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

Abstract

The present invention provides a multi-sensor fusion estimation method and system based on a token bucket traffic shaping mechanism, belonging to the field of multi-sensor control. The method aims to solve the communication resource scheduling problem existing in existing multi-sensor fusion estimation, as well as the problem of how to handle the state estimation and censored measurement of nonlinear systems. The present invention designs a new communication protocol, combines the trace of the upper bound of the local estimation error covariance with a trigger function designed based on tokens as a judgment condition for whether to perform transmission measurement, and decides whether to pass the measurement value of each node to the local estimator, giving full play to the characteristics of token traffic shaping; designs the local Tobit Kalman filter gain of each node by minimizing the trace of the filter error covariance matrix; transmits the local estimate from each node to the fusion center, generates a global estimate using a federated fusion rule, and sends the global estimate with appropriate weights back to each node for prediction in the subsequent local filter.

Description

Technical Field

[0001] The present invention relates to the field of multi-sensor control technology, 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 the integration of 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. In contrast, the latter approach involves the fusion center fusing the available estimates from local filters to generate an optimal or suboptimal 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 widespread attention to distributed fusion filtering.

[0003] Due to the limited measurement capabilities of low-cost sensors, censored measurements are ubiquitous in practical engineering. Censored measurements are often described by the Tobit model, which effectively handles problems involving censored data and provides estimates of unobserved variables. Because system measurement noise exhibits non-Gaussian properties near the censored region, traditional Kalman filtering methods cannot directly address it. Allik et al. first used the Tobit model to design a Tobit Kalman filter, integrating unilateral and bilateral Tobit regression models into the recursive form of the Kalman filter. However, this approach does not fully explore the useful information contained in the censored region. A new conditional expectation method has been recently published in the literature to study the Tobit Kalman filter problem for random parameter systems. Subsequent research on the Tobit Kalman filter has considered several interesting phenomena, such as dynamic bias and cyclical protocols, channel fading, and dynamic event triggering mechanisms. However, these studies have been limited to linear systems, which is clearly impractical. Most systems in practical engineering are nonlinear, so the problem of state estimation for nonlinear systems in the presence of censored measurements is of great interest.

[0004] Unlike traditional automatic control systems, networked systems explicitly account for the limitations of the communication medium between sensors and controllers / filters. These limitations become particularly pronounced when network congestion occurs, where request allocations exceed the network's sustainable transmission rate, severely impacting optimal performance. A well-established paradigm for addressing this issue is the event-triggered protocol. The concept of an event-triggered protocol is to reduce the number of transmissions only when the event triggering condition is met. This protocol can effectively conserve communication resources. However, this does not guarantee that the transmission network will not be overutilized, especially when the required performance level requires a high transmission rate. Existing literature has introduced event-triggered protocols that, while maintaining reasonable performance, unilaterally conserve network bandwidth resources by reducing the number of information transmissions. However, such protocols are not practical for real-world engineering scenarios. In a shared network with limited bandwidth, it is difficult to maintain sufficient bandwidth when multiple information transmission requests are encountered. It is important to note that existing results cannot directly describe the dynamic changes in communication resources, and therefore do not fully reflect the role of event-triggered protocols. Summary of the Invention

[0005] The technical problems to be solved by the present invention are:

[0006] In order to solve the communication resource scheduling problem in the existing multi-sensor fusion estimation, and how to deal with the state estimation and missing measurement problems of nonlinear systems.

[0007] The present invention is to solve the above technical problems using the following technical solutions:

[0008] The present invention provides a multi-sensor fusion estimation method based on a token bucket traffic shaping mechanism, comprising the following steps:

[0009] S100, establish nonlinear network dynamics model;

[0010] S200, establish a bilateral censored measurement model based on the Tobit model;

[0011] 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;

[0012] S400, designing a filter, providing a prediction of a local estimator and an upper bound of the filter error covariance;

[0013] S500, providing a gain matrix of a local estimator;

[0014] S600: The local estimation results are fused and estimated using a federal fusion criterion at the fusion center to obtain a final estimation value.

