A distributed elastic fusion filtering method based on generalized inverted pendulum system

Abstract

The application relates to a distributed elastic fusion filtering method based on a generalized inverted pendulum system and relates to the technical field of information fusion filtering. A dynamic model of a generalized inverted pendulum system under a multi-sensor network with colored measurement noise is constructed, the dynamic model is converted into a dynamic model of a non-generalized inverted pendulum system, a local elastic filter is designed according to the measurement information of each node to filter the state of the system, a correction parameter matrix is calculated and substituted into the local elastic filter, the local state filtering of the generalized inverted pendulum system and the upper bound of the filtering covariance are obtained, and finally, an inverse covariance cross fusion method is used to obtain the best fusion filtering process. The application can effectively solve the fusion filtering problem of the generalized inverted pendulum system under the multi-sensor network affected by the colored measurement noise and the change of the filter parameters, can objectively fit the real engineering scene, is easy to realize online iterative calculation, and can improve the state estimation precision and the filtering algorithm performance.

Description

Technical Field

[0001] This invention relates to the field of information fusion filtering technology, specifically a distributed elastic fusion filtering method based on a generalized inverted pendulum system. Background Technology

[0002] The generalized inverted pendulum system is a typical multivariable, high-order, nonlinear, and naturally unstable system in the field of control. A generalized model constructed by introducing algebraic constraint equations can more accurately characterize its complex dynamics, possessing significant research value and application potential in intelligent control, robot balancing systems, and aerospace attitude control. However, accurately estimating the state of the generalized inverted pendulum system is a core prerequisite for ensuring stable system control.

[0003] Distributed fusion filtering algorithms, in state estimation, can utilize not only the observation information of a node itself but also fuse relevant measurement data from neighboring nodes. They possess advantages such as strong scalability, high computational efficiency, and minimal impact of local faults on overall performance, effectively adapting to the multivariate coupling characteristics of generalized inverted pendulum systems. Therefore, researching distributed fusion filtering methods based on generalized inverted pendulum systems can not only overcome the performance limitations of traditional single-node filtering but also provide a new technical path for state estimation of complex nonlinear systems, possessing significant theoretical value and practical application significance.

[0004] In multi-sensor networks, existing technologies typically assume that the measurement noise of sensors at different sampling times is independent and does not affect each other. However, in real-world engineering scenarios, due to factors such as differences in sensor sampling frequencies, measurement noise can be correlated with noise at adjacent sampling times. This type of noise is often referred to as colored measurement noise, which is a significant factor that cannot be ignored in state estimation algorithms. Furthermore, during actual operation, filters are highly sensitive to rounding errors in calculated values, parameter changes, and equipment aging, which can easily lead to a decline in filtering performance. Therefore, designing a generalized elastic fusion filtering method for inverted pendulum systems that is suitable for environments with colored measurement noise and has robustness to parameter perturbations can more objectively fit real-world engineering scenarios and has significant engineering value.

[0005] Existing fusion filtering methods are insufficient to simultaneously address the elastic fusion filtering problem of a generalized inverted pendulum system in a multi-sensor network under the influence of colored measurement noise and filter parameter variations. They suffer from low performance of fusion filtering algorithms and insufