Distributed adaptive estimation method based on fusion trigger detection and quantized transmission

Abstract

The distributed adaptive estimation method based on fusion trigger detection and quantized transmission of the present application, nodes do not interact with neighbor nodes at the beginning, only use local information for single point estimation. When the fusion trigger condition is reached, communication with all neighbor nodes and fusion estimation are carried out, thereby reducing the communication times of distributed adaptive estimation. Further, the nodes only send quantized information in the fusion process, thereby reducing the communication data volume.

Description

Technical Field

[0001] This invention relates to the technical field of distributed information processing methods, and in particular to a distributed adaptive estimation method based on fusion-triggered detection and quantized transmission. Background Technology

[0002] Distributed adaptive estimation combines distributed optimization theory and adaptive estimation theory. Nodes estimate the parameter vectors of interest through information exchange with neighboring nodes and local computation. Compared to centralized methods, distributed methods offer advantages in robustness and scalability. Distributed adaptive estimation techniques can be categorized according to their information exchange methods: incremental strategies, consensus strategies, and diffusion strategies. Among these, diffusion strategies offer better stability and are widely used in target cooperative localization and tracking in sensor networks, and formation, path planning, and navigation in unmanned swarms. Traditional diffusion adaptive estimation requires nodes to send their local estimation results to all neighboring nodes at every time step and receive local estimates from all neighboring nodes. By fusing the local estimates from themselves and their neighbors, estimation accuracy can be significantly improved. However, in application scenarios with limited inter-node communication bandwidth or node energy, requiring nodes to exchange estimation information at every time step introduces significant communication overhead. For example,

[0003] 1) Existing methods use information compression to reduce the amount of communication data, but this method requires local implementation of compression and decompression algorithms, which is complex and has low estimation accuracy;

[0004] 2) A probabilistic communication method was adopted, randomly selecting some neighboring nodes for information exchange. This method reduced the number of local communications; however, it failed to effectively utilize all neighboring node information, resulting in low estimation accuracy.

[0005] 3) The method of communication fusion is adopted only at fixed intervals, which reduces the number of communications, but the estimation accuracy of this method is poor. Summary of the Invention

[0006] In view of this, the distributed adaptive estimation method based on fusion-triggered detection and quantization transmission provided by the present invention solves the technical problem of low estimation accuracy of existing calculation methods.

[0007] A distributed adaptive estimation method based on fusion-triggered detection and quantized transmission is disclosed. The distributed system comprises N nodes, which perform distributed adaptive calculations on unknown parameters over time T to determine estimated values. The method includes...

[0008] Step 1: Initialize the time interval to i = 0, j = 0, and begin estimating the estimated value.

[0009] Each node performs initial fusion estimation and local estimation, let w k,0 =0, ψ k,0 =0, where w k,0 and ψ k,0 Let δ represent the initial fusion value and the initial local estimate of the k-th node at initial time 0, respectively, where k = 1, 2, ..., N, and N represents the total number of nodes; k,0 =0 indicates that the initial value of the estimated difference of the k-th node at the initial time 0;

[0010] Fusion indicator vector I k =[I k (1),I k (2),…,I k (j),…I k [(J)] = 0, where J is the preset fusion indicator vector length and f is the fusion trigger flag. k =0 indicates that no fusion is performed at the initial time, and the quantization flag q k,0 =0 indicates that no quantization is performed at the initial time of 0;

[0011] Step 2: The update at time i is represented as i = i + 1, and each node adaptively updates its parameter vector based on the local information at time i to obtain a local estimate. The expression for the local estimate is:

[0012]

[0013] In the formula, ψ k,i Let w be an M×1 dimensional vector representing the local estimate of node k at time i; k,i-1 Let x be an M×1 dimensional vector representing the fusion estimate of node k at time i-1; k,i Let d be an M×1 dimensional vector representing the input autoregressive vector of node k at time i; k,i Let be a real number representing the observation of node k at time i, and T denote the transpose;

[0014] Step 3: If f k =1, jump to fusion step 6; if f k =0, then let w k,i =ψ k,i And calculate the estimated difference with the previous time step, the expression for the estimated difference is,

[0015] δ k,i =λ||w k,i -w k,i-1 || 2 +(1-λ)δ k,i-1

[0016] wherein, λ represents a smoothing factor, 0<λ<1, which is used to perform smooth filtering on the estimated difference value to filter out the influence of noise; ||·|| represents the 2-norm of a vector;

