Multi-sensor fusion estimation method and system based on token bucket traffic shaping mechanism

Abstract

The invention provides a multi-sensor fusion estimation method and system based on a token bucket traffic shaping mechanism, and belongs to the field of multi-sensor control. The problem of scheduling communication resources in existing multi-sensor fusion estimation and the problem of how to process state estimation and censoring measurement of a nonlinear system are solved. According to the method, a new communication protocol is designed, a trace of an upper bound of a local estimation error covariance and a trigger function designed based on a token are combined to serve as a judgment condition for whether transmission measurement is carried out or not, whether a measurement value of each node is transmitted to a local estimator or not is determined, and the characteristic of token traffic shaping is fully exerted; designing a local Tobit Kalman filter gain of each node by minimizing a trace of a filtering error covariance matrix; local estimates from each node are transmitted to a fusion center, global estimates are generated using federated fusion rules, and global estimates with appropriate weights are sent back to each node for prediction at subsequent local filters.

Description

Technical Field

[0001] The present invention relates to the technical field of multi-sensor control, and in particular, to a multi-sensor fusion estimation method and system based on a token bucket traffic shaping mechanism. Background Art

[0002] As is well known, multi-sensor fusion filtering refers to integrating information from different sensors to improve the performance of filtering methods. Generally speaking, multi-sensor fusion can be divided into two categories: centralized and distributed. In the former, the raw data from each sensor is directly transmitted to the fusion center for filtering processing. In contrast, the latter involves the fusion center fusing the available estimates from local filters to generate an optimal or sub-optimal estimate. Although the accuracy of distributed fusion filtering may not be as good as that of centralized fusion, its advantages include reducing the burden on the central processor, lowering the communication bandwidth requirements, and improving the reliability and robustness of the system. These significant advantages have attracted extensive attention to distributed fusion filtering.

[0003] Due to the limited measurement capabilities of low-cost sensors, censored measurements are prevalent in practical engineering. Censored measurements are usually described by the Tobit model, which can effectively handle problems involving censored data and provide estimates of unobserved variables. Since the system measurement noise exhibits non-Gaussian characteristics near the censored region, traditional Kalman filtering methods cannot directly handle it. Allik et al. first designed the Tobit Kalman filter using the Tobit model, in which the one-sided and two-sided Tobit regression models were integrated into the recursive form of the Kalman filter. However, it does not fully explore the useful information contained in the censored region. Currently, a new conditional expectation method has been disclosed in the existing literature to study the Tobit Kalman filtering problem of stochastic parameter systems. Subsequent studies on Tobit Kalman filtering have considered some interesting phenomena, such as dynamic bias and cyclic protocols, channel fading, dynamic event-triggering mechanisms, etc. But the above studies are only limited to linear systems, which obviously does not conform to reality. Most systems in practical engineering are nonlinear, so it is very meaningful to handle the state estimation problem of nonlinear systems in the case of censored measurements.

[0004] Different from traditional automatic control systems, networked systems explicitly consider the limitations of the communication medium between sensors and controllers / filters. Especially when network congestion occurs and requests allocate more than the sustainable transmission rate of the network, these limitations become more obvious, which will have a serious impact on the ideal performance. A well-established paradigm for solving this problem is the event-triggered protocol. The idea of the event-triggered protocol is to reduce the number of transmissions only when the event-triggering condition is met. This protocol can effectively save communication resources. However, this does not guarantee that the transmission network will not be overused, especially when a high transmission rate is required for the desired performance level. In the existing references, the event-triggered protocol is introduced to unilaterally save network bandwidth resources by reducing the number of information transmissions on the premise of a certain performance. However, such a protocol cannot be used in actual engineering scenarios. In a shared network with limited bandwidth, it is difficult to have sufficient bandwidth resources when multiple information transmission requests are encountered. It should be noted that the dynamic changes of communication resources cannot be directly described in the existing results, so the role of the event-triggered protocol cannot be fully reflected. Summary of the Invention

[0005] The technical problem to be solved by the present invention is: To solve the scheduling problem of communication resources in existing multi-sensor fusion estimation, and how to handle the state estimation of non-linear systems and censored measurements.

