Event-driven asynchronous network distributed parameter estimation method based on M estimation

Abstract

The invention discloses an event-driven asynchronous network distributed parameter estimation method based on M estimation. The method mainly comprises the following steps: A, constructing a distributed measurement model; b, calculating a local error ei (n); c, constructing an M estimation cost function; d, setting a random step size to describe the uncertainty of the nodes; e, adaptively updating the intermediate estimation hi (n + 1); f, setting an event driving mechanism, and judging a satisfaction condition of an event driving condition; g, setting a random combination coefficient to describe the uncertainty of the connection between the nodes; h, aggregating the intermediate estimations of the neighbor nodes to obtain updated parameter estimations wi (n + 1); and I, iterating, and repeating the steps from A to H until the distributed parameter estimation is finished. According to the method, interference of non-Gaussian noise can be overcome in an asynchronous network environment, each node only carries out information interaction at the event triggering moment, and the distributed parameter estimation capability with lower communication consumption is achieved.

Description

Technical Field

[0001] The present invention belongs to the technical field of digital signal processing, and in particular relates to an event-driven asynchronous network distributed parameter estimation method based on M estimation. Background Art

[0002] In the field of digital signals, parameter estimation involves estimating changes in system states by analyzing and identifying system dynamics based on observed measurement data. The core of parameter estimation is to dynamically adjust system response parameters by monitoring real-time changes in system input and output signals. For models with unknown system parameters, adaptive learning methods can be used to adjust parameters based on information from the real system and sensor devices. This allows for rapid and accurate identification of model parameters and recognition of unknown system characteristics. This is of great significance in fields such as information processing and system control.

[0003] Distributed parameter estimation is a key application in the field of information and control, playing a vital role in modern communication systems, network systems, and industrial control systems. In real-world networked systems, uncertainties such as changes in network topology, random connection failures, and node disconnections and reconnections often arise. Asynchronous networks are often used to model these systems. Traditional distributed least mean-square (DLMS) methods can provide an effective decision-making basis for distributed parameter estimation in asynchronous networks. Furthermore, actual measurement data from networked systems can be subject to interference from uncertain noise, necessitating the adoption of reliable adaptive learning methods to enhance the accuracy and robustness of parameter estimation.

[0004] The non-Gaussian noise encountered in actual networked systems has more pronounced pulse characteristics than Gaussian noise, manifested in a longer tail effect on the probability density. In asynchronous network environments, the performance of traditional DLMS methods will be significantly reduced or even lead to divergence when interfered with by non-Gaussian noise. Therefore, distributed methods need to be able to resist the interference of non-Gaussian noise and alleviate the impact of non-Gaussian noise on parameter estimation results. Reference 1 "Yu Y, He H, Yang T, et al. Diffusion normalized least mean M-estimate algorithms: Design and performance analysis [J]. IEEE Transactions on SignalProcessing, 2020, 68: 2199-2214." proposes a distributed adaptive learning method based on M-estimation. This method determines whether outlier samples deviate from the normal value by comparing the threshold with the amplitude of the observed sample, ensuring the robustness of the adaptive method under non-Gaussian noise interference. However, in networked systems, as network size expands and resource utilization increases, a large amount of communication overhead is required between nodes to maintain network operation, which imposes a large communication load and consumes communication resources. Therefore, in asynchronous network environments, it is necessary to further propose a distributed processing method that saves communication resources and ensures robust and efficient distributed parameter estimation. Summary of the Invention

[0005] The purpose of the present invention is to provide an event-driven asynchronous network distributed parameter estimation method based on M estimation. The method is suitable for asynchronous network environments, combines the M estimation method to resist the interference of non-Gaussian noise, and sets an event-driven communication mechanism. Information exchange is only performed when an event occurs. It has excellent convergence performance and can save a large amount of communication resources.

[0006] The technical solution adopted by the present invention to achieve the above-mentioned object is as follows: in an asynchronous network environment, an M estimation function is used to determine abnormal values in the update process by comparing a threshold with the amplitude of an observed sample. When an abnormality exists, the update is stopped to avoid interference from the spike characteristic. In addition, an event-driven mechanism is set up to exchange information only when the system monitoring estimation information changes significantly, thereby reducing the consumption of communication resources.

