CN106507275A - A kind of robust Distributed filtering method and apparatus of wireless sensor network - Google Patents
A kind of robust Distributed filtering method and apparatus of wireless sensor network Download PDFInfo
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- CN106507275A CN106507275A CN201610896232.9A CN201610896232A CN106507275A CN 106507275 A CN106507275 A CN 106507275A CN 201610896232 A CN201610896232 A CN 201610896232A CN 106507275 A CN106507275 A CN 106507275A
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- H—ELECTRICITY
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Abstract
The invention discloses a kind of robust Distributed filtering method and apparatus of wireless sensor network, including：Set up the mathematical model of random uncertain time-varying wireless sensor network；Any two wireless sensor network node mutually transfers respective measurement output information；Mathematical model, current control input information according to wireless sensor network, each network node obtain when pre-test output information and Augmentation approach determine the filter model of wireless sensor network；State estimation is carried out to the perceptive object of each wireless sensor network node monitoring using filter model.Therefore, uncertainty structure can be independent of using the present invention, solve while having time-varying topology structure, random topology is uncertain, with the Distributed filtering problem of the probabilistic wireless sensor network of stochastic model, the effective guarantee application demand of perceptive object running status real time on-line monitoring.
Description
Technical field
A kind of the present invention relates to signal processing technology field, more particularly to the robust Distributed filtering of wireless sensor network
Method and apparatus.
Background technology
Wireless sensor network is made up of a large amount of cheap microsensor node in monitored area, by radio communication
The network system that mode is formed.The three elements of wireless sensor network be sensor, perceptive object and observer, extensive at present
For fields such as process monitoring, environmental monitoring, intelligent transportation.
The filtering method of wireless sensor network is generally divided into centralized filtering method and Distributed filtering method.Relative collection
Chinese style is filtered, and Distributed filtering has amount of calculation little, and reliability is high, energy and the low advantage of bandwidth demand, therefore range of application
Wider.In practical application, the failure of one side sensor node or monitoring function adjustment etc. can change network topological information, cause nothing
Line sensor network topological structure has time-varying characteristics.On the other hand, environmental change and electromagnetic interference etc. can be made to radio communication
Into interference, cause network topology structure of wireless sensor that there is uncertain characteristic at random.Further, since there is Parameter Perturbation and outer
The factors such as boundary's interference, perceptive object inevitably have stochastic model uncertain.
At present, effective method is there is no to solve while having time-varying topology structure, random topology is uncertain, and with
The Distributed filtering problem of the wireless sensor network of machine model uncertainty.Additionally, existing robust Distributed filtering method is tight
Uncertainty structure is relied on again.
Content of the invention
The technical problem to be solved is to provide a kind of while having time-varying topology structure, and random topology does not know
Property, and the Distributed filtering method and apparatus of the probabilistic wireless sensor network of stochastic model.
In order to solve above-mentioned technical problem, the invention provides a kind of robust Distributed filtering side of wireless sensor network
Method, including：
Set up the mathematical model of random uncertain time-varying wireless sensor network；
Any two wireless sensor network node mutually transfers respective measurement output information；
Determine the current control input information of wireless sensor network；
Determine the Augmentation approach of the wireless sensor network, the Augmentation approach is by each wireless sensor network section
The correlated variabless of point are extended and obtain；
Mathematical model, current control input information, each network node according to the wireless sensor network is obtained
When pre-test output information and Augmentation approach, the filter model of the wireless sensor network is determined；
State estimation is carried out to the perceptive object of each wireless sensor network node monitoring using the filter model.
In one embodiment, the mathematical model of the random uncertain time-varying wireless sensor network, is according to described
The state equation of the perceptive object of radio sensor network monitoring, the distributed measurement equation of the wireless sensor network and
The random time-dependent topology controlment of the wireless sensor network is set up.
In one embodiment,
The state equation of the perceptive object of the radio sensor network monitoring is represented using expression formula one,
Expression formula one：X (k+1)=(Ac(k)+Aδ(k))x(k)+(Bc(k)+Bδ(k)) u (k)+w (k),
Wherein, x (k+1) represents that the perceptive object state variable at k+1 moment, x (k) represent the perceptive object state at k moment
Variable, u (k) represent that the control input signal at k moment, w (k) represent the process noise signal at k moment, AcK () represents the k moment
First central process parameter matrix, BcK () represents the second central process parameter matrix at k moment, AδK () represents the first of k moment
Stochastic process parameter uncertainty, BδK () represents the second stochastic process parameter uncertainty at k moment；
The distributed measurement equation of the wireless sensor network is represented using expression formula two,
Expression formula two：yi(k)=(Cc,i(k)+Cδ,i(k))x(k)+vi(k), i ∈ (1, N),
Wherein, yiK () represents the measurement output signal of k i-th wireless sensor network node of moment, viWhen () represents k k
Carve the measurement noise signal of i-th wireless sensor network node, Cc,iK () represents i-th wireless sensor network section of k moment
The center measurement parameter matrix of point, Cδ,iK () represents that the random measurement parameter of k i-th wireless sensor network node of moment is not true
Qualitative, total numbers of the N for wireless sensor network node；
The random time-dependent topology controlment of the wireless sensor network is represented using expression formula three,
Expression formula three：
Wherein, G represents directed graph,Represent that the set on wireless sensor network summit, ε (k) represent wireless sensor network
Network connects the set on side, HcK () represents wireless sensor network center weight matrix, HδK () represents that wireless sensor network is random
Weight is uncertain.
