A distributed state fusion estimation method based on event-triggered asynchronous feedback

Abstract

The present invention proposes an event-triggered asynchronous feedback distributed state fusion estimation method, including: step 1: obtaining original observation data; step 2: converting the iterative multi-sensor multi-rate system based on the Send‑on‑Delta event trigger mechanism into an equivalent single-rate system model; step 3: obtaining a local state filter with feedback and a local state predictor in the sense of linear minimum variance based on the obtained original observation data; step 4: obtaining a fusion forecast estimate based on the local state filter estimate; step 5: calculating a fusion filter estimate with feedback based on the prediction result of the forecast fusion estimate with feedback from the fusion center; step 6: repeating steps 3-5 to obtain the fusion filter estimate at the next moment. The present invention not only avoids the high amount of calculation of centralized fusion, but also can provide the same optimal estimation accuracy, meeting the high accuracy requirements of actual systems such as target tracking and positioning.

Description

Technical Field

[0001] The invention relates to an asynchronous feedback distributed state fusion estimation method based on event triggering, and belongs to the technical field of wireless sensor network security. Background Art

[0002] With the continuous development of sensor technology and the widespread application of computer networks, the state estimation of networked multi-sensor systems has been widely used in public transportation, environmental monitoring, industrial control, target tracking and positioning, and other fields. Due to the limitations of communication bandwidth and battery energy in actual systems or devices, it is very important to introduce event triggering mechanisms to ensure the accuracy of state estimation while reducing network communication rates and avoiding unnecessary energy waste. Compared with traditional timed transmission, event triggering mechanisms reduce communication overhead and energy consumption, making the system more energy-efficient and responsive, and providing an efficient communication strategy for devices with limited resources. With the expansion and development of sensor systems, there are many types of sensors. In actual processes, sensors often have different sampling rates and sampling times, resulting in asynchronous multi-sensor information fusion problems, which are widely present in civil, military and industrial fields. At the same time, asynchronous sampling systems can provide richer information about targets and have become a hot topic of research. With the continuous improvement of the integration and automation of control systems, the various interferences and noises that systems are subject to in actual applications show greater diversity and complexity. In the estimation problem of networked systems, the existence of these problems needs to be considered to ensure the stable operation of the system and provide more accurate estimation results.

[0003] The invention patent with the patent publication number CN112270039A discloses a nonlinear state estimation method for a wire-controlled chassis vehicle based on distributed asynchronous fusion. It designs a nonlinear state time-delay volume Kalman fusion filter to perform real-time fusion estimation on the sampling frequencies of different on-board sensors. The invention patent with the patent publication number CN111817626A discloses a distributed state fusion estimation method for a wind turbine generator, which estimates the generator state by obtaining the optimal gain and weighted fusion matrix through multi-sensor distributed fusion. However, the above two patents do not adopt a recursive iterative structure, which is not suitable for real-time applications, and do not deal with the limited resources and bandwidth limitations in network data transmission. In addition, the prior art has the following defects: 1. The existing model lacks a comprehensive description and explanation of the above problems, which may lead to the problem of low state estimation accuracy. 2. Complex system model conversion problem. Multi-rate sampling systems need to be synchronized modeling, and the model conversion of multi-factor systems will be more complicated. 3. The problem of proposing an appropriate fusion estimation method. Due to the asynchronous sampling mechanism, a fusion method that is both efficient and has high estimation accuracy needs to be developed. At the same time, the traditional centralized fusion estimation method has a large computational burden and is not convenient for practical application. Appropriate fusion methods also need to be expanded. The parallel structure of the distributed fusion estimation structure enables it to have good robustness and stability, and can provide estimation results with high estimation accuracy. Therefore, the present invention proposes a new event-triggered asynchronous feedback distributed fusion estimation method based on an event-triggered mechanism for systems with complex factors such as correlated noise, attenuated observations, multiplicative noise and multi-rate sampling. Summary of the invention

[0004] In order to solve the technical problem that the traditional centralized fusion estimation method in the prior art has a large computational burden and is not convenient for practical application, the present invention further proposes an asynchronous feedback distributed state fusion estimation method based on event triggering.