[0017] Step 4: update the time instant as j=j+1, if j>J, then let j=1, update the fusion indication vector I k (j), if δ k,i <Th, then I k (j)=1, otherwise I k (j)=0, wherein Th is a preset difference threshold;

[0018] Step 5: update the fusion trigger identifier, if ||I k ||₁>TH, then f k =1, otherwise f k =0, ||·||₁ is the 1-norm of a vector, which represents the number of non-zero elements in the vector, 0<TH<J is a preset value, jump to step 2 and perform estimation at the next time instant;

[0019] Step 6: perform a fusion step:

[0020] Step 7: if i=T, and T is the total time length, then end the estimation of the estimated value.

[0021] Advantageous Effects

[0022] In this method, nodes do not exchange information with neighboring nodes at the beginning, and only use local information to perform single-point estimation. When the fusion trigger condition is satisfied, the nodes communicate with all neighboring nodes and fuse estimations, thereby reducing the number of communications in distributed adaptive estimation. Further, during fusion, nodes only send quantized information, thereby reducing the amount of communication data. Description of Drawings

[0023] In order to more clearly illustrate the technical solutions of the embodiments of the present disclosure, the accompanying drawings required for the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present disclosure. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative effort.

[0024] as shown in Figure 1 it is a composition diagram of a multi-node distributed system according to an embodiment of the present invention. The distributed system in this embodiment includes 20 nodes, and there is a communication link between each node and its neighboring nodes;

[0025] as shown in Figure 2 it is a flowchart of a distributed adaptive estimation method according to an embodiment of the present invention. Detailed Embodiments

[0026] The embodiments of this disclosure will now be described in detail with reference to the accompanying drawings.

[0027] The following specific examples illustrate the implementation of this disclosure. Those skilled in the art can easily understand other advantages and effects of this disclosure from the content disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of this disclosure, and not all of them. This disclosure can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of this disclosure. It should be noted that, in the absence of conflict, the following embodiments and features in the embodiments can be combined with each other. Based on the embodiments in this disclosure, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this disclosure.

[0028] It should be noted that various aspects of embodiments within the scope of the appended claims are described below. It will be apparent that the aspects described herein can be embodied in a wide variety of forms, and any particular structure and / or function described herein is merely illustrative. Based on this disclosure, those skilled in the art will understand that one aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number of aspects set forth herein can be used to implement the device and / or practice the method. Additionally, this device and / or method can be implemented using other structures and / or functionalities besides one or more of the aspects set forth herein.

[0029] It should also be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of this disclosure. The drawings only show the components related to this disclosure and are not drawn according to the number, shape and size of the components in actual implementation. In actual implementation, the form, quantity and proportion of each component can be arbitrarily changed, and the layout of the components may also be more complex.

[0030] Furthermore, specific details are provided in the following description to facilitate a thorough understanding of the examples. However, those skilled in the art will understand that these aspects can be practiced without these specific details.

[0031] See Figures 1 to 2 The distributed adaptive estimation method based on fusion-triggered detection and quantized transmission shown is suitable for data processing in distributed systems. Preferably, the distributed system is suitable for sensor networks or unmanned swarm systems. The distributed system contains N nodes and performs distributed adaptive calculations on unknown parameters within a time interval T to determine the estimated values. The method includes...

[0032] Step 1: Initialize the time interval to i = 0, j = 0, and begin estimating the estimated value.

[0033] Each node performs initial fusion estimation and local estimation, at the initial time i=0, j=

[0034] 0, let w k,0 =0, ψ k,0 =0, where w k,0 and ψ k,0 Let δ represent the initial fusion value and the initial local estimate of the k-th node at initial time 0, respectively, where k = 1, 2, ..., N, and N represents the total number of nodes; k,0 =0 indicates that the initial value of the estimated difference of the k-th node at the initial time 0;

[0035] Fusion indicator vector I k =[I k (1),I k (2),…,I k (j),…I k [(J)] = 0, where J is the preset fusion indicator vector length and f is the fusion trigger flag. k =0 indicates that no fusion is performed at the initial time, and the quantization flag q k,0 =0 indicates that no quantization is performed at the initial time of 0;

[0036] Step 2: The update at time i is represented as i = i + 1, and each node adaptively updates its parameter vector based on the local information at time i to obtain a local estimate. The expression for the local estimate is:

[0037]

