CN110516198A - A kind of distribution type non-linear kalman filter method - Google Patents

A kind of distribution type non-linear kalman filter method Download PDF

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CN110516198A
CN110516198A CN201910645592.5A CN201910645592A CN110516198A CN 110516198 A CN110516198 A CN 110516198A CN 201910645592 A CN201910645592 A CN 201910645592A CN 110516198 A CN110516198 A CN 110516198A
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node
function
moment
posterior distrbutionp
indicate
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CN110516198B (en
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夏威
任媛媛
孙美秋
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University of Electronic Science and Technology of China
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/18—Complex mathematical operations for evaluating statistical data, e.g. average values, frequency distributions, probability functions, regression analysis
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L41/00—Arrangements for maintenance, administration or management of data switching networks, e.g. of packet switching networks
    • H04L41/12—Discovery or management of network topologies
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00—Reducing energy consumption in communication networks
    • Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks

Abstract

Invention belongs to field of signal processing, specially a kind of distribution type non-linear kalman filter method, the time of day of target is described with Posterior distrbutionp function, and with the function of an ED~* class come the approximate Posterior distrbutionp function；Firstly, the present invention obtains intermediate state estimation by optimizing the backward KL divergence among each node between Posterior distrbutionp approximate function and true Posterior distrbutionp function；Then, the end-state estimated result of each node is calculated by optimizing the convex combination of forward direction KL divergence between the final Posterior distrbutionp approximate function of each node and the intermediate Posterior distrbutionp approximate function of its neighbor node.Fast convergence rate of the present invention, and in such a way that multiple nodes work at the same time, can effectively save calculating cost, greatly improve computational efficiency, be widely used in being related to the positioning of distributed wireless sensor and nonlinear dynamic system, in the fields such as target following.

