CN118350193A - Method for designing set member filter based on incomplete measurement information - Google Patents
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Abstract
The application relates to the technical field of member-collecting filtering, and discloses a member-collecting filter design method based on incomplete measurement information in a complex network, which comprises the following steps: step one: establishing a complex network system model; step two: controlling noise in the system in an ellipsoidal set; step three: controlling a nonlinear function in the system in a fan-shaped bounded condition; step four: introducing measurement output of an RR protocol scheduling system; step five: modeling to describe incomplete measurements; step six: designing a set member filter based on incomplete measurement; step seven: the problem of member collection filtering of a complex network system which is incompletely measured under the RR protocol is solved; step eight: the feasibility of the proposed filtering scheme was demonstrated using numerical examples. The incomplete measurement information is reflected by establishing a complex network model, so that the distributed filtering problem of a discrete nonlinear complex network with network bandwidth limitation is solved.
Description
Technical Field
The invention relates to the technical field of member-collecting filtering, in particular to a member-collecting filter design method based on incomplete measurement information.
Background
In the past few decades, complex networks have received great attention due to their wide use in various real world systems, and unlike isolated nodes, the state estimation of each node in a complex network is not only determined by itself but also by its neighbors, so that conventional isolated node filtering cannot be directly applied to complex networks, in order to solve this problem, various state estimation strategies of complex networks have been proposed, such as distributed ≡filtering, extended kalman filtering and member filtering, and a recursive state estimator has also been proposed in which the gain matrix of each node is determined by optimizing the upper bound matrix.
In the above-described methods, many filtering schemes have been developed, most of which require system noise under a random framework, including process noise and measurement noise, such as kalman filtering, which not only result in requirements on the mean and variance of the noise, but also cannot guarantee that the states are included in the region.
To overcome these difficulties, a set-top estimation method is currently proposed that provides a set of state estimates that contain the assumption that the true state of the system is unknown, but that are bounded by noise rather than random descriptions, on the other hand, it has been recognized that the application of set-top filtering is more convenient than kalman filtering.
Accordingly, the present invention is directed to a method of crew filter design based on incomplete measurement information to improve the uncertainty problem in the system model.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a member filter design method based on incomplete measurement information, and aims to solve the distributed filtering problem of a discrete nonlinear complex network with network bandwidth limitation.
In order to achieve the above purpose, the invention is realized by the following technical scheme: a method for designing a set member filter based on incomplete measurement information in a complex network comprises the following steps:
step one: establishing a complex network system model;
Step two: controlling noise in the system in an ellipsoidal set;
Step three: controlling a nonlinear function in the system in a fan-shaped bounded condition;
step four: introducing measurement output of an RR protocol scheduling system;
Step five: modeling to describe incomplete measurements;
Step six: designing a set member filter based on incomplete measurement;
Step seven: the problem of member collection filtering of a complex network system which is incompletely measured under the RR protocol is solved;
Step eight: the feasibility of the proposed filtering scheme was demonstrated using numerical examples.
Preferably, the complex network system model in the first step is:
yi,k＝Ci,kxi,k+Di,kvi,k
Where i and k represent node and time, respectively, x i,k is the state of the system, y i,k is the measured output of the system, f (·) is a known nonlinear function, Γ is the internal coupling matrix, ω ij is the external coupling matrix, w i,k is the process noise, v i,k is the measured noise, and a i,K,Bi,K,Ci,k,Di,k is a known dimensionality matrix.
Preferably, in the second step, the noise control is as follows:
wherein S i,Ri is a known fitting positive definite matrix.
Preferably, the step three controls the nonlinear function in the system within a fan-shaped bounded condition:
[fi(x)-fi(y)-U1(x-y)]Τ[fi(x)-fi(y)-U2(x-y)]≤0
wherein the nonlinear function f i (·) is continuous, satisfying f i(0)＝0,U1,U2 is a known fit matrix.
Preferably, the measurement output of the RR protocol scheduling system introduced in the fourth step is:
Wherein, Delta (·) is a Kronecker-delta function, θ k-l =l when k-l < 0; y k＝y0,y0 is the initial measurement when k.ltoreq.0.
Preferably, the measurement output of the RR protocol scheduling system, the required introduction variable θ i,k,θi,k is defined as:
Wherein, theta i,k epsilon {1,2, (ii) the method comprises the steps of (1), m }, θ k+m＝θk according to the periodicity of the RR protocol.
