CN117895920A - Distributed consistency Kalman filtering method for sensor network under communication link fault - Google Patents
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Abstract
The invention discloses a distributed consistency Kalman filtering method of a sensor network under communication link faults, which comprises the following steps: step 1, based on a standard Kalman filtering algorithm, carrying out local measurement update according to measurement information of a sensor network under a communication link fault to obtain local optimal estimation, wherein the local optimal estimation comprises an optimal estimation value and an estimation error covariance matrix of the sensor network; and 2, carrying out information consistency fusion on the local optimal estimation, and updating an optimal estimation value and an estimation error covariance matrix of the sensor network after the consistency fusion is completed. The invention can compensate the influence of the loss of the measured data on the filtering precision, calculates the error covariance matrix and the state estimation variance matrix of the augmentation system by means of matrix theory and random analysis technology, further obtains the updating equation of the distributed filter, can ensure the integral working performance of the whole distributed sensing network, and is suitable for the problem of distributed state estimation when the communication link fails.
Description
Technical Field
The invention belongs to the technical field of signal processing, and particularly relates to a distributed consistency Kalman filtering method of a sensor network under a communication link fault.
Background
The Kalman filter is used as a classical online optimal recursive filter, is widely applied in the fields of target tracking, industrial system state estimation and the like, and is widely focused at home and abroad when being popularized to a distributed sensor network.
It should be noted that, in the actual implementation process, some sensor nodes in the sensor network may fail due to energy exhaustion or environmental interference. Meanwhile, in order to compensate for the failure node and improve the monitoring precision, some new sensor nodes are supplemented into the network. In addition, routing algorithms are commonly employed to reduce power consumption, and these factors can cause changes in the communication links between network sensor nodes. Obviously, the communication link between the sensors is extremely easy to be broken down due to the influence of various complex factors, so that transmission data is lost, distributed resource sharing cannot be realized, the overall performance of the network is further destroyed, filtering precision is reduced, even estimation errors are dispersed, and therefore, the influence of the communication link fault on the distributed filtering performance of the sensor network is required to be studied deeply.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a distributed consistency Kalman filtering method of a sensor network under the fault of a communication link, develops the research of a distributed filtering algorithm with robustness to the fault of the communication link, eliminates adverse effects caused by data loss as much as possible, deeply improves the existing filtering method to ensure that the existing filtering method is suitable for the problem of estimating the distributed state when the fault of the communication link exists, particularly compensates the influence of the loss of measured data on the filtering precision by introducing a new online data iterative updating strategy, solves the problem of difficult deduction of a time updating equation and a measuring updating equation, successfully realizes the design of relevant parameters which can meet the robustness requirement to the uncertainty factor of the link, and ensures that the distributed consistency Kalman filter has good performance under the influence of the fault of the communication link, thereby ensuring the whole working performance of the whole distributed sensing network.
In order to achieve the technical purpose, the invention adopts the following technical scheme:
The distributed consistency Kalman filtering method of the sensor network under the fault of the communication link comprises the following steps:
Step 1, based on a standard Kalman filtering algorithm, carrying out local measurement update according to measurement information of a sensor network under a communication link fault to obtain local optimal estimation, wherein the local optimal estimation comprises an optimal estimation value and an estimation error covariance matrix of the sensor network;
And 2, carrying out information consistency fusion on the local optimal estimation, and updating an optimal estimation value and an estimation error covariance matrix of the sensor network after the consistency fusion is completed.
In order to optimize the technical scheme, the specific measures adopted further comprise:
the local measurement update process in the step 1 is as follows:
；
；
Wherein represents the optimal estimated value of the ith sensor at the k moment; the/> represents the estimated error covariance matrix of the ith sensor at time k; the value of i-th sensor at time k is denoted by/> ; the/> represents the measurement matrix of the i-th sensor; the/> represents a one-step predicted value of the ith sensor at time k; the/> represents a one-step prediction error estimation error covariance matrix of the ith sensor at the k moment; and/> is the Kalman filtering gain matrix of the ith sensor at k time.
Described above;
where T represents the matrix transpose and represents the estimated error covariance matrix of the noise signal in the ith sensor measurement.