[0015] Furthermore, in step S100, it includes:

[0016] The moving target considered is described by the following discrete nonlinear state space equation:

[0017] (1)

[0018] in, is the state vector; is Gaussian white noise with zero mean and is process noise; is a matrix of known appropriate dimension; is a continuously differentiable nonlinear function;

[0019] (2)

[0020] Nonlinear part It is the resistance encountered by a ballistic object when it rises. It is a force opposite to the target velocity and also an exponential decay model, namely:

[0021] (3)

[0022] The air density function ; 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;

[0023] Using the following identity:

[0024] ;

[0025] Transform formula (3) into:

[0026] (4)

[0027] for and have:

[0028]

[0029] The coefficient matrices of each item in formula (2) are given below:

[0030]

[0031] in, is the time interval between radar measurements;

[0032] 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:

[0033] (5)

[0034] in, is the coefficient related to process noise;

[0035] In radar target tracking applications, the collected measurement data includes the distance between the radar and the target and the radar's elevation angle , coordinate conversion is performed through the measurement values ​​observed by the radar, and it is converted into a rectangular coordinate system. The specific conversion formula is: ;

[0036] The observation model is as follows:

[0037] (6)

[0038] in, , is the zero-mean Gaussian white measurement noise, which is different from the process noise is irrelevant, and the variance is ;

[0039] In summary, the nonlinear state space equation of the discretized ballistic object is:

[0040] (7)

[0041] in, for Moment The observation value of each node, are Gaussian white noise with zero mean, are matrices of known appropriate dimensions.

[0042] Furthermore, in step S200, it includes:

[0043] Build a bilateral Tobit measurement model:

[0044] (8)

[0045] in, , represents the first Quantity, and is the measurement censoring value, and Node The left and right censoring thresholds of ;

[0046] 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:

[0047] (9)

[0048] (10)

[0049] Get the probability distribution:

[0050] (11)

[0051] in, and is a known non-negative constant;

[0052] Assumptions and and and the initial system state of the system Uncorrelated; censoring probability and Approximated by the following method:

[0053] (12)

[0054] (13)

[0055] in, Indicates that it comes from a node right predictions, and They are and No. elements, is the cumulative distribution function of the standard normal distribution;

[0056] set up:

[0057]

[0058] get:

[0059] (14).

[0060] Furthermore, in step S300, it includes:

[0061] use Indicates the trigger time series:

[0062] (15)

[0063] in, is the forecast error covariance, and the trigger function is as follows:

[0064] (16)

[0065] set up Indicates The number of tokens in the current bucket at this moment, its initial value is The number of tokens in each node's bucket changes as follows:

[0066] (17)

[0067] 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;

[0068] Under given parameterization conditions, the number of tokens The dynamic changes within the trigger function are described as:

[0069] (18)

[0070] 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:

[0071] (19)

[0072] Furthermore, in step S400, it includes:

[0073] exist Moment, yes The filter design of each node is as follows:

[0074] (20)

[0075] remember and are the prediction error and the estimation error respectively; the prediction error covariance and the filtering error covariance are defined as and ; is the filter gain to be designed;

[0076] According to equations (1) and (20), the prediction error is:

[0077] (twenty one)

[0078] Similarly, the estimated error is:

[0079] (twenty two)

[0080] Use Taylor expansion method centered on Expressed as:

[0081] (twenty three)

[0082] in, , the higher-order terms are denoted as ,get ,in Represents a 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 ;

[0083] According to formulas (21) and (23), we can obtain:

[0084] (twenty four)

[0085] The upper bound of the forecast error covariance is:

[0086] (25)

[0087] According to equations (20) to (24), the estimated error is:

[0088] (26)

[0089] in, ;

[0090] The estimated error covariance is:

[0091] (27)

[0092] in,

[0093]

[0094] Two lemmas are introduced to derive the upper bound of the filtering error covariance;

[0095] Lemma 1. For any two real vectors and , the following inequality holds:

[0096] ,

[0097] in, is a real number greater than zero;

[0098] Lemma 2. Let is a real matrix, is a random diagonal matrix, then:

[0099]

[0100] in, For Hadamard;

[0101] Using the basic inequality in Lemma 1, we can calculate The upper bound of is:

[0102] (28)

[0103] in, ;

[0104] According to Lemma 2 and Equation (28), we can conclude that:

[0105] (29)

[0106] set up: is a positive scalar; the upper bound of the filtering error covariance is:

[0107] (30)

[0108] The initial value is ,in:

[0109]

[0110] in, are all constants greater than zero.

