Distributed estimation method in wireless sensor networks under time-varying topology

Abstract

This invention discloses a distributed estimation method for wireless sensor networks with time-varying topologies, belonging to the field of signal processing technology. The distributed estimation method for wireless sensor networks with time-varying topologies includes modeling the wireless sensor network system under time-varying topologies, distributed state estimation of the time-varying topology network structure, and a distributed state estimation method for asynchronous sensor sampling. The wireless sensor network system takes into account inter-node communication constraints, providing the number of nodes and communication topology connections. The distributed state estimation method for asynchronous sensor sampling includes the design of distributed filters for asynchronous sampling, which can be used for wireless sensors with fixed topologies and sensors with time-varying topologies. It can reduce energy consumption, facilitate research on distributed state estimation of wireless sensor networks, and provide corresponding filter parameter design and optimization methods to compensate for the adverse effects of interference factors on state estimation.

Description

Technical Field

[0001] This invention belongs to the field of signal processing technology, and more specifically, relates to a distributed estimation method in wireless sensor networks with time-varying topology. Background Technology

[0002] Wireless sensor networks consist of a large number of miniature intelligent sensor nodes deployed in a monitoring area. The nodes collect and process information about the objects being sensed in the monitoring area and exchange the information collected by the sensors in real time through wireless communication. Compared with traditional sensing systems, wireless sensor networks have significant advantages such as self-organization, adaptability, robustness and low cost. Therefore, wireless sensor network technology is used in various fields of industry and life.

[0003] While wireless sensor networks have irreplaceable advantages in information sensing, sensor nodes are powered by batteries, and the space available for power supply modules in miniature sensor nodes is very limited. Therefore, the design of sensor nodes must aim to save energy to the greatest extent possible. Data acquisition and wireless communication account for a significant proportion of the total energy consumption of the sensor node. To save energy to the greatest extent, more economical data acquisition methods and transmission communication protocols are needed. Sometimes, to achieve higher energy efficiency, it is even necessary to sacrifice some other system performance indicators. Due to the above characteristics of wireless sensor networks, sensor nodes are inevitably constrained by node energy, which in turn brings some limitations to the information interaction between nodes.

[0004] Furthermore, wireless sensor networks often operate in complex environments. Communication between nodes may be obstructed by objects such as people, vehicles, animals, and trees, or interfered with by wireless communication signals from electronic devices such as mobile phones, routers, and mobile communication stations. Electromagnetic interference caused by natural phenomena such as lightning can also lead to communication link loss, i.e., changes in network topology. The loss of communication links between sensor nodes results in a dynamic change in the network's communication topology. In this situation, traditional distributed state estimation algorithms based on the assumption of real-time, unrestricted signal transmission may no longer be applicable to wireless sensor networks. This presents a new challenge to the distributed state estimation problem. Therefore, research on distributed estimation problems in wireless sensor networks under time-varying topology environments is of great significance. Summary of the Invention

[0005] The technical problem to be solved by this invention is to provide a distributed estimation method in wireless sensor networks with time-varying topology. It can reduce energy consumption while carrying out distributed state estimation research in wireless sensor networks, and provide corresponding filter parameter design and optimization methods to compensate for the adverse effects of interference factors on state estimation.

[0006] The distributed estimation method in wireless sensor networks under time-varying topology of the present invention includes system modeling of wireless sensor networks under time-varying topology, distributed state estimation of time-varying topology network structure, and distributed state estimation method for obtaining asynchronous sensor sampling.

[0007] The wireless sensor network system, while taking into account the communication constraints between nodes, provides the number of nodes and the communication topology of the wireless sensor network.

[0008] Distributed state estimation of time-varying topology network structures is based on selecting a utility function to evaluate bandwidth utilization and estimation performance as needed, and is given through optimal estimation theory, mathematical optimization methods and stability theory;

[0009] The distributed state estimation method for asynchronous sensor sampling includes the design of a distributed filter for asynchronous sampling, which can be used for wireless sensors with fixed topology and sensors with time-varying topology.

