CN115906413A - Dirichlet process mixed model node self-positioning method based on importance sampling - Google Patents
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Abstract
The invention provides a Dirichlet process mixed model node self-positioning method based on importance sampling.A node position coordinate is taken as a time variable, a sensor node self-positioning model is constructed by combining a Dirichlet process mixed model on the basis, and a node position posterior probability density function is directly sampled in a Gibbs iteration process to obtain a node position; by using the importance sampling principle in the Monte Carlo sampling approximation method, the suggested distribution of the posterior probability distribution of the target node is searched, the sampling difficulty of the posterior probability distribution is simplified, and the positioning precision performance of the sensor network node is improved. The invention solves the problem that the sensor network measures the influence of multipath interference in practice, so that the sensor can self-adaptively adjust the underwater multipath interference information; and a new node self-positioning model is constructed, so that the actual situation is effectively fitted, the sampling difficulty of 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 statistical signal processing, non-parametric Bayesian theory and high-precision node self-positioning under the conditions of underwater complex multipath environment and sensor network node drift.
Background
The scientific researches on the aspects of the construction and development of oceans, the underwater acoustic sensors which cannot be opened, the tracking, positioning and fusion and the like are all based on a high-performance underwater acoustic sensor network, and the importance of the underwater acoustic network is increasingly highlighted. The self-positioning of the underwater acoustic sensor network on the sensor nodes in the network is the basis for realizing various functions of the high-performance underwater acoustic sensor network, is an indispensable component in the initialization process of 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, the self-positioning accuracy of the node is improved, and the method has important significance for 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 unparameterized Bayes estimation carries out adaptive learning on actual data is introduced into the self-positioning of the underwater acoustic network node, the positioning performance and the adaptive capacity of the self-positioning algorithm in the multipath environment are improved, the accuracy of the underwater acoustic sensor network is improved, and the overall performance of the underwater acoustic sensor network system can be improved in the actual marine environment.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a Dirichlet process mixed model node self-positioning method based on importance sampling. Regarding the conditions of multipath effect and node drift in the actual underwater acoustic environment, the position coordinates of the nodes are regarded as time variables, and a sensor node self-positioning model is constructed by combining a Dirichlet process mixed model on the basis. Simultaneously, directly sampling a posterior probability density function of the node position in a Gibbs iteration process to obtain the node position; aiming at the problems of difficult Sampling and difficult solution of the posterior probability of the target position, the suggested distribution of the posterior probability distribution of the target node IS searched by utilizing the Importance Sampling principle (IS) in the Monte Carlo Sampling approximation method, the Sampling difficulty of the posterior probability distribution IS simplified, and the positioning precision performance of the sensor network node IS improved.
The technical scheme adopted by the invention for solving the technical problem comprises the following specific steps:
step 1: establishing a node self-positioning model based on a Dirichlet process mixed model, wherein a target node position state transition probability model is as follows:
X t ＝X t-1 +v t (1)
wherein, X t ＝[x t ,y t ]Is the location information of the target node at time t, x t ，y t Coordinates in the X and Y directions of the node are respectively;
step 2: establishing a measurement model of a target node and an ith anchor node of the underwater acoustic sensor network, wherein the measurement model comprises the following steps:
R it ＝f i (X t )+ε it (3)
wherein R is it Is measurement information, target node X t True distance to the ith anchor node is
A i ＝[x i ,y i ] T Coordinates of an ith anchor node in the underwater acoustic sensor network; />