[0007] The steps of this method are as follows:

[0008] A. Building a distributed measurement model

[0009] Establish a distributed network system with N nodes. At the i-th node, use the M-dimensional input signal u at the current n-th moment i (n)=[u i (n),u i (n-1),...,u i (n-M+1)] T , the M-dimensional unknown parameter vector w to be estimated o =[w1,w2,...,w M ] T , actual measurement information where v i (n) represents the additive noise with mean value of 0;

[0010] B. Calculating local errors

[0011] Let w i (n)=[w i,1 (n),w i,2 (n),...,w i,M (n)] T For each node pair parameter w o For each node, the local error can be calculated:

[0012]

[0013] Construction of C and M estimation cost function

[0014] Using the M estimation function as the cost function, the optimization problem is described as:

[0015]

[0016] Where E{·} represents the mathematical expectation;

[0017] M estimates the function ψ(e i (n)) is a piecewise continuous function, expressed as:

[0018]

[0019] where ξ i =κσ e,i (n) is the threshold parameter, constant κ = 2.576;

[0020] Represents the error signal e i The estimated variance of (n) is calculated as follows:

[0021]

[0022] Among them, 0<τ<1 is the forgetting factor, τ eis the correlation factor, med(·) represents the mathematical median operation, 5≤M e ≤9 represents the number of windows, setting τ=0.99, τ e =1.483[1+5 / (M e -1)];

[0023] ψ(e i (n)) to e i (n) Taking the partial derivative we get:

[0024]

[0025] D. Set random step size

[0026] To describe the uncertainty of nodes in asynchronous networks, the step size is described by the following distribution:

[0027]

[0028] where μ i (n) = 0 means that node i fails at time n, p i Indicates the probability that a node in the network is working properly;

[0029] E. Adaptive Update of Intermediate Estimates

[0030] Use the stochastic gradient method to update the intermediate estimate, and the update rule is:

[0031]

[0032] F. Set up event-driven mechanism

[0033] Define event-driven conditions as:

[0034]

[0035] where δ i (n) represents the event occurrence threshold;

[0036] Prior error Indicates the intermediate estimate h of the node at the current moment i (n+1) and the last information transmission estimate When the event driving condition is met, the information exchange between nodes is triggered and Otherwise, no information exchange occurs between nodes and

[0037] G. Set random combination coefficient

[0038] To describe the uncertainty of connections between nodes in an asynchronous network, the combination coefficient is described by the following distribution:

[0039]

[0040] where a j,i (n) = 0 means that the connection between node i and node j fails at time n, q j,i Indicates the probability that the connection between nodes in the network is working properly;

[0041] In addition, set the node's own combination coefficient to:

[0042]

[0043] H. Aggregation

[0044] After updating the intermediate estimate, each node aggregates and obtains a new collaborative estimate:

[0045]

[0046] I. Iteration

[0047] Repeat steps A to H until the distributed parameter estimation is completed.

[0048] The beneficial effects of the present invention are:

[0049] In an asynchronous network environment, the present invention constructs a cost function through the M-estimation strategy, reduces the sensitivity to large outliers in the adaptive update process, and sets an event-triggered driving mechanism so that information exchange between network nodes occurs only when necessary, greatly reducing communication overhead and saving communication resources in the network. It has a robust and low-communication-consumption distributed adaptive parameter estimation capability. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 This is a graph showing the network mean square deviation of the method of the present invention, the method of reference 1, and the traditional DLMS method in an asynchronous network environment under Bernoulli-Gaussian noise interference.

[0051] Figure 2 This is the node information triggering time diagram of the method of the present invention in Experiment 1;

[0052] Figure 3 This is a graph showing the network mean square deviation of the method of the present invention, the method of reference 1, and the traditional DLMS method in Experiment 2 under uniform noise interference in an asynchronous network environment.