[0006] The technical solution adopted by the present invention to solve the above technical problems: The present invention provides a multi-sensor fusion estimation method based on a token bucket traffic shaping mechanism, including the following steps: S100. Establish a non-linear networked dynamics model; S200. Establish a bilateral censored measurement model based on the Tobit model; S300. Use the token bucket traffic shaping method to design a trigger function based on the censored measurement model in step S200, and design a communication protocol; S400. Design a filter, and give the prediction of the local estimator and the upper bound of the filtering error covariance; S500. Give the gain matrix of the local estimator; S600. Fuse and estimate the local estimation results at the fusion center using the federated fusion criterion to obtain the final estimated value.

[0007] Further, in step S100, it includes, The moving target considered is described by the following discrete non-linear state space equation: (1) Where, is the state vector; is Gaussian white noise with zero mean and is the process noise; is a matrix with a known appropriate dimension; is a continuously differentiable nonlinear function; (2) The nonlinear part is the drag force acting on the ballistic object during ascent, is a force opposite to the direction of the target velocity, and is also an exponential decay model, i.e.: (3) Among them, the air density function ; is the acceleration due to gravity, is the ballistic coefficient; is the displacement of the object in the horizontal direction, is the horizontal velocity of the object, is the displacement of the object in the vertical direction, is the vertical velocity of the object; Using the following identity: ; Convert Equation (3) into: (4) For and there is:

[0008] The coefficient matrices of each term in Equation (2) are given separately below:

[0009] Among them, is the time interval between radar measurements; Considering the problem of interference on the system, the process noise in Equation (1) is assumed to be Gaussian white noise with zero mean and the variance is ; In order to achieve a more accurate consideration, the following modeling of the process noise aims to cover the potential sudden variables in Equation (2) of the model, as well as various deviations between the model and the actual situation: (5) Among them, is the coefficient related to the process noise; In radar target tracking applications, the collected measurement data includes the distance between the radar and the target and the elevation angle of the radar , the measurement values observed by the radar are subjected to coordinate transformation and converted into a rectangular coordinate system. The specific transformation formula is as follows: ; The observation model is as follows: (6) Wherein, , is Gaussian white measurement noise with zero mean, which is independent of the process noise and has a variance of ; In summary, the nonlinear state space equation after discretization of the ballistic object is: (7) Wherein, is the th observation value at time ; are Gaussian white noises with zero mean respectively, are matrices with known appropriate dimensions respectively.

[0010] Furthermore, in step S200, it includes Establish a bilateral Tobit measurement model: (8) Wherein, , representing the th component in the transmission vector, and is the measurement censoring value, and are the left censoring threshold and the right censoring threshold of node respectively; Based on the Tobit observation model formula (8), define Bernoulli random variables and , and the bilateral censored measurement model of is as follows: (9) (10) Obtain the probability distribution: (11) Wherein, and are known non - negative constants; Assume that and are independent of and the initial system state of the system ; The censoring probabilities and are approximated by the following method: (12) (13) Among them, represents the prediction from node for The prediction of and are respectively and The th element of is the cumulative distribution function of the standard normal distribution; Let:

[0011] Get: (14)

[0012] Furthermore, in step S300, it includes, Use to represent the trigger time series: (15) Among them, is the prediction error covariance, and the trigger function is as follows: (16) Let represent the number of tokens in the current bucket at time , and its initial value is ; The change in the number of tokens in the bucket of each node is as follows: (17) Among them, represents the size of the token bucket, represents the cost of each transmission, represents the rate of token generation in the bucket, represents the balance factor; Under the given parameterization conditions, the dynamic change of the number of tokens inside the trigger function is described as: (18) It can be seen from equation (18) that ; When the number of tokens exceeds the transmission cost , that is, , it means that there are sufficient transmission resources in the communication network at this time, and then update the trigger sequence ; The final measurement transmission model is: (19)

[0013] Further, in step S400, it includes At moment, the filter design for nodes is as follows: (20) Denote and as the prediction error and the estimation error respectively; the prediction error covariance and the filtering error covariance are defined as and ; is the filtering gain to be designed; According to equations (1) and (20), the prediction error is obtained as: (21) Similarly, the estimation error is: (22) Using the Taylor expansion method centered on , the non - linear function is expressed as: (23) where , the high - order term is denoted as , and we get where represents a known scaling matrix related to the motion of the ballistic object; represents a known matrix for adjusting the filter; represents an unknown matrix for describing the linearization error, and ; According to equations (21) and (23), we get: (24) The upper bound of the prediction error covariance is: (25) According to equations (20) to (24), the estimation error is obtained as: (26) where ; The estimation error covariance is: (27) where

[0014]

[0015] Introduce two lemmas to derive the upper bound of the filtering error covariance; Lemma 1. For any two real vectors and , the following inequality holds: , where is a real number greater than zero; Lemma 2. Let be a real matrix, and be a random diagonal matrix. Then:

[0016] where is the Hadamard product; Using the basic inequality in Lemma 1, the upper bound of is calculated as: (28) where ; According to Lemma 2 and Equation (28), it is obtained that: (29) Suppose: is a positive scalar; the upper bound of the filtering error covariance is obtained as: (30) The initial value is , where:

[0017] where are all constants greater than zero.