Description

A kind of distribution type non-linear kalman filter method
Technical field
The invention belongs to field of signal processing, are related to the Target Tracking Problem of field of signal processing, more particularly to distribution Target Tracking Problem on formula wireless sensor network, specially a kind of distribution type non-linear kalman filter method.
Background technique
Since Kalman filtering is highly suitable for real time signal processing and large-scale state-space model, since the advent of the world, In The fields such as communication system, electric system, aerospace, environment pollution control, Industry Control, Radar Signal Processing suffer from extensively Application, achieve many achievements.In recent years, with the explosive growth of sequence and flow data, Kalman filter is in machine Also extensive application in study.
Kalman filtering is a kind of using linear system state equation, observation data is inputted by system, to system mode Carry out the algorithm of optimal estimation.However, typical Kalman filtering is only applicable to linear signal model, and in real life, it is past It is more non-linear loop border toward encountering.Currently, it is quite active to the research of general Nonlinear Filtering Problem, it is common non-thread Property filtering have Extended Kalman filter (EKF), unscented kalman filter (UKF) etc.；However, these algorithms are all to nonlinear card Germania has done linear approximation processing, and the method for recycling linear Kalman filter system is handled.
Common centralization, which calculates, to be needed to consume a lot of time and resources, and distributed method by PROBLEM DECOMPOSITION at many small Part, distribute to multiple stage computers and handled, calculating cost can be saved in this way, greatly improve computational efficiency.In recent years, Cooperation diffusion type processing on distributed wireless sensor network has been increasingly becoming a kind of effective data processing technique；It is this Processing mode substantially increases the scalability and flexibility of network, is widely used in environmental monitoring, disaster relief management, and parameter is estimated Meter, the fields such as target following.However, existing distribution type non-linear Kalman filtering is all based on greatly spreading kalman or not at present Quick Kalman filtering has done linear approximation processing to nonlinear Kalman when calculating the state estimation of each node.
Summary of the invention
It is an object of the invention to propose a kind of distribution type non-linear kalman filter method, using point of an exponential family Cloth function q (x) carrys out approximate true Posterior distrbutionp, and measures gap between the two with KL divergence, and optimization KL divergence is minimum, The closest true Posterior distrbutionp p of guarantee q (x) (x | y).
To achieve the above object, The technical solution adopted by the invention is as follows:
A kind of distribution type non-linear kalman filter method, comprising the following steps:
Step 1. is directed to node k, according to the Posterior distrbutionp function at its t-1 momentWith state transfer side The prior density function of journey calculating t moment
Step 2. sets the suggestion distribution function of the sampling of t momentIt is distributed according to suggestion Function is sampled, so that each particle independent same distribution is distributed in suggestion:
Wherein, S is input sample population,Indicate the state vector for s-th of particle that node k is sampled in t moment；
Step 3: the particle weights of calculate node k according to the following formula, and be normalized:
Wherein,Indicate that node k samples the weight of particle, W at s-th of t momentk,tIndicate that node k is adopted t moment is all The sum of weight of like-particles, yl,tIndicate observation of the neighbor node l in t moment of node k；Indicate neighbours' section L pairs of pointThe prediction of observation；Indicate node k to particle s state vectorPrediction；
Step 4: Posterior distrbutionp approximate function among the granular Weights Computing acquired according to above formulaMean valueWith Covariance matrix
It obtainsDistribution function are as follows:
Step 5: in distributed network, intermediate Posterior distrbutionp approximate function that each node is obtainedExpanded It dissipates, according to the intermediate Posterior distrbutionp approximate function of each neighbor node of node kThe end-state that node k is calculated is estimated Count qk(xk,t):
Wherein, al,kIt is neighbor node l to the weight of present node k, meetsAnd calculate qk(xk,t) mean value μk,tWith covariance matrix Σk,t:
μk,tState estimation vector as node k.
The beneficial effects of the present invention are:
A kind of nonlinear distributed kalman filter method proposed by the present invention has the advantages that
1. algorithm proposed by the present invention is suitable for non-linear environment, compared to classical linear Kalman filter algorithm, application Range is wider；
2. distributed algorithm proposed by the present invention need to only obtain the observation information of its neighbor node at each node, allow Each node is handled simultaneously, is not needed to send all observation informations to fusion center and is handled, the communication energy needed Amount is less, and has higher operation efficiency；
3. proposed by the present invention is a kind of distributed algorithm, it is stronger steady to have compared with corresponding centralized algorithm Property.For centralization, when processing center when something goes wrong, whole system can not work normally, and distributed algorithm can have Effect, which avoids fusion center when something goes wrong, leads to the risk of whole system collapse；
4. the present invention is directly optimized unbiased in the intermediate state estimation for calculating each node based on Monte Carlo technique Algorithm directly optimizes the backward KL divergence between APPROXIMATE DISTRIBUTION and true Posterior distrbutionp, does not need to carry out nonlinear function linear It is approximate；
5. the present invention is realized by spreading the intermediate state estimated result of each node in its neighborhood.Work as distribution When the topological structure interior joint number and the more corresponding neighbor node number of each node of network, method of the invention is than corresponding collection The steady-state error fluctuation of Chinese style method is smaller.
Detailed description of the invention
Fig. 1 is the flow diagram of each node in distribution type non-linear kalman filter method proposed by the present invention.
Fig. 2 is distributed network topology structure used in the examples (for having 10 nodes in network).
Fig. 3 is the tracking knot of the present invention and some node in certain Monte Carlo Experiment of centralization in embodiment Fruit figure.
Fig. 4 is the MSE comparison diagram of the present invention and the position of centralization in embodiment.
Fig. 5 is the MSE comparison diagram of the present invention and the speed of centralization in embodiment.
Specific embodiment
Present invention will be further explained below with reference to the attached drawings and examples.
In the present invention, consider haveThe distributed network structure of a node, in each node point of one exponential family Cloth functionCarry out the Posterior distrbutionp function of the approximate nodeIt is approximate referred to as intermediate Posterior distrbutionp Function, the present invention takeFor Gaussian function, gap between the two is measured with KL divergence；Define the backward of each node KL divergence expression formula are as follows:
Wherein, k indicates k-th of node of entire topological structure, NkIndicate the proximity network (including oneself) of node k；xk,t Indicate the state vector of k-th of node t moment；yk,tIndicate node k in the observation data of t moment；Assuming that the neighbor node of k point It does not useIt indicates, thenIndicate that all neighbor nodes of k obtain observation data acquisition system in t moment:y1:tIndicate the set of 1~t moment observation information；Indicate all neighbor nodes of node k In the set of 1~t moment observation information
Assuming that the observation information of each neighbor node is independent of one another, i.e.,Between independently of one another；Indicate the posteriority state that node k is obtained according to its all neighbor node in the cumulative observations information of 1~t moment Estimation；
The backward KL divergence for optimizing each node enables its minimum, obtains dividing under the rear divergence meaning to KL with true posteriority The immediate intermediate Posterior distrbutionp approximate function of clothBecause choosingFunction is Gaussian Profile, by rightWithMatch by moment is done, is obtained:E indicates expectation；It calculatesI.e. It obtainsMean value and assist poor matrix, that is, can determineFunction.
A kind of distribution type non-linear kalman filter method is provided in the present embodiment, process is as shown in Figure 1；The present embodiment In, a state estimation result is calculated to each node in distributed network；
Specific step is as follows:
Step 1. is directed to node k, according to the Posterior distrbutionp function of its t-1With state transition equation meter Calculate the prior density function at t moment Indicate node k according to its all neighbor node The prior state estimation that the observation information of (including oneself) at 1~t-1 moment obtains；
Step 2. sets the suggestion distribution function of the sampling of t momentIt is distributed according to suggestion Function is sampled, so that each particle independent same distribution is distributed in suggestion:
Wherein, S is input sample population,Indicate the state vector for s-th of particle that node k is sampled in t moment；
Step 3: the particle weights of calculate node k according to the following formula, and be normalized:
Wherein,Indicate that node k samples the weight of particle, W at s-th of t momentk,tIndicate that node k is adopted t moment is all The sum of weight of like-particles, yl,tIndicate observation of the neighbor node l in t moment of node k；Indicate neighbours' section L pairs of pointThe prediction of observation, is calculated by observational equation；Indicate node k to the state of particle s to AmountPrediction, be calculated by state transition equation；
Step 4: the granular Weights Computing acquired according to above formula
ThereforeDue to forGauss of distribution function is to get arrivingDistribution Function is as follows:
Wherein,
Step 5: in distributed network, intermediate Posterior distrbutionp approximate function that each node is obtainedExpanded It dissipates, according to the intermediate Posterior distrbutionp approximate function of each neighbor node of node kThe state estimation of node k is repaired Just, the end-state estimation q of node k is obtainedk(xk,t)；
The end-state of definition node k estimates the forward direction KL between the intermediate Posterior distrbutionp approximate function of its neighbor node Divergence are as follows:
Wherein, al,kIt is neighbor node l to the weight of present node k, meets
It enables above-mentioned forward direction KL divergence minimum, obtains:Because whereinIt obeys high This distribution, therefore qk(xk,t) also Gaussian distributed, the q being calculate by the following formulak(xk,t) mean μk,tWith covariance matrix Σk,t
Obtain final state estimation: qk(xk,t)~N (μk,t,Σk,t), qk(xk,t) mean value is that the state of the node is estimated Count vector；
Step 6: carrying out time iteration, obtain the state estimation result of subsequent time.
Simulated conditions
Emulation experiment: method proposed by the present invention is used in the target following of distributed network, with article The centralized approach that " Nonlinear Kal- man Filtering With Divergence Minimization " is proposed It is compared.The topological structure of entire distributed network totally 10 nodes, topological structure is as shown in Fig. 2, one at each node Sensor respectively tracks target, and the observation noise power of each node is the same；The state-space model of target movement is as follows:
xt=Ftxt-1+wt,wt~N (0, Qt)
yt=h (xt)+vt,vt~N (0, Rt)
Wherein, FtIndicate state-transition matrix, h (xt) indicate observation function, wtIt is state-noise, vtIt is observation noise, wt With vtBe mean value be zero, covariance matrix is respectively QtAnd RtWhite Gaussian noise:
Wherein, s indicates the location information of sensor；Constant measurement rate is taken in the present invention, enables Δ t=1, σCV= 10-2；The covariance matrix of observation noise isσR=20.State vector is four-dimensional:Packet The location information of both direction is included, the second peacekeeping fourth dimension indicates the velocity information of both direction；Sample population 500, iteration 300 times, Monte Carlo Experiment 100 times.The non-linear Kalman filtering of the method for the present invention and centralization is compared, the two Simulation result is as shown in Fig. 3,4,5.
Fig. 3 shows that distribution type non-linear kalman filter method proposed by the present invention can effectively track target. Fig. 4,5 show distributed method proposed by the present invention and " Nonlinear Kalman Filtering With Divergence The centralized approach (" centralization " is labeled as in figure) that Minimization " is proposed is compared, and the MSE of position and speed estimation is bent The convergence rate of line is all identical, but the steady-state error fluctuation of method proposed by the present invention is smaller, and the steady-state performance of this method Even it is slightly better than the algorithm of centralization.
The above description is merely a specific embodiment, any feature disclosed in this specification, except non-specifically Narration, can be replaced by other alternative features that are equivalent or have similar purpose；Disclosed all features or all sides Method or in the process the step of, other than mutually exclusive feature and/or step, can be combined in any way.

