the high-performance underwater acoustic sensor network, is an indispensable component part of the process of initializing the underwater acoustic sensor network, and is also an important link in the aspects of target detection, positioning and tracking, submarine navigation, ocean resource development and utilization and the like. Therefore, improving the self-positioning accuracy of the nodes is of great significance to the underwater acoustic sensor network. The influence of multipath effect on the traditional positioning algorithm in the actual underwater acoustic environment is considered, the characteristic that the Dirichlet process mixed model in the non-parameterized Bayesian estimation carries out self-adaptive learning on the actual data is introduced into the self-positioning of the underwater acoustic network node, the positioning performance and the adaptability of the self-positioning algorithm in the multipath environment are improved, the network precision of the underwater acoustic sensor is improved, and the overall performance of the underwater acoustic sensor network system can be improved in the actual ocean environment.
Disclosure of Invention
In order to overcome the defects in the prior art, the invention provides a self-positioning method for a Dirichlet process mixed model node. Aiming at the situation that multipath effect and node have drift in the actual underwater sound environment, the node position coordinates are regarded as time variables, and a sensor node self-positioning model is built by combining a Dirichlet process mixed model on the basis. Meanwhile, directly sampling the posterior probability density function of the node position in the Gibbs iteration process to obtain the node position; aiming at the problem that posterior probability of a target position IS difficult to sample and solve, an importance sampling principle (Importance Sampling, IS) in a Monte Carlo sampling approximation method IS utilized to find the suggested distribution of posterior probability distribution of a target node, the sampling difficulty of the posterior probability distribution IS simplified, and the positioning accuracy performance of the sensor network node IS improved.
The technical scheme adopted by the invention for solving the technical problems comprises the following specific steps:
step 1: a node self-positioning model based on a Dirichlet process mixed model is established, wherein a target node position state transition probability model is as follows:
X t ＝X t-1 +v t (1)
wherein X is t ＝[x t ,y t ]Is the position information of the target node at the time t, x t ，y t Coordinates in the X and Y directions of the nodes respectively;
step 2: a measurement model of a target node and an ith anchor node of the underwater acoustic sensor network is established, and the measurement model is as follows:
R it ＝f i (X t )+ε it (3)
wherein R is it Is measurement information, target node X t The true distance to the ith anchor node isA i ＝[x i ,y i ] T An ith anchor node coordinate in the underwater acoustic sensor network;
step 3: due to the position coordinates X of the target node t Is a time variable, thus distance information f i (X t ) Is a variable, and under the node self-positioning model and the measuring model constructed in the step 1 and the step 2, X is needed to be calculated t Posterior probability of (2)Performing deduction; first to TOAMeasuring error variable epsilon it Indicated variable z of (2) it Mathematical inference is performed on the error indication variable z measured for the ith anchor node it For instance, when z it Pointing to the identified kth multipath, the indicator variable z can be deduced by means of knowledge of the probability map model it The posterior is:
wherein n is k,-i For the number mu of the observation information of the kth multipath in the ith anchor node measurement information ik Parameters for the identified kth multipath;
at the same time, new information R is collected at the moment of the ith anchor point t it The corresponding parameter mu of the kth multipath needs to be updated ik The update equation is as follows:
when indicating variable z it Pointing to K+1 indicates that the measurement information is from unidentified multipath, indicating the variable z it The posterior probability of (2) is:
when z it Pointing to K+1, indicating a new multipath parameter u i,K+1 Must be from a priori base clothGenerating new mu for K+1st multipath i,K+1 The new parameter is independent of other parameters, and the posterior probability of the parameter is only related to the current distance measurement data R it Related, mu i,K+1 The probability distribution is as follows:
step 4: under the node self-positioning model and the measuring model constructed in the step 1 and the step 2, the X is to be calculated t Deducing the posterior probability of (3) the error indication variable z of the measurement it Is inferred from (a); step 4, deducing the position coordinates of the target node, and knowing the position coordinates X of the target node from the established mathematical model t The probability distribution is not only the coordinate X at the previous moment t-1 Related to the distance measurement value R at the current moment it Related to; from Bayes formula, X t The posterior probability distribution of (2) is as follows:
from formula (9), X t The posterior probability distribution is continuous and irregular, meaning that the probability density function cannot be directly generatedThus solving for X by means of importance sampling (Importance Sampling) in Monte Carlo sampling t A problem of difficulty in sampling; suggested distribution pair X using (10) t Sampling:
q(X t )＝γN(X t-1 ,Σ v ) (10)
wherein:
where σ is the measurement variance, at which time the distribution q (X t ) Not only very close to the original distribution p (X t ) Moreover, gaussian distribution is formally easy to generate sample points;
step 5: q (X) mentioned in step 4 t ) Substituting the target node into the importance sampling process, and performing N Monte Carlo sampling experiments to obtain the position information of the target node.