[0111] Furthermore, in step S500, it also includes:

[0112] In formula (30), The trace is:

[0113] (31)

[0114] right Taking the partial derivative we get:

[0115] (32)

[0116] Let equation (32) be zero, and we get the gain matrix :

[0117]

[0118] in,

[0119]

[0120] Furthermore, in step S600, when the local estimation error covariance and the local estimation value are known, the fusion center adopts a federation fusion criterion, including:

[0121] The first stage is to initialize and distribute information, and set the local filter initial estimation error covariance and the initial process noise matrix to the system error covariance and process noise respectively. Times:

[0122]

[0123] The second stage local filter processes the received observations to update the state estimate:

[0124]

[0125] In the third stage, the fusion center fuses all the estimation results to obtain the global optimal fusion estimation:

[0126]

[0127] In the fourth phase, the information is reset and distributed. The fusion center will The fusion results are distributed to each local estimator with a weight of times:

[0128]

[0129] and After that, the update time will return to the second stage.

[0130] A multi-sensor fusion estimation system based on a token bucket traffic shaping mechanism has a program module corresponding to the above steps, and executes the steps in the multi-sensor fusion estimation method based on a token bucket traffic shaping mechanism during operation.

[0131] A computer-readable storage medium stores a computer program 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.

[0132] Compared with the prior art, the present invention has the following beneficial effects:

[0133] A multi-sensor fusion estimation method based on the token bucket traffic shaping mechanism was invented. It adopts a fully distributed fusion method to reduce the computational burden, lower the requirements for the central processing unit, and increase system reliability. The communication protocol adopts a token bucket design, which reduces the communication burden and increases the estimation accuracy of the local estimator. At the same time, it takes into account nonlinear systems and bilateral censored measurement models, which is more in line with actual engineering needs. BRIEF DESCRIPTION OF THE DRAWINGS

[0134] Figure 1 This is a structural block diagram of a multi-sensor fusion estimation method based on a token bucket traffic shaping mechanism in an embodiment of the present invention;

[0135] Figure 2 This is a graph showing the change in the number of tokens before fusion estimation in an embodiment of the present invention;

[0136] Figure 3 This is a diagram of a trigger sequence for the number of tokens before fusion estimation in an embodiment of the present invention;

[0137] Figure 4 This is a state estimation diagram of node 1 in an embodiment of the present invention;

[0138] Figure 5 This is a state estimation diagram of node 2 in an embodiment of the present invention;

[0139] Figure 6 This is a state estimation diagram of node 3 in an embodiment of the present invention;

[0140] Figure 7 This is a comparative analysis diagram of the error of node 1 before and after fusion in an embodiment of the present invention;

[0141] Figure 8 This is a comparative analysis diagram of the errors of node 2 before and after fusion in an embodiment of the present invention;

[0142] Figure 9 This is a comparative analysis diagram of the error of node 3 before and after fusion in an embodiment of the present invention;

[0143] Figure 10 This is a graph showing changes in the number of tokens after fusion estimation in an embodiment of the present invention;

[0144] Figure 11 This is a diagram of the trigger sequence of the number of tokens before fusion estimation in an embodiment of the present invention. DETAILED DESCRIPTION

[0145] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, specific implementation examples of the present invention are described in detail below with reference to the accompanying drawings.

[0146] Specific implementation scheme 1: The present invention provides a multi-sensor fusion estimation method based on a token bucket traffic shaping mechanism, comprising the following steps:

[0147] S100, establish a nonlinear network dynamics model; specifically including,

[0148] Before building the model, the following assumptions are made:

[0149] 1) First, the force is simplified:

[0150] Gravity: Assume that the main force acting on the target is gravity, which is always directed vertically downward. The acceleration due to gravity is ;

[0151] Resistance: Assume that there is air resistance, its direction is opposite to the direction of the object's movement, and its magnitude is proportional to the square of the speed, that is, ,in is the ballistic coefficient, which depends on the target's mass, shape, and cross-sectional area perpendicular to the direction of motion. At supersonic speeds, it is constant. is the air density, is the velocity of the object;

[0152] 2) Ignore other forces:

[0153] Centrifugal acceleration: Ignore the centrifugal acceleration caused by the rotation of the earth;

[0154] Coriolis acceleration: Ignore the Coriolis acceleration caused by the rotation of the earth;

[0155] Wind: Ignore the effect of wind on the movement of objects;

[0156] Lift: Ignore the effect of lift on the object's motion;