[0005] The technical solution adopted by the present invention to solve the above problems is: the present invention comprises:

[0006] Step 1: Obtain raw sensor observation data;

[0007] Step 2: Obtain the equivalent single-rate system of the iteratively running multi-sensor multi-rate system based on the SOD event trigger mechanism;

[0008] Step 3: Fusion center's distributed fusion forecaster prediction results Feedback is given to each local estimator to obtain a local state filter and a local state predictor with feedback in the sense of linear minimum variance;

[0009] Step 4: Use the estimation result of the local state predictor as the input of the fusion estimation, establish the fusion estimation of the fusion center with feedback, and obtain the fusion prediction value based on the fusion estimation of the fusion center with feedback.

[0010] Step 5: Using the estimation result of the local state filter as the input of the fusion estimation, the fusion filter estimation with feedback is calculated based on the forecast fusion estimation with feedback of the fusion center.

[0011] Step 6: Repeat steps 3 to 5, and feed back the fusion prediction estimate obtained by the fusion center to each local sensor to obtain the fusion filter estimate at the next moment.

[0012] Optionally, obtain the original sensor observation data in step 1:

[0013] Each sensor at time n i k collects original observation data y i (n i k),i=1,2,…,L,;k≥0.

[0014] Where L is the number of sensors; is a positive integer, h0 is the system state update rate, h i is the sampling rate of the i-th sensor observation.

[0015] Optionally, the step of obtaining an equivalent single-rate system of the multi-sensor multi-rate system in step 2 includes:

[0016] Step 2.1: Obtaining the state equation and observation equation of each sensor based on the original sensor observation data;

[0017] Step 2.2: Obtain the SOD event triggering mechanism of each sensor;

[0018] Step 2.3: Introduce variable τ into the event trigger mechanism of each sensor i (k) performing synchronization;

[0019] Step 2.4: Based on the synchronization variable τ i (k) Convert the iterative multi-sensor multi-rate system into an equivalent single-rate system model;

[0020] Step 2.5: Calculate the statistics of the new noise based on the single-rate system model.

[0021] The state equation and the multi-rate sampling observation equation of the i-th sensor are:

[0022]

[0023] In formula (1), x(k)∈R n is the state of the sensor at time k, Φ0, Φ1, Γ, H 0i and H 1i are all stationary system matrices of appropriate dimensions, w(k) has zero mean and variance Q w The system noise, v i (n i k) is zero and its variance is The observation noise of different sensors v i (n i k) and v j (n j k) is correlated at the same time, and the covariance is w(k) and v i (n i k) is correlated at the same time, and the covariance is η(k) means zero mean and variance is Q η The multiplicative noise, ξ i (n i k) indicates zero mean and variance is The multiplicative noise, β i (n i k) represents a random variable describing the attenuation observation phenomenon, taking values ​​in the interval [0,1], with an expectation of α i , the variance is The expression of the SOD event triggering mechanism of the i-th sensor is:

[0024]

[0025] In formula (2), m is a fixed threshold, T is the transposition, and l i (n i (k-1)) is the last triggering moment;

[0026] l i (n i The expression for (k-1) is:

[0027]

[0028] The asynchronous sampling system is synchronized by pseudo observation method. For the asynchronous sampling system based on event triggering, the variable τ i The expression of (k) is:

[0029]

[0030] In formula (4), τ i (k) is a variable consisting of 0 and 1.

[0031] The equivalent single-rate system model is expressed as:

[0032]

[0033] In formula (5), is the new system noise, V i (k) is the new observation noise, and the calculation formula of its statistical information is:

[0034]

[0035]

[0036]

[0037]

[0038]

[0039] Optionally, the step of obtaining a local state filter with feedback in the sense of linear minimum variance in step 3 includes:

[0040] Step 3.1.1: Based on the new noise statistics, the steady-state system matrix and the fusion prediction error variance matrix Calculating a local filter gain of a local state filter;

[0041] Step 3.1.2: Based on the local filter gain of the local state filter and the observation y i (k) and the prediction results of the distributed fusion predictor Compute local state filters;

[0042] Step 3.1.3: Based on the local state filter gain and fusion prediction error variance matrix Calculate the local filter error square matrix.

