A partially event-triggered distributed adaptive bernoulli filter method

Abstract

The application discloses a kind of partial event triggered distributed adaptive Bernoulli filtering method, it is related to sensor target tracking field.Each sensor node performs adaptive Bernoulli filtering locally, and obtains local Bernoulli posterior.Edge is carried out to node local measurement noise variable, and event trigger discrimination is constructed based on public global variable. By calculating the symmetric Kullback-Leibler divergence between current posterior and reference Bernoulli density, the difference between current information and shared information is measured.According to the size relationship between reference target existence probability and preset target existence threshold, event trigger discrimination is divided into empty set situation and single-element set situation. Partial trigger mode is used for information transmission for single-element set situation. In the distributed fusion stage, flooding communication protocol and geometric mean fusion strategy are used.The application can consider communication burden, computational complexity and tracking accuracy, effectively reduce average trigger rate and communication burden.

Description

Technical Field

[0001] This invention relates to the field of sensor target tracking, and more particularly to a distributed adaptive Bernoulli filtering method triggered by partial events. Background Technology

[0002] Distributed sensor networks (DSNs) possess excellent scalability and robustness, and have been widely applied in scenarios such as area surveillance, unmanned systems, autonomous driving, the Internet of Things (IoT), and collaborative sensing. In distributed target tracking tasks, each sensor node typically first independently obtains a target state estimate using local measurements, then shares the estimate information through inter-node communication, and fuses information from other nodes to obtain a more accurate and consistent global estimation result.

[0003] However, frequent transmission of complete posterior information between nodes can lead to communication channel congestion and increased energy consumption, especially in wireless sensor networks and battery-powered nodes. Event-triggered communication mechanisms, by transmitting only when the estimated information changes significantly, can reduce the frequency of communication of low-information-gain data, and are an important means of reducing the communication burden of distributed estimation.

[0004] In real-world target tracking environments, clutter, false alarms, and missed detections are common. In these situations, compared to triggering mechanisms based on measurements or state estimates, event-triggered mechanisms based on posterior distributions can retain more information such as the probability of target presence and state uncertainty, making them more suitable for target tracking within a stochastic finite set framework. Bernoulli stochastic finite sets can simultaneously describe both the empty set case ("target does not exist") and the single-element set case ("a single target exists"), making them an effective tool for modeling single targets in cluttered and missed detection environments.

[0005] Existing event-triggered Bernoulli filtering methods often assume that the detection probability, process noise covariance, and measurement noise covariance are known or fixed. In practical applications, these parameters are often unknown, time-varying, or vary from node to node. Adaptive Bernoulli filtering can incorporate the target motion state, target features related to the detection probability, process uncertainty, and measurement noise uncertainty into the augmented state for estimation, but its posterior distribution contains more unknown variables, leading to a significant increase in the amount of information that needs to be transmitted and fused.

[0006] Meanwhile, the spatial probability density of adaptive Bernoulli filtering is often characterized by a Gaussian-inverse Gamma-inverse Wishart Mixture (GIGIWM) distribution. Calculating the information difference between the posterior and the reference posterior for the complete mixture distribution typically requires a Monte Carlo approximation, which incurs high computational costs and increases real-time processing pressure on distributed nodes.

[0007] Therefore, those skilled in the art are dedicated to developing a partially event-triggered distributed adaptive Bernoulli filtering method that can balance communication burden, computational complexity, and tracking accuracy. Summary of the Invention

[0008] In view of the above-mentioned deficiencies of the prior art, the technical problem to be solved by the present invention is how to reduce the amount of communication between nodes and reduce the computational burden in the event triggering discrimination and distributed fusion process while ensuring target tracking performance in a distributed sensor network with clutter, missed detection and uncertain parameters.

[0009] To achieve the above objectives, the present invention provides a partially event-triggered distributed adaptive Bernoulli filtering method, which includes an event-triggered distributed adaptive Bernoulli filtering method, using the symmetric Kullback-Leibler divergence between the current Bernoulli posterior and the reference Bernoulli density predicted by the most recently transmitted posterior as an information difference measure, and setting triggering conditions for the empty set case and the single-element set case respectively.

[0010] Furthermore, each node propagates the posterior only when the information difference between the current posterior and the reference posterior exceeds a threshold; when the probability of the reference target's existence is not higher than the target's existence threshold, the empty set difference term is used for discrimination, and when the probability of the reference target's existence is higher than the target's existence threshold, the single-element set difference term is used for discrimination, so that the triggering rule is consistent with the Bernoulli random finite set structure.

[0011] Furthermore, including a partial event triggering mechanism, only the possible mixed components of the target with weights greater than a threshold in the spatial probability density are retained, and the corresponding reference density is constructed by selecting the component with the largest weight from the reference spatial probability density.

[0012] Furthermore, the possible components of the target are paired with the reference maximum weight component, and the information difference between the GIGIWM mixed distributions is transformed into a weighted sum of the Kullback-Leibler divergences between the Gaussian distribution, the inverse Gamma distribution, and the inverse Wishart distribution, forming a closed event triggering criterion.

[0013] Furthermore, the augmented state is decomposed into common global variables and node local variables, and the node local measurement noise covariance is marginalized, with only the posterior of the common global variables being transmitted and fused.

[0014] Furthermore, the common global variables include the target motion state, the target features related to the detection probability, and the prediction error covariance.

[0015] Furthermore, after obtaining the augmented state posterior through local adaptive Bernoulli filtering, the node local variables are integrated and marginalized to form a Bernoulli posterior only with respect to the common global variables; after fusion, the common global variable posterior and the local variables of this node are reconstructed into a local fused posterior.

[0016] Furthermore, based on the flooding communication protocol and the geometric mean fusion strategy, the current posterior prediction results of triggered nodes and the reference posterior prediction results of untriggered nodes are fused respectively, and different posterior quality indicators and fusion weights are designed for the empty set case and the single-element set case.

[0017] Furthermore, in each flooding step, the node divides the newly received information into a triggered set and a non-triggered set; in the case of a single-element set, the quality index is determined by the target state covariance and posterior timeliness, and in the case of an empty set, the quality index is determined by the detection probability confidence and posterior timeliness. Then, the weights are normalized and geometric mean fusion is performed.

[0018] Furthermore, each sensor node performs adaptive Bernoulli filtering locally, combining the target motion state, target detection features, prediction error covariance, and node measurement noise covariance into an augmented state to obtain the local Bernoulli posterior. Local measurement noise variables at nodes are marginalized, and only common global variables consisting of target motion state, detection features and prediction error covariance are retained. Event trigger discrimination is constructed based on common global variables. The reference Bernoulli density is obtained from the node's most recently transmitted posterior prediction up to the current time. The difference between the current information and the shared information is measured by calculating the symmetric Kullback-Leibler divergence between the current posterior and the reference density. Based on the relationship between the probability of the reference target's existence and the preset threshold for the existence of the target, the event triggering judgment is divided into the empty set case and the single-element set case. In the empty set case, the triggering condition is set only based on the difference in the probability of the target not existing. In the single-element set case, the triggering condition is set based on the joint difference in the probability of the target's existence and the probability density of the common global variable space. Filter possible mixed components of the target in the spatial probability density with weights greater than a threshold; select the largest weighted component from the reference spatial probability density to construct a reference spatial probability density corresponding to the number and weight of possible mixed components of the target; convert the difference in mixed distribution information into a weighted sum of the divergences of Gaussian, inverse Gamma, and inverse Wishart distributions Kullback-Leibler, and obtain the closed event triggering criterion; In the distributed fusion phase, a flooding communication protocol and a geometric mean fusion strategy are adopted. For triggered nodes, the current posterior is fused; for untriggered nodes, the reference posterior prediction results are fused. The fusion weights are designed according to the empty set and single-element set cases of Bernoulli random finite sets, and are normalized in combination with posterior quality and posterior timeliness.

[0019] When the detection probability, process noise covariance, and measurement noise covariance are unknown or time-varying, the posterior of the distributed adaptive Bernoulli filter includes the target existence probability and a multidimensional spatial probability density. Continuously transmitting the complete posterior between nodes would significantly increase communication burden and energy consumption. This invention constructs an event-triggered distributed adaptive Bernoulli filtering method, using the symmetric Kullback-Leibler divergence between the current Bernoulli posterior and the reference Bernoulli density predicted by the most recently transmitted posterior as an information difference measure, and setting triggering conditions for both the empty set and single-element set cases. In this invention, each node only propagates the posterior when the information difference between the current posterior and the reference posterior exceeds a threshold; when the reference target existence probability is not higher than the target existence threshold, the empty set difference term is used for discrimination; when the reference target existence probability is higher than the target existence threshold, the single-element set difference term is used for discrimination, making the triggering rules consistent with the Bernoulli random finite set structure. This invention avoids transmitting low-value information when the target does not exist or the posterior change is small, reduces the communication frequency and energy consumption between nodes, and retains the posterior description of the target's existence probability, state uncertainty and unknown parameters, thereby maintaining target tracking performance with reduced communication.

[0020] In the case of a single-element set, the spatial probability density is represented by a GIGIMWM mixture distribution containing multiple unknown variables. Completely calculating the Kullback-Leibler divergence between two mixture distributions typically relies on approximate sampling, resulting in high computational complexity and hindering real-time node triggering. This invention proposes a partial event triggering mechanism, retaining only the target's possible mixture components with weights greater than a threshold in the spatial probability density, and constructing a corresponding reference density by selecting the component with the largest weight from the reference spatial probability density. This invention pairs the target's possible components with the reference component with the largest weight, transforming the information difference between GIGIMWM mixture distributions into a weighted sum of the Kullback-Leibler divergences between Gaussian, inverse Gamma, and inverse Wishart distributions, thus forming a closed-form event triggering criterion. This invention reduces Monte Carlo sampling or complex approximation calculations of the complete mixture distribution, lowers the computational overhead of distributed nodes, improves the real-time performance of event triggering, and achieves higher communication and computational efficiency at a certain cost to accuracy.

[0021] The measurement noise covariance of each sensor node is a local variable. If it is directly transmitted and fused along with the augmented state, it will increase the communication dimensionality and may cause node-specific noise information to affect the global target state fusion. This invention decomposes the augmented state into a common global variable C = (target motion state, detection probability-related target features, prediction error covariance) and node local variables R, marginalizing the node local measurement noise covariance and transmitting and fusing only the posterior of the common global variable. After obtaining the augmented state posterior through local adaptive Bernoulli filtering, this invention performs integral marginalization on the node local variable R to form a Bernoulli posterior only about the common global variable; after fusion, the posterior of the common global variable and the local variable of the node are reconstructed into a local fused posterior. This invention reduces the dimensionality of the posterior to be transmitted, reduces unnecessary local parameter exchanges, and retains the adaptive estimation ability of each node for its own measurement noise, making distributed fusion more focused on shared target information.

[0022] Existing distributed fusion methods typically fail to simultaneously consider node triggering, Bernoulli empty set / single-element set differences, posterior quality, and posterior timeliness, potentially leading to low-quality or expired posteriors occupying unreasonable weights in the fusion process. This invention, based on a flooding communication protocol and a geometric mean fusion strategy, fuses the current posterior predictions of triggered nodes and the reference posterior predictions of non-triggered nodes separately, and designs different posterior quality indices and fusion weights for the empty set and single-element set scenarios. In each flooding step, nodes divide newly received information into triggered and non-triggered sets. In the single-element set scenario, the quality index is determined by the target state covariance and posterior timeliness; in the empty set scenario, it is determined by the detection probability reliability and posterior timeliness. The weights are then normalized and geometric mean fusion is performed. This invention provides higher-quality, more timely posteriors with greater weight in the fusion, improving the reliability of the fused posterior. When the number of flooding steps is not less than the network diameter and all nodes are triggered, each node can obtain a consistent fused posterior. Even when not all nodes are triggered, reference posteriors can still participate in the fusion process, reducing communication burden.

[0023] This invention provides a distributed adaptive Bernoulli filter target tracking method based on partial event triggering and geometric mean fusion, and the technical solution adopted is as follows: First, each sensor node performs adaptive Bernoulli filtering locally, combining the target motion state, target detection features, prediction error covariance, and node measurement noise covariance into an augmented state to obtain the local Bernoulli posterior.

[0024] Secondly, since the fusion between nodes only requires the transmission of common global variables related to the target, this invention marginalizes the local measurement noise variables of the nodes, retains only the common global variables composed of the target motion state, detection features and prediction error covariance, and constructs event trigger discrimination based on the common global variables.

[0025] Furthermore, this invention introduces a reference Bernoulli density. This reference Bernoulli density is obtained from the node's most recently transmitted posterior prediction up to the current time. The difference between the current information and the shared information is measured by calculating the symmetric Kullback-Leibler divergence between the current posterior and the reference density.

[0026] Furthermore, this invention categorizes event triggering into an empty set scenario and a single-element set scenario based on the relationship between the probability of the reference target's existence and a preset target existence threshold. In the empty set scenario, the triggering condition is set solely based on the difference in the probability of the target's non-existence; in the single-element set scenario, the triggering condition is set based on the joint difference between the target's existence probability and the probability density of the common global variable space.

[0027] Furthermore, to address the complexity of calculating the differences in complete GIGIMWM distribution information in the case of a single-element set, this invention proposes a partial event triggering mechanism: filtering potential mixed components with weights greater than a threshold in the spatial probability density; selecting the component with the largest weight from the reference spatial probability density to construct a reference spatial probability density corresponding to the number and weight of potential mixed components; and converting the differences in mixed distribution information into a weighted sum of the divergences of Gaussian, inverse Gamma, and inverse Wishart distributions (Kullback-Leibler divergences) to obtain a closed-form event triggering criterion.