[0010] As a further improvement of the present invention, the modeling of wireless sensor network systems under time-varying topology includes the following steps: calculating and obtaining the impact of randomness, dynamics and nonlinearity on system analysis and synthesis; using appropriate nonlinear functions and stochastic difference equations to establish a state-space model; reasonably abstracting and modeling the communication routing algorithms and signal transmission constraints used in practical applications; and using tools such as graph theory, Markov processes, and switching system theory to establish a mathematical model of network topology changes.

[0011] As a further improvement of the present invention, the modeling process of a wireless sensor network system under a time-varying topology includes: For a wireless sensor network with n sensor nodes, we can use a graph G = (V, E, S) to describe the communication topology of the wireless sensor network, where V = {v1, v2, ..., v...} n Let ) be the node set, E = V × V be the edge set, and S = [a ij ] n×n For a weighted neighbor matrix; connecting edges (V i V j )∈E indicates that the i-th sensor node can receive information from the j-th sensor node, at which point a ij Greater than 0, otherwise equal to 0.

[0012] As a further improvement of the present invention, the steps of inter-node communication constraint include: letting γ i (k) indicates whether the i-th sensor transmits information at time k (γ). i (k) = 1 indicates transmission, γ i (k) = 0 indicates no transmission); at this time, the communication frequency constraint is expressed as Where δ iIt is a scalar with a value between 0 and 1.

[0013] As a further improvement of the present invention, the distributed state estimation of time-varying topology network structures includes the following steps:

[0014] The impact of dynamic communication topology on data sharing between nodes is analyzed, and communication scheduling strategies such as event triggering, signal quantization, and effective data dimension transmission are designed accordingly to allocate limited communication resources.

[0015] Based on the designed communication scheduling strategies, a distributed state estimator expression for wireless sensor networks is constructed. A utility function that comprehensively considers bandwidth consumption and distributed algorithm estimation performance is established. The parameters of the distributed estimator are solved by optimizing this utility function.

[0016] The performance of the distributed filter is analyzed to obtain the convergence of the estimation error and its relationship with bandwidth resources, and the robustness of the algorithm to parameter perturbations is calculated.

[0017] As a further improvement of the present invention, the process of establishing distributed state estimation for time-varying topological network structures includes:

[0018] Consider a discrete system: x k+1 =Ak x +f(x k ξ k )+Γ k w k ;

[0019] The sensor network for target observation is as follows:

[0020] Define event triggering functions based on the triggering mechanism to reduce unnecessary energy consumption:

[0021]

[0022] Constructing a distributed filter consists of two parts: prediction and update.

[0023]

[0024] Based on the communication scheduling mechanism, the network transmission frequency under this mechanism is obtained, the expression of the system estimation error covariance matrix is ​​obtained, and the filter gain is designed under certain criteria to obtain the relationship between filter performance and threshold.

[0025] As a further improvement of the present invention, the establishment of distributed state estimation for time-varying topological network structures also includes:

[0026] When the system is affected by the non-ideal condition of noise correlation, especially when the system noise and measurement noise are correlated, the predictor of the filter is:

[0027] Then, a method for updating the covariance of the estimation error of the local filter is set up. By using a matrix-weighted linear combination of local filters, the optimal distributed fusion estimator is given.

[0028] As a further improvement to the present invention, the asynchronous sampling distributed filter design includes:

[0029] A distributed filter design method for constructing a multi-rate sampling system in a wireless sensor network with a fixed topology is obtained. The equivalent noise covariance of the estimation error system is calculated using a set of multi-rate recursive formulas. The observer parameters are optimized based on the orthogonal projection theorem, and the algorithm performance is analyzed.

[0030] Based on the impact of time-varying topology on multi-rate distributed sensors, a distributed estimation method based on a two-layer fusion strategy is designed to enable each node to make full use of neighbor information to improve its local estimation results. At the same time, the performance loss of the estimator caused by the information transmission frequency is analyzed to achieve a reasonable trade-off between energy saving and estimator performance.