Described above;
Wherein represents the estimated value of the ith sensor at time k-1; the/> represents the estimated error covariance matrix of the ith sensor at time k-1; the/> represents a process noise estimation error covariance matrix in the target system model; a represents a state matrix in the target system model.
The step 2 specifically includes:
Setting initial parameters and/> according to the locally optimal estimate;
and carrying out -step information consistency fusion based on the initial parameters, and after finishing the information consistency fusion, recalculating and updating the optimal estimated value and the estimated error covariance matrix of the sensor network.
The information consistency fusion formula in the th step is as follows:
；
wherein represents the inverse matrix of the local optimal estimation error covariance matrix of the ith sensor at the k moment after/> step fusion; the/> is equal to/> times the locally optimal estimate of the ith sensor at time k; Representing the inverse matrix of the local optimal estimation error covariance matrix of the ith sensor at the k moment after the/> steps of fusion; the/> is equal to/> times the locally optimal estimate of the ith sensor at time k; the expression of/> denotes a set of neighbor nodes of an ith sensor in the sensor network; and/> is a weight.
Described above;
Wherein represents the weight of direct information transmission between the ith sensor and the jth sensor in the sensor network; Indicating random packet loss of the link.
The optimal estimated value and the estimated error covariance matrix of the updated sensor network are as follows:
；
Wherein represents the inverse matrix of the local optimal estimation error covariance matrix of the ith sensor at the k moment after/> step fusion; the/> is equal to/> times the locally optimal estimate of the ith sensor at time k.
The invention has the following beneficial effects:
The distributed consistency filtering algorithm robust to communication link faults provided by the invention firstly compensates the influence of measured data loss on filtering precision by introducing a new online data iterative updating strategy in the structural design process of a filter; secondly, the current state estimation is used to update the estimation error variance matrix in each iteration, which essentially linearizes the system equation and the measurement equation around the state estimation, and in this process, linearization errors are necessarily generated, and also the norm-bounded uncertainty term brought by the logarithmic quantizer is introduced. Therefore, compared with the existing distributed Kalman filtering scheme, the method not only considers the difficulty brought by the introduction of a new compensation strategy to the filter design and analysis, but also further considers the robustness of design parameters to link uncertainty factors. In the specific research process, calculating an optimal estimated value and an estimated error covariance matrix of the augmentation system by means of matrix theory and a random analysis technology, and further obtaining an updating equation of the distributed filter; finally, the theory and algorithm are further perfected by utilizing numerical simulation, and an evaluation result is given.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a diagram of a sensor network topology;
fig. 3 is a graph of the mean square estimation error of each sensor.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
Although the steps of the present invention are arranged by reference numerals, the order of the steps is not limited, and the relative order of the steps may be adjusted unless the order of the steps is explicitly stated or the execution of a step requires other steps as a basis. It is to be understood that the term "and/or" as used herein relates to and encompasses any and all possible combinations of one or more of the associated listed items.
As shown in fig. 1, the distributed consistency kalman filtering method of the sensor network under the fault of the communication link of the invention comprises the following steps:
Step 1, based on a standard Kalman filtering algorithm, carrying out local measurement update according to measurement information of a sensor network under a communication link fault to obtain local optimal estimation, wherein the local optimal estimation comprises an optimal estimation value and an estimation error covariance matrix of the sensor network;
And 2, carrying out information consistency fusion on the local optimal estimation, and updating an optimal estimation value and an estimation error covariance matrix of the sensor network after the consistency fusion is completed.
When the algorithm of the invention is used for filtering, the filtering result is as follows: the estimated values of all the sensors can accurately track the state of the target system after distributed fusion. And obtaining the state estimation of the sensor network.
The covariance matrix in the algorithm refers to covariance of the estimation error of the sensor network, and because the estimation error is a random quantity, statistical information, covariance, is needed, and because the estimation error is a vector, the covariance matrix is needed. The covariance matrix is used for completing the updating of the subsequent estimated value and is also an evaluation index of the estimation accuracy.