[0157] Rotational motion: Ignore the effect of the object's own rotational motion on the trajectory;

[0158] 3) Flat Earth Hypothesis:

[0159] Flat Earth: Assuming the Earth is flat is a common approximation in short-range trajectory estimation problems. Under this assumption, the motion of an object can be described using a two-dimensional rectangular coordinate system, where: Axis: represents the horizontal displacement of an object; Axis: Indicates the vertical displacement of an object; is the horizontal displacement of the object, is the object's horizontal speed, is the vertical displacement of the object, is the velocity of the object in the numerical direction, thus we get

[0160] The moving target considered is described by the following discrete nonlinear state space equation:

[0161]

[0162] in, is the state vector; is Gaussian white noise with zero mean and is process noise; is a matrix of known suitable dimension; is a continuously differentiable nonlinear function;

[0163] (2)

[0164] Nonlinear part It is the resistance encountered by a ballistic object when it rises. It is a force opposite to the target velocity and also an exponential decay model, namely:

[0165] (3)

[0166] The air density function ; is the acceleration due to gravity, is the ballistic coefficient;

[0167] Using the following identity:

[0168] ;

[0169] Transform formula (3) into:

[0170] (4)

[0171] for and have:

[0172]

[0173] The coefficient matrices of each item in formula (2) are given below:

[0174]

[0175] in, is the time interval between radar measurements;

[0176] 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 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:

[0177] (5)

[0178] in, is the coefficient related to process noise;

[0179] In radar target tracking applications, the collected measurement data includes the distance between the radar and the target and the radar's elevation angle , coordinate conversion is performed through the measurement values ​​observed by the radar, and it is converted into a rectangular coordinate system. The specific conversion formula is: After this transformation, the observation equation is in linear form, which is convenient for subsequent processing and analysis;

[0180] The observation model is as follows:

[0181] (6)

[0182] in, , is the zero-mean Gaussian white measurement noise, which is different from the process noise is irrelevant, and the variance is ;

[0183] In summary, by comprehensively considering various factors and corresponding processing methods, the nonlinear state space equation of the discretized ballistic object is finally derived, while considering that there are multiple radars observing the target:

[0184] (7)

[0185] in, is the state vector, nonlinear function is continuously differentiable, for Moment The observation value of each node, are Gaussian white noise with zero mean, are matrices of known appropriate dimensions;

[0186] S200, establish a bilateral censored measurement model based on the Tobit model, specifically including:

[0187] According to the Tobit measurement model, the two-sided measurement censoring model is as follows:

[0188] (8)

[0189] in, , represents the first Quantity, and is the measurement censoring value, and Node The left and right censoring thresholds of ;

[0190] Based on the Tobit measurement model (8), we define a series of Bernoulli random variables and To adjust The double-sided censoring case is defined as follows:

[0191] (9)

[0192] (10)

[0193] You can get the probability distribution:

[0194] (11)

[0195] in, and is a known non-negative constant; in addition, it is assumed that and and and the initial system state Not relevant; the deletion threshold can be known through statistical experiments of actual sensor measurements; therefore and It can also be approximately calculated as follows:

[0196] (12)

[0197] (13)

[0198] in, Indicates that it comes from a node right predictions, and The observation noise is and the observation equation No. elements, is the cumulative distribution function of the standard normal distribution;

[0199] To make the notation more concise, we define:

[0200]

[0201] Therefore, in (8) It can be rewritten as follows:

[0202] (14)

[0203] S300, using the token bucket traffic shaping method, designing a trigger function based on the censored measurement model of step S200, and designing a communication protocol, specifically including:

[0204] use To represent the trigger moment sequence value:

[0205] (15)

[0206] in, is the forecast error covariance, and:

[0207] (16)

[0208] set up Indicates The number of tokens in the current bucket at this moment, its initial value is :

[0209] (17)

[0210] 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;

[0211] Under the given parameterization conditions, the trigger function in Eq. (16) The evolution of is as follows:

[0212] (18)

[0213] From formula (18), we can see 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 When the trigger sequence should be updated, indicating that a transfer occurred and some tokens were consumed; it is worth mentioning that when the number of tokens is less than the transfer cost When , the formula (16) is equal to 0, which is obviously contradictory because it is in the denominator. To solve this problem, we should multiply both sides of (16) by As discussed above, when the number of tokens is greater than the transfer cost, the transfer may not be triggered. To avoid the situation where the transfer is not triggered despite there being enough tokens, a balance factor should be introduced in the trigger function. This feature can be used to adjust the scheduling of trigger sequences. Therefore, this feature allows for the design of appropriate communication networks based on the given parameters of the token bucket model. This design aims to leverage the smooth and stable transmission characteristics of the token bucket. Furthermore, the scheduling of communication resources within the network can be clearly observed through the number of tokens in the bucket, further integrating the state estimation algorithm with the token bucket traffic shaping mechanism.