[0018] Furthermore, in step S500, it also includes

[0019] The trace of in Equation (30) is: (31) Taking the partial derivative of yields: (32) Let Equation (32) be zero to obtain the gain matrix :

[0020] where

[0021] Furthermore, in step S600, given the local estimation error covariance and the local estimation value, the fusion center adopts the federated fusion criterion, including In the first stage, information initialization and distribution are performed, and the initial estimation error covariance of the local filter and the initial process noise matrix are respectively set to the system error covariance and times of the process noise:

[0022] In the second stage, the local filter processes the received observations to update the state estimation:

[0023] In the third stage, the fusion center fuses all the estimation results to obtain the globally optimal fusion estimation:

[0024] In the fourth stage, information reset and distribution are performed. The fusion center distributes the fused result to each local estimator according to times of the weight:

[0025] And then the update time returns to the second stage.

[0026] A multi-sensor fusion estimation system based on the token bucket traffic shaping mechanism. The system has program modules corresponding to the above steps and executes the steps in the above multi-sensor fusion estimation method based on the token bucket traffic shaping mechanism when running.

[0027] A computer-readable storage medium stores a computer program configured to implement the steps of the multi-sensor fusion estimation method based on the token bucket traffic shaping mechanism when called by a processor. Compared with the prior art, the beneficial effects of the present invention are:

[0028] A multi-sensor fusion estimation method based on the token bucket traffic shaping mechanism is invented. A fully distributed fusion method is adopted, reducing the computational burden, lowering the requirements for the central processing unit, and increasing the system reliability; the communication protocol adopts the token bucket design, which reduces the communication burden and increases the estimation accuracy of the local estimator; at the same time, a non-linear system and a bilateral censored measurement model are considered, which better meets the actual engineering needs. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 is a structural block diagram of the multi-sensor fusion estimation method based on the token bucket traffic shaping mechanism in an embodiment of the present invention; Figure 2 is a diagram of the change in the number of tokens before fusion estimation in an embodiment of the present invention; Figure 3Trigger sequence diagram of the number of tokens before fusion estimation in the embodiments of the present invention; Figure 4 State estimation diagram of Node 1 in the embodiments of the present invention; Figure 5 State estimation diagram of Node 2 in the embodiments of the present invention; Figure 6 State estimation diagram of Node 3 in the embodiments of the present invention; Figure 7 Error comparison and analysis diagram of Node 1 before and after fusion in the embodiments of the present invention; Figure 8 Error comparison and analysis diagram of Node 2 before and after fusion in the embodiments of the present invention; Figure 9 Error comparison and analysis diagram of Node 3 before and after fusion in the embodiments of the present invention; Figure 10 Variation diagram of the number of tokens after fusion estimation in the embodiments of the present invention; Figure 11 Trigger sequence diagram of the number of tokens before fusion estimation in the embodiments of the present invention. Detailed implementation manners

[0030] To make the above objects, features and advantages of the present invention more obvious and understandable, the following detailed description of the specific embodiments of the present invention will be given with reference to the accompanying drawings.

[0031] Specific implementation manner 1: The present invention provides a multi-sensor fusion estimation method based on a token bucket traffic shaping mechanism, including the following steps: S100. Establish a non-linear networked dynamics model; specifically including, Before establishing the model, the following assumptions are made: 1) First is the simplification of the acting force: Gravity: Assume that the main force acting on the target is gravity, whose direction is always vertically downward, and the gravitational acceleration is ; Drag: Assume that there is air drag, whose direction is opposite to the direction of the object's motion, and its magnitude is proportional to the square of the velocity, i.e., where is the ballistic coefficient, which depends on the mass, shape and cross-sectional area perpendicular to the direction of motion of the target, and is constant at supersonic speeds specifically; is the air density, is the velocity of the object; 2) Ignore other forces: Centrifugal acceleration: Ignore the centrifugal acceleration caused by the rotation of the earth; Coriolis acceleration: Ignore the Coriolis acceleration caused by the rotation of the earth; Wind: Neglect the influence of wind on the motion of an object; Lift: Neglect the influence of lift on the motion of an object; Rotational motion: Neglect the influence of the object's own rotational motion on the trajectory; 3) Flat Earth assumption: Flat Earth: Assume that the Earth is flat, which is a commonly used approximation in short-range ballistic estimation problems; Under this assumption, a two-dimensional rectangular coordinate system can be used to describe the motion of an object; where: axis: Represents the horizontal displacement of the object; axis: Represents the vertical displacement of the object; Denote as the displacement of the object in the horizontal direction, as the horizontal motion speed of the object, as the vertical displacement of the object, as the motion speed of the object in the vertical direction, thus obtaining