[0028] Finally, this invention employs a flooding communication protocol and a geometric mean fusion strategy in the distributed fusion phase. For triggered nodes, their current posterior is fused; for untriggered nodes, their reference posterior prediction results are fused. The fusion weights are designed separately for the empty set / single-element set cases of Bernoulli random finite sets, and normalized by combining posterior quality and posterior timeliness.

[0029] This invention is a software-implementable distributed target tracking method that can be deployed in multi-sensor networks such as radar, sonar, lidar, visual sensors, IoT sensing nodes, unmanned platforms, and area surveillance systems. Each node only needs to have local measurement processing, neighbor communication, and basic matrix operation capabilities, without relying on a central fusion station, making it suitable for point-to-point distributed networks and scenarios with limited communication resources.

[0030] From a technical perspective, this invention can operate under conditions of clutter, missed detection, and uncertain or time-varying detection probabilities, process noise covariance, and measurement noise covariance, making it closer to real-world application environments than traditional event-triggered Bernoulli filtering that assumes fixed parameters. Through the marginalization of common global variables and a partial event-triggered mechanism, both the dimensionality of the information to be transmitted and the computational complexity of triggering discrimination are reduced.

[0031] In terms of performance metrics, compared with the distributed adaptive Bernoulli filter with continuous transmission, the event triggering method of this invention can effectively reduce the average triggering rate and communication burden, and the decrease in tracking accuracy is less than the decrease in communication burden; some event triggering implementations can also obtain closed triggering criteria, which is suitable for node devices that are sensitive to real-time performance and energy consumption.

[0032] From an industrial application perspective, this invention can be embedded as a software module in existing target tracking links of distributed sensing systems, for scenarios with limited communication bandwidth, limited node power supply, or complex detection environments, such as collaborative sensing by unmanned vehicles / drones, border or park security monitoring, distributed surveillance of sea and air targets, and abnormal target tracking in the Industrial Internet of Things. This invention does not require changes to the sensor hardware structure and has good feasibility for engineering implementation and commercialization.

[0033] Compared with the prior art, the present invention has the following obvious substantive features and significant advantages: 1. This invention designs event triggering discrimination conditions for the empty set case and the single-element set case of Bernoulli random finite sets, respectively, which can avoid transmitting low-value posterior when the target does not exist or the information changes little, thereby reducing the communication burden.

[0034] 2. This invention is applicable to target tracking scenarios where the detection probability, process noise covariance, and measurement noise covariance are unknown or time-varying, and can perform distributed target estimation under conditions closer to actual applications.

[0035] 3. The partial event triggering mechanism proposed in this invention only triggers and distinguishes the mixed components with a high probability of target, avoiding a large number of Monte Carlo samples for the complete GIGIWM mixed distribution and reducing the computational overhead of nodes.

[0036] 4. This invention designs fusion weights for single-element set cases and empty set cases respectively, so that the target state estimation accuracy, detection probability reliability and posterior timeliness all participate in the fusion weight allocation, thereby improving the quality of fusion results.

[0037] 5. This invention combines a flooding protocol to achieve distributed multi-node fusion. When the number of flooding steps is not less than the network diameter and all nodes are triggered, each node can obtain a consistent fusion post-test.

[0038] The following will further explain the concept, specific structure, and technical effects of the present invention in conjunction with the accompanying drawings, so as to fully understand the purpose, features, and effects of the present invention. Attached Figure Description

[0039] Figure 1 This is a flowchart of a preferred embodiment of the distributed adaptive Bernoulli filter target tracking method of the present invention. Figure 2This is a flowchart of an event triggering discrimination method based on the empty set case and the single-element set case, which is a preferred embodiment of the present invention. Figure 3 This is a flowchart of a partial event triggering mechanism of a preferred embodiment of the present invention; Figure 4 This is a flowchart of an event-triggered distributed fusion process based on a flooding protocol, according to a preferred embodiment of the present invention. Figure 5 This is a flowchart of the reconstruction of fused public global variables and node local variables according to a preferred embodiment of the present invention. Detailed Implementation

[0040] The following description, with reference to the accompanying drawings, illustrates several preferred embodiments of the present invention to make its technical content clearer and easier to understand. The present invention can be embodied in many different forms, and the scope of protection of the present invention is not limited to the embodiments mentioned herein.