In one embodiment, w (k), viK the average of () is respectively 0, its covariance matrix is respectively
Aδ(k)、Bδ(k)、Cδ,iK the average of () is respectively 0, its covariance matrix is respectivelyEqual
It is worth for 0, its covariance matrix is
In one embodiment, the Augmentation approach of the wireless sensor network includes following arbitrary variable or its group
Close：y(k)、v(k)、 K(k)、Hc,i(k)、Hδ,i(k)、Hc(k)、Hδ(k)、Hi(k)、H(k)、Fi、F；
Above-mentioned variable is respectively adopted expression formula four to 25 expression of expression formula,
Expression formula four：
Expression formula five：
Expression formula six：
Expression formula seven：Y (k)=coli∈(1,N){yi(k) },
Expression formula eight：
Expression formula nine：V (k)=coli∈(1,N){vi(k) },
Expression formula ten：
Expression formula 11：
Expression formula 12：
Expression formula 13：
Expression formula 14：
Expression formula 15：
Expression formula 16：K (k)=rowj∈(1,N){coli∈(1,N){Kij(k) } },
Expression formula 17：
Expression formula 18：
Expression formula 19：
Expression formula 20：Hc(k)=coli∈(1,N){Hc,i(k) },
Expression formula 21：Hδ(k)=coli∈(1,N){Hδ,i(k) },
Expression formula 22：Hi(k)=Hc,i(k)+Hδ,i(k),
Expression formula 23：H (k)=Hc(k)+Hδ(k),
Expression formula 24：
Expression formula 25：F=rowi∈(1,N){Fi,
Wherein,Represent estimating for the perceptive object state variable that i-th wireless sensor network node of k moment is monitored
Meter error,RepresentAugmented matrix,The augmented matrix of x (k) is represented,Represent the augmentation square of u (k)
Battle array, y (k) represent yiThe augmented matrix of (k),Represent that the augmented matrix of w (k), v (k) represent viThe augmented matrix of (k),Represent AcThe augmented matrix of (k),Represent AδThe augmented matrix of (k),Represent BcThe augmented matrix of (k),Represent BδThe augmented matrix of (k),Represent Cc,iThe augmented matrix of (k),Represent Cδ,iThe augmented matrix of (k),
KijK () represents that j-th wireless sensor network node increases to wave filter during i-th wireless sensor network node transmission information
Benefit, K (k) represent KijThe augmented matrix of (k),The state estimation of k i-th wireless sensor network node of moment is represented,RepresentAugmented matrix, hc,ij(k)j∈(1,N)Represent j-th wireless sensor network node of k moment to i-th nothing
Center weight matrix during line sensor network nodes transmission information,Represent nyiDimension unit matrix, Hc,iK () representsAugmented matrix, hδ,ij(k)j∈(1,N)Represent that j-th wireless sensor network node of k moment is wireless to i-th
Random weight during sensor network nodes transmission information is uncertain, Hδ,iK () representsAugmented matrix,
Hc,iK () represents the center weight matrix of k i-th wireless sensor network node of moment, Hδ,iK () represents that i-th of k moment is wireless
The random weight of sensor network nodes is uncertain.
In one embodiment,
The distributed filter gain of each wireless sensor network node is according to the mathematical model and described current
Control input information determines；
The augmentation distributed filter gain of the wireless sensor network is according to each wireless sensor network described
The distributed filter gain of node determines.
In one embodiment, described according to the mathematical model and the current control input information determines that each is wireless
The distributed filter gain of sensor network nodes, specifically includes：
Determine the state second moment of the state estimation initial value and the perceptive object of the perceptive object；
State second order according to the Augmentation approach, the state estimation initial value of the perceptive object and the perceptive object
Square determines the distributed filter gain of each wireless sensor network node.
In one embodiment,
The state estimation initial value of the perceptive object is by expressions below 26, expression formula 27 and expression formula
Arbitrary expression formula or its combination determination in 28,
Expression formula 26：
Wherein,The meansigma methodss of perceptive object original state variable are represented,Represent constant；
Expression formula 27：Σx(0)=Σ0,
Wherein, Σx(0)Represent the second moment of perceptive object original state variable, Σ0Represent constant；
Expression formula 28：P (0)=P0,
Wherein, P (0) represents the covariance of perceptive object original state variable, P0Represent constant；
The state second moment of the perceptive object is determined by expression formula 29,
Expression formula 29：
Wherein, Σx(k)Represent the second moment of the perceptive object state variable at k moment, Σx(k-1)Represent the perception at k-1 moment
The second moment of Obj State variable,Represent Aδ(k-1) second moment with x (k-1) product, Aδ(k-1) k-1 is represented
The first stochastic process parameter uncertainty at moment, x (k-1) represent the perceptive object state variable at k-1 moment, Σu(k-1)Represent
The second moment of u (k-1),Represent Bδ(k-1) second moment with u (k-1) product, Bδ(k-1) the of the k-1 moment is represented
Two stochastic process parameter uncertainties, Σw(k-1)Represent that the covariance matrix of w (k-1), w (k-1) represent that the process at k-1 moment is made an uproar
Acoustical signal.