And step 3: due to the position coordinate X of the target node t Is a time variable, so the distance information f i (X t ) Is variable, and needs to be matched with X under the node self-positioning model and the measuring model constructed in the steps 1 and 2 t A posteriori probability of
Carrying out derivation; firstly, measure the error variable epsilon of TOA it Is an indicator variable z it Making a mathematical extrapolation of the error-indicating variable z measured for the ith anchor node it In other words, when z is it Pointing to the identified kth multipath, the indicator variable z can be derived by means of knowledge of the probabilistic graphical model it A posteriori of：
Wherein n is k,-i The number of observed information, mu, belonging to k-th multipath in the ith anchor node measurement information ik Parameters for the identified kth multipath;
meanwhile, new information R is collected at the moment of the ith anchor point t it The corresponding parameter mu of k-th multipath needs to be updated ik The update equation is as follows:
when indicating variable z it Pointing at K +1, indicating that the measurement information is from an unidentified multipath, indicates the variable z it The posterior probability of (a) is:
when z is it Pointing to K +1, a parameter u indicating the newly identified multipath i,K+1 Must first examine the basic cloth
Generating new mu for K +1 type multipath i,K+1 The new parameter is not related to other parameters, and the posterior probability of the parameter is only related to the current distance measurement data R it Related to, mu i,K+1 The probability distribution is as follows: />
And 4, step 4: under the node self-positioning model and the measurement model constructed in the steps 1 and 2, X is subjected to self-positioning t The posterior probability of (3) is deduced, and the measured error indicating variable z is completed it An inference of (2); step 4, the position coordinates of the target nodes are deduced, and the position coordinates X of the target nodes can be known from the established mathematical model t Probability distribution not only with the previous time coordinate X t-1 The relation also relates to the distance measurement value R at the current moment it (ii) related; known from Bayesian formula, X t The posterior probability distribution of (a) is as follows:
from the formula (9), X t The posterior probability distribution is continuous and irregular, meaning that the obedient probability density function cannot be generated directly
Thus solving for X by means of the Importance Sampling (importation Sampling) method in monte carlo Sampling t The problem of difficulty in sampling; proposed distribution pairs X using equation (10) t Sampling:
q(X t )＝γN(X t-1 ,Σ v ) (10)
wherein:
where σ is the measurement variance, then the distribution q (X) is proposed t ) Not only very close to the original distribution p (X) t ) And, formally, a gaussian distribution is easy to generate sample points;
and 5: q (X) mentioned in step 4 t ) And substituting the importance sampling process with the Monte Carlo sampling test for N times to obtain the position information of the target node.
In said step 1, v t Position noise of target node, noise obeying mean value to zero, variance to sigma v Is shown in formula (2):
v t ～N(0,Σ v ) (2)。
in step 2, the error ε in the model is measured it The non-parametric Bayes is adopted to carry out the following construction:
wherein alpha is i And
for prior information of a mixed model of the Dirichlet process, GEM (. Smallcircle.) represents a broken stick structure in the Dirichlet process, and N (u, σ) 2 ) Means and variance u and σ, respectively 2 Normal distribution,. Pi i Distribution, μ, constructed for Dirichlet procedures ik A k-th type multipath parameter observed for the ith anchor node; using z it Combining the measurement information with multiple paths, each path corresponding to a z it Therefore, the problem that the measurement information and the multipath source are unknown in the complex underwater acoustic environment is solved.
The importance sampling process is as follows:
first, let j =1, from the proposed distribution q (X) t ) Generating sample points X according to probability distribution j t And find q (X) j t ) A value of (i) i.e. X j t Substitution into equation (10) to calculate q (X) t ) To obtain q (X) t ) The value of (d);
the second step is that: sample point X j t Substituting the true distribution p (X) t ) In (b) to obtain p (X) j t ) I.e. X j t Substituted into the formula (9) to calculate
The value of (d);
the third step: calculating importance weight, and normalizing the importance weight, wherein the normalization mode is shown as formula (12):
the 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; (ii) a
The fifth step: obtained in the first to fourth steps
And performing weighted summation, wherein the specific operation is as follows:
finally obtaining a target node X at the time t t And (4) completing node positioning.