[0041] In the accompanying drawings, components with the same structure are indicated by the same numerical designation, and components with similar structures or functions are indicated by similar numerical designations. The dimensions and thicknesses of each component shown in the drawings are arbitrary, and the present invention does not limit the dimensions and thicknesses of each component. To make the illustrations clearer, the thickness of some components has been appropriately exaggerated in the drawings.

[0042] Example 1: System Modeling and Local Adaptive Bernoulli Filtering

[0043] Consider including A distributed sensor network of 12 sensor nodes, each node possessing local measurement, information processing, and neighbor communication capabilities. For targets within the monitoring area, the 12th sensor node... Each sensor node at time The equations of motion and measurement can be expressed as:

[0044] in, Here is the state transition matrix. For the first Measurement matrix of each node For process noise, For measuring noise.

[0045] Under conditions of clutter and missed detections, the target state is modeled using a Bernoulli random finite set. The augmented state of each node is:

[0046] in, For the target motion state, For target features related to detection probability, To predict the error covariance, For the first Measurement noise covariance of each node.

[0047] No. A Bernoulli random finite set of nodes The Bernoulli posterior density is:

[0048] in, Let represent the probability that the target exists at node i at time k. Let be the spatial probability density.

[0049] Spatial probability density is represented by the GIGIBIM mixture distribution:

[0050] in, For the first The weights of the mixed components, The number of mixed components. , and Let represent the probability density functions of Gaussian, inverse Gamma, and inverse Wishart distributions, respectively, with each weight being non-negative and satisfying the normalization condition.

[0051] Example 2: Marginalization of Public Global Variables

[0052] Since different nodes do not need to transmit their own node-specific measurement noise variables when fusing target states, In this embodiment, the augmented state is decomposed into common global variables and node local variables:

[0053] right After being marginalized, the first Each node yields its Bernoulli density with respect to a common global variable:

[0054] The probability density of the common global variable space can be expressed as:

[0055] Example 3: Event Triggering Determination Method

[0056] No. Each node at time... A reference Bernoulli density is provided. This reference density is predicted from the node's most recently transmitted posterior density and is used to characterize information about this node that is known or inferred by other nodes. For example... Figure 2 As shown.

[0057] To determine whether a transmission is needed in the current posterior dimension, this embodiment calculates the current Bernoulli density. Compared with reference Bernoulli density Symmetric Kullback-Leibler divergence between:

[0058] in, express and Kullback-Leibler divergence between them.

[0059] Based on the structure of Bernoulli random finite sets, this symmetric divergence is decomposed into an empty set difference term and a single-element set difference term:

[0060] The empty set difference term is defined as:

[0061] The difference term for a single element set is defined as:

[0062] Set a threshold for the probability of the target existing. When the reference exists, the probability is... When, it is considered that the current discrimination is in the case of an empty set; when At this time, it is considered that the current judgment is in the case of a single-element set. The event trigger condition is:

[0063] If one of the above conditions is met, then the first Each node broadcasts the current public global variable posterior to its neighboring nodes. And update the current posterior to the new reference posterior; if the above conditions are not met, then the first... One node does not broadcast its current posterior, while other nodes use the reference posterior obtained from the most recent received posterior prediction of that node up to the current time when merging.

[0064] Example 4: Implementation of Full Event Triggering

[0065] In the full event triggering implementation, the single-element set difference item and Calculations are based on the complete GIGIWM mixture distribution. Since there is usually no direct closed Kullback-Leibler divergence expression between GIGIWM mixture distributions, the Monte Carlo approximation can be used.

[0066] by For example, from Extraction Individual samples , And calculate:

[0067] Full event triggering utilizes the complete spatial probability density for discrimination, resulting in high accuracy, but it incurs high computational overhead when the number of samples is large.

[0068] Example 5: Partial Event Triggering Mechanism

[0069] To reduce the computational overhead of the Monte Carlo approximation in the full event triggering implementation, this embodiment provides a partial event triggering mechanism. This mechanism utilizes the high-weighted mixed component in the spatial probability density that best represents the target for event triggering discrimination. For example... Figure 3 As shown.

[0070] The first step is to preserve the target components. Set weight thresholds. Preservation space probability density The mixed components with a weight greater than this threshold are selected. Assume the number of mixed components retained is... Then we obtain the spatial probability density of the possible components of the reconstructed target:

[0071] in, These are the retained mixed component weights. In practice, the original mixed component weights can be used directly, or the retained weights can be normalized. The probability of existence corresponding to the spatial probability density of the possible components of the target is its value and Consistent.