In one embodiment, the sense using the filter model to each wireless sensor network node monitoring
Knowing that object carries out the state estimation of state estimation is determined by expression formula 30,
Expression formula 30：Wherein,It is by expression formula three
11 determinations, rjK () is determined by expression formula 32,Represent i-th wireless sensor network of k moment
One step status predication value of network node, rjK () represents the new breath of k j-th wireless sensor network node of moment；
Expression formula 31：
Wherein, Ac(k-1) the first central process parameter matrix at k-1 moment, B are representedc(k-1) the second of the k-1 moment is represented
Central process parameter matrix,Represent the state estimation of i-th wireless sensor network node at k-1 moment, u (k-
1) the control input signal at k-1 moment is represented；
Expression formula 32：
According to a further aspect in the invention, a kind of robust distributed filtering device of wireless sensor network is additionally provided,
Including：
MBM, for setting up the mathematical model of random uncertain time-varying wireless sensor network；
Information transfer module, mutually transfers respective measurement output letter for any two wireless sensor network node
Breath；
First determining module, for determining the current control input information of wireless sensor network；
Second determining module, for determining the Augmentation approach of the wireless sensor network, the Augmentation approach is will be each
The correlated variabless of individual wireless sensor network node are extended and obtain；
3rd determining module, for the mathematical model according to the wireless sensor network, current control input information, each
Individual network node obtain when pre-test output information and Augmentation approach determine the wave filter mould of the wireless sensor network
Type；
State estimation module, for the perception using the filter model to each wireless sensor network node monitoring
Object carries out state estimation.
In one embodiment, MBM is further used for the perceptive object according to the radio sensor network monitoring
State equation, the distributed measurement equation of the wireless sensor network and the wireless sensor network random time-dependent
Topology controlment sets up the mathematical model of the random uncertain time-varying wireless sensor network.
In one embodiment, the 3rd determining module is further used for：
Dividing for each wireless sensor network node is determined according to the mathematical model and the current control input information
Cloth filter gain；
Distributed filter gain according to each wireless sensor network node determines the wireless sensor network
The augmentation distributed filter gain of network.
In one embodiment, the 3rd determining module is further used for：
Determine the state second moment of the state estimation initial value and the perceptive object of the perceptive object；
State second order according to the Augmentation approach, the state estimation initial value of the perceptive object and the perceptive object
Square determines the distributed filter gain of each wireless sensor network node.
Compared with prior art, one or more embodiments of the invention can have the advantage that：
The robust Distributed filtering scheme of the wireless sensor network that the present invention is provided can be solved while opening up with time-varying
Structure is flutterred, random topology is uncertain, and the Distributed filtering problem of the probabilistic wireless sensor network of stochastic model.
Other features and advantages of the present invention will be illustrated in the following description, also, partly be become from description
Obtain it is clear that or being understood by implementing the present invention.The purpose of the present invention and other advantages can pass through in description, right
In claim and accompanying drawing, specifically noted structure is realizing and obtain.
Description of the drawings
Accompanying drawing is used for providing a further understanding of the present invention, and constitutes a part for description, the reality with the present invention
Apply example to be provided commonly for explaining the present invention, be not construed as limiting the invention.In the accompanying drawings：
Fig. 1 is the flow process of the robust Distributed filtering method of wireless sensor network according to a first embodiment of the present invention
Figure；
Fig. 2 is the mathematical model that foundation according to a first embodiment of the present invention does not know time-varying wireless sensor network at random
Flow chart；
Fig. 3 is the topological structure directed graph of wireless sensor network according to a first embodiment of the present invention；
Fig. 4 is the sensor node measurement output curve diagram of wireless sensor network according to a first embodiment of the present invention；
Fig. 5 is that the distributed filter of determination each wireless sensor network node according to a first embodiment of the present invention increases
The flow chart of benefit；
Fig. 6 is the estimated error mean squares difference curve of the state one of wireless sensor network according to a first embodiment of the present invention
Figure；
Fig. 7 is the estimated error mean squares difference curve of the state two of wireless sensor network according to a first embodiment of the present invention
Figure；
Fig. 8 is that the structure of the robust distributed filtering device of wireless sensor network according to a second embodiment of the present invention is shown
It is intended to.
Specific embodiment
For making the object, technical solutions and advantages of the present invention clearer, below in conjunction with drawings and Examples to the present invention
Embodiment be described in further detail, to the present invention, how application technology means solving technical problem, and reach whereby
Realize that process can fully understand and implement according to this into technique effect.As long as it should be noted that do not constitute conflict, in the present invention
Each embodiment and each embodiment in each feature can be combined with each other, the technical scheme for being formed the present invention
Within protection domain.
In addition, can be in the department of computer science of such as one group of computer executable instructions the step of the flow process of accompanying drawing is illustrated
Execute in system, and, although show logical order in flow charts, but in some cases, can be being different from herein
Order execute shown or described step.