Preferably, in the fifth step, a model is built to describe the incomplete measurement as:
Wherein y i,k is the actual received information ,Πk＝diag{π1,k,π2,k,···,πm,k},πi,k∈[πi,πi],0≤πi≤πi≤1,i＝1,2,···,m; order
Wherein,
Preferably, in the sixth step, a set member filter based on incomplete measurement is designed:
Where x i,k is the estimate of x i,k and L k is the set-member filter gain matrix.
Preferably, in the seventh step, the problem of member filtering of the complex network system that is not completely measured under the RR protocol is solved:
For a given set of matrices P k+1 >0, the guaranteed filtering error e k+1＝xk+1-xk+1 can satisfy:
The appropriate gain matrix L K is selected to minimize the trace of matrix P k+1.
The invention provides a set member filter design method based on incomplete measurement information. The beneficial effects are as follows:
1. The invention reduces network transmission burden by using polling protocol, for the random variables which exist in the system matrix function and are independent of each other, the random variables are assumed to be uniformly distributed in a known limited range, the process noise and the measurement noise are unknown and are bounded to be limited to a specified ellipsoid set, all allowable unknown but bounded noises are converted into inequality constraint processing, known deterministic input and incomplete measurement are carried out, so that the ellipsoid set, including all possible states, can determine a convex optimization method and probability constraint, and the invention has the advantages of simple periodicity, convenient operation and the like.
2. The invention builds a model to reflect incomplete measurement based on incomplete measurement output acquired by sensors due to intermittent faults, abrupt structural changes, aging, network noise and the like in engineering practice, has certain reliability and practicability, and solves the problem of distributed filtering of a discrete nonlinear complex network with network bandwidth limitation.
Drawings
FIG. 1 is a schematic flow chart of the method of the present invention;
FIG. 2 is a schematic diagram of a numerical example system according to the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and fully with reference to the accompanying drawings, in which it is evident that the embodiments described are only some, but not all embodiments of the invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Examples:
referring to fig. 1-2, an embodiment of the present invention provides a method for designing a set-top filter based on incomplete measurement information in a complex network, including the following steps:
step one: establishing a complex network system model;
Step two: controlling noise in the system in an ellipsoidal set;
Step three: controlling a nonlinear function in the system in a fan-shaped bounded condition;
step four: introducing measurement output of an RR protocol scheduling system;
Step five: modeling to describe incomplete measurements;
Step six: designing a set member filter based on incomplete measurement;
Step seven: the problem of member collection filtering of a complex network system which is incompletely measured under the RR protocol is solved;
step eight: the feasibility of the proposed filtering scheme is demonstrated by using numerical examples;
further, the complex network system model in the first step is:
yi,k＝Ci,kxi,k+Di,kvi,k
Where i and k represent node and time, respectively, x i,k is the state of the system, y i,k is the measured output of the system, f () is a known nonlinear function, Γ is the internal coupling matrix, ω ij is the external coupling matrix, w i,k is the process noise, v i,k is the measured noise, and a i,K,Bi,K,Ci,k,Di,k is a known dimensionality matrix.
Further, in the second step, the noise is controlled in the ellipsoidal set as follows:
wherein S i,Ri is a known fitting positive definite matrix.
Further, step three controls the nonlinear function in the system within the fan-bounded condition:
[fi(x)-fi(y)-U1(x-y)]Τ[fi(x)-fi(y)-U2(x-y)]≤0
Wherein the nonlinear function f i (·) is continuous, satisfying f i(0)＝0,U1,U2 as a known dimensionality matrix:
Further, in the fourth step, the measurement output of the RR protocol scheduling system is introduced as follows:
Wherein, Delta (·) is a Kronecker-delta function, θ k-l =l when k-l < 0; y k＝y0,y0 is the initial measurement when k.ltoreq.0.
Introducing measurement output of an RR protocol scheduling system, which is characterized in that: considering the measured output of an RR protocol scheduling system, the required introduction variable θ i,k,θi,k can be defined as:
Wherein, theta i,k epsilon {1,2, (ii) the method comprises the steps of (1), m }, θ k+m＝θk according to the periodicity of the RR protocol.
Further, the modeling in step five describes the incomplete measurement as:
wherein y i,k is the actual received information ,Πk＝diag{π1,k,π2,k,···,πm,k},πi,k∈[πi,πi],0≤πi≤πi≤1,i＝1,2,···,m. order
Wherein,
Further, in step six, a set membership filter based on incomplete measurement is designed:
Where x i,k is the estimate of x i,k and L k is the set-member filter gain matrix.
Further, in the seventh step, the problem of member filtering of the complex network system which is incompletely measured under the RR protocol is solved:
Definition:
For a given set of matrices P k+1 >0, the guaranteed filtering error e k+1＝xk+1-xk+1 can satisfy:
The appropriate gain matrix L K is selected to minimize the trace of matrix P k+1.