[0214] After the above transmission mechanism is scheduled, the filter uses prediction to compensate when no new measurement values ​​are received. The transmission model is as follows:

[0215] (19)

[0216] S400, designing a filter, giving the prediction of the local estimator and the upper bound of the filter error covariance, specifically including:

[0217] exist Moment, yes The design of the filter for each node is summarized as follows:

[0218] (20)

[0219] Among them, and are the prediction error and the estimation error respectively; the prediction error covariance and the filtering error covariance are defined as and ; is the filter gain to be designed;

[0220] According to formulas (1) and (20), the prediction error of node m is The calculation is as follows:

[0221] (twenty one)

[0222] Similarly, filtering error for:

[0223] (twenty two)

[0224] Use Taylor expansion method centered on It can be expressed as:

[0225] (twenty three)

[0226] in, , the higher-order terms are denoted as , we can get

[0227] ,in Represents the 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 ;

[0228] According to equations (21) and (23), we can obtain:

[0229] (twenty four)

[0230] Measurement Censoring Model Based on system status The conditional expectation of is:

[0231] (25)

[0232] (26)

[0233] in, They are the probability density function and cumulative distribution function under the standard normal distribution respectively;

[0234] The above formula is also called the Tobit retrospective model, using Approximation (25) and (26) , we can deduce :

[0235] (27)

[0236] in, ;

[0237] According to equations (22), (23) and (27), it can be rewritten as follows:

[0238] (28)

[0239] in, According to (24) and the definition of covariance, it is easy to conclude that formula (28) is valid;

[0240] The forecast error covariance follows the following recursive relationship:

[0241] (29)

[0242] The filter error covariance can be calculated recursively:

[0243] (30)

[0244] in,

[0245]

[0246] Two lemmas are introduced to derive the upper bound of the filtering error covariance;

[0247] Lemma 1: For any two real vectors and , the following inequality holds:

[0248]

[0249] in, is a real number greater than zero;

[0250] Lemma 2: Let is a real matrix, is a random diagonal matrix, then:

[0251]

[0252] in, For Hadamard;

[0253] Next, we further reduce some of the uncertainties in (30) and use the basic inequality in Lemma 1 to calculate The upper bound of is:

[0254] (31)

[0255] in, ;and is a real number greater than zero.

[0256] According to Lemma 2 and (30), we can conclude that:

[0257] (32)

[0258] This derivation also applies to other similar terms in (30); in summary, according to (31) and (32), the upper bound of the covariance of the filtering error in (30) can be systematically derived; for the local filter of each sensor, let: is a positive scalar; the upper bound of the filtering error covariance can be obtained as:

[0259] (33)

[0260] The initial value is ,in:

[0261]

[0262] Then (33) is The upper bound of ; (33) The trace of the filter error covariance matrix can be expressed as:

[0263] (34)

[0264] Therefore, in formula (34) The partial derivatives of are as follows:

[0265] (35)

[0266] Let the above formula be 0, we can calculate :

[0267]

[0268]

[0269] S600: The local estimation results are fused and estimated at the fusion center using a federation fusion criterion to obtain a final estimation value, which specifically includes the following:

[0270] The first stage is to initialize and distribute information, and set the local filter initial estimation error covariance and the initial process noise matrix to the system error covariance and process noise respectively. Times:

[0271]

[0272] The second stage local filter processes the received observations to update the state estimate:

[0273]

[0274] In the third stage, the fusion center fuses all the estimation results to obtain the global optimal fusion estimation:

[0275]

[0276] In the fourth phase, the information is reset and distributed. The fusion center will The fusion results are distributed to each local estimator with a weight of times, so as to provide a prediction value for the initialization update of the local estimator at the next moment.

[0277]

[0278] and After that, the update time will return to the second stage.