[0043] The local filter gain of the local state filter at time k is:

[0044]

[0045] Design the local state filter with feedback at time k as:

[0046]

[0047] In formula (12), I n is the identity matrix of appropriate dimension;

[0048] The error variance matrix of the local state filter with feedback at time k is designed to be:

[0049]

[0050] Optionally, the step of obtaining a local state predictor with feedback in the sense of linear minimum variance in step 3 includes:

[0051] Step 3.2.1: Based on the new noise statistics, the steady-state system matrix and the fusion prediction error variance matrix Calculate local forecast gain;

[0052] Step 3.2.2: Based on the local prediction gain and observation y i (k) and the prediction results of the distributed fusion predictor Construct a local state predictor with feedback for the next moment;

[0053] Step 3.2.3: Based on the local state predictor gain and the fusion prediction error variance matrix Calculate the local forecast error variance matrix for the next moment;

[0054] The local prediction gain is:

[0055]

[0056] The local state predictor with feedback in the linear minimum variance sense at time k+1 is designed as:

[0057]

[0058] The local forecast error variance matrix at time k+1 is designed to be:

[0059]

[0060] Optionally, the step of obtaining the forecast fusion estimate with feedback from the fusion center in step 4 includes:

[0061] Step 4.1: Use the local forecast results as the input of the fusion estimation, and calculate the optimal fusion forecast gain at the next moment based on the optimal fusion forecast error variance matrix and the local forecast gain;

[0062] Step 4.2: Based on local forecast results Establish a fusion center forecast fusion estimate with feedback with the optimal fusion forecast gain matrix to obtain a fusion forecast estimate with feedback

[0063] Step 4.3: Calculate the optimal fusion prediction error variance matrix at the next moment based on the fusion prediction gain with feedback and the optimal fusion prediction error variance matrix.

[0064] The optimal fusion prediction gain matrix is:

[0065]

[0066]

[0067]

[0068]

[0069]

[0070] The forecast fusion estimate with feedback from the fusion center at time k+1 is designed as:

[0071]

[0072] In formula (22), J = [I n …I n ] is composed of an identity matrix of appropriate dimension;

[0073] Design the optimal fusion prediction error variance matrix at time k+1 as:

[0074]

[0075] Optionally, in step 5, the fusion filter estimate with feedback is calculated The steps include:

[0076] Step 5.1: Use the local filtering result as the input of the fusion estimation, based on the fusion prediction error variance matrix and local filter gain to calculate the optimal fusion filter gain;

[0077] Step 5.2: Filter the results based on the local state Establish a fusion filter estimation with feedback with the prediction fusion estimation with feedback of the fusion center

[0078] Step 5.3: Calculate the optimal fusion filter error variance matrix based on the fusion filter gain with feedback and the optimal fusion prediction error variance matrix;

[0079] The expression of the optimal fusion filter gain matrix is:

[0080]

[0081]

[0082] In formula (24) and formula (25),

[0083] The filter fusion estimation with feedback of the fusion center at time k is designed as:

[0084]

[0085] The expression of the optimal cross-covariance matrix of fusion filter error at time k is designed as:

[0086]

[0087] The beneficial effects of the present invention are:

[0088] 1. The estimation method proposed in the present invention is suitable for multi-rate systems in complex network environments.

[0089] 2. The asynchronous distributed fusion method in the present invention has good reliability and robustness due to its parallel structure.

[0090] 3. The distributed fusion method technology proposed in the present invention avoids the high and complex calculation amount of centralized fusion, while providing the same optimal estimation accuracy, meeting the high accuracy requirements of the actual system.

[0091] 4. The present invention introduces a SOD event triggering mechanism and proposes a distributed fusion method technology, which can effectively deal with the limited resources and bandwidth limitations in network data transmission, meet the needs of actual systems to save energy while ensuring estimation accuracy.

[0092] 5. The distributed fusion filtering method and technology with feedback proposed by the present invention has higher estimation accuracy than the matrix-weighted distributed fusion estimation method and avoids the calculation of the cross-covariance matrix; at the same time, the accuracy is higher than the distributed fusion estimation method without feedback. This estimation method is simple and easy to operate.

[0093] 6. The estimation method proposed in the present invention has a recursive iterative structure and is suitable for real-time applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0094] Figure 1 It is a structural block diagram of an event-triggered distributed fusion algorithm with feedback provided in an embodiment of the present invention.

[0095] Figure 2 It is a tracking diagram of the event-triggered centralized (ECFF) when m=1, the event-triggered matrix-weighted distributed (EMWFF), the event-triggered distributed without feedback (EDOLFF), and the proposed event-triggered distributed fusion with feedback (EDOLFFWF) method provided in the embodiment of the present invention;

[0096] Figure 3 This is a comparison of the root mean square errors (RMSEs) curves of the EMWFF, EDOLFF, and EDOLFFWF algorithms from 0 to 150 steps provided by the embodiment of the present invention after 100 Monte Carlo tests.