[0031] The results are extended to non-ideal measurement environments such as measurement noise correlation, channel attenuation, and transmission delay to obtain the maximum allowable packet loss rate and the upper bound of transmission delay when the distributed estimation method is effective.

[0032] As a further improvement of the present invention, the steps of constructing a distributed filter based on a multi-rate sampling system of a wireless sensor network with a fixed topology include:

[0033] The asynchronous uniform sampling networked multi-sensor discrete system model is as follows:

[0034] x((k+1)T)=Ax(kT)+Γ(kT)w(kT), k=12,...;

[0035] y i (n i kT ) = C i (n i kT )x(n i kT )+v i (n i kT ), i = 1, 2, ..., M;

[0036]

[0037] Where x kIt is a periodically evolving state variable to be estimated, y i (n i kT) is the sampling rate n i The measurement information of sensor i in kT, M represents the number of sensors, let h x h is the state update rate. i Let i be the observation sampling rate of sensor i, then Let T be a positive integer; for ease of description, let T = 1.

[0038] Among them, random parameters It follows a Bernoulli distribution and satisfies:

[0039] Based on the system description, a multi-rate estimator of the following form is constructed:

[0040]

[0041]

[0042] Estimate the state equation and filter, and construct expressions for the estimation error and its covariance:

[0043]

[0044] Then, the parameters are optimized in the sense of minimizing the mean square error, thereby completing the filter design.

[0045] As a further improvement of the present invention, the step of constructing a distributed filter based on the influence of time-varying topology on multi-rate distributed sensors includes: for asynchronous sampling systems under non-ideal measurement conditions, designing a distributed estimator for asynchronous sampling systems with data loss and observation delay respectively. Taking the system with observation delay as an example, the following model is constructed: x((k+1)T)=Ax(kT)+Γw(kT), k=1,2,...; y i (n i kT ) = C i x (n i kT -d i T )+v i (n i kT ), i = 1, 2, ..., M; where x k The state variable to be estimated is x. k Sensor i has a known constant single time delay and satisfies 1 ≤ d i ≤d, where d is the upper limit of the time delay, d i Both d and d are positive integers;

[0046] Obtain the state-space model of the sensor at the observation sampling points: in The new system noise and measurement noise are as follows:

[0047] Depending on the delay (d) i ≤n i and d i >n i Based on the expression for noise, the corresponding second-order statistical matrices are obtained to complete the design of the distributed state estimator.

[0048] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0049] (1) It can reduce energy consumption while taking into account several non-ideal conditions such as system noise correlation, measurement information delay, and channel attenuation, and carry out distributed state estimation research of wireless sensor networks; in order to reveal the impact of signal transmission strategy, asynchronous sampling strategy and non-ideal conditions on estimator design, and provide corresponding filter parameter design and optimization methods to compensate for the adverse effects of the above factors on state estimation.

[0050] (2) When performing mathematical modeling of wireless sensor networks, the network constraints and the characteristics of the monitoring objects and measurement systems should be fully considered. Through reasonable simplification, induction and assumption, specific mathematical models should be abstracted. Existing research tools should be modified or new research methods should be explored to solve the design problem of distributed state estimation algorithms under energy and bandwidth constraints. This has implications for designing more applicable, lower cost and lower energy consumption sensors.

[0051] (3) Explore the relationship between constraints, network topology, system parameters and the convergence of the distributed state estimation algorithm, give the conditions to ensure the convergence of the estimation error system, and evaluate the complexity, convergence speed, robustness and other properties of the algorithm; these studies lay the theoretical foundation for the practical application of distributed estimation algorithms in wireless sensor networks; solve the problem that communication limitations impose constraints on the communication process between sensors, resulting in a certain degree of information loss in data sharing between sensors;

[0052] (4) In addition, dynamic communication topology will hinder the propagation of sensor information in wireless sensor networks. Both pose serious challenges to the design and analysis of distributed state estimation algorithms. This invention comprehensively reflects the utility function that reflects estimation performance, energy and bandwidth loss, and provides optimal or suboptimal distributed estimation algorithms. It judges the relationship between constraints and the convergence of the estimation error system, and analyzes the robustness of the algorithm to parameter perturbations. This is conducive to further expanding the application advantages of wireless sensors and broadening their application scenarios and scope of application. Attached Figure Description