In an embodiment, the specific implementation process of the invention comprises the following steps: the sensor obtains local optimal estimation based on a standard Kalman filtering algorithm according to self measurement information; setting iteration initial parameters; carrying out local information fusion in an information consistency mode; after the consistency is completed, the updated estimation error covariance matrix and the estimation equation are recalculated and recorded as the estimation error covariance matrix and the estimation value of the sensor at the moment. The finite nature of the estimation error at finite coherence steps and infinite coherence steps is demonstrated. The concrete introduction is as follows:
firstly, constructing and analyzing a sensor network architecture model:
Consider the following type of linear system described by a state space model: ;
Wherein is the state vector of the system. The measurement model of the/> sensor nodes is described as follows:
；
Wherein is the measurement of the/> sensors at the/> moment, the disturbance terms/> and/> are zero-mean and mutually independent gaussian white noise, and the estimated error covariance matrices are/> and/> respectively. The initial state/> is gaussian noise with zero mean and estimation error covariance matrix/> and is independent of/> and/> ; the/> and/> are known matrices with suitable dimensions.
In fact, directed graph may describe the communication topology of the network, where/> is the node set,/> is the edge set, and/> is the weighted adjacency matrix. Side/> means that the/> node can receive information from the/> node. The weighted adjacency matrix/> is a row random matrix (i.e., the sum of each row of elements is 1), where each element/> is non-negative; if/> then/> , otherwise/> . In addition, since the node does not need to communicate to obtain its own information,/> . At this time, considering that the network node and the link mode may change randomly in a complex environment, a markov process is used to describe the communication topology change of the sensor network. The evolution of the graph/> is determined by the homogeneous markov process/> , which takes on values in the finite set/> . Accordingly, we can get the node set/> , the edge set/> , the weighted adjacency matrix/> , and the adjacency node set/> at the current time, and the transition probability matrix of the markov process is/> .
Then on the basis, a distributed consistency Kalman filtering algorithm meeting the Markov switching topological structure is designed, and the accurate and reliable estimation of the target state is completed under the condition of dynamic topology. The design of the distributed consistency Kalman filtering algorithm is specifically as follows:
each sensor node adopts a Kalman distributed filtering algorithm to estimate the state of the target system.
Firstly, the sensor obtains a local optimal estimation based on a standard Kalman filtering algorithm according to self measurement information. The one-step state prediction process of the Kalman filtering algorithm is as follows:
；
Wherein represents the estimated value of the ith sensor at time k-1; the/> represents the estimated error covariance matrix of the ith sensor at time k-1; the/> represents a process noise estimation error covariance matrix in the target system model; a represents a state matrix in the target system model.
The local measurement update procedure is as follows:
；
；
Wherein represents the optimal estimated value of the ith sensor at the k moment; the/> represents the estimated error covariance matrix of the ith sensor at time k; the value of i-th sensor at time k is denoted by/> ; the/> represents the measurement matrix of the i-th sensor; the/> represents a one-step predicted value of the ith sensor at time k; the/> represents a one-step prediction error estimation error covariance matrix of the ith sensor at the k moment; and/> is the Kalman filtering gain matrix of the ith sensor at k time.
The Kalman filter gain matrix is given by:
；
Where T represents the matrix transpose and represents the estimated error covariance matrix of the noise signal in the ith sensor measurement.
The collaborative estimation is given using the distributed consensus kalman filter algorithm as shown in table 1:
；
In table 1, step 3, represents the inverse of the locally optimal estimation error covariance matrix of the i-th sensor at k-time after/> step fusion; the/> is equal to/> times the locally optimal estimate of the ith sensor at time k; the expression/> is the inverse matrix of the local optimal estimation error covariance matrix of the ith sensor at the k moment after the fusion of the/> steps; the/> is equal to/> times the locally optimal estimate of the ith sensor at time k; the expression of/> denotes a set of neighbor nodes of an ith sensor in the sensor network; and/> is a weight.
In table 1, step 4, represents the inverse of the locally optimal estimation error covariance matrix of the i-th sensor at k-time after/> step fusion; the/> is equal to/> times the locally optimal estimate of the ith sensor at time k.
In table 1, step 3, the adjacent sensing nodes need to implement information interaction through a network and acquire information vectors and information matrixes, that is, the sensors need to mutually transmit the information vectors and the information matrixes with the adjacent sensing nodes through the network, so that local information fusion estimation is completed. The process is carried out in an information consistency mode, L steps of consistency coordination steps are shared in consideration of time k, and information is required to be transmitted outwards in each step of sensor network. It is not difficult to find that the consistency process information transfer at this time depends on the real-time topology of the sensor network.