[0072] The second step is to construct the reference spatial probability density. From the reference spatial probability density obtained from the most recent posterior prediction to the current time step, the element with the largest weight is selected. The first component is a mixture. The marginal distributions of each variable in the mixture component construct the reference space probability density:

[0073] The reference spatial probability density has the same number and weight of mixed components as the retained partial spatial probability density, which facilitates component matching calculation.

[0074] The third step is to calculate the closed-form event triggering criterion. Based on the above construction, the difference term for the single-element set under partial event triggering is:

[0075] The Kullback-Leibler divergence between Gaussian distributions can be calculated using the following closed-form formula:

[0076] in, Let be the state dimension. and The first The mean and covariance of each Gaussian component.

[0077] The Kullback-Leibler divergence between inverse Gamma distributions can be calculated using the following closed-form formula:

[0078] in, For the Gamma function, For the digamma function.

[0079] The Kullback-Leibler divergence between inverse Wishart distributions can be calculated using the following closed formula:

[0080] in, Represents the determinant of a matrix. Represents the trace of a matrix. for dimensional Gamma function, for The dimensional digamma function.

[0081] Through the above steps, the partial event-triggered mechanism converts the calculation of information differences between the complete GIGIMWM mixture distributions into a weighted sum of the differences in Gaussian, inverse Gamma, and inverse Wishart edge distributions in each retained mixture component, avoiding a large amount of sampling and making it suitable for real-time execution on resource-constrained sensor nodes.

[0082] Example 6: Event-triggered distributed fusion based on flooding protocol and geometric mean

[0083] like Figure 4As shown, after each node completes the local event trigger determination, this embodiment uses a flooding protocol for distributed information fusion. In each flooding step, nodes The set of nodes that have newly received information is denoted as . The set of nodes whose events have been triggered is denoted as . The set of nodes that have not been triggered is denoted as ,and:

[0084] for ,node Use nodes The posterior broadcast at the current moment ;for ,node Use the most recent receiving node The posterior and the reference posterior obtained by predicting up to the current time. The geometric mean fusion is obtained by solving the following equation:

[0085] The solution is:

[0086] Regarding Bernoulli density, this embodiment sets weights for the empty set case and the single-element set case respectively:

[0087] In the A flooding step, node The fusion space probability density is updated as follows:

[0088] The probability of the existence of the fusion target is updated by the following formula:

[0089] in,

[0090] In the above formula and Determine based on trigger status:

[0091] in, and From node The posterior of the current broadcast trigger, and From node For nodes The most recent received posterior prediction to the reference posterior at the current time.

[0092] Example 7: Fusion Weight Design

[0093] This embodiment designs the fusion weights for both the single-element set and empty set cases. For the single-element set case, if the node... The state covariance corresponding to the largest weighted mixed component in the posterior is The smaller the uncertainty of the state, the higher the posterior quality. Considering the timeliness of the posterior, a quality index for a single-element set is defined as follows:

[0094] For the case of an empty set, if the node The higher the detection probability of a target, the more reliable the judgment that the target does not exist. Considering posterior timeliness, an empty set quality index is defined:

[0095] in, Forgetting factor, ; For nodes The time difference between the posterior generation time and the current time. The larger the time difference, the better. The smaller the value, the less weight is needed to prevent stale posterior references of untriggered nodes from having an excessively high weight in the fusion process. Let:

[0096] Then for , No. The fusion weights in each flooding step are:

[0097] The above weights satisfy the normalization condition, so that the cumulative posterior that has been integrated in the previous flooding step participates in the current flooding step integration as a whole, and the weights of newly arrived nodes are assigned according to their quality indicators.

[0098] Example 8: Algorithm Flow

[0099] The event-triggered distributed adaptive Bernoulli filter target tracking method provided by this invention can be executed according to the following steps. For example... Figure 1 As shown.

[0100] Step 1: Each node inputs the local posterior from the previous time step. and reference posterior .

[0101] Step 2: Each node performs adaptive Bernoulli filtering prediction and update based on local measurements to obtain the current local posterior. .

[0102] Step 3: Local variables of nodes Marginalization is performed to obtain information about the common global variables. posterior .

[0103] Step 4: Refer to the posterior Predicting up to the current moment, we get .

[0104] Step 5: If Calculate the difference term of the empty set Otherwise, calculate the difference term for the single-element set. .

[0105] Step 6: If the difference term of the empty set is greater than Or the difference term of a single element set is greater than If the node triggers and broadcasts the current public global variable posterior to its neighbors, it sets the current posterior as the new reference posterior; otherwise, the node does not broadcast and approximates the current posterior with the prediction result of the reference posterior in subsequent fusion.