[0038] In the formula, ψ k,i Let w be an M×1 dimensional vector representing the local estimate of node k at time i; k,i-1 Let x be an M×1 dimensional vector representing the fusion estimate of node k at time i-1; k,i Let d be an M×1 dimensional vector representing the input autoregressive vector of node k at time i; k,i Let be a real number representing the observation of node k at time i, and T denote the transpose;

[0039] Step 3: If f k =1, jump to fusion step 6; if f k =0, then let w k,i =ψ k,i And calculate the difference between the estimate and the previous time step (i.e., the difference between the estimate at time "i" and the estimate at time "i-1"). The expression for the difference is:

[0040] δ k,i =λ||w k,i -wk,i-1 || 2 +(1-λ)δ k,i-1

[0041] wherein λ represents a smoothing factor, 0<λ<1, which is used for performing smoothing filtering on the estimated difference to filter out the influence of noise; |||| represents the 2-norm of a vector.

[0042] Step 4: update the time step as j=j+1, if j>J, then set j=1, update the fusion indication vector I k (j), if δ k,i <Th, then I k (j)=1, otherwise I k (j)=0, wherein Th is a preset difference threshold;

[0043] Step 5: update the fusion trigger identifier, if ||I k ||₁>TH, then f k =1, otherwise f k =0, ||||₁ is the 1-norm of the vector, which represents the number of non-zero elements in the vector, 0<TH<J is a preset value, then the process jumps to step 2 for estimation at the next moment, it should be noted that: ||I k ||₁>TH indicates that within consecutive J time periods, there are more than TH times that the estimated difference is less than the preset difference threshold, which indicates that the local estimation parameter of the node has converged, then fusion is performed and the process jumps to step 6. The purpose of this is to further improve the estimation accuracy, and a preset larger TH can effectively eliminate the interference of noise;

[0044] Step 6: perform fusion, specifically,

[0045] 6.1) if q k =0, each node sends the local estimation ψ k,i to respective neighbor nodes, and updates the fusion estimation value:

[0046]

[0047] wherein a lk is the fusion coefficient for the estimation obtained by node k from neighbor node l, which satisfies the condition: when l∈N k , a lk >0, otherwise a lk =0, and N k is the set of neighbor nodes of node k;

[0048] node k records the estimation ψ of the neighbor node at the current time l，i as a quantization reference, set the quantization range as [a,b], wherein a=-2ψ l，i , b=2ψ l，i ; and set qk = 1, which is the condition set for quantization at the next moment.

[0049] 6.2) If q k = 1, each node sends the locally estimated bit quantization value q(ψ k,i ) to its respective neighboring nodes (neighboring nodes refer to nodes that can communicate directly, all are regarded as adjacent nodes; preferably, nodes with a direct communication link are taken as neighboring nodes), and update the fusion estimated value:

[0050]

[0051] In the formula, is the quantization value q(ψ of node l k,i ) corresponding estimated value,

[0052] Step 7: If i = T, where T is the total time length, end the estimation of the estimated value; specifically,

[0053] 7.1) If i < T and w k,i ∈ (a,b), jump to step 2;

[0054] 7.2) If i < T and w k,i = a or w k,i = b, it indicates that the parameter to be estimated has changed greatly and quantization overflow has occurred. It is necessary to re-perform single-point adaptive update and update the quantization range to avoid a large estimation deviation. Then, let f k = 0, q k = 0, and then jump to step 2.

[0055] The method can reduce the communication overhead of distributed adaptive estimation. In this method, nodes do not exchange information with neighboring nodes in the initial stage, and only use local information for single-point estimation. This is because the local estimation results of each node have not converged in the initial stage, and fusion at this time cannot effectively improve the estimation accuracy. When the fusion trigger condition is reached, the nodes communicate with all neighboring nodes and fuse the estimation to improve the estimation accuracy, thereby reducing the number of communications in distributed adaptive estimation. Further, in the fusion process, nodes only send quantized information, thereby reducing the amount of communication data. In quantization, a difficulty lies in the selection of the quantization range, and the estimated value of the unknown parameter may exceed the quantization range and cause overflow. In this solution, when the fusion condition is reached, the node already has a preliminary relatively accurate estimation locally. Selecting the quantization range on this basis can effectively avoid the risk of overflow, and this solution provides a mechanism for re-selecting the quantization range, whose advantages are:

[0056] (1) A fusion trigger detection mechanism is provided to determine whether the estimation in the adaptive stage has converged, avoiding the situation that communication fusion at this time provides limited help for improving estimation accuracy;

[0057] (2) The difference detection of the fusion trigger mechanism adopts a smoothing process and a long-term statistical strategy to avoid noise influence and cause incorrect judgment;

[0058] (3) Provide a quantization range selection strategy for unknown estimates and provide a mechanism for reselecting the range under time-varying parameters.