Lemma 1 (Shur lemma) if the dimension-adaptive matrices S 1,S2 and S 3 exist, thenEquivalent to:
Or (b)
Lemma 2 (S procedure) is knownIs aboutIs a quadratic function of (2)(j＝0,1,…,p)，If the real number epsilon 1≥0,ε2≥0,…,εP is more than or equal to 0, the method leads
Theorem 1 gives a set of P k > 0 such that the filtering error e k satisfiesIf matrix P k+1 >0 is present, the filter gain matrix L k and the real number epsilon j >0 (j=1, 2, …, 8) are such that the following matrix inequality holds:
Specifically, in the above formula:
g k is a given matrix In the set of ellipsoids, the filter error e k+1 is considered to be constrained to the set of ellipsoidsAnd (3) inner part. There is a vector Z k satisfying Z k 1 so that the following formula holds
xk＝xk+GkZk
Wherein: g k is a given matrixIs a matrix of factors of (a).
The filter error e k+1 is calculated as follows, defined as:
Because of Thus:
Redefining:
Then:
ek+1＝Ωkηk
wherein: Thus, it is possible to obtain:
the following inequality holds:
wherein:
Thus, it can be expressed as η k:
From the non-linear function f (x) belonging to the sector [ U 1,U2 ], it can therefore be deduced that:
[f(xk)-f(xk)-U1(xk-xk)]Τ[f(xk)-f(xk)-U2(xk-xk)]≤0 Substituting x k＝xk+GkZk into the above formula yields:
Equivalent to:
wherein:
Applying lemma 2, if there is a real number epsilon j > 0 (j=1, 2, …, 10), let the following hold:
Then there is The same is true.
Thus, the formula may also be abbreviated as:
By means of the primer 1, The sufficient condition is thatThis is true. Thus, if the matrix is inequalityIf so, the filtering error e k+1 can be constrained to the set of ellipsoidsAnd (3) inner part. Based on the mathematical induction method,Hold true, and the syndrome is complete.
Inference 1, if positive definite matrix P k+1 is present, filter gain matrix L k and real epsilon j > 0 (j=1, 2, …, 10) so that the following optimization problem is solved:
a minimum ellipsoid set sequence can be obtained.
Further, in the step eight, the feasibility of the proposed filtering scheme is demonstrated by using a numerical example, and in this step, in order to demonstrate the feasibility of the proposed filtering scheme, the following advantages are obtained by performing simulation and analysis using the numerical example:
the signal characteristics before and after filtering can be sufficiently compared: selecting a specific signal as input, simulating the characteristics of the signal before and after filtering, and comparing the waveform, frequency spectrum and other related characteristics before and after filtering to show the influence of the filtering scheme on the signal;
specifically, by using a numerical example, input signals with different frequencies, amplitudes and phases can be simulated, responses of the filter to the signals are observed, and the suppression effect of the filter on different frequency components can be evaluated by analyzing the filtered output signals, so that the effectiveness of a filtering scheme is proved;
Further, if there are a plurality of filtering schemes available for selection, the superiority of the selected filtering scheme can be demonstrated by comparing the filtering effects of different types of filters (such as low-pass filters, band-pass filters, etc.) under the same input signal through numerical simulation;
The application of the numerical calculation example can also calculate various performance indexes of the filtered signal, such as signal-to-noise ratio, distortion degree, phase delay and the like, and the indexes can help to quantify the advantages and disadvantages of the filtering scheme;
Therefore, the step eight of the embodiment of the invention utilizes the numerical calculation example to verify and analyze the provided filtering scheme, thereby being capable of fully verifying the feasibility and the benefit of the scheme of the invention and providing theoretical support and guidance for the practical application of the filtering scheme.
Specifically, in this embodiment, by reducing the network transmission load by using the polling protocol, there are some benefits in reducing the network transmission load and the aggregate filtering, including:
The polling protocol generally adopts a mode of active polling or passive polling, and obtains the data of the sensor nodes according to the need in a polling mode, compared with a traditional transmission mode, the polling protocol can reduce unnecessary data transmission, thereby saving the use of network bandwidth, and being beneficial to reducing the network transmission burden, in particular in a large-scale sensor network.
In the polling protocol, data is typically transmitted by the sensor nodes to the data sink nodes, which may centrally process and filter the received data. The centralized filtering mode can effectively reduce the data quantity transmitted in the network, and can utilize the computing power of the data sink node to perform more complex data processing and filtering operation, thereby improving the efficiency and accuracy of data processing.