First embodiment
Fig. 1 is the flow process of the robust Distributed filtering method of wireless sensor network according to a first embodiment of the present invention
Figure.This method is illustrated with reference to Fig. 1.
Step S110, sets up the mathematical model of random uncertain time-varying wireless sensor network.
In actual application, when the change of wireless sensor network topology information can cause wireless sensor network to have
Become characteristic, the radio communication between wireless sensor network node is interfered can cause network topology structure of wireless sensor to have
There is stochastic uncertainty, the perceptive object of wireless sensor network has the factors such as Parameter Perturbation and external interference can be caused to perceive
Object has stochastic model uncertain.Time-varying characteristics for wireless sensor network, random topology are uncertain and random
Model uncertainty, founding mathematical models describe the wireless sensor network.
What the introduction of lower mask body did not knew the mathematical model of time-varying wireless sensor network at random sets up process.
Preferably, the mathematical model of the random uncertain time-varying wireless sensor network, is according to the wireless sensing
The state equation of the perceptive object of device network monitor, the distributed measurement equation of the wireless sensor network and described wireless
The random time-dependent topology controlment of sensor network is set up.
Fig. 2 is the mathematical model for not knowing time-varying wireless sensor network according to the foundation of first embodiment of the invention at random
Flow chart, referring to Fig. 2, describe each step in detail.
As long as it should be noted that do not constitute conflict, can be different from following logical orders execute disclosed below
The step of.
Step S210, determines the state equation of the perceptive object of radio sensor network monitoring.
Preferably, the state equation of the perceptive object of the radio sensor network monitoring is using one expression of expression formula
,
Expression formula one：X (k+1)=(Ac(k)+Aδ(k))x(k)+(Bc(k)+Bδ(k)) u (k)+w (k),
Wherein, x (k+1) represents that the perceptive object state variable at k+1 moment, x (k) represent the perceptive object state at k moment
Variable, u (k) represent that the control input signal at k moment, w (k) represent the process noise signal at k moment, AcK () represents the k moment
First central process parameter matrix, BcK () represents the second central process parameter matrix at k moment, AδK () represents the first of k moment
Stochastic process parameter uncertainty, BδK () represents the second stochastic process parameter uncertainty at k moment.
Step S220, determines the distributed measurement equation of wireless sensor network.
Preferably, the distributed measurement equation of the wireless sensor network is represented using expression formula two,
Expression formula two：yi(k)=(Cc,i(k)+Cδ,i(k))x(k)+vi(k), i ∈ (1, N),
Wherein, yiK () represents the measurement output signal of k i-th wireless sensor network node of moment, viWhen () represents k k
Carve the measurement noise signal of i-th wireless sensor network node, Cc,iK () represents i-th wireless sensor network section of k moment
The center measurement parameter matrix of point, Cδ,iK () represents that the random measurement parameter of k i-th wireless sensor network node of moment is not true
Qualitative, total numbers of the N for wireless sensor network node.
Step S230, determines the random time-dependent topology controlment of wireless sensor network.
Preferably, the random time-dependent topology controlment of the wireless sensor network is represented using expression formula three,
Expression formula three：
Wherein, G represents directed graph,Represent that the set on wireless sensor network summit, ε (k) represent wireless sensor network
Network connects the set on side, HcK () represents wireless sensor network center weight matrix, HδK () represents that wireless sensor network is random
Weight is uncertain.
Preferably, w (k), viK the average of () is respectively 0, its covariance matrix is respectively Σw(k)、Aδ(k)、Bδ
(k)、Cδ,iK the average of () is respectively 0, its covariance matrix is respectivelyHδK the average of () is 0,
Its covariance matrix is
Step S240, the state equation, wireless sensor network according to the perceptive object of radio sensor network monitoring
It is wireless that the random time-dependent topology controlment of distributed measurement equation and wireless sensor network sets up uncertain time-varying at random
The mathematical model of sensor network.
Step S120, any two wireless sensor network node mutually transfer respective measurement output information.
Any two wireless sensor network node is exchanged with each other metrical information, or each nothing by communication
Line sensor network nodes at least can be with other wireless sensor network nodes communication.The i-th of wireless sensor network
Individual sensor node gathers the information of j-th sensor node according to topological structure real-time radio.Fig. 3 is according to the present invention first
The topological structure directed graph of the wireless sensor network of embodiment, as illustrated, the information of sensor node 1 is passed in real time
Sensor node 2,3,4, the information of sensor node 2 pass to sensor node 1 in real time.Fig. 4 is to be implemented according to the present invention first
The sensor node measurement output curve diagram of the wireless sensor network of example, the measurement output letter of 4 in Fig. 3 sensor node
Breath is as shown in Figure 4.
Step S130, determines the current control input information of wireless sensor network.
In this step, the control of its perceptive object that monitors of each network node Real-time Collection of wireless sensor network
Input information.
Step S140, determines the Augmentation approach of the wireless sensor network, and the Augmentation approach is wirelessly to pass each
The correlated variabless of sensor network node are extended and obtain.