[0279] Specific implementation scheme 2: The present invention provides a multi-sensor fusion estimation system based on a token bucket traffic shaping mechanism. The system has a program module corresponding to the above steps, and executes the steps in the above-mentioned multi-sensor fusion estimation method based on a token bucket traffic shaping mechanism during operation.

[0280] The other combinations and connection relationships of this embodiment are the same as those of the first embodiment.

[0281] Specific implementation scheme three: The present invention provides 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 a multi-sensor fusion estimation method based on a token bucket traffic shaping mechanism when called by a processor.

[0282] The other combinations and connection relationships of this embodiment are the same as those of the first embodiment.

[0283] Simulation experiment

[0284] The proposed multi-sensor fusion estimation method based on token bucket traffic shaping mechanism is simulated and verified through a ballistic missile trajectory tracking example. , ballistic coefficient: , radar sensor detection time interval: , the correlation coefficient of process noise: .

[0285] Initial state: , radar observation noise variance: Noise variance during ballistic missile motion: .

[0286] Process noise matrix: .

[0287] Radar sensor left censoring threshold: ,

[0288] Radar sensor right censoring threshold: .

[0289] Linearization error parameters:

[0290] Scaling factor , initial value of covariance: .

[0291] Token bucket related parameters: Trade-off coefficient: , token generation rate: , token bucket capacity: , transmission cost: .

[0292] According to the communication protocol designed in step S200, Figure 2 and Figure 3 The dynamic changes of the number of tokens inside the three transmission nodes before fusion and the triggered transmission situations at each moment are described in detail.

[0293] Going to step S300, based on the censoring threshold value given in the simulation, it is determined whether censoring occurs on the transmission values ​​of the three nodes at each moment.

[0294] Perform steps S400, S500 and S600, Figures 4 to 6 The three local filters respectively show the state estimates of the target position and velocity of the ballistic object. In each sub-figure, the solid black line accurately indicates the true state, while the blue and red dashed lines correspond to the local and fused estimates, respectively. It is clear from the figures that these estimates accurately match the true state of the system. Due to the large numerical values ​​involved, some parts of the figure have been zoomed in to provide a more intuitive view of the details.

[0295] In order to further explore the difference between local estimation accuracy and fusion estimation accuracy, this paper conducts comparative analysis from the perspective of mean square error in the logarithmic sense. First, the mean square error is defined as follows:

[0296]

[0297] Specifically, Figure 7 In the figure, the black solid line represents the mean square error before fusion. The green solid line corresponds to the estimated mean square error after fusion It can be clearly seen from the figure that the black solid line value is much higher than the green solid line, indicating that the estimation accuracy is significantly improved after fusion. Figure 8 In the figure, the black solid line is very close to the green solid line, which reflects that the difference in estimation accuracy before and after fusion is small in this scenario. Figure 9 , the difference in mean square error before and after fusion is larger than that of local filter 1. The reason for this is that the token generation rate of node 1 is the same as that of node 3, 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 capacity of its transmission resources. Although the transmission cost of node 2 is comparable to that of node 1, due to its advantage in token generation rate, it can store more transmission resources at each moment, and then obtain more observations to update local estimates, effectively improving the estimation accuracy of the local estimator. In contrast, node 3 not only has a lower token generation rate, but also a higher transmission cost, resulting in relatively poor estimation performance. This phenomenon has effectively verified from the side that there is a close correlation between the transmission protocol designed in the present invention and the estimation accuracy.

[0298] After the fusion center completes information fusion using the federated fusion rules, each node will share information and obtain the global optimal estimate. The global optimal estimate is based on the synthesis of all local estimates. Given that nodes 1 and 3 have insufficient filtering performance, in order to improve the accuracy of the global 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 Figure 8 The reason why the black solid line is very close to the green solid line is that the estimation accuracy after fusion has not decreased significantly compared with that before fusion, and the global optimal estimation value effectively compensates for the performance disadvantages of nodes 1 and 3.

[0299] exist Figures 7 to 9 Middle, solid blue line With red solid line Represent the traces of the estimation error covariance before and after fusion, respectively. As can be seen from the figure, the red solid line shows a more stable change trend than the blue solid line. This phenomenon fully highlights the significant advantages of the distributed federated fusion method adopted by 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 highlights its superiority in multi-node collaborative estimation, providing a strong guarantee for high-precision target state estimation.