[0097] Figure 4This is a comparison chart of the RMSEs curves of the ECFF and EDOLFFWF algorithms from 0 to 150 steps provided by the embodiment of the present invention after 100 Monte Carlo tests.

[0098] Figure 5 is a comparison chart of RMSEs curves after 100 Monte Carlo tests of the EDOLFFWF algorithm provided by an embodiment of the present invention when the thresholds from 0 to 150 steps are m=0, m=1, m=1.5, and m=2 respectively;

[0099] In the figure, ECFF is an event-triggered centralized algorithm, EMWFF is an event-triggered matrix-weighted distributed algorithm, EDOLFF is an event-triggered distributed algorithm without feedback, and EDOLFFWF is an event-triggered distributed fusion algorithm with feedback. Example

[0100] Combination Figure 1-Figure 5 This embodiment is described as follows. Figure 1 As shown, the steps of an asynchronous distributed state fusion estimation method based on event triggering provided by this embodiment include:

[0101] Step S1: Given initial value Get the sensor's observation data y of the state i (k).

[0102] Step S2: By integrating the distributed fusion predictor at the fusion center Feedback to each local estimator to calculate the local filter with feedback Local Predictor with Feedback Filter gain and prediction gain And sent together to the fusion center.

[0103] Step S3: Local sensor prediction As the input of the fusion estimation, calculate the fusion prediction gain with feedback and the filter gain matrix and the intermediate matrix

[0104] Step S4: Calculate the error variance matrix of the fusion filter with feedback and the fusion prediction error variance matrix Calculate the fusion filter estimate with feedback and fusion forecast estimate And feed back to each local sensor.

[0105] Step S5: Repeat steps S1 to S5 to obtain the fusion filter estimation at the next moment.

[0106] In this embodiment, the following target tracking system with three sensors is considered:

[0107] x(k+1)=(Φ0+η(k)Φ1)x(k)+Γw(k) (1)

[0108] y i (n i k)=β i (n i k)(H 0i +ξ i (n i k)H 1i )x(n i k)+v i (n i k),i=1,2,3 (2)

[0109] In formulas (1) and (2), the state s(k), and They represent the position, velocity and acceleration of the target at time k respectively.

[0110] The relevant parameters used in the embodiment are as follows:

[0111] H 03 =[0 0 1], H 11 =[0.1 0 0], H 12 =[0 0.1 0], H 13 =[0 0 0.1]. Let T = 0.01s, n1 = 1, n2 = 2, n3 = 3. Take the initial value x(0) = [0.5 0.5 0.5] T , μ0=[0.1 0.1 0.1], P0=0.5I3.

[0112] The multiplicative noise used in this embodiment is as follows:

[0113] η(kT) and ξ i (n i kT) is uncorrelated white noise with an expected value of 0 and variances of Q η =0.2,

[0114] The process noise and observation noise used in this embodiment satisfy the following relationship:

[0115] v i (n i kT)=ι i w(n i kT)+κ i (ni kT) (3)

[0116] In formula (3), process noise w(kT) and κ i (k) is a Gaussian white noise with zero mean and independent correlation, and the variances are Q w =0.49, Q κ1 =0.25, Q κ2 =0.16, Q κ3 =0.09. Take ι1=5, ι2=4, ι3=1.

[0117] The attenuation observation phenomenon used in this embodiment is described as follows:

[0118] Random variable beta i (n i k), i = 1, 2, 3 represents the attenuation observation of the three sensors, taking values ​​in the interval [0, 1], and the probability function for:

[0119] After calculation, β i (n i k), i=1, 2, 3, the expectations are α1=0.5, α2=0.4, α3=0.8, and the variances are

[0120] In the embodiment, the thresholds for event triggering are m=1, m=1.5, and m=2 respectively.

[0121] In order to demonstrate the superior performance of the method of the present invention, a comparison is made with related methods in this embodiment, as follows:

[0122] like Figure 2 As shown, Figure 2 The trace graphs of the event-triggered centralized (ECFF), event-triggered matrix-weighted distributed (EMWFF), event-triggered distributed without feedback (EDOLFF), and event-triggered distributed fusion with feedback (EDOLFFWF) algorithms are given when m=1. Figure 2 It can be seen that the estimation method proposed in the present invention has the same tracking performance as the centralized estimation method and is superior to other methods.