Preferably, the Augmentation approach of the wireless sensor network includes following arbitrary variable or its combination： y(k)、v(k)、K
(k)、Hc,i(k)、Hδ,i(k)、Hc(k)、Hδ(k)、Hi(k)、H(k)、Fi、F；
Above-mentioned variable is respectively adopted expression formula four to 25 expression of expression formula,
Expression formula four：
Expression formula five：
Expression formula six：
Expression formula seven：Y (k)=coli∈(1,N){yi(k) },
Expression formula eight：
Expression formula nine：V (k)=coli∈(1,N){vi(k) },
Expression formula ten：
Expression formula 11：
Expression formula 12：
Expression formula 13：
Expression formula 14：
Expression formula 15：
Expression formula 16：K (k)=rowj∈(1,N){coli∈(1,N){Kij(k) } },
Expression formula 17：
Expression formula 18：
Expression formula 19：
Expression formula 20：Hc(k)=coli∈(1,N){Hc,i(k) },
Expression formula 21：Hδ(k)=coli∈(1,N){Hδ,i(k) },
Expression formula 22：Hi(k)=Hc,i(k)+Hδ,i(k),
Expression formula 23：H (k)=Hc(k)+Hδ(k),
Expression formula 24：
Expression formula 25：F=rowi∈(1,N){Fi,
Wherein,Represent estimating for the perceptive object state variable that i-th wireless sensor network node of k moment is monitored
Meter error,RepresentAugmented matrix,The augmented matrix of x (k) is represented,Represent the augmentation square of u (k)
Battle array, y (k) represent yiThe augmented matrix of (k),Represent that the augmented matrix of w (k), v (k) represent viThe augmented matrix of (k),Represent AcThe augmented matrix of (k),Represent AδThe augmented matrix of (k),Represent BcThe augmented matrix of (k),Represent BδThe augmented matrix of (k),Represent Cc,iThe augmented matrix of (k),Represent Cδ,iThe augmented matrix of (k),
KijK () represents that j-th wireless sensor network node increases to wave filter during i-th wireless sensor network node transmission information
Benefit, K (k) represent KijThe augmented matrix of (k),The state estimation of k i-th wireless sensor network node of moment is represented,RepresentAugmented matrix, hc,ij(k)j∈(1,N)Represent j-th wireless sensor network node of k moment to i-th nothing
Center weight matrix during line sensor network nodes transmission information,Represent nyiDimension unit matrix, Hc,iK () representsAugmented matrix, hδ,ij(k)j∈(1,N)Represent that j-th wireless sensor network node of k moment is wireless to i-th
Random weight during sensor network nodes transmission information is uncertain, Hδ,iK () representsAugmented matrix,
Hc,iK () represents the center weight matrix of k i-th wireless sensor network node of moment, Hδ,iK () represents that i-th of k moment is wireless
The random weight of sensor network nodes is uncertain.
Step S150, mathematical model, current control input information according to the wireless sensor network, each network section
Point obtain when pre-test output information and Augmentation approach, determine the filter model of the wireless sensor network.
The meter of the distributed filter gain and augmentation distributed filter gain of wireless sensor network is described below
Calculation process.
Preferably, the distributed filter gain of each wireless sensor network node is according to the mathematical model and institute
State what current control input information determined；
The augmentation distributed filter gain of the wireless sensor network is according to each wireless sensor network described
The distributed filter gain of node determines.
Fig. 5 is that the distributed filter of determination each wireless sensor network node according to first embodiment of the invention increases
The flow chart of benefit, referring to Fig. 5, describes each step in detail.
As long as it should be noted that do not constitute conflict, can be different from following logical orders execute disclosed below
The step of.
Step S510, determines the state estimation initial value of perceptive object.
Preferably, the state estimation initial value of the perceptive object is by expressions below 26, expression formula 27
And the arbitrary expression formula in expression formula 28 or its combine determine,
Expression formula 26：
Wherein,The meansigma methodss of perceptive object original state variable are represented,Represent constant；
Expression formula 27：Σx(0)=Σ0,
Wherein, Σx(0)Represent the second moment of perceptive object original state variable, Σ0Represent constant；
Expression formula 28：P (0)=P0,
Wherein, P (0) represents the covariance of perceptive object original state variable, P0Represent constant；
Step S520, determines the state second moment of perceptive object.
The state second moment of the perceptive object is determined by expression formula 29,
Expression formula 29：
Wherein, Σx(k)Represent the second moment of the perceptive object state variable at k moment, Σx(k-1)Represent the perception at k-1 moment
The second moment of Obj State variable,Represent Aδ(k-1) second moment with x (k-1) product, Aδ(k-1) when representing k-1
The the first stochastic process parameter uncertainty that carves, x (k-1) represent the perceptive object state variable at k-1 moment, Σu(k-1)Represent u
(k-1) second moment,Represent Bδ(k-1) second moment with u (k-1) product, Bδ(k-1) the of the k-1 moment is represented
Two stochastic process parameter uncertainties, Σw(k-1)Represent that the covariance matrix of w (k-1), w (k-1) represent that the process at k-1 moment is made an uproar
Acoustical signal.
Step S530, determines the Augmentation approach of wireless sensor network.