In the step 1, v t The position noise of the target node, the noise obeys the mean value to be zero, and the variance to be sigma v As shown in formula (2):
v t ～N(0,Σ v ) (2)。
in the step 2, the error epsilon in the model is measured it The following construction was performed using non-parameterized bayesian:
wherein alpha is i Andfor prior information of the Dirichlet process hybrid model, GEM (·) represents the broken stick configuration in the Dirichlet process, N (u, σ) 2 ) Representing mean and variance as u and sigma, respectively 2 Normal distribution, pi i Distribution, μ constructed for Dirichlet procedure ik The kth multipath parameter observed for the ith anchor node; by z it Combining the measured information with the multipath, each path corresponding to one z it Thus solving the problems of unknown measurement information and multipath sources in the complex underwater acoustic environment.
The importance sampling process is as follows:
in a first step, let j=1 first, from the proposed distribution q (X t ) Generating sample points X according to probability distribution j t Q (X) j t ) I.e. X j t Substituting into formula (10) to calculate q (X) t ) To obtain q (X) t ) Is a numerical value of (2);
and a second step of: sample Point X j t Substituting the true distribution p (X t ) In (1), p (X) j t ) I.e. X j t Substituting into the formula (9) to calculateIs a numerical value of (2);
and a third step of: calculating importance weights, and normalizing the importance weights, wherein the normalization mode is shown as a formula (12):
fourth step: if j is equal to N, entering a fifth step, if j is smaller than N, adding 1 to j, returning to the first step, and circulating for N times; the method comprises the steps of carrying out a first treatment on the surface of the
Fifth step: the first step to the fourth stepThe weighted summation is carried out as follows:
finally, a target node X at the moment t is obtained t And (3) completing node positioning.
The invention has the beneficial effects that:
1. a non-parametric Bayesian method is introduced to solve the problem that in practice, the sensor network measures the influence of multipath interference, so that the sensor can adaptively adjust the interference information of underwater multipath;
2. providing a node drift model of the sensor network, combining the node drift model with non-parametric Bayes, and constructing a new node self-positioning model, so that the actual situation is effectively fitted;
3. the Monte Carlo method is introduced, and the proposal distribution adapting to the model is provided, so that the sampling difficulty of the node position state is reduced, and the self-positioning precision of the sensor network is improved.
Drawings
Fig. 1 is a Dirichlet process hybrid model-based underwater acoustic network node self-localization probability map model.
Fig. 2 is a position diagram of an anchor node and a target node.
FIG. 3 is a graph showing the RMSE of the location results of the least squares algorithm, taylor algorithm, and the Dirichlet process mixture model algorithm based on importance sampling (ISDP, proposed by this patent) in each Monte Carlo experiment.
Fig. 4 is a RMSE histogram of the positioning results of various algorithms.
Detailed Description
The invention will be further described with reference to the drawings and examples.
The steps of the embodiment of the invention are as follows:
step 1: a node self-positioning model based on a Dirichlet process mixed model is established, as shown in fig. 1, wherein a target node position state transition probability model is as follows:
X t ＝X t-1 +v t
wherein the target node position is X 0 ＝[4822.5,2707.0]Position noise v of target node t Obeying the mean value to be zero and the variance to beAs shown in formula (13):
step 2: establishing a measurement model of a target node and an ith anchor node of the underwater acoustic sensor network, wherein the positions of the anchor node and the target node are shown in figure 2, setting the total anchor node number to 3, and the position information of the three anchor nodes is A respectively 1 ＝[4123.6,2787.9] T ,A 2 ＝[1287.46059] T ,A 3 ＝[3969.1,3616.5] T The measurement model is shown in formula (14):
R it ＝f i (X t )+ε it (14)
target node X t The true distance to the ith anchor node isError epsilon in metrology model it The following construction is performed using non-parameterized Bayes, the error ε it The specific construction is shown as formula (4), wherein the super parameter of the Dirichlet process mixing model isSigma (sigma) 2 =50, randomly generating 3 groups of mixed Gaussian noise with multipath number of 2, each group of 1000 data, and adding 3 groups of measurement errors to 3 groups of actual distances R it In which 3 sets of distance measurement data are obtained.
Step 3: for TOA measurement error variable epsilon it Indicated variable z of (2) it Mathematical inferences are made.
Step 4: for X t Posterior probability of (2)By inference, using a proposed distribution q (X t ) The monte carlo sampling experiment was performed n=5000 times, as already explained in step 4, detailed description of the procedure, to obtain N particle states +.>The particle states are weighted and summed to finally obtain a target node X at the moment t t And the node self-positioning is realized. The final results are shown in fig. 3 and fig. 4, fig. 3 is a RMSE showing the positioning results of the least square algorithm, the Taylor algorithm, the Dirichlet process mixed model algorithm based on importance sampling (ISDP, the algorithm proposed in the patent) in each monte carlo experiment, and fig. 4 is a RMSE histogram of the positioning results of various algorithms.