[0053] Figure 1 This is a schematic diagram of the present invention;

[0054] Figure 2 This is a diagram of the asynchronous uniform sampling structure of the present invention. Detailed Implementation

[0055] Limited by the hardware resources and battery supply of sensor nodes, sensor nodes inevitably suffer from energy constraints. Since data sampling and information exchange consume the majority of the power, adopting novel sampling and communication methods is an effective way to extend the lifespan of sensor nodes.

[0056] Reducing the sampling frequency of sensors can obviously reduce energy consumption, and designing a reasonable communication scheduling mechanism to reduce the signal transmission frequency can also reduce communication volume and transmission energy.

[0057] Asynchronous sampling is a common method for reducing sensor sampling frequency and an effective means of reducing energy consumption. An asynchronous sampling system refers to a multi-sensor system in which each sensor has a different sampling rate or two or more sampling rates (multi-rate); the ratio between the sampling rates of different sensors can be a rational number or an irrational number; the estimation problem of asynchronous sampling systems often needs to be transformed into the estimation problem of synchronous systems, that is, the asynchronous sampling system needs to be synchronized, and then the estimation algorithm can be studied using the existing estimation theory of synchronous systems.

[0058] Existing technologies employ iterative system state equation model transformation methods and present research on fusion algorithms. For asynchronous non-uniform sampling, based on multi-scale theory, data blocks are used to describe and establish multi-rate system models. Within each data block, the state is updated uniformly at the finest scale, while different sensors sample non-uniformly at different sampling rates at the coarse scale, with the sampling rates between different sensors being integer multiples of each other. In this technique, local sensors use the moving average of the system state within a data block as their state to establish the state-space model of the observed sampling points, thus obtaining the augmented state and observation equations. However, if the data block is large, this augmentation method incurs a significant computational burden. To date, comprehensive reports on state fusion estimation for asynchronous sampling networked systems with time delays, lost observations, and correlated noise remain incomplete, and many problems and challenges need to be addressed.

[0059] Regarding methods to reduce signal transmission frequency, existing literature proposes a sensor selection algorithm, provides a corresponding optimal state estimator design scheme and estimation error convergence conditions. Subsequently, researchers further explored a random sensor activation scheme in wireless sensor networks, where each sensor only broadcasts its own information when activated, presenting an optimal distributed estimation algorithm and using the properties of linear matrix inequalities and the Riccati equation to give upper and lower bounds on the estimation error covariance. They also established a multi-rate sensor network where sensors communicate at a slower rate and perform state estimation at a faster rate, designing a distributed state estimation algorithm using the lift-up method. However, while these methods can reduce the signal transmission frequency of sensors to some extent, they do not selectively exclude certain types of signals from transmission, potentially leading to the loss of some critical information and deterioration of the overall estimation performance of the sensor network.

[0060] Specific Implementation Example 1: Based on the aforementioned limitations in reducing energy consumption and the problems of communication link loss and network link topology changes caused by environmental factors, please refer to... Figure 1 Distributed estimation methods in wireless sensor networks with time-varying topologies include system modeling of wireless sensor networks with time-varying topologies, distributed state estimation of time-varying topology networks, and distributed state estimation methods for asynchronous sensor sampling.

[0061] Communication between nodes may be affected by obstructions from objects, interference from electronic devices, and electromagnetic influences from natural phenomena, leading to the loss of some communication links. Furthermore, in practical applications, the objects monitored by wireless sensor networks typically possess more complex dynamic characteristics than traditional objects. To reduce or avoid the impact of these factors, it is necessary to model the wireless sensor network system with a time-varying topology, including the following steps:

[0062] (1) Calculate and obtain the impact of randomness, dynamics and nonlinearity on system analysis and synthesis, and use appropriate nonlinear functions and stochastic difference equations to establish a state-space model;

[0063] (2) Reasonably abstract and model the communication routing algorithms and signal transmission constraints used in practical applications, and establish a mathematical model of network topology changes by using tools such as graph theory, Markov process, and switching system theory.