[0053] Figure 4 This is the node information triggering time diagram of the method of the present invention in Experiment 2. DETAILED DESCRIPTION

[0054] Example:

[0055] The event-driven asynchronous network distributed parameter estimation method based on M estimation in this embodiment has the following specific steps:

[0056] A. Building a distributed measurement model

[0057] Establish a distributed network system with N nodes. At the i-th node, use the M-dimensional input signal u at the current n-th moment i (n)=[u i (n),u i (n-1),...,u i (n-M+1)] T , the M-dimensional unknown parameter vector w to be estimated o =[w1,w2,...,w M ] T , actual measurement information where v i (n) represents the additive noise with mean value of 0;

[0058] B. Calculating local errors

[0059] Let w i (n)=[w i,1 (n),w i,2 (n),...,w i,M (n)] T For each node pair parameter w o For each node, the local error can be calculated:

[0060]

[0061] Construction of C and M estimation cost function

[0062] Using the M estimation function as the cost function, the optimization problem is described as:

[0063]

[0064] Where E{·} represents the mathematical expectation;

[0065] M estimates the function ψ(e i (n)) is a piecewise continuous function, expressed as:

[0066]

[0067] where ξ i =κσ e,i (n) is the threshold parameter, constant κ = 2.576;

[0068] Represents the error signal e iThe estimated variance of (n) is calculated as follows:

[0069]

[0070] Among them, 0<τ<1 is the forgetting factor, τ e is the correlation factor, med(·) represents the mathematical median operation, 5≤M e ≤9 represents the number of windows, setting τ=0.99, τ e =1.483[1+5 / (M e -1)];

[0071] ψ(e i (n)) to e i (n) Taking the partial derivative we get:

[0072]

[0073] D. Set random step size

[0074] To describe the uncertainty of nodes in asynchronous networks, the step size is described by the following distribution:

[0075]

[0076] where μ i (n) = 0 means that node i fails at time n, p i Indicates the probability that a node in the network is working properly;

[0077] E. Adaptive Update of Intermediate Estimates

[0078] Use the stochastic gradient method to update the intermediate estimate, and the update rule is:

[0079]

[0080] F. Set up event-driven mechanism

[0081] Define event-driven conditions as:

[0082]

[0083] where δ i (n) represents the event occurrence threshold;

[0084] Prior error Indicates the intermediate estimate h of the node at the current moment i (n+1) and the last information transmission estimate When the event driving condition is met, the information exchange between nodes is triggered and Otherwise, no information exchange occurs between nodes and

[0085] G. Set random combination coefficient

[0086] To describe the uncertainty of connections between nodes in an asynchronous network, the combination coefficient is described by the following distribution:

[0087]

[0088] where a j,i (n) = 0 means that the connection between node i and node j fails at time n, q j,i Indicates the probability that the connection between nodes in the network is working properly;

[0089] In addition, set the node's own combination coefficient to:

[0090]

[0091] H. Aggregation

[0092] After updating the intermediate estimate, each node aggregates and obtains a new collaborative estimate:

[0093]

[0094] I. Iteration

[0095] Repeat steps A to H until the distributed parameter estimation is completed.

[0096] Numerical simulation experiment:

[0097] In order to verify the effectiveness of the present invention, numerical simulation experiments were conducted and compared with the method of existing document 1 and the traditional DLMS method.

[0098] In the numerical simulation, the distributed network system consists of 10 nodes. The unknown parameters to be estimated are a set of randomly generated 5-dimensional parameter vectors. The input signal of each node is a Gaussian signal sequence. The additional noise of each node is a mixed noise signal of zero-mean Gaussian noise and Bernoulli-Gaussian noise, where the variance of the Gaussian noise signal is The probability of occurrence of Bernoulli-Gaussian noise is 0.01, and its variance is

[0099] The probability p of nodes and connections working properly in an asynchronous network environment i =q j,i =0.8. In Experiment 1, the parameter values of the method of the present invention are: i =0.07,δ i (n) = 0.006; the step size parameter of the method in Reference 1 is: μi =0.07; the step size parameter of the traditional DLMS method is: μ i =0.07.

[0100] In distributed parameter estimation experiments, the network mean squared deviation (MSD) is typically used as a performance evaluation metric. During the experiment, 100 independent tests were performed. The faster the MSD curve converges and the lower the steady-state value, the better the distributed parameter estimation performance.

[0101] Figure 1 This is the network mean square deviation curve of the method of the present invention, the method of document 1 and the traditional DLMS method in Experiment 1. Figure 1 As can be seen, the traditional DLMS method uses mean square error as the cost function, which is not robust to Bernoulli-Gaussian noise interference and has severe performance degradation. The method of the present invention and the method in Reference 1 are both able to effectively resist Bernoulli-Gaussian noise interference, and their overall performance is similar, but the communication method of the present invention is more efficient.