[0059] For example, a distributed system consists of 20 nodes, and each node has communication links with its neighboring nodes. Figure 2 As shown, in this embodiment, time is T, and the method is as follows:

[0060] Step 1: Initialize the estimated values ​​at time i = 0, j = 0; initialize the fusion estimate w at each node. k,0 =0, local estimate ψ k,0 =0, where w k,0 and ψ k,0 Let δ represent the initial fusion value and the initial local estimate of the k-th node at initial time 0, respectively, where k = 1, 2, ..., N, and N represents the total number of nodes; k,0 =0 indicates the initial value of the estimated difference of the k-th node at initial time 0; fusion indicator vector I k =[I k (1),I k (2),…,I k (j),…I k [(J)] = 0, where J is the preset fusion indicator vector length; fusion trigger flag f k =0 indicates that no fusion is performed at the initial time, and the quantization flag q k,0 =0 indicates that no quantization is performed at the initial time of 0.

[0061] Step 2: Adaptive step, updating i = i + 1 at every moment, each node adaptively updates the local estimated value of the parameter vector based on local information:

[0062]

[0063] In the formula, ψ k,i Let w be an M×1 dimensional vector representing the local estimate of node k at time i; k,i-1 Let x be an M×1 dimensional vector representing the fusion estimate of node k at time i-1; k,i Let d be an M×1 dimensional vector representing the input autoregressive vector of node k at time i; k,i Let be a real number, representing the observation of node k at time i; This indicates transpose.

[0064] Step 3: If f k =1, jump to fusion step 6. If fk = 0, let w k,ii = ψ k,i , calculate the estimated difference from the previous moment:

[0065] δ k,i = λ||w k,i -w k,i-1 || 2 +(1-λ)δ k,i-1

[0066] where 0<λ<1 represents a smoothing factor, which is used to perform smooth filtering on the estimated difference to filter out the influence of noise; ||·|| represents the 2-norm of a vector.

[0067] Step 4: time update j = j+1, if j>J, then j = 1; update the fusion indication vector I k (j), if δ k,i < Th, then I k (j) = 1, otherwise I k (j) = 0, where Th is a preset difference threshold.

[0068] Step 5: update the fusion trigger identifier, if ||I k ||₁>TH, then f k = 1, otherwise f k = 0, ||·||₁ is the 1-norm of a vector, which represents the number of non-zero elements in the vector, 0<TH<J is a preset value. ||I k ||₁>TH indicates that within consecutive J time periods, the number of estimated differences smaller than the preset difference threshold is greater than TH, which means that the local estimation parameters of the node have converged, and fusion can be performed to further improve the estimation accuracy. Setting a large preset TH can eliminate the interference of noise. After updating the fusion trigger identifier, jump back to Step 2.

[0069] Step 6: Fusion step:

[0070] If q k = 0, each node sends the local estimation ψ k,i to its respective neighbor nodes, and update the fusion estimation value:

[0071]

[0072] where a lk is the fusion coefficient of the estimation of neighbor node l by node k, which satisfies the condition: when l∈N k , a lk > 0, otherwise a lk = 0, and N k is the set of neighbor nodes of node k. Node k records the estimation ψ of neighbor nodes at this time l，iAs a quantitative reference, let the quantization range be [a,b], where a=-2ψ l，i , b=2ψ l，i ; and let q k =1, which sets a condition for quantization at the next moment.

[0073] If q k =1, each node transmits the locally estimated bit quantization value q(ψ k,i ) to its respective neighbor nodes, and updates the fused estimation value:

[0074]

[0075] wherein is the estimated value corresponding to the quantization value q(ψ k,i ) of node l.

[0076] Step 7: if i=T, where T is the total time length, the estimation ends; if i<T and w k,i ∈(a,b), jump back to step 2; if i<T and w k,i =a or w k,i =b, it indicates that the parameter to be estimated has changed greatly and quantization overflow occurs. Single-point adaptive update and quantization range update need to be performed again, let f k =0, q k =0, and jump back to step 2.