[0300] Next, Figure 10 and Figure 11 Conduct in-depth analysis. Figure 10 The dynamic changes of the number of tokens in the three transmission nodes after fusion are shown. Figure 11 The trigger transmission situation at each moment is depicted. In order to present the comparison effect more intuitively, Figure 2 、 Figure 3 and Figure 10 、 Figure 11 Conduct comprehensive analysis in parallel.

[0301] From an overall perspective, whether it is the dynamic changes in the number of tokens within the node or the trigger transmission at each moment, the fused data shows significantly smaller changes, stronger regularity, and higher stability. The fundamental reason for this phenomenon is that the estimation performance is significantly improved after fusion, which greatly reduces the time of trigger transmission, such as Figure 10 Focusing further on the local details, the number of internal tokens in node 3 changes the most before fusion, followed by node 1, while the change in node 2 is closer to the state after fusion, which is consistent with the previous analysis from the perspective of mean square error. Figures 7 to 9The analysis results are consistent with those of Node 3. For frequently transmitted data like Node 3, the token bucket traffic shaping mechanism can accurately characterize the scheduling of transmission resources. It is worth mentioning that when multiple transmission resources need to be called upon in the face of emergencies, the token bucket shaping mechanism not only ensures transmission stability but also meets transmission needs as much as possible, effectively responding to emergencies. From an overall perspective, whether before or after fusion, the dynamic changes in the number of internal tokens in each node show regularity, which further highlights the excellent performance of the token bucket shaping mechanism in terms of stability and reliability, and fully demonstrates its efficiency and adaptability in multi-node transmission resource management.

[0302] Although the present invention is disclosed as above, the scope of protection disclosed by the present invention is not limited thereto. Those skilled in the art of the present invention may make various changes and modifications without departing from the spirit and scope of the present invention, and these changes and modifications will fall within the scope of protection 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; include, The moving target considered is described by the following discrete nonlinear state space equation: ； in, is the state vector; is Gaussian white noise with zero mean and is process noise; is a matrix of known appropriate dimension; is a continuously differentiable nonlinear function; （2）； Nonlinear part It is the resistance encountered by a ballistic object when it rises. It is a force opposite to the target velocity and also an exponential decay model, namely: （3）； The air density function ; g 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 physical vertical displacement, is the vertical speed of the object; Using the following identity: （4）； Transform formula (3) into: ； for and have: （6）； The coefficient matrices of each item in formula (2) are given below: ； Where T 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: ； in, is the coefficient related to process noise; In radar target tracking applications, the collected measurement data includes the distance r between the radar and the target and the radar elevation angle θ. The measurement values ​​observed by the radar are converted into a rectangular coordinate system through coordinate transformation. The specific conversion formula is: ; The observation model is as follows: ； in, , , is the zero-mean Gaussian white measurement noise, which is different from the process noise is irrelevant, and the variance is ; In summary, the nonlinear state space equation of the discretized ballistic object is: ； in, is the observation value of the mth node at time k, are Gaussian white noise with zero mean, are matrices of known appropriate dimensions; S200, establish a bilateral censored measurement model based on the Tobit model; including, Build a bilateral Tobit measurement model: ； in, , represents the jth component in the transmission vector, and is the measurement censoring value, and are the left censoring threshold and right censoring threshold of node m respectively; Based on the Tobit observation model (11), the Bernoulli random variable is defined as and ,specification The bilaterally censored measurement model for is as follows: （12）； （13）； Get the probability distribution: ； 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 the following method: （15）； （16）； in, Represents the number of nodes from node m predictions, and They are and The jth element of is the cumulative distribution function of the standard normal distribution; set up: ； get: ； 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 the filter error covariance; S500, providing a gain matrix of a local estimator; S600: The local estimation results are fused and estimated using a federated fusion criterion at the fusion center 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 S300, it includes: use Indicates the trigger time series: ； in, is the forecast error covariance, and the trigger function is as follows: ； set up Indicates the number of tokens in the current bucket at time k, and its initial value is The number of tokens in each node's bucket changes as follows: ； 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: ； From formula (22), 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: 。 3. A multi-sensor fusion estimation system based on a token bucket traffic shaping mechanism, characterized by: The system has a program module corresponding to the steps described in claim 1 or 2, and executes the steps in the multi-sensor fusion estimation method based on the token bucket traffic shaping mechanism during operation.

4. 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 claim 1 or 2 when called by a processor.

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