[0106] Step 7: [Regarding...] In the flooding step, a node receives information from its neighbors, distinguishes between the set of triggered nodes and the set of non-triggered nodes, and calculates the fusion weight based on the quality index of the empty set / single-element set.

[0107] Step 8: In each flooding step, the nodes update the fused spatial probability density and the target presence probability using geometric mean fusion.

[0108] Step 9: Complete After each flooding step, the nodes obtain the a posteriori of the merged public global variables.

[0109] Step 10: The node reconstructs the fused common global variable posterior with the local measurement noise variable of its own node to obtain the local fused posterior usable in the next filtering cycle. For example... Figure 5 As shown.

[0110] Example 9: Parameter Setting Method

[0111] In practical applications The settings can be configured based on the target existence determination requirements. If the system wants to more conservatively confirm the target's existence, the settings can be improved. If the system wants to enter the single-element set discrimination earlier, it can reduce... .

[0112] Empty set trigger threshold This value controls the communication frequency when the target is not present. The smaller the value, the easier it is for the node to trigger when the probability of the target's presence changes little; the larger the value, the lower the communication frequency.

[0113] Single-element set trigger threshold This is used to control the communication frequency in the presence of the target. Its value can be set according to the tolerance for state estimation error, the range of detection probability variation, and the range of covariance variation.

[0114] Weight threshold This controls the number of mixed components retained in the partial event triggering mechanism. A higher value means fewer components are retained, resulting in faster computation, but some information may be lost; a lower value means more components are retained, leading to a judgment closer to full event triggering.

[0115] Forgetting factor Used to control the decay rate of old a posteriori during fusion. The closer it is to 1, the slower the historical reference posterior decays; The smaller the value, the faster the weight of old information from untriggered nodes decreases during fusion.

[0116] Flooding Steps It can be set according to network diameter, communication bandwidth, and real-time requirements. When the number of flooding steps is not less than the network diameter and all nodes are triggered, each node can receive information from all network nodes and obtain a consistent geometric mean fusion result.

[0117] Example 10: Technical Effects

[0118] By employing the method of this invention, nodes transmit data only when the current posterior has sufficient information gain relative to the reference posterior, thereby reducing unnecessary communication during the target absence phase and the phase where the posterior changes little.

[0119] By adopting a partial event-triggered mechanism, in the case of a single element set, it is not necessary to perform a large number of Monte Carlo samplings on the complete GIGIMWM mixture distribution. Instead, the discrimination is completed by calculating the possible components of the target and the closed Kullback-Leibler divergence, which can reduce the computational burden on the nodes.

[0120] By adopting a fusion weight that separates the empty set / single-element set, when the target exists, more emphasis is placed on the posterior with lower uncertainty in state estimation and more recent updates; when the target does not exist, more emphasis is placed on the posterior with higher detection probability and more recent updates, thereby improving the credibility of the fusion posterior.

[0121] By employing a flooding protocol, this invention can progressively propagate information in a distributed network without a central node, making it suitable for point-to-point sensor network structures. When communication conditions permit, increasing the number of flooding steps can improve fusion consistency within the network.

[0122] Terms and Symbols

[0123] Bernoulli random finite set: A random finite set used to represent the existence or non-existence of a single objective. When the objective does not exist, the random finite set is empty. When the target exists, the random finite set is a single-element set.

[0124] Adaptive Bernoulli Filter (ABF): A Bernoulli filtering method that incorporates uncertain parameters such as unknown detection probabilities, process noise covariance, and measurement noise covariance into the augmented state, and jointly estimates the target state and related unknown parameters within a Bayesian filtering framework.

[0125] GIGIWM distribution: A Gaussian-inverse Gamma-inverse Wishart mixture distribution used to describe the joint spatial probability density of target motion state, detection features, prediction error covariance, and measurement noise covariance in augmented states.

[0126] Event-triggered communication: A communication method in which a node transmits posterior information only when the information difference between the current posterior and the reference posterior exceeds a threshold.

[0127] Geometric mean fusion: A fusion method obtained by minimizing the weighted Kullback-Leibler divergence between the fused posterior and each posterior to be fused.

[0128] Flooding protocol: A distributed communication protocol in which nodes transmit information that has not yet been broadcast to neighboring nodes in multiple communication steps, so that information in the network is gradually spread to more nodes.

[0129] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A partially event-triggered distributed adaptive Bernoulli filtering method, characterized in that, This includes an event-triggered distributed adaptive Bernoulli filtering method, which uses the symmetric Kullback-Leibler divergence between the current Bernoulli posterior and the reference Bernoulli density predicted by the most recently transmitted posterior as a measure of information difference, and sets trigger conditions for the empty set case and the single-element set case respectively.