Step S540, the state second moment and wireless sensing of state estimation initial value, perceptive object according to perceptive object
The Augmentation approach of device network determines the distributed filter gain of each wireless sensor network node.
The detailed calculating process of the distributed filter gain of each wireless sensor network node is as follows.
The state two of the state estimation initial value and perceptive object of perceptive object has been calculated by step S510 and step S520
After rank square, intermediate variable is next calculated.
The process for calculating intermediate variable is as follows：
Wherein, P (k-1) represents the state estimation error covariance at k-1 moment；
In Practical CalculationDuring, need to knowValue, and augmentation perceptive object state become
The average of amountCalculating can adopt expression formula：The average of perceptive object state variable
Calculating can adopt expression formula：
According to the distributed filter gain that above-mentioned intermediate variable calculates sensor node.
According to the augmentation distributed filter gain that the distributed filter gain of sensor node calculates sensor node.
Wherein,Represent that the augmentation distributed filter gain at k moment, K (k) represent each sensor section at k moment
The matrix of the distributed filter gain composition of point.
Step S160, is carried out to the perceptive object of each wireless sensor network node monitoring using the filter model
State estimation.
Below to step S160 be embodied as illustrate.
Perceptive object state estimation initial value is set first,
State estimation is carried out to the perceptive object of each wireless sensor network node monitoring using the filter model.
Preferably, described the perceptive object of each wireless sensor network node monitoring is entered using the filter model
The state estimation of row state estimation is determined by expression formula 30,
Expression formula 30Wherein,It is by expression formula
31 determinations, rjK () is determined by expression formula 32,Represent i-th wireless senser of k moment
One step status predication value of network node, rjK () represents the new breath of k j-th wireless sensor network node of moment；
Expression formula 31：
Wherein, Ac(k-1) the first central process parameter matrix at k-1 moment, B are representedc(k-1) the second of the k-1 moment is represented
Central process parameter matrix,Represent the state estimation of i-th wireless sensor network node at k-1 moment, u (k-
1) the control input signal at k-1 moment is represented；
Expression formula 32：
State estimation error mean square is calculated according to state estimation poor.Fig. 6 is according to the wireless of first embodiment of the invention
The estimated error mean squares dygoram of the state one of sensor network, Fig. 7 are the wireless sensing according to first embodiment of the invention
The estimated error mean squares dygoram of the state two of device network, state one and two different shapes that state two is perceptive object
State.Poor according to the state estimation error mean square that above-mentioned enforcement can obtain wireless sensor network as shown in Figure 6 and Figure 7.
Calculate state estimation error covariance
It follows that uncertainty structure can be independent of by this method, solve while have time-varying topology structure,
Random topology is uncertain, and the Distributed filtering problem of the probabilistic wireless sensor network of stochastic model.
In sum, the robust Distributed filtering method of the wireless sensor network of the present embodiment, has in engineering monitoring
There is actual directive significance.
Second embodiment
Based on same inventive concept, a kind of robust of wireless sensor network is additionally provided in the embodiment of the present invention distributed
Filter, due to the robust Distributed filtering method phase of principle and a kind of wireless sensor network of these equipment solve problems
Seemingly, therefore the enforcement of these equipment may refer to the enforcement of method, repeats part and repeats no more.
Fig. 8 is that the structure of the robust distributed filtering device of the wireless sensor network according to second embodiment of the invention is shown
It is intended to, below according to each ingredient that figure describes the system in detail.
MBM 810, for setting up the mathematical model of random uncertain time-varying wireless sensor network；
Information transfer module 820, mutually transfers respective measurement output for any two wireless sensor network node
Information；
First determining module 830, for determining the current control input information of wireless sensor network；
Second determining module 840, for determining the Augmentation approach of the wireless sensor network, the Augmentation approach be by
The correlated variabless of each wireless sensor network node are extended and obtain；
3rd determining module 850, believes for the mathematical model according to the wireless sensor network, current control input
Breath, each network node obtain when pre-test output information and Augmentation approach determine the filtering of the wireless sensor network
Device model；
State estimation module 860, for monitored to each wireless sensor network node using the filter model
Perceptive object carries out state estimation.
Preferably, MBM is further used for the state side of the perceptive object according to the radio sensor network monitoring
The random time-dependent topological structure of journey, the distributed measurement equation of the wireless sensor network and the wireless sensor network
The mathematical model of the random uncertain time-varying wireless sensor network set up by model.
Preferably, the 3rd determining module is further used for：
Dividing for each wireless sensor network node is determined according to the mathematical model and the current control input information
Cloth filter gain；
Distributed filter gain according to each wireless sensor network node determines the wireless sensor network
The augmentation distributed filter gain of network.
Preferably, the 3rd determining module is further used for：
Determine the state second moment of the state estimation initial value and the perceptive object of the perceptive object；
State second order according to the Augmentation approach, the state estimation initial value of the perceptive object and the perceptive object
Square determines the distributed filter gain of each wireless sensor network node.