[0032] The moving target under consideration is described by the following discrete nonlinear state space equation:

[0033] where, is the state vector; is Gaussian white noise with zero mean and is the process noise; is a matrix with a known appropriate dimension; is a continuously differentiable nonlinear function; (2) Nonlinear part is the drag force experienced by the ballistic object during ascent, which is a force opposite to the direction of the target velocity and is also an exponential decay model, i.e.: (3) where, the air density function ; is the acceleration due to gravity, is the ballistic coefficient; Using the following identity: ; Convert Equation (3) into: (4) For and there is:

[0034] The coefficient matrices of each term in Equation (2) are given separately below:

[0035] Among them, is the time interval between radar measurements; Next, consider the interference problem of the system. The process noise in Equation (1) is assumed to be zero-mean Gaussian white noise and the variance is ; In order to achieve a more accurate consideration, the following modeling of the process noise aims to cover the potential burst variables in Model (2), as well as various deviations between the model and the actual situation: (5) Among them, is the coefficient related to the process noise; In radar target tracking applications, the collected measurement data includes the distance between the radar and the target and the elevation angle of the radar . Through coordinate transformation of the measurement values observed by the radar, it is converted into a rectangular coordinate system. The specific transformation formula is: After this transformation, the observation equation is in a linear form, which is convenient for subsequent processing and analysis; The observation model is as follows: (6) Among them, , is zero-mean Gaussian white measurement noise, which is independent of the process noise and the variance is ; To sum up, by comprehensively considering various factors and corresponding processing methods, the nonlinear state space equation after discretization of the ballistic object is finally derived, and it is also considered that multiple radars observe the target: (7) Among them, is the state vector, and the nonlinear function is continuously differentiable, is the observation value of the th node at time are respectively zero-mean Gaussian white noises, are respectively matrices with known appropriate dimensions; S200. Establish a bilateral censored measurement model based on the Tobit model, specifically including, According to the Tobit measurement model, the bilateral measurement censored model is as follows: (8) Among them, , representing the th component in the transmission vector, and To measure the censored values, and are the left censoring threshold and the right censoring threshold of node respectively; Based on the Tobit measurement model (8), we define a series of Bernoulli random variables and to adjust the bilateral censoring situation of as follows: (9) (10) The probability distribution can be obtained: (11) where, and are known non - negative constants; in addition, it is also assumed that and are not related to and the initial system state ; the censoring thresholds can be obtained through actual measurement and statistical experiments of sensors; therefore and can also be approximately calculated in the following way: (12) (13) where, represents the prediction of by node , and are the th element of the observation noise and the observation equation respectively, is the cumulative distribution function of the standard normal distribution; To make the notation more concise, we define:

[0036] Therefore, in (8) can be rewritten in the following form: (14) S300. Using the token - bucket traffic shaping method, design a trigger function based on the censoring measurement model in step S200, and design a communication protocol, specifically including, Use to represent the sequence values of trigger times: (15) where, is the prediction error covariance, and: (16) Let represent the number of tokens in the current bucket at time , and its initial value is : (17) where represents the size of the token bucket, represents the cost of each transmission, represents the rate of token generation in the bucket, represents the balance factor; Under the given parameterization, the evolution of in the trigger function in Equation (16) is described as follows: (18) It can be seen from Equation (18) that ; on the other hand, the trigger function (16) is designed based on the token bucket traffic shaping mechanism (17); it can be guaranteed that when the number of tokens exceeds the transmission cost , the trigger sequence should be updated, which indicates that a transmission has occurred and some tokens have been consumed; it is worth mentioning that when the number of tokens is less than the transmission cost , in Equation (16) is equal to 0, and since it is in the denominator position, this is obviously contradictory; to solve this problem, we should multiply both sides of (16) by ; just as it was discussed earlier that a transmission may not be triggered even when the number of tokens is greater than the transmission cost, to avoid the situation where a transmission is not triggered despite having enough tokens, a balance factor should be introduced into the trigger function to adjust the scheduling of the trigger sequence; therefore, this feature can directly design a suitable communication network according to the given parameters of the token bucket model; the above design aims to utilize the smooth and stable transmission characteristics of the token bucket, and at the same time, the scheduling of communication resources in the network can be clearly observed through the number of tokens in the bucket, and the state estimation algorithm and the token bucket traffic shaping mechanism are more fully combined; After the above transmission mechanism scheduling, when the filter does not receive new measurement values, prediction is used for compensation, and the transmission model is as follows: (19) S400. Design a filter to give the prediction of the local estimator and the upper bound of the filtering error covariance, specifically including, At time , for The design overview of the filter with [number of] nodes is as follows: (20) Among them, let and be the prediction error and the estimation error respectively; the prediction error covariance and the filtering error covariance are defined as and ; is the filtering gain to be designed; According to formulas (1) and (20), the prediction error of node m is calculated as follows: (21) Similarly, the filtering error is: (22) Using the Taylor expansion method centered on , the non - linear function can be expressed as: (23) Among them, , the high - order term is denoted as , and we can get , where represents the scaling matrix related to the motion of the ballistic object; represents a known matrix used to adjust the filter; represents an unknown matrix used to describe the linearization error, and ; According to equations (21) and (23), we can get: (24) The measurement censoring model based on the conditional expectation of the system state is: (25) (26) Among them, are the probability density function and the cumulative distribution function under the standard normal distribution respectively; The above formula is also called the Tobit regression model. Using to approximate in (25) and (26), we can deduce : (27) Among them, ; It can be rewritten in the following form according to equations (22), (23) and (27): (28) where ; according to (24) and the definition of covariance, it is easy to conclude that equation (28) holds; The prediction error covariance follows the following recurrence relation: (29) The filtering error covariance can be calculated recursively: (30) where

[0037] Two lemmas are introduced to derive the upper bound of the filtering error covariance; Lemma 1: For any two real vectors and , the following inequality holds:

[0038] where is a real number greater than zero; Lemma 2: Let be a real matrix and be a random diagonal matrix, then:

[0039] where is the Hadamard product; Next, some uncertainties in (30) are further reduced. Using the basic inequality in Lemma 1, the upper bound of is calculated as: (31) where ; and is a real number greater than zero.

[0040] According to Lemma 2 and (30), it can be concluded that: (32) This derivation result also applies to other similar terms in (30); in summary, according to (31) and (32), the upper bound of the filtering error covariance in (30) can be systematically derived; for the local filter of each sensor, let: be a positive scalar; the upper bound of the filtering error covariance can be obtained as: (33) The initial value is , where:

[0041] Then (33) is the upper bound of, that is ; The trace of the (33) filtering error covariance matrix can be expressed as: (34) Therefore, the partial derivative of in Equation (34) is as follows: (35) Let the above equation be 0, and can be calculated:

[0042]

[0043] S600. The local estimation results are fused and estimated at the fusion center using the federated fusion criterion to obtain the final estimated value, which specifically includes the following: In the first stage, information is initialized and distributed. The initial estimation error covariance of the local filter and the initial process noise matrix are respectively set to times the system error covariance and the process noise:

[0044] In the second stage, the local filter processes the received observation values to update the state estimation:

[0045] In the third stage, the fusion center fuses all the estimation results to obtain the globally optimal fusion estimation:

[0046] In the fourth stage, information is reset and distributed. The fusion center will times the weight to distribute the fused result to each local estimator, so as to provide a predicted value for the initialization update of the local estimator at the next moment.

[0047]

[0048] And then return to the second stage at the next update moment.

[0049] Specific implementation method two: A multi-sensor fusion estimation system based on the token bucket traffic shaping mechanism of the present invention. The system has program modules corresponding to the above steps and executes the steps in the above multi-sensor fusion estimation method based on the token bucket traffic shaping mechanism when running.

[0050] Other combinations and connection relationships in this implementation scheme are the same as those in the first specific implementation scheme.