[0102] Figure 2 This is the node information triggering time diagram of the method of the present invention in Experiment 1. Figure 2 It can be seen that the method of the present invention adopts an event-driven mechanism, and performs information interaction only at the moment when an event occurs, rather than at every moment, thereby saving a lot of communication overhead.

[0103] Experiment 2 also constructs a 10-node distributed network system. The unknown parameters to be estimated are a set of randomly generated 6-dimensional parameter vectors. The input signal to each node is a Gaussian signal sequence. The additional noise at each node is a mixture of zero-mean Gaussian noise and uniform noise. The variance of the Gaussian noise signal is distributed in [0.01, 0.07]. The probability of occurrence of the uniform noise is 0.1, and its uniform distribution is [-20, 20].

[0104] The probability p of nodes and connections working properly in an asynchronous network environment i =q j,i =0.9. In Experiment 1, the parameter values of the method of the present invention are: i =0.06,δ i (n) = 0.005; the step size parameter of the method in Reference 1 is: μ i =0.06; the step size parameter of the traditional DLMS method is: μ i =0.06.

[0105] Figure 3 This is the network mean square deviation curve of the method of the present invention, the method of document 1 and the traditional DLMS method in Experiment 3. Figure 3It can be seen that the performance of the traditional DLMS method is seriously degraded under uniform noise interference. The convergence performance of the method of the present invention and the method of reference 1 under uniform noise interference is similar overall, but the method of the present invention saves communication resources.

[0106] Figure 4 This is the node information triggering time diagram of the method of the present invention in Experiment 2. Figure 4 As can be seen, the method of the present invention uses an event-driven mechanism, where all nodes in the network only interact with each other when an event is triggered, rather than at every moment. This significantly reduces the communication cost in the network. The method of the present invention has high communication efficiency and excellent distributed parameter estimation results.

Claims

1. An event-driven asynchronous network distributed parameter estimation method based on M estimation, the steps of which are: A. Building a distributed measurement model Establish a distributed network system with N nodes. At the i-th node, use the M-dimensional input signal u at the current n-th moment i (n)=[u i (n),u i (n-1),...,u i (n-M+1)] T , the M-dimensional unknown parameter vector w to be estimated o =[w1,w2,...,w M ] T , actual measurement information where v i (n) represents the additive noise with a mean of 0; B. Calculating local errors Let w i (n)=[w i,1 (n),w i,2 (n),...,w i,M (n)] T For each node pair parameter w o For each node, the local error can be calculated: Construction of C and M estimation cost function Using the M estimation function as the cost function, the optimization problem is described as: Where E{·} represents the mathematical expectation; M estimates the function ψ(e i (n)) is a piecewise continuous function, expressed as: where ξ i =κσ e,i (n) is the threshold parameter, constant κ = 2.576; Represents the error signal e i The estimated variance of (n) is calculated as follows: Among them, 0<τ<1 is the forgetting factor, τ e is the correlation factor, med(·) represents the mathematical median operation, 5≤M e ≤9 represents the number of windows, setting τ=0.99, τ e =1.483[1+5 / (M e -1)]; ψ(e i (n)) to e i (n) Taking the partial derivative we get: D. Set random step size To describe the uncertainty of nodes in asynchronous networks, the step size is described by the following distribution: where μ i (n) = 0 means that node i fails at time n, p i Indicates the probability that a node in the network is working properly; E. Adaptive Update of Intermediate Estimates Use the stochastic gradient method to update the intermediate estimate, and the update rule is: F. Set up event-driven mechanism Define event-driven conditions as: where δ i (n) represents the event occurrence threshold; Prior error Indicates the intermediate estimate h of the node at the current moment i (n+1) and the last information transmission estimate When the event driving condition is met, the information exchange between nodes is triggered and Otherwise, no information exchange occurs between nodes and G. Set random combination coefficient To describe the uncertainty of connections between nodes in an asynchronous network, the combination coefficient is described by the following distribution: where a j,i (n) = 0 means that the connection between node i and node j fails at time n, q j,i Indicates the probability that the connection between nodes in the network is working properly; In addition, set the node's own combination coefficient to: H. Aggregation After updating the intermediate estimate, each node aggregates and obtains a new collaborative estimate: I. Iteration Repeat steps A to H until the distributed parameter estimation is completed.

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