[0123] like Figure 3 As shown, Figure 3 The root mean square error (RMSEs) curves of EMWFF, EDOLFF, and EDOLFFWF algorithms from 0 to 150 steps after 100 Monte Carlo tests are compared. Figure 3It can be seen that the accuracy of the EDOLFFWF algorithm is higher than that of the EDOLFF algorithm, and both of them are higher than the accuracy of the EMWFF algorithm. That is, the estimation method proposed by the present invention has the highest estimation accuracy.

[0124] like Figure 4 As shown, Figure 4 A comparison chart of the RMSEs curves of the ECFF and EDOLFFWF algorithms from 0 to 150 steps after 100 Monte Carlo tests is given. It can be seen that the ECFF algorithm and the EDOLFFWF algorithm have the same accuracy, but EDOLFFWF does not require observation augmentation and is easy to diagnose and isolate faults.

[0125] like Figure 5 As shown, Figure 5 The RMSEs curve comparison of the EDOLFFWF algorithm after 100 Monte Carlo tests when the thresholds are m=0, m=1, m=1.5, and m=2 from 0 to 150 steps is given. It can be seen from the figure that the smaller the threshold, the smaller the RMSE, that is, the higher the accuracy. Increasing the threshold reduces the communication rate of the observation information and reduces energy consumption.

[0126] The above is only a preferred embodiment of the present invention and does not limit the present invention in any form. Although the present invention has been disclosed as a preferred embodiment as above, it is not used to limit the present invention. Any technician familiar with this profession can make some changes or modify the technical contents disclosed above into equivalent embodiments without departing from the scope of the technical solution of the present invention. However, any simple modification, equivalent replacement and improvement made to the above embodiments without departing from the content of the technical solution of the present invention, based on the technical essence of the present invention, within the spirit and principles of the present invention, still fall within the protection scope of the technical solution of the present invention.

Claims

1. An event-triggered asynchronous feedback distributed state fusion estimation method, characterized in that: The steps of the event-triggered asynchronous distributed state fusion estimation method include: Step 1: Obtain raw sensor observation data; Step 2: Obtain the equivalent single-rate system of the iteratively running multi-sensor multi-rate system based on the SOD event trigger mechanism; Step 3: Fusion center's distributed fusion forecaster prediction results Feedback is given to each local estimator to obtain a local state filter and a local state predictor with feedback in the sense of linear minimum variance; Step 4: Use the estimation result of the local state predictor as the input of the fusion estimation, establish the fusion estimation of the fusion center with feedback, and obtain the fusion prediction value based on the fusion estimation of the fusion center with feedback. Step 5: Using the estimation result of the local state filter as the input of the fusion estimation, the fusion filter estimation with feedback is calculated based on the forecast fusion estimation with feedback of the fusion center. Step 6: Repeat steps 3 to 5, and feed back the fusion prediction estimate obtained by the fusion center to each local sensor to obtain the fusion filter estimate at the next moment.

2. The method for distributed state fusion estimation based on event-triggered asynchronous feedback according to claim 1, characterized in that: The steps of obtaining the original sensor observation data in step 1 include: Each sensor at time n i k collects original observation data y i (n i k), i = 1, 2, ..., L, k ≥ 0; where L is the number of sensors, is a positive integer, h0 is the system state update rate, h i is the sampling rate of the i-th sensor observation.

3. The method for distributed state fusion estimation based on event-triggered asynchronous feedback according to claim 1, characterized in that: The steps of obtaining the equivalent single-rate system of the multi-sensor multi-rate system in step 2 include: Step 2.1: Obtaining the state equation and observation equation of each sensor based on the original sensor observation data; Step 2.2: Obtain the SOD event triggering mechanism of each sensor; Step 2.3: Introduce variable τ into the event trigger mechanism of each sensor i (k) performing synchronization; Step 2.4: Based on the synchronization variable τ i (k) Convert the iterative multi-sensor multi-rate system into an equivalent single-rate system model; Step 2.5: Calculate new noise statistics based on the single-rate system model; The state equation and the multi-rate sampling observation equation of the i-th sensor are: In formula (1), x(k)∈R n is the state of the sensor at time k, Φ0, Φ1, Γ, H 0i and H 1i are all stationary system matrices of appropriate dimensions, w(k) has zero mean and variance Q w The system noise, v i (n i k) is zero and its variance is The observation noise of different sensors v i (n i k) and v j (n j k) is correlated at the same time, and the covariance is w(k) and v i (n i k) is correlated at the same time, and the covariance is η(k) means zero mean and variance is Q η The multiplicative noise, ξ i (n i k) indicates zero mean and variance is The multiplicative noise, β i (n i k) represents a random variable describing the attenuation observation phenomenon, taking values ​​in the interval [0,1], with an expectation of α i , the variance is The expression of the SOD event triggering mechanism of the i-th sensor is: In formula (2), m is a fixed threshold, T is the transposition, and l i (n i (k-1)) is the last triggering moment; l i (n i The expression for (k-1) is: Variable τ i The expression of (k) is: In formula (4), τ i (k) is a variable consisting of 0 and 1; The equivalent single-rate system model is expressed as: In formula (5), is the new system noise, V i (k) is the new observation noise, and the calculation formula of statistical information is:

4. The method for distributed state fusion estimation based on event-triggered asynchronous feedback according to claim 1, characterized in that: The steps of obtaining a local state filter with feedback in the sense of linear minimum variance in step 3 include: Step 3.1.1: Based on the new noise statistics, the steady-state system matrix and the fusion prediction error variance matrix Calculating a local filter gain of a local state filter; Step 3.1.2: Based on the local filter gain of the local state filter and the observation y i (k) and the prediction results of the distributed fusion predictor Compute local state filters; Step 3.1.3: Based on the local state filter gain and fusion prediction error variance matrix Calculate the local filter error square matrix; The local filter gain of the local state filter at time k is: Design the local state filter with feedback at time k as: In formula (12), I n is the identity matrix of appropriate dimension; The error variance matrix of the local state filter with feedback at time k is designed to be:

5. The method for distributed state fusion estimation based on event-triggered asynchronous feedback according to claim 1, characterized in that: The steps of obtaining the local state predictor with feedback in the sense of linear minimum variance in step 3 include: Step 3.2.1: Based on the new noise statistics, the steady-state system matrix and the fusion prediction error variance matrix Calculate local forecast gain; Step 3.2.2: Based on the local prediction gain and observation y i (k) and the prediction results of the distributed fusion predictor Construct a local state predictor with feedback for the next moment; Step 3.2.3: Based on the local state predictor gain and the fusion prediction error variance matrix Calculate the local forecast error variance matrix for the next moment; The local prediction gain is: The local state predictor with feedback in the linear minimum variance sense at time k+1 is designed as: The local forecast error variance matrix at time k+1 is designed to be:

6. The method for distributed state fusion estimation based on event-triggered asynchronous feedback according to claim 1, characterized in that: The steps of obtaining the forecast fusion estimate with feedback from the fusion center in step 4 include: Step 4.1: Use the local forecast results as the input of the fusion estimation, and calculate the optimal fusion forecast gain at the next moment based on the optimal fusion forecast error variance matrix and the local forecast gain; Step 4.2: Based on local forecast results Establish the forecast fusion estimation with feedback from the fusion center and the optimal fusion forecast gain matrix to obtain the fusion forecast estimation with feedback Step 4.3: Calculate the optimal fusion prediction error variance matrix at the next moment based on the fusion prediction gain with feedback and the optimal fusion prediction error variance matrix; The optimal fusion prediction gain matrix is: The forecast fusion estimate with feedback from the fusion center at time k+1 is designed as: In formula (22), J = [I n …I n ] is composed of an identity matrix of appropriate dimension; Design the optimal fusion prediction error variance matrix at time k+1 as:

7. The method for distributed state fusion estimation based on event-triggered asynchronous feedback according to claim 1, characterized in that: In step 5, the fusion filter estimate with feedback is calculated The steps include: Step 5.1: Use the local filtering result as the input of the fusion estimation, based on the fusion prediction error variance matrix and local filter gain to calculate the optimal fusion filter gain; Step 5.2: Filter the results based on the local state Establish a fusion filter estimation with feedback with the prediction fusion estimation with feedback of the fusion center Step 5.3: Calculate the optimal fusion filter error variance matrix based on the fusion filter gain with feedback and the optimal fusion prediction error variance matrix; The expression of the optimal fusion filter gain matrix is: In formula (24) and formula (25), The filter fusion estimation with feedback of the fusion center at time k is designed as: The expression of the optimal cross-covariance matrix of fusion filter error at time k is designed as:

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