[0051] Specific implementation scheme three: A computer-readable storage medium of the present invention, characterized in that: the computer-readable storage medium stores a computer program, and the computer program is configured to implement the steps of a multi-sensor fusion estimation method based on a token bucket traffic shaping mechanism when called by a processor.

[0052] Other combinations and connection relationships in this implementation scheme are the same as those in the first specific implementation scheme.

[0053] Simulation experiment A simulation verification is carried out on the method of multi-sensor fusion estimation based on the token bucket traffic shaping mechanism proposed by the present invention through an example of tracking the trajectory of a ballistic missile. Related state parameters of the ballistic missile motion physical system: gravitational acceleration: , ballistic coefficient: , radar sensor detection time interval: , correlation coefficient of process noise: .

[0054] Initial state: , radar observation noise variance: Ballistic missile motion process noise variance: .

[0055] Process noise matrix: .

[0056] Left censoring threshold of the radar sensor: , Right censoring threshold of the radar sensor: .

[0057] Linearization error parameter:

[0058] Scaling coefficient , covariance initial value: .

[0059] Token bucket related parameters: trade-off coefficient: , token generation rate: , token bucket capacity: , transmission cost: .

[0060] According to the communication protocol designed in step S200, Figure 2 and Figure 3 respectively depict in detail the dynamic changes of the number of tokens inside the first three transmission nodes before fusion, as well as the triggering transmission situations at each moment.

[0061] Perform step S300, and determine whether censor occurs for the transmission values of the three nodes at each moment according to the given censor threshold in the simulation.

[0062] Perform steps S400, S500, and S600. Figures 4 to 6 Then, it respectively shows the state estimation situations of the three local filters for the target coordinate positions and velocities of the ballistic objects. In each subfigure, the black solid line accurately marks the true state, while the blue and red dashed lines respectively correspond to the local estimated values and the fused estimated values. It can be clearly observed from the figure that these estimated values can accurately fit the true state of the system. Due to the large values involved, some parts of the figure are locally magnified for a more intuitive presentation of the details.

[0063] In order to deeply explore the differences between the local estimation accuracy and the fused estimation accuracy, the present invention conducts a comparative analysis from the perspective of the mean square error in the log sense. First, the mean square error is defined as follows:

[0064] Specifically, Figure 7 in, the black solid line represents the mean square error before fusion , and the green solid line corresponds to the estimated mean square error after fusion . It can be clearly seen from the figure that the value of the black solid line is much higher than that of the green solid line, indicating that the estimated accuracy after fusion is significantly improved. However, in Figure 8 , the black solid line and the green solid line are very close, which reflects that the difference in the estimated accuracy before and after fusion is small in this scenario. Further observing Figure 9 , the gap between the mean square errors before and after fusion is larger than that of local filter 1. The reason is that the token generation rates of node 1 and node 3 are the same, but the token generation rate of node 2 is higher. This means that node 2 can obtain more tokens at each moment, thereby increasing the storage amount of its transmission resources. Although the transmission cost of node 2 is equivalent to that of node 1, due to the advantage of its token generation rate, it can store more transmission resources at each moment, and then obtain more observation values to update the local estimated values, effectively improving the estimation accuracy of the local estimator. In contrast, node 3 not only has a low token generation rate but also a high transmission cost, resulting in relatively poor estimation performance. This phenomenon strongly verifies from the side that there is a close correlation between the transmission protocol designed in the present invention and the estimation accuracy.

[0065] After information fusion is completed using the federated fusion rule at the fusion center, each node will achieve information sharing and thus obtain the globally optimal estimate value. This globally optimal estimate value is obtained by synthesizing all local estimates. Given the deficiencies in the filtering performance of Node 1 and Node 3, in order to improve the accuracy of the globally optimal estimate, the fusion center will be more inclined to adopt the estimated state of Node 2 and make more use of the information of Node 2. This is exactly the reason why Figure 8 the black solid line and the green solid line in [reference] are very close, indicating that the estimation accuracy after fusion has no obvious decline compared with that before fusion, and the globally optimal estimate value effectively makes up for the performance disadvantages of Node 1 and Node 3.

[0066] In Figures 7 to 9 [reference], the blue solid line and the red solid line represent the traces of the estimated error covariance before and after fusion respectively. It can be seen from the figure that the red solid line shows a more stable change trend compared with the blue solid line. This phenomenon fully highlights the significant advantages of the distributed federated fusion method adopted in the present invention in terms of stability and reliability. The overall estimation performance after fusion is significantly better than that before fusion, which not only reflects the effectiveness of the fusion algorithm but also demonstrates its superiority in multi-node collaborative estimation, providing a strong guarantee for high-precision target state estimation.