In Table 1, step 3 thus completes the local information fusion process. That is, the consistency process is affected by random packet loss during communication, and thus the weight is defined as follows:
；
Wherein represents the weight of direct information transmission between the ith sensor and the jth sensor in the sensor network; Indicating random packet loss of the link, which obeys an independent co-distributed Bernoulli distribution. Specifically, in the/> step consistency filtering process at time k, communication between the nodes/> and/> is successful at , otherwise packet loss occurs. For each communication link, it is assumed that the packet loss rate is less than 1, namely:
；
wherein holds for all/> and/> . There is/> ,/> because the node can obtain its own information regardless of the network conditions. Let the random variable/> be independent of process noise/> , measurement noise/> , and initial state/> . Thus far, a distributed consistency Kalman filter algorithm under the condition of link failure is given.
Finally, deep performance analysis is carried out on the algorithm, and the convergence condition of the algorithm is discussed.
The convergence analysis of the distributed consistency kalman filter algorithm is as follows:
To analyze convergence, the algorithm proposed by the present invention will be described as having consistency. "compatibility" here means that the resulting covariance of the algorithm must be the upper bound of the system's true covariance matrix. First, the true one-step prediction error covariance is defined as follows:
；
The true estimation error covariance is as follows:
；
the true estimated error covariance after multi-step consistency synergy/fusion is as follows:
；
It is easy to verify that the consistent kalman filtering algorithm under the markov switching topology is coherent, i.e.:
；
Assuming that the sensor network is globally observable, i.e., is observable, wherein/> ;
In applications where sensor nodes are limited in functionality, it is difficult for a single node to be able to perform the task of target tracking, and the assumption of local observability is often not reasonable. As a whole, the sensor network comprises different types of sensors, and the defects of the performance of a single sensor can be generally overcome through cooperation among the sensors, so that global observability is realized, and the assumption is reasonable.
Under globally observable conditions/concepts, the following results can be demonstrated:
(1) Estimation error bounded analysis under finite consistency step size: if the sensing network is globally considerable and the link fault probability is not constant 1, then the estimated error covariance is randomly bounded, namely:
；
(2) Estimation error bounded analysis under infinite consistency step size: if the sensing network is globally observable, the link failure probability is not constant at 1, the number of consistency steps is large enough, then there is a positive scalar to establish the following consistent bounded condition,
；
Almost certainly true for .
Therefore, the system convergence is influenced by link faults, and has deep requirements on the network topology structure in addition to the requirements on the observation performance of the sensors in the sensor network. If the topology structure cannot meet the condition of communication in the mean value sense, the network part nodes are likely to be isolated nodes, and the information of the network part nodes cannot be shared globally, so that the task fails.
In order that the practice of the invention may be better understood by those skilled in the art, the invention is simulated using Matlab software.
The linear system model considered is as follows:
；
Where is the sampling period,/> is zero mean and variance is the gaussian distribution/> . Assume that initial state/> satisfies a gaussian distribution with mean 0 and variance/> . For convenience, the weights are set to/> for all/> . The probability of no packet loss of the communication link is given to be 10%. The topology of the hypothetical network is already given.
The individual sensor measurement matrices are as follows:
；
Wherein obeys a gaussian distribution with a mean of 0 variance/> .
The network is not difficult to verify to meet global observability, and the mean square estimation error (MSE) obtained by the proposed distributed consistency filtering algorithm can be verified to have consistency through the simulation result graph, and the overall requirement of error convergence is met. In fact, for a single sensor, the estimation error curve will diverge because of not satisfying observability itself, but the estimation error remains converged as a whole for the sensor network, thus it can be seen that the performance of the present invention is significantly better than that of a single sensor algorithm.
Fig. 2 is a network topology structure diagram arbitrarily given, and fig. 3 is a simulation result of mean square estimation error (MSE) of each sensor, from which MSE can be found to have consistency and successfully meet the overall requirement of error convergence, which verifies the effectiveness of the present invention.