Those skilled in the art should be understood that each module or each step of the invention described above can be filled with general calculating
Put to realize, they can be concentrated on single computing device, or be distributed on the network constituted by multiple computing devices,
Optionally, they can be realized with the executable program code of computing device, it is thus possible to be stored in storage device
In executed by computing device, or they are fabricated to each integrated circuit modules respectively, or by the multiple moulds in them
Block or step are fabricated to single integrated circuit module to realize.So, the present invention is not restricted to any specific hardware and software
In conjunction with.
Although disclosed herein embodiment as above, described content only to facilitate understand the present invention and adopt
Embodiment, is not limited to the present invention.Technical staff in any the technical field of the invention, without departing from this
On the premise of the disclosed spirit and scope of invention, any modification and change can be made in the formal and details that implements,
But the scope of patent protection of the present invention, still needs to be defined by the scope of which is defined in the appended claims.
Claims (13)
1. a kind of robust Distributed filtering method of wireless sensor network, including：
Set up the mathematical model of random uncertain time-varying wireless sensor network；
Any two wireless sensor network node mutually transfers respective measurement output information；
Determine the current control input information of wireless sensor network；
Determine the Augmentation approach of the wireless sensor network, the Augmentation approach is by each wireless sensor network node
Correlated variabless are extended and obtain；
It is current that mathematical model, current control input information, each network node according to the wireless sensor network is obtained
Measurement output information and Augmentation approach determine the filter model of the wireless sensor network；
State estimation is carried out to the perceptive object of each wireless sensor network node monitoring using the filter model.
2. method according to claim 1, it is characterised in that the number of the random uncertain time-varying wireless sensor network
Model is learned, is the state equation of perceptive object according to the radio sensor network monitoring, the wireless sensor network
The random time-dependent topology controlment of distributed measurement equation and the wireless sensor network is set up.
3. method according to claim 2, it is characterised in that：
The state equation of the perceptive object of the radio sensor network monitoring is represented using formula one,
Formula one：X (k+1)=(Ac(k)+Aδ(k))x(k)+(Bc(k)+Bδ(k)) u (k)+w (k),
Wherein, x (k+1) represents that the perceptive object state variable at k+1 moment, x (k) represent the perceptive object state variable at k moment,
U (k) represents that the control input signal at k moment, w (k) represent the process noise signal at k moment, AcK () represents the first of k moment
Central process parameter matrix, BcK () represents the second central process parameter matrix at k moment, AδK the first of () expression k moment is random
Procedure parameter is uncertain, BδK () represents the second stochastic process parameter uncertainty at k moment；
The distributed measurement equation of the wireless sensor network is represented using formula two,
Formula two：yi(k)=(Cc,i(k)+Cδ,i(k))x(k)+vi(k), i ∈ S (1, N),
Wherein, yiK () represents the measurement output signal of k i-th wireless sensor network node of moment, viK () represents the k moment i-th
The measurement noise signal of individual wireless sensor network node, Cc,iK () is represented in i-th wireless sensor network node of k moment
Heart measurement parameter matrix, Cδ,iK () represents the random measurement parameter uncertainty of k i-th wireless sensor network node of moment；
The random time-dependent topology controlment of the wireless sensor network is represented using formula three,
Formula three：
Wherein, G represents directed graph,Represent that the set on wireless sensor network summit, ε (k) represent wireless sensor network connection
The set on side, HcK () represents wireless sensor network center weight matrix, HδK () represents the random weight of wireless sensor network not
Definitiveness.
4. method according to claim 3, it is characterised in that w (k), viK the average of () is respectively 0, its covariance matrix
Respectively Σw(k)、Aδ(k)、Bδ(k)、Cδ,iK the average of () is respectively 0, its covariance matrix is respectivelyHδK the average of () is 0, its covariance matrix is
5. method according to claim 4, it is characterised in that the Augmentation approach of the wireless sensor network includes following arbitrary change
Amount or its combination：y(k)、v(k)、
K(k)、Hc,i(k)、Hδ,i(k)、Hc(k)、Hδ(k)、Hi(k)、H(k)、Fi、F；
Above-mentioned variable is respectively adopted formula four to 25 expression of formula,
Formula four：
Formula five：
Formula six：
Formula seven：
Formula eight：
Formula nine：
Formula ten：
Formula 11：
Formula 12：
Formula 13：
Formula 14：
Formula 15：
Formula 16：
Formula 17：
Formula 18：
Formula 19：
Formula 20：
Formula 21：
Formula 22：Hi(k)=Hc,i(k)+Hδ,i(k),
Formula 23：H (k)=Hc(k)+Hδ(k),
Formula 24：
Formula 25：
Wherein,Represent that the estimation of the perceptive object state variable of i-th wireless sensor network node monitoring of k moment is missed
Difference,RepresentAugmented matrix,The augmented matrix of x (k) is represented,Represent the augmented matrix of u (k), y
K () represents yiThe augmented matrix of (k),Represent that the augmented matrix of w (k), v (k) represent viThe augmented matrix of (k),
Represent AcThe augmented matrix of (k),Represent AδThe augmented matrix of (k),Represent BcThe augmented matrix of (k),Table
Show BδThe augmented matrix of (k),Represent Cc,iThe augmented matrix of (k),Represent Cδ,iThe augmented matrix of (k), Kij(k) table
Show j-th wireless sensor network node to filter gain during i-th wireless sensor network node transmission information, K (k)
Represent KijThe augmented matrix of (k),The state estimation of k i-th wireless sensor network node of moment is represented,Table
ShowAugmented matrix,Represent j-th wireless sensor network node of k moment to i-th wireless senser
Center weight matrix during network node transmissions information,Represent nyiDimension unit matrix, Hc,iK () representsAugmented matrix,Represent that j-th wireless sensor network node of k moment is wireless to i-th
Random weight during sensor network nodes transmission information is uncertain, Hδ,iK () representsAugmented matrix,
Hc,iK () represents the center weight matrix of k i-th wireless sensor network node of moment, Hδ,iK () represents that i-th of k moment is wireless
The random weight of sensor network nodes is uncertain.