[0064] Specifically, the computational modeling process for modeling a wireless sensor network system with a time-varying topology is as follows:

[0065] Wireless sensor networks are composed of a large number of sensor nodes that self-organize. The network topology that represents the communication connection relationship between sensor nodes in the network can be characterized using relevant knowledge in graph theory.

[0066] Specifically, for a wireless sensor network with n sensor nodes, we can use a graph G = (V, E, S) to describe the communication topology of the wireless sensor network, where V = {v1, v2, ..., v...} n Let} be the node set, E = V × V be the edge set, and S = [a ij ] n×n This is a weighted neighbor matrix;

[0067] Connect edges (V) i V j )∈E indicates that the i-th sensor node can receive information from the j-th sensor node, at which point a ij Greater than 0, otherwise equal to 0.

[0068] Through the above modeling method, Figure G provides a relatively complete structural feature of the wireless sensor network, and gives the number of nodes and communication topology of the wireless sensor network. This will greatly help in the further design and analysis of distributed state estimation algorithms.

[0069] It should be noted that the communication frequency directly determines the energy consumption of sensor nodes and the network bandwidth usage. Therefore, by establishing the relationship between energy and bandwidth loss and the communication frequency, we can transform the original problem into one that considers communication frequency constraints. Thus, in the above modeling process, it is also necessary to take into account the communication constraints between nodes. The steps are as follows:

[0070] Let γ i (k) indicates whether the i-th sensor transmits information at time k (γ). i (k) = 1 indicates transmission, γ i (k) = 0 indicates no transmission);

[0071] The communication frequency constraint can be represented by the following model:

[0072]

[0073] Where δ i It is a scalar with a value between 0 and 1.

[0074] Due to the limitations of the established time-varying topology wireless sensor network and communication constraints, distributed state estimation of the time-varying topology network structure is required. Based on practical engineering needs, a utility function for evaluating bandwidth utilization and estimation performance is selected. Using optimal estimation theory, mathematical optimization methods, and stability theory, a corresponding optimal distributed state estimation algorithm is presented, and the impact of bandwidth constraints on the estimation error and system performance is discussed. The process includes the following steps:

[0075] (1) Analyze the impact of data sharing between nodes in the dynamic communication topology, and design communication scheduling strategies such as event triggering, signal quantization, and data effective dimension transmission to allocate limited communication resources.

[0076] (2) Based on the designed communication scheduling strategies, construct the expression of the distributed state estimator for the wireless sensor network, establish a utility function that comprehensively considers bandwidth loss and distributed algorithm estimation performance, and solve the parameters of the distributed estimator by optimizing the utility function;

[0077] (3) Analyze the performance of the distributed filter, further obtain the convergence of the estimation error and its relationship with bandwidth resources, and calculate the robustness of the algorithm to parameter perturbation;

[0078] Specifically, the steps for obtaining and analyzing the distributed state estimate of a time-varying topology network include:

[0079] First, assume that the external environment of the sensor network coverage area has the same impact on all sensors, and that the sensors are from the same manufacturer and batch of products. Therefore, the probability of a sensor experiencing a communication failure due to interference or being removed from the network due to a failure is the same.

[0080] In this case, we propose to use Markov processes and graph theory to characterize the real-time communication topology of wireless sensor networks and define a switching topology that follows a Markov process.

[0081] Subsequently, a suitable distributed estimation algorithm is constructed to provide a state estimate of the target system using its own information and neighbor sensor information;

[0082] It is worth noting that distributed estimation requires collaboration from all sensor nodes. During communication topology switching, a series of disconnected topologies may occur, preventing sensor information from being shared within the network, which severely hinders the collaboration process. To address this issue, we will consider that the Markov process has reached a steady-state distribution. Subsequently, using Lyapunov stability theory combined with recursive Riccati equations, Markov convergence criteria, and the spectral properties of the Laplace matrix of graphs, we will obtain sufficient conditions for the almost inevitable convergence of the estimation error system, revealing the direct relationship between convergence and system parameters such as network topology and the Markov process transition probability matrix.