It will be evident to those skilled in the art that the invention is not limited to the details of the foregoing illustrative embodiments, and that the present invention may be embodied in other specific forms without departing from the spirit or essential characteristics thereof. The present embodiments are, therefore, to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein. Any reference sign in a claim should not be construed as limiting the claim concerned.
Furthermore, it should be understood that although the present disclosure describes embodiments, not every embodiment is provided with a separate embodiment, and that this description is provided for clarity only, and that the disclosure is not limited to the embodiments described in detail below, and that the embodiments described in the examples may be combined as appropriate to form other embodiments that will be apparent to those skilled in the art.
Claims (5)
1. The distributed consistency Kalman filtering method of the sensor network under the communication link fault is characterized by comprising the following steps:
Step 1, based on a standard Kalman filtering algorithm, carrying out local measurement update according to measurement information of a sensor network under a communication link fault to obtain local optimal estimation, wherein the local optimal estimation comprises an optimal estimation value and an estimation error covariance matrix of the sensor network;
The local measurement updating process comprises the following steps:
；
；
Wherein represents the optimal estimated value of the ith sensor at the k moment; the/> represents the estimated error covariance matrix of the ith sensor at time k; the value of i-th sensor at time k is denoted by/> ; the/> represents the measurement matrix of the i-th sensor; Representing a one-step predicted value of an ith sensor at a time k; the/> represents a one-step prediction error estimation error covariance matrix of the ith sensor at the k moment; the value of the Kalman filtering gain matrix of the ith sensor at the k moment is/;
；
Wherein T represents a matrix transpose, represents an estimated error covariance matrix of the noise signal in the ith sensor measurement;
；
Wherein represents the estimated value of the ith sensor at time k-1; the/> represents the estimated error covariance matrix of the ith sensor at time k-1; the/> represents a process noise estimation error covariance matrix in the target system model; a represents a state matrix in a target system model;
And 2, carrying out information consistency fusion on the local optimal estimation, and updating an optimal estimation value and an estimation error covariance matrix of the sensor network after the consistency fusion is completed.
2. The distributed consistency kalman filtering method of the sensor network under the fault of the communication link according to claim 1, wherein the step2 specifically includes:
Setting initial parameters and/> according to the locally optimal estimate;
And carrying out -step information consistency fusion based on the initial parameters, and after finishing the information consistency fusion, recalculating and updating the optimal estimated value and the estimated error covariance matrix of the sensor network.
3. The distributed consistency kalman filtering method of sensor network under communication link failure according to claim 2, wherein the information consistency fusion formula in the th step is:
；
Wherein represents the inverse matrix of the local optimal estimation error covariance matrix of the ith sensor at the k moment after/> step fusion; the/> is equal to/> times the locally optimal estimate of the ith sensor at time k; the expression/> is the inverse matrix of the local optimal estimation error covariance matrix of the ith sensor at the k moment after the fusion of the/> steps; Equal to/> times the local optimum estimate of the ith sensor at time k; the expression of/> denotes a set of neighbor nodes of an ith sensor in the sensor network; and/> is a weight.
4. The distributed consistency kalman filtering method of sensor network under communication link failure according to claim 3, wherein ;
Wherein represents the weight of direct information transmission between the ith sensor and the jth sensor in the sensor network; Indicating random packet loss of the link.
5. The distributed consistency kalman filtering method of sensor network under communication link failure according to claim 4, wherein the updated optimal estimated value and estimated error covariance matrix of the sensor network are:
；
Wherein represents the inverse matrix of the local optimal estimation error covariance matrix of the ith sensor at the k moment after/> step fusion; the/> is equal to/> times the locally optimal estimate of the ith sensor at time k.
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| CN115603845A (en) * | 2022-09-19 | 2023-01-13 | 安徽理工大学（Cn） | Optimal distributed filter cooperative target tracking method based on consistency strategy |
| CN116186643A (en) * | 2023-04-27 | 2023-05-30 | 北京航空航天大学 | Multi-sensor collaborative target tracking method, system, equipment and medium |
| CN116699598A (en) * | 2023-07-10 | 2023-09-05 | 哈尔滨工业大学 | Multi-sensor target tracking method, system and equipment based on consistency filtering |
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