6. method according to claim 5, it is characterised in that：
The distributed filter gain of each wireless sensor network node is according to the mathematical model and the current control
Input information determines；
The augmentation distributed filter gain of the wireless sensor network is according to each wireless sensor network node described
Distributed filter gain determine.
7. method according to claim 6, it is characterised in that described according to the mathematical model and described currently control defeated
Enter the distributed filter gain that information determines each wireless sensor network node, specifically include：
Determine the state second moment of the state estimation initial value and the perceptive object of the perceptive object；
True according to the state second moment of the Augmentation approach, the state estimation initial value of the perceptive object and the perceptive object
The distributed filter gain of each wireless sensor network node fixed.
8. method according to claim 7, it is characterised in that：
The state estimation initial value of the perceptive object be by following formula 26, formula 27 and formula 28 in
Arbitrary formula or its combine determine,
Formula 26：
Wherein,The meansigma methodss of perceptive object original state variable are represented,Represent constant；
Formula 27：Σx(0)=Σ0,
Wherein, Σx(0)Represent the second moment of perceptive object original state variable, Σ0Represent constant；
Formula 28：P (0)=P0,
Wherein, P (0) represents the covariance of perceptive object original state variable, P0Represent constant；
The state second moment of the perceptive object is determined by formula 29,
Formula 29：
Wherein, Σx(k)Represent the second moment of the perceptive object state variable at k moment, Σx(k-1)Represent the perceptive object at k-1 moment
The second moment of state variable,Represent Aδ(k-1) second moment with x (k-1) product, Aδ(k-1) the k-1 moment is represented
First stochastic process parameter uncertainty, x (k-1) represent the perceptive object state variable at k-1 moment, Σu(k-1)Represent u (k-1)
Second moment,Represent Bδ(k-1) second moment with u (k-1) product, Bδ(k-1) represent the k-1 moment second with
Machine procedure parameter is uncertain, Σw(k-1)Represent that the covariance matrix of w (k-1), w (k-1) represent the process noise letter at k-1 moment
Number.
9. method according to claim 7, it is characterised in that described using the filter model to each wireless sensing
The perceptive object of device network node monitoring carries out the state estimation of state estimation to be determined by formula 30,
Formula 30：
Wherein,It is to be determined by formula 31, rjK () is determined by formula 32,Represent a step status predication value of k i-th wireless sensor network node of moment, rjJ-th of (k) expression k moment
The new breath of wireless sensor network node；
Formula 31：
Wherein, Ac(k-1) the first central process parameter matrix at k-1 moment, B are representedc(k-1) second center at k-1 moment is represented
Procedure parameter matrix,Represent the state estimation of i-th wireless sensor network node at k-1 moment, u (k-1) table
Show the control input signal at k-1 moment；
Formula 32：
10. the robust distributed filtering device of a kind of wireless sensor network, including：
MBM, for setting up the mathematical model of random uncertain time-varying wireless sensor network；
Information transfer module, mutually transfers respective measurement output information for any two wireless sensor network node；
First determining module, for determining the current control input information of wireless sensor network；
Second determining module, for determining the Augmentation approach of the wireless sensor network, the Augmentation approach is by each nothing
The correlated variabless of line sensor network nodes are extended and obtain；
3rd determining module, for the mathematical model according to the wireless sensor network, current control input information, each net
What network node was obtained determines the filter model of the wireless sensor network when pre-test output information and Augmentation approach；
State estimation module, for the perceptive object using the filter model to each wireless sensor network node monitoring
Carry out state estimation.
11. devices according to claim 10, it is characterised in that MBM is further used for according to the wireless sensing
The state equation of the perceptive object of device network monitor, the distributed measurement equation of the wireless sensor network and described wireless
The random time-dependent topology controlment of sensor network sets up the mathematical modulo of the random uncertain time-varying wireless sensor network
Type.
12. devices according to claim 10, it is characterised in that：3rd determining module is further used for：
The distributed of each wireless sensor network node is determined according to the mathematical model and the current control input information
Filter gain；
Distributed filter gain according to each wireless sensor network node determines the wireless sensor network
Augmentation distributed filter gain.
13. devices according to claim 12, it is characterised in that the 3rd determining module is further used for：
Determine the state second moment of the state estimation initial value and the perceptive object of the perceptive object；
True according to the state second moment of the Augmentation approach, the state estimation initial value of the perceptive object and the perceptive object
The distributed filter gain of each wireless sensor network node fixed.
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