[0067] Next, in-depth analysis is carried out on Figure 10 and Figure 11 . Figure 10 [reference] shows the dynamic changes of the number of tokens inside the three transmission nodes after fusion, while Figure 11 depicts the triggering transmission situation at each moment. In order to more intuitively present the comparison effect, Figure 2 , Figure 3 and Figure 10 , Figure 11 are comprehensively analyzed side by side.

[0068] From an overall perspective, whether it is the dynamic changes of the number of tokens inside the nodes or the triggering transmission situation at each moment, the data after fusion shows significantly smaller change amplitudes, stronger regularities, and higher stabilities. The fundamental reason for this phenomenon is the significant improvement in the estimation performance after fusion, which makes the moments of triggering transmission greatly reduced, as clearly shown in Figure 10 . Further focusing on the local details, before fusion, the change amplitude of the number of tokens inside Node 3 is the largest, followed by Node 1, while the change situation of Node 2 is already relatively close to the state after fusion, which is consistent with the previous analysis from the perspective of mean square error for Figures 7 to 9The analysis results are consistent. For data with frequent transmissions like Node 3, the token bucket traffic shaping mechanism can accurately depict the scheduling of transmission resources. It is worth mentioning that when multiple transmission resources need to be invoked in the face of emergencies, the token bucket shaping mechanism can not only ensure transmission stability but also meet transmission requirements as much as possible, effectively coping with emergencies. From an overall perspective, whether before or after fusion, the dynamic changes in the internal token quantity of each node show regularity, which further highlights the excellent performance of the token bucket shaping mechanism in terms of stability and reliability, fully demonstrating its efficiency and adaptability in multi-node transmission resource management.

[0069] Although the present invention is disclosed as above, the protection scope of the present invention is not limited thereto. Those skilled in the art of the present invention can make various changes and modifications without departing from the spirit and scope of the present invention, and these changes and modifications will all fall within the protection scope of the present invention.

Claims

1. A multi-sensor fusion estimation method based on token bucket traffic shaping mechanism, characterized in that: The following steps are involved: S100, establish nonlinear network dynamics model; S200, establish a bilateral censored measurement model based on the Tobit model; S300, using a token bucket traffic shaping method, designing a trigger function based on the censored measurement model of step S200, and designing a communication protocol; S400, designing a filter, providing a prediction of a local estimator and an upper bound of a filter error covariance; S500, providing a gain matrix of a local estimator; S600: The local estimation results are fused and estimated at the fusion center using a federal fusion criterion to obtain a final estimation value.

2. The multi-sensor fusion estimation method based on token bucket traffic shaping mechanism according to claim 1 is characterized in that: In step S100, it includes: The moving target considered is described by the following discrete nonlinear state space equation: ； in, is the state vector; is a Gaussian white noise with zero mean and is process noise; is a matrix of known suitable dimension; is a continuously differentiable nonlinear function; ； Nonlinear part It is the resistance encountered by a ballistic object when it rises. It is a force in the opposite direction of the target velocity and also an exponential decay model, namely: ； The air density function is ; is the acceleration due to gravity, is the ballistic coefficient; is the horizontal displacement of the object, is the object's horizontal speed, is the vertical displacement of the object, is the speed of the object in the numerical direction; Using the following identity: ； Transform formula (3) into: （4） for and have: ； The coefficient matrices of each item in formula (2) are given below: ； in, is the time interval between radar measurements; Considering the interference problem of the system, the process noise in equation (1) is assumed to be zero-mean Gaussian white noise. And the variance is ; In order to achieve more accurate considerations, the following process noise modeling aims to cover the potential sudden variables in model equation (2) and various deviations between the model and the actual situation: （5） in, is the coefficient related to process noise; In radar target tracking applications, the collected measurement data includes the distance between the radar and the target and the elevation angle of the radar , coordinate transformation is performed through the measurement values ​​observed by the radar, and it is converted into a rectangular coordinate system. The specific conversion formula is: ; The observation model is as follows: （6） in, , is the zero-mean Gaussian white measurement noise, which is different from the process noise is independent, and the variance is ; In summary, the nonlinear state space equation of the discretized ballistic object is: （7） in, for Moment The observed value of each node, are zero-mean Gaussian white noise, are matrices of known appropriate dimensions.