[0083] Consider a discrete system:

[0084] x k+1 =Ak x +f(x k ξ k )+Γ k w k

[0085] The sensor network for target observation is as follows:

[0086]

[0087] To reduce unnecessary energy consumption, event triggering functions are defined according to the triggering mechanism:

[0088]

[0089] Based on this, a distributed filter is constructed, comprising two parts: prediction and update.

[0090]

[0091]

[0092] Next, based on the communication scheduling mechanism, we will analyze the network transmission frequency under this mechanism, obtain the expression for the system estimation error covariance matrix, design the filter gain under certain criteria, and further derive the relationship between filter performance and threshold.

[0093] It should be noted that when the system is affected by the non-ideal condition of noise correlation, especially when the system noise and measurement noise are correlated, the filter design needs to be changed, that is, the predictor is changed to:

[0094]

[0095] This change makes it difficult to obtain the recursive expression for the estimation error covariance matrix. It is necessary to redesign the estimation error covariance update method of the local filter and give the optimal distributed fusion estimator by adopting matrix-weighted linear combination of local filters.

[0096] To further reduce energy consumption and lower the sampling frequency of some sensors (i.e., asynchronous sampling), multi-rate sampling presents challenges for data fusion at local nodes, becoming another difficulty in designing multi-rate network distributed systems. Therefore, a distributed state estimation method based on asynchronous sensor sampling is needed. This method includes the design of distributed filters for asynchronous sampling.

[0097] (1) A distributed filter design method for constructing a multi-rate sampling system of a wireless sensor network under a fixed topology is obtained. The equivalent noise covariance of the estimation error system is calculated using a set of multi-rate recursive formulas. Then, the observer parameters are optimized based on the orthogonal projection theorem, and the algorithm performance is analyzed.

[0098] (2) Based on the influence of time-varying topology on multi-rate distributed sensors, a distributed estimation method based on a two-layer fusion strategy is designed so that each node can make full use of neighbor information to improve its local estimation results. At the same time, the performance loss of the estimator caused by the information transmission frequency is analyzed to achieve a reasonable trade-off between energy saving and estimator performance.

[0099] (3) Extend the research results to non-ideal measurement environments such as measurement noise correlation, channel attenuation, and transmission delay to obtain the maximum allowable packet loss rate and the upper bound of transmission delay when the distributed estimation method is effective.

[0100] Specifically, the design of an asynchronously sampled distributed filter includes the following steps:

[0101] First, consider an asynchronous uniform sampling system, assuming the state update rate is an integer multiple of the observation sampling rate, and the initial sampling time is the same as the state update time, such as... Figure 2 The asynchronous uniform sampling structure is shown in the diagram (taking two sensors as an example).

[0102] The asynchronous uniform sampling networked multi-sensor discrete system model is as follows:

[0103] x((k+1)T)=Ax(kT)+Γ(kT)w(kT), k=1, 2,...

[0104] y i (n i kT)=C i (n i kT)x(n i kT)+v i (n ikT), i = 1, 2, ..., M

[0105]

[0106] Where x k It is a periodically evolving state variable to be estimated, y i (n i kT) is the sampling rate n i The measurement information of sensor i in kT, M represents the number of sensors, let h x h is the state update rate. i Let i be the observation sampling rate of sensor i, then Let T be a positive integer; for ease of description, let T = 1.

[0107] Among them, random parameters It follows a Bernoulli distribution and satisfies:

[0108]

[0109] Based on the system description, a multi-rate estimator of the following form is constructed:

[0110]

[0111]

[0112] Furthermore, the above formula can be simplified to an equivalent form:

[0113]

[0114]

[0115] Estimate the state equation and filter, and construct the estimation error:

[0116]

[0117] And the expression for the estimated error covariance:

[0118]

[0119] Then, the parameters are optimized in the sense of minimizing the mean square error, thereby completing the filter design.