2. In the partially event-triggered distributed adaptive Bernoulli filtering method as described in claim 1, each node propagates the posterior only when the information difference between the current posterior and the reference posterior exceeds a threshold; when the probability of the reference target's existence is not higher than the target's existence threshold, the empty set difference term is used for discrimination; when the probability of the reference target's existence is higher than the target's existence threshold, the single-element set difference term is used for discrimination, so that the triggering rule is consistent with the Bernoulli random finite set structure.

3. The partially event-triggered distributed adaptive Bernoulli filtering method as described in claim 1 includes a partially event-triggered mechanism, which retains only the possible mixed components of the target with weights greater than a threshold in the spatial probability density, and selects the component with the largest weight from the reference spatial probability density to construct the corresponding reference density.

4. The distributed adaptive Bernoulli filtering method with partial event triggering as described in claim 3 pairs the possible components of the target with the reference maximum weight component, transforms the information difference between the GIGIMWM mixed distributions into a weighted sum of the Kullback-Leibler divergences between the Gaussian distribution, the inverse Gamma distribution, and the inverse Wishart distribution, and forms a closed event triggering criterion.

5. The partially event-triggered distributed adaptive Bernoulli filtering method as described in claim 1 decomposes the augmented state into common global variables and node local variables, marginalizes the node local measurement noise covariance, and only transmits and fuses the posterior of the common global variables.

6. The distributed adaptive Bernoulli filtering method triggered by partial events as described in claim 5, wherein the common global variables include the target motion state, the target features related to the detection probability, and the prediction error covariance.

7. The distributed adaptive Bernoulli filtering method triggered by partial events as described in claim 5, after obtaining the augmented state posterior through local adaptive Bernoulli filtering, performs integral marginalization on the local variables of the nodes to form a Bernoulli posterior only with respect to the common global variables; after fusion, the posterior of the common global variables and the local variables of the node are reconstructed into a local fused posterior.

8. The partially event-triggered distributed adaptive Bernoulli filtering method as described in claim 1, based on the flooding communication protocol and the geometric mean fusion strategy, fuses the current posterior prediction results of triggered nodes and the reference posterior prediction results of untriggered nodes respectively, and designs different posterior quality indicators and fusion weights for the empty set case and the single-element set case.

9. In the partially event-triggered distributed adaptive Bernoulli filtering method as described in claim 8, in each flooding step, the node divides the newly received information into a triggered set and a non-triggered set; in the case of a single-element set, the quality index is determined by the target state covariance and posterior timeliness; in the case of an empty set, the quality index is determined by the detection probability reliability and posterior timeliness; then the weights are normalized and geometric mean fusion is performed.

10. The distributed adaptive Bernoulli filtering method triggered by partial events as described in claim 1, wherein each sensor node performs adaptive Bernoulli filtering locally, and combines the target motion state, target detection features, prediction error covariance and node measurement noise covariance into an augmented state to obtain the local Bernoulli posterior. Local measurement noise variables at nodes are marginalized, and only common global variables consisting of target motion state, detection features and prediction error covariance are retained. Event trigger discrimination is constructed based on common global variables. The reference Bernoulli density is obtained from the node's most recently transmitted posterior prediction up to the current time. The difference between the current information and the shared information is measured by calculating the symmetric Kullback-Leibler divergence between the current posterior and the reference density. Based on the relationship between the probability of the reference target's existence and the preset threshold for the existence of the target, the event triggering judgment is divided into the empty set case and the single-element set case. In the empty set case, the triggering condition is set only based on the difference in the probability of the target not existing. In the single-element set case, the triggering condition is set based on the joint difference in the probability of the target's existence and the probability density of the common global variable space. Filter possible mixed components of the target in the spatial probability density with weights greater than a threshold; select the largest weighted component from the reference spatial probability density to construct a reference spatial probability density corresponding to the number and weight of possible mixed components of the target; convert the difference in mixed distribution information into a weighted sum of the divergences of Gaussian, inverse Gamma, and inverse Wishart distributions Kullback-Leibler, and obtain the closed event triggering criterion; In the distributed fusion phase, a flooding communication protocol and a geometric mean fusion strategy are adopted. For triggered nodes, the current posterior is fused; for untriggered nodes, the reference posterior prediction results are fused. The fusion weights are designed according to the empty set and single-element set cases of Bernoulli random finite sets, and are normalized in combination with posterior quality and posterior timeliness.

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