3. The multi-sensor fusion estimation method based on token bucket traffic shaping mechanism according to claim 1 is characterized in that: In step S200, it includes: Build a bilateral Tobit measurement model: （8） in, , which means the first Quantity, and is the measurement missing value, and Node The left and right censoring thresholds of ; Based on the Tobit observation model (8), the Bernoulli random variable is defined as and ,specification The bilaterally censored measurement model for is as follows: （9） （10） Get the probability distribution: （11） in, and is a known non-negative constant; Assumptions and and and the initial system state of the system Uncorrelated; censoring probability and Approximated by: （12） （13） in, Indicates that it comes from the node right predictions, and They are and No. elements, is the cumulative distribution function of the standard normal distribution; set up: ； get: （14）。 4. The multi-sensor fusion estimation method based on token bucket traffic shaping mechanism according to claim 1 is characterized in that: In step S300, it includes: use Indicates the trigger time series: （15） in, is the forecast error covariance, and the trigger function is as follows: （16） set up Indicated in The number of tokens in the current bucket at this moment, and its initial value is ; The number of tokens in the bucket of each node changes as follows: （17） in, Indicates the size of the token bucket. represents the cost of each transmission, Represents the rate at which tokens are generated in the bucket. represents the balance factor; Under given parameterization conditions, the number of tokens The dynamic changes within the trigger function are described as: （18） From formula (18), we can see that ; When the number of tokens exceeds the transfer cost When , indicating that there are sufficient transmission resources in the communication network at this time, and then the trigger sequence is updated ; The final measurement transmission model is: （19）。 5. The multi-sensor fusion estimation method based on token bucket traffic shaping mechanism according to claim 1 is characterized in that: In step S400, it includes: exist Moment, yes The filter design of each node is as follows: （20） remember and are prediction error and estimation error respectively; the prediction error covariance and filtering error covariance are defined as and ; is the filter gain to be designed; According to equations (1) and (20), the prediction error is: （21） Similarly, the estimated error is: （22） Use Taylor expansion method centered on It is expressed as: （23） in, , the higher-order terms are denoted as ,get ,in represents the known scaling matrix associated with the motion of a ballistic object; represents a known matrix used to adjust the filter; represents an unknown matrix describing the linearization error, and ; According to equations (21) and (23), we get: （24） The upper bound of the forecast error covariance is: （25） According to equations (20) to (24), the estimated error is: （26） in, ; The estimated error covariance is: （27） in, ； Two lemmas are introduced to derive the upper bound of the filtering error covariance; Lemma 1. For any two real vectors and , the following inequality holds: ， in, is a real number greater than zero; Lemma 2. Let is a real matrix, is a random diagonal matrix, then: ； in, For Hadamard; Using the basic inequality in Lemma 1, we can calculate The upper bound of is: （28） in, ； According to Lemma 2 and formula (28), we can conclude that: (29) set up: is a positive scalar; the upper bound of the filtering error covariance is: （30） The initial value is ,in: ； in, are all constants greater than zero.

6. The multi-sensor fusion estimation method based on token bucket traffic shaping mechanism according to claim 1 is characterized in that: In step S500, it also includes: In formula (30), The trace is: ； right Taking partial derivatives we get: （32） Let equation (32) be zero, and we get the gain matrix : ； in, 。 7. The multi-sensor fusion estimation method based on token bucket traffic shaping mechanism according to claim 1 is characterized in that: In step S600, when the local estimation error covariance and the local estimation value are known, the fusion center adopts the federation fusion criterion, including: In the first stage, the information is initialized and distributed. The local filter initial estimation error covariance and the initial process noise matrix are set to the system error covariance and process noise respectively. Times: ； The second stage local filter processes the received observations to update the state estimate: ； In the third stage, the fusion center fuses all the estimation results to obtain the global optimal fusion estimation: ； In the fourth phase, the fusion center will reset and distribute information according to The fused results are distributed to each local estimator with a weight of times: ； and After that, the update time will return to the second stage.

8. A multi-sensor fusion estimation system based on token bucket traffic shaping mechanism, characterized by: The system has a program module corresponding to the steps of any one of claims 1 to 7, and executes the steps of the multi-sensor fusion estimation method based on the token bucket traffic shaping mechanism during operation.

9. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, and the computer program is configured to implement the steps of the multi-sensor fusion estimation method based on the token bucket traffic shaping mechanism according to any one of claims 1 to 7 when called by a processor.

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