[0120] For asynchronous sampling systems under non-ideal measurement conditions, we develop distributed estimators for asynchronous sampling systems with data loss and observation delays. Taking the system with observation delay as an example, consider the following model:

[0121] x((k+1) T )=Ax(kT)+Γw(kT), k=1, 2,...

[0122] y i (n i kT ) = C i x (n i kT -d i T )+v i (n i kT ), i = 1, 2, ..., M

[0123] Where x k The state variable to be estimated is x. k Sensor i has a known constant single time delay and satisfies 1 ≤ d i ≤d, where d is the upper limit of the time delay, d i Both d and d are positive integers;

[0124] Obtain the state-space model of the sensor at the observation sampling points:

[0125] x(n i (k+1))=A i x(n i k)+W i (n i k)

[0126]

[0127] in The new system noise and measurement noise are as follows:

[0128]

[0129]

[0130] Depending on the delay (d) i ≤n i and d i >n i Based on the expression for noise, the corresponding second-order statistical matrices are obtained to complete the design of the distributed state estimator.

Claims

1. A distributed estimation method in a wireless sensor network under time-varying topology, characterized in that: This includes modeling of wireless sensor network systems with time-varying topologies, distributed state estimation of time-varying topology networks, and distributed state estimation methods for obtaining asynchronous sensor samples. The wireless sensor network system, while taking into account the communication constraints between nodes, provides the number of nodes and the communication topology of the wireless sensor network. Distributed state estimation of time-varying topology network structures is based on selecting a utility function to evaluate bandwidth utilization and estimation performance as needed, and is given through optimal estimation theory, mathematical optimization methods and stability theory; The distributed state estimation method for asynchronous sensor sampling includes the design of a distributed filter for asynchronous sampling, which can be used for wireless sensors with fixed topology and sensors with time-varying topology.

2. The method according to claim 1, wherein: Modeling wireless sensor network systems with time-varying topologies includes the following steps: calculating and obtaining the impact of randomness, dynamism, and nonlinearity on system analysis and synthesis; establishing a state-space model using appropriate nonlinear functions and stochastic difference equations; reasonably abstracting and modeling the communication routing algorithms and signal transmission constraints used in practical applications; and establishing a mathematical model of network topology changes using tools such as graph theory, Markov processes, and switching system theory.

3. The method according to claim 2, wherein: The modeling process for a wireless sensor network system with a time-varying topology includes: For a wireless sensor network with n sensor nodes, we can use a graph G = (V, E, S) to describe the communication topology of the wireless sensor network, where V = {v1, v2, ..., v...} n Let ) be the node set, E = V × V be the edge set, and S = [a ij ] n×n For a weighted neighbor matrix; connecting edges (V i V j )∈E indicates that the i-th sensor node can receive information from the j-th sensor node, at which point a ij Greater than 0, otherwise equal to 0.

4. The method according to claim 1, wherein: The steps for constraining inter-node communication include: Let γ i (k) indicates whether the i-th sensor transmits information at time k (γ). i (k) = 1 indicates transmission, γ i (k) = 0 indicates no transmission); at this time, the communication frequency constraint is expressed as Where δ i It is a scalar with a value between 0 and 1.

5. The method according to claim 1, wherein: Distributed state estimation of time-varying topology networks includes the following steps: The impact of dynamic communication topology on data sharing between nodes is analyzed, and communication scheduling strategies such as event triggering, signal quantization, and effective data dimension transmission are designed accordingly to allocate limited communication resources. Based on the designed communication scheduling strategies, a distributed state estimator expression for wireless sensor networks is constructed. A utility function that comprehensively considers bandwidth consumption and distributed algorithm estimation performance is established. The parameters of the distributed estimator are solved by optimizing this utility function. The performance of the distributed filter is analyzed to obtain the convergence of the estimation error and its relationship with bandwidth resources, and the robustness of the algorithm to parameter perturbations is calculated.