The invention has the beneficial effects that:
1. a non-parametric Bayes method is introduced to solve the problem of influence of multipath interference in the measurement of a sensor network in practice, so that the sensor can self-adaptively adjust the underwater multipath interference information;
2. a node drift model of the sensor network is provided, and is combined with the non-parametric Bayes to construct a new node self-positioning model, so that the actual situation is effectively fitted;
3. a Monte Carlo method is introduced, and suggested distribution adaptive to the model is provided, so that the sampling difficulty of the node position state is reduced, and the self-positioning accuracy of the sensor network is improved.
Drawings
FIG. 1 is a Dirichlet process hybrid model-based underwater acoustic network node self-positioning probability map model.
Fig. 2 is a location diagram of an anchor node and a target node.
FIG. 3 is a diagram showing the RMSE of the positioning results of the least squares algorithm, taylor algorithm, and the Dirichlet process mixed model algorithm based on importance sampling (ISDP, the algorithm proposed in this patent) in each Monte Carlo experiment.
FIG. 4 is a histogram of the RMSE positioning results of various algorithms.
Detailed Description
The invention is further illustrated with reference to the following figures and examples.
The steps of the embodiment of the invention are as follows:
step 1: establishing a node self-positioning model based on a Dirichlet process mixed model, as shown in FIG. 1, wherein the 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 Obedience mean is zero and variance is
Gaussian noise of (4), as shown in equation (13):
and 2, step: establishing measurement models of target nodes and ith anchor nodes of the underwater acoustic sensor network, setting the positions of the anchor nodes and the target nodes as shown in figure 2, setting the number of all anchor nodes to be 3, and setting the position information of the three anchor nodes to be A 1 ＝[4123.6,2787.9] T ,A 2 ＝[1287.46059] T ,A 3 ＝[3969.1,3616.5] T The measurement model is shown as formula (14):
R it ＝f i (X t )+ε it (14)
target node X t True distance to the ith anchor node is
Error in metrology model ε it Using unparameterized Bayes, the error epsilon is constructed it The specific structure is as shown in formula (4), wherein the hyper-parameter of the Dirichlet process mixed model is alpha 0 ＝1,/>
And σ 2 =50, randomly generating mixed Gaussian noise embodying multipath number 23 sets of sound, 1000 data for each set, and adding 3 sets of measurement errors to 3 sets of actual distances R it In (1), 3 sets of distance measurement data are obtained.
And step 3: for TOA measurement error variable epsilon it Is a variable z it A mathematical inference is made.
And 4, step 4: to X t A posteriori probability of
Making an inference using the proposed distribution q (X) t ) N =5000 Monte Carlo sampling experiments were performed, as already explained in step 4 of the detailed procedural summary, to obtain N particle states->
Carrying out weighted summation on the particle states to finally obtain a target node X at the time t t And (3) to implement node self-positioning. The final result is shown in fig. 3 and fig. 4, fig. 3 is an RMSE showing the positioning result of the least square algorithm, the Taylor algorithm, and the Dirichlet process mixed model algorithm based on importance sampling (ISDP, the algorithm proposed by the present patent) in each monte carlo experiment, and fig. 4 is an RMSE histogram showing the positioning result of various algorithms. />
Claims (4)
1. A Dirichlet process hybrid model node self-positioning method based on importance sampling is characterized by comprising the following steps:
step 1: establishing a node self-positioning model based on a Dirichlet process mixed model, wherein the target node position state transition probability model is as follows:
X t ＝X t-1 +v t (1)
wherein X t ＝[x t ,y t ]Is the location information of the target node at time t, x t ，y t Coordinates in the X and Y directions of the node are respectively;
and 2, step: establishing a measurement model of a target node and an ith anchor node of the underwater acoustic sensor network, wherein the measurement model comprises the following steps:
R it ＝f i (X t )+ε it (3)
wherein R is it Is measurement information, target node X t True distance to the ith anchor node is
A i ＝[x i ,y i ] T Coordinates of an ith anchor node in the underwater acoustic sensor network;
and 3, step 3: firstly, measure the error variable epsilon of TOA it Is an indicator variable z it Making a mathematical inference of the error-indicating variable z measured for the ith anchor node it In other words, when z is it Pointing to the identified kth multipath, the indicator variable z can be derived by means of knowledge of the probabilistic graphical model it The posterior is:
wherein n is k,-i The number of observed information, mu, belonging to k-th multipath in the ith anchor node measurement information ik Parameters for the identified kth multipath;
meanwhile, 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 at K +1, indicating that the measurement information is from unidentified multipath, and indicating variable z it The posterior probability of (a) is:
when z is it Pointing to K +1, indicating a new recognitionDeriving a multipath parameter u i,K+1 Must first examine the basic cloth
Generating new mu for K +1 type multipath i,K+1 The new parameter is not related to other parameters, and the posterior probability of the parameter is only related to the current distance measurement data R it Related to, mu i,K+1 The probability distribution is as follows:
and 4, step 4: under the node self-positioning model and the measurement model constructed in the steps 1 and 2, X is subjected to self-positioning t The posterior probability of (3) is deduced, and the measured error indicating variable z is completed it An inference of (2); step 4, the position coordinates of the target nodes are deduced, and the position coordinates X of the target nodes can be known from the established mathematical model t Probability distribution not only with the previous time coordinate X t-1 The relation also relates to the distance measurement value R at the current moment it (ii) related; known from Bayesian formula, X t The posterior probability distribution of (a) is as follows:
from the formula (9), X t The posterior probability distribution is continuous and irregular, meaning that the obedient probability density function cannot be generated directly
Sample points of (a), thus solving for X by means of the significance sampling method in Monte Carlo sampling t The problem of difficulty in sampling; proposed distribution pair X using equation (10) t Sampling:
q(X t )＝γN(X t-1 ,Σ v ) (10)
wherein:
where σ is the measurement variance, where the distribution q (X) is proposed t ) Not only very close to the original distribution p (X) t ) And, formally, a gaussian distribution is easy to generate sample points;
and 5: q (X) mentioned in step 4 t ) And substituting the obtained data into an importance sampling process to perform N Monte Carlo sampling experiments so as to obtain the position information of the target node.
2. The importance sampling-based Dirichlet process hybrid model node self-localization method of claim 1, wherein:
in said step 1, v t Position noise of target node, noise obeying mean value to zero, variance to sigma v Is shown in formula (2):
v t ～N(0,Σ v ) (2)。
3. the importance sampling-based Dirichlet process hybrid model node self-localization method of claim 1, wherein:
in the step 2, the error epsilon in the model is measured it The non-parametric Bayes is adopted to carry out the following construction:
wherein alpha is i And
as prior information of a mixed model of the Dirichlet process, GEM (. Cndot.) represents a broken stick structure in the Dirichlet process, and N (u, sigma) 2 ) Means and variance u and σ, respectively 2 Normal distribution,. Pi i Distribution, μ, constructed for Dirichlet procedures ik Is as followsThe k-th multipath parameters observed by the i anchor nodes; using z it Combining the measured information with multiple paths, each path corresponding to a z it Therefore, the problem that the measurement information and the multipath source are unknown in the complex underwater acoustic environment is solved.
4. The importance sampling-based Dirichlet process hybrid model node self-localization method of claim 1, wherein:
the importance sampling process is as follows:
first, let j =1, from the proposed distribution q (X) t ) Generating sample points X according to probability distribution j t And find q (X) j t ) A value of (i) i.e. X j t Substitution into equation (10) to calculate q (X) t ) To obtain q (X) t ) The value of (d);
the second step is that: sample point X j t Substitution into the true distribution p (X) t ) In (b) to obtain p (X) j t ) I.e. X j t Substituted into the formula (9) to calculate
The value of (d);
the third step: calculating the importance weight, and normalizing the importance weight, wherein the normalization mode is shown as formula (12):
the 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; (ii) a
The fifth step: obtained in the first to fourth steps
And performing weighted summation, wherein the specific operation is as follows:
finally obtaining a target node X at the time t t And (4) finishing node positioning.
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