Claims (3)
1. The Dirichlet process mixed model node self-positioning method is characterized by comprising the following steps of:
step 1: a node self-positioning model based on a Dirichlet process mixed model is established, wherein a target node position state transition probability model is as follows:
X t ＝X t-1 +v t (1)
wherein X is t ＝[x t ,y t ]Is the position information of the target node at the time t, x t ，y t Coordinates in the X and Y directions of the nodes respectively; v t For the position noise of the target node, the noise obeys to have a mean value of zero and a variance of Σ v As shown in formula (2):
v t ～N(0,Σ v ) (2)
step 2: a measurement model of a target node and an ith anchor node of the underwater acoustic sensor network is established, and the measurement model is as follows:
R it ＝f i (X t )+ε it (3)
wherein R is it Is measurement information, target node X t The true distance to the ith anchor node isA i ＝[x i ,y i ] T Is the coordinate epsilon of the ith anchor node in the underwater acoustic sensor network it Measuring an error variable for TOA;
step 3: first, for TOA measuring error variable epsilon it Indicated variable z of (2) it Mathematical inference is performed on the error indication variable z measured for the ith anchor node it For instance, when z it Pointing to the identified kth multipath, the indicator variable z can be deduced by means of knowledge of the probability map model it The posterior probability of (2) is:
wherein n is k,-i For the number mu of the observation information of the kth multipath in the ith anchor node measurement information ik Parameters for the identified kth multipath;
at the same time, new information R is collected at the moment of the ith anchor point t it The corresponding parameter mu of the kth multipath needs to be updated ik The update equation is as follows:
when indicating variable z it Pointing to K+1 indicates that the measurement information is from unidentified multipath, indicating the variable z it The posterior probability of (2) is:
when z it Pointing to K+1, indicating a new multipath parameter u i,K+1 Must be from a priori base clothGenerating new mu for K+1st multipath i,K+1 Parameter u at this time i,K+1 Independent of other parameters, the posterior probability of the parameter is only related to the current distance measurement data R it Related, mu i,K+1 The probability distribution is as follows:
wherein u is the mean value;
step 4: under the node self-positioning model and the measuring model constructed in the step 1 and the step 2, the X is to be calculated t Deducing the posterior probability of (3) the error indication variable z of the measurement it Is inferred from (a); step 4, deducing the position coordinates of the target node, and knowing the position coordinates X of the target node from the established mathematical model t The probability distribution is not only the coordinate X at the previous moment t-1 Related to the distance measurement value R at the current moment it Related to; from Bayes formula, X t The posterior probability distribution of (2) is as follows:
wherein Σ is v For the target node defined in equation (2)From the variance of the position noise of (2), X is known from the formula (9) t The posterior probability distribution is continuous and irregular, meaning that the probability density function cannot be directly generatedThus solving for X by means of importance sampling method in monte carlo sampling t A problem of difficulty in sampling; suggested distribution pair X using (10) t Sampling:
q(X t )＝γN(X t-1 ,Σ v ) (10)
wherein:
where σ is the measurement variance, at which time the distribution q (X t ) Not only very close to the original distribution p (X t ) Moreover, gaussian distribution is formally easy to generate sample points;
step 5: q (X) mentioned in step 4 t ) Substituting the target node into the importance sampling process, and performing N Monte Carlo sampling experiments to obtain the position information of the target node.
2. The Dirichlet process hybrid model node self-positioning method according to claim 1, wherein:
in the step 2, the error epsilon in the model is measured it The following construction was performed using non-parameterized bayesian:
wherein alpha is i Andfor prior information of the Dirichlet process hybrid model, GEM (·) represents the broken stick configuration in the Dirichlet process,N(u,σ 2 ) Representing mean and variance as u and sigma, respectively 2 Normal distribution, pi i Distribution, μ constructed for Dirichlet procedure ik The kth multipath parameter observed for the ith anchor node; by z it Combining the measured information with the multipath, each path corresponding to one z it Thus solving the problems of unknown measurement information and multipath sources in the complex underwater acoustic environment.
3. The Dirichlet process hybrid model node self-positioning method according to claim 1, wherein:
the importance sampling process is as follows:
in a first step, let j=1 first, from the proposed distribution q (X t ) Generating sample points X according to probability distribution j t Q (X) j t ) I.e. X j t Substituting into formula (10) to calculate q (X) t ) To obtain q (X) t ) Is a numerical value of (2);
and a second step of: sample Point X j t Substituting the true distribution p (X t ) In (1), p (X) j t ) I.e. X j t Substituting into the formula (9) to calculateIs a numerical value of (2);
and a third step of: calculating importance weights, and normalizing the importance weights, wherein the normalization mode is shown as a formula (12):
fourth step: if j is equal to N, entering a fifth step, if j is smaller than N, adding 1 to j, returning to the first step, and circulating for N times;
fifth step: the first step to the fourth stepAddingThe weight sums are specifically operated as follows:
finally, a target node X at the moment t is obtained t And (3) completing node positioning.
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