6. The method according to claim 5, wherein: The process of establishing distributed state estimation for time-varying topology networks includes: Consider a discrete system: x k+1 = Ak x + f(x k , ξ k ) + Γ k w k ; The sensor network for observing the target is: According to the trigger mechanism, the event trigger function is defined to reduce unnecessary energy loss: The distributed filter is constructed to include both a prediction and an update, i.e.: Based on the communication scheduling mechanism, the network transmission frequency under this mechanism is obtained, the expression of the system estimation error covariance matrix is ​​obtained, and the filter gain is designed under certain criteria to obtain the relationship between filter performance and threshold.

7. The method according to claim 6, wherein: The establishment of distributed state estimation for time-varying topology networks also includes: When the system is affected by the non-ideal condition of noise correlation, especially the correlation between the system noise and the measurement noise, the predictor of the filter is: Then, a method for updating the covariance of the estimation error of the local filter is set up. By using a matrix-weighted linear combination of local filters, the optimal distributed fusion estimator is given.

8. The method according to claim 1, wherein: The design of asynchronous sampling distributed filters includes: A distributed filter design method for constructing a multi-rate sampling system in a wireless sensor network with a fixed topology is obtained. The equivalent noise covariance of the estimation error system is calculated using a set of multi-rate recursive formulas. The observer parameters are optimized based on the orthogonal projection theorem, and the algorithm performance is analyzed. Based on the impact of time-varying topology on multi-rate distributed sensors, a distributed estimation method based on a two-layer fusion strategy is designed to enable each node to make full use of neighbor information to improve its local estimation results. At the same time, the performance loss of the estimator caused by the information transmission frequency is analyzed to achieve a reasonable trade-off between energy saving and estimator performance. The results are extended to non-ideal measurement environments such as measurement noise correlation, channel attenuation, and transmission delay to obtain the maximum allowable packet loss rate and the upper bound of transmission delay when the distributed estimation method is effective.

9. The method according to claim 8, wherein: The steps for constructing a distributed filter based on a multi-rate sampling system in a wireless sensor network with a fixed topology include: The asynchronous uniform sampling networked multi-sensor discrete system model is as follows: x((k+1) T ) = Ax(kT) + Γ(kT)w(kT), k = 1, 2,...; y i (n i kT )=C i (n i kT )x(n i kT )+v i (n i kT ),i=1,2,...,M; Where x k It is a periodically evolving state variable to be estimated, y i (n i kT) is the sampling rate n i The measurement information of sensor i in kT, M represents the number of sensors, let h x h is the state update rate. i Let i be the observation sampling rate of sensor i, then Let T be a positive integer; for ease of description, let T = 1. wherein the random parameters are subject to a Bernoulli distribution and satisfy: Based on the system description, a multi-rate estimator of the following form is constructed: The estimation state equation and filter are constructed, and the expression of the estimation error and the estimation error covariance are constructed: Then, the parameters are optimized in the sense of minimizing the mean square error, thereby completing the filter design.

10. The distributed estimation method in wireless sensor networks with time-varying topology according to claim 8, characterized in that: The steps for constructing a distributed filter based on the influence of time-varying topology on multi-rate distributed sensors include: for asynchronous sampling systems under non-ideal measurement conditions, designing a distributed estimator for asynchronous sampling systems with data loss and observation delay respectively. Taking the system with observation delay as an example, the following model is constructed: x((k+1) T ) = Ax(kT) + Tw(kT), k = 1, 2,... y i (n i kT )=C i x (n i kT -d i T )+v i (n i kT ),i=1,2,...,M Where x k The state variable to be estimated is x. k Sensor i has a known constant single time delay and satisfies 1 ≤ d i ≤d, where d is the upper limit of the time delay, d i Both d and d are positive integers; Obtain the state-space model of the sensor at the observation sampling points: x(n) i (k+1))=A i x(n i k)+W i (n i k) in The new system noise and measurement noise are as follows: According to the different of delay (d i ≤n i and d i >n i ), based on the expression of noise, the corresponding second-order statistical matrix is obtained, respectively, to complete the design of the distributed state estimator.

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