Claims (1)

1. a kind of distribution type non-linear kalman filter method, comprising the following steps:
Step 1. is directed to node k, according to the Posterior distrbutionp function at its t-1 momentWith state transition equation meter Calculate the prior density function of t moment
Step 2. sets the suggestion distribution function of the sampling of t momentAccording to suggestion distribution function It is sampled, so that each particle independent same distribution is distributed in suggestion:
Wherein, S is input sample population,Indicate the state vector for s-th of particle that node k is sampled in t moment；
Step 3: the particle weights of calculate node k according to the following formula, and be normalized:
Wherein,Indicate that node k samples the weight of particle, W at s-th of t momentk,tIndicate node k in all sampling grains of t moment The sum of the weight of son, yl,tIndicate observation of the neighbor node l in t moment of node k；Indicate l pairs of neighbor nodeThe prediction of observation；Indicate node k to particle s state vectorPrediction；
Step 4: Posterior distrbutionp approximate function among the granular Weights Computing acquired according to above formulaMean valueWith association side Poor matrix
It obtainsDistribution function are as follows:
Step 5: in distributed network, intermediate Posterior distrbutionp approximate function that each node is obtainedIt is diffused, According to the intermediate Posterior distrbutionp approximate function of each neighbor node of node kThe end-state estimation q of node k is calculatedk (xk,t):
Wherein, al,kIt is neighbor node l to the weight of present node k, meetsAnd calculate qk(xk,t) mean μk,tWith Covariance matrix Σk,t:
μk,tState estimation vector as node k.
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