In a polling protocol, a sensor node may sleep in a non-operational state, only being awakened and transmitting data when it is polled. The working mode with low power consumption can save the energy consumption of the sensor nodes, prolong the working life of the sensor network and save the energy consumption.
Further, through the polling protocol, the data sink node can perform quality control and filtering operation on the received data, eliminate abnormal data or noise, and improve accuracy and reliability of the data. This is important for some application scenarios where the data accuracy requirements are high.
In general, the benefits of the polling protocol in terms of reducing network transmission load and centralized filtering are mainly reflected in terms of saving network bandwidth, implementing centralized processing and filtering, saving energy consumption, improving data quality control, and the like. These benefits make the polling protocol have important application value in large-scale sensor networks and application scenarios with high requirements for data quality.
Meanwhile, the embodiment of the invention builds a model to reflect incomplete measurement based on the situation that the measurement output acquired by the sensor may be incomplete due to reasons such as intermittent faults, abrupt structural changes, aging, network noise and the like of the sensor in engineering practice, has certain reliability and practicability, and effectively solves the problem of distributed filtering of a discrete nonlinear complex network with network bandwidth limitation.
Although embodiments of the present invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made therein without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.
Claims (9)
1. The method for designing the set member filter based on the incomplete measurement information in the complex network is characterized by comprising the following steps of:
step one: establishing a complex network system model;
Step two: controlling noise in the system in an ellipsoidal set;
Step three: controlling a nonlinear function in the system in a fan-shaped bounded condition;
step four: introducing measurement output of an RR protocol scheduling system;
Step five: modeling to describe incomplete measurements;
Step six: designing a set member filter based on incomplete measurement;
Step seven: the problem of member collection filtering of a complex network system which is incompletely measured under the RR protocol is solved;
Step eight: the feasibility of the proposed filtering scheme was demonstrated using numerical examples.
2. The method for designing a set membership filter based on incomplete measurement information in a complex network according to claim 1, wherein the complex network system model in the step one is:
yi,k＝Ci,kxi,k+Di,kvi,k
Where i and k represent node and time, respectively, x i,k is the state of the system, y i,k is the measured output of the system, f (·) is a known nonlinear function, Γ is the internal coupling matrix, ω ij is the external coupling matrix, w i,k is the process noise, v i,k is the measured noise, and a i,K,Bi,K,Ci,k,Di,k is a known dimensionality matrix.
3. The method for designing a set member filter based on incomplete measurement information in a complex network according to claim 1, wherein the noise control in the step two is as follows:
wherein S i,Ri is a known fitting positive definite matrix.
4. The method for designing a set membership filter based on incomplete measurement information in a complex network according to claim 1, wherein said step three controls a nonlinear function in the system within a fan-shaped bounded condition:
[fi(x)-fi(y)-U1(x-y)]Τ[fi(x)-fi(y)-U2(x-y)]≤0
wherein the nonlinear function f i (·) is continuous, satisfying f i(0)＝0,U1,U2 is a known fit matrix.
5. The method for designing a set membership filter based on incomplete measurement information in a complex network according to claim 1, wherein the measurement output of the RR protocol scheduling system introduced in the fourth step is:
Wherein, Delta (·) is a Kronecker-delta function, θ k-l =l when k-l < 0; y k＝y0,y0 is the initial measurement when k.ltoreq.0.
6. The method for designing a set-up filter based on incomplete measurement information in a complex network according to claim 5, wherein the measurement output of the RR protocol scheduling system, the required introduction variable θ i,k,θi,k is defined as:
Wherein, theta i,k epsilon {1,2, (ii) the method comprises the steps of (1), m }, θ k+m＝θk according to the periodicity of the RR protocol.
7. The method for designing a set-top filter based on incomplete measurement information in a complex network according to claim 1, wherein in the fifth step, a model is built to describe the incomplete measurement as:
Wherein, For the information actually received, pi k＝diag{π1,k,π2,k,···,πm,k,Order the
Wherein,
8. The method for designing the set membership filter based on incomplete measurement information in the complex network according to claim 1, wherein the method comprises the following steps: in the sixth step, a set member filter based on incomplete measurement is designed:
Wherein, Is an estimate of x i,k, and L k is the set-membership filter gain matrix.
9. The method for designing the set membership filter based on incomplete measurement information in the complex network according to claim 1, wherein the method comprises the following steps: in the seventh step, the problem of member filtering of the complex network system which is incompletely measured under the RR protocol is solved:
for a given set of matrices P k+1 > 0, the filtering error is guaranteed Can satisfy:
The appropriate gain matrix L K is selected to minimize the trace of matrix P k+1.
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