[0077] The above is only specific implementations of the present disclosure. The protection scope of the present disclosure is not limited thereto. Any change or replacement that can be easily conceived by a person skilled in the art within the technical scope disclosed in the present disclosure shall be covered by the protection scope of the present disclosure. Therefore, the protection scope of the present disclosure shall be subject to the protection scope of the claims.

Claims

1. A distributed adaptive estimation method based on fusion-triggered detection and quantized transmission, applicable to data processing in distributed systems, characterized in that, The distributed system comprises N nodes, which perform distributed adaptive computation on unknown parameters over time T to determine estimated values. The methods include... Step 1: Initialize the time interval to i = 0, j = 0, and begin estimating the estimated value. Each node performs initial fusion estimation and local estimation, let w k,0 =0, ψ k,0 =0, where w k,0 and ψ k,0 Let δ represent the initial fusion value and the initial local estimate of the k-th node at initial time 0, respectively, where k = 1, 2, ..., N, and N represents the total number of nodes; k,0 =0 indicates that the initial value of the estimated difference of the k-th node at the initial time 0; Fusion indicator vector I k =[I k (1),I k (2),…,I k (j),…I k [(J)] = 0, where J is the preset fusion indicator vector length and f is the fusion trigger flag. k =0 indicates that no fusion is performed at the initial time, and the quantization flag q k,0 =0 indicates that no quantization is performed at the initial time of 0; Step 2: The update at time i is represented as i = i + 1, and each node adaptively updates its parameter vector based on the local information at time i to obtain a local estimate. The expression for the local estimate is: In the formula, ψ k,i Let w be an M×1 dimensional vector representing the local estimate of node k at time i; k,i-1 Let x be an M×1 dimensional vector representing the fusion estimate of node k at time i-1; k,i Let d be an M×1 dimensional vector representing the input autoregressive vector of node k at time i; k,i Let be a real number representing the observation of node k at time i, and T denote the transpose; Step 3: If f k =1, jump to fusion step 6; if f k =0, then let w k,i =ψ k,i And calculate the estimated difference with the previous time step, the expression for the estimated difference is, d k,i =λ||w k,i -w k,i-1 || 2 +(1-λ)δ k,i-1 In the formula, λ represents the smoothing factor, and 0 < λ < 1, which is used to smooth the estimated difference to filter out the influence of noise; |||| represents the 2-norm of the vector; Step 4: Update constantly denoted as j=j+1, if j>J, then let j=1, and update the fusion indication vector I k (j), if δ k,i <Th, then I k (j)=1, otherwise I k (j)=0, wherein Th is a preset difference threshold; Step 5: Update the fusion trigger flag, if ||I k ||1>TH, then f k = 1, otherwise f k = 0, ||·||1 is the 1-norm of a vector, which represents the number of non-zero elements in the vector, 0<TH<J is a preset value, skip to step 2, and perform estimation at the next moment; Step 6: Perform the fusion; Step 7: If i = T, where T is the total time length, then the estimation of the estimated value ends.

2. The distributed adaptive estimation method according to claim 1, characterized in that, The fusion process includes, If q k =0, each node sends its local estimate ψ k,i Update the fusion estimate to each of its neighboring nodes: In the formula, a lk Let be the fusion coefficient of node k for its estimated neighboring node l, which satisfies the condition: when l∈N k At that time, a lk >0, otherwise a lk =0, and N k Let k be the set of its neighboring nodes; Node k records the estimated ψ of its neighboring nodes at this moment. l,i As a quantization reference, let the quantization range be [a, b], where a = -2ψ l,i b = 2ψ l,i And let q k =1, serving as the condition for quantization at the next moment.

3. The distributed adaptive estimation method according to claim 2, characterized in that, The fusion process also includes, If q k =1, each node sends its locally estimated bit quantization value q(ψ) k,i Reach each neighboring node and update the fusion estimate: In the formula, The quantization value q(ψ) for node l k,i The corresponding estimated value.

4. The distributed adaptive estimation method according to claim 3, characterized in that, The estimation of the estimated value is complete, including, If i<T and w k,i ∈(a,b), proceed to step 2.

5. The distributed adaptive estimation method according to claim 4, characterized in that, The estimation of the estimated value is complete, and it also includes, If i<T and w k,i =a or w k,i =b, then let f k =0, q k =0, and jump to step 2.

6. The distributed adaptive estimation method according to claim 1, characterized in that, The distributed system is suitable for sensor networks or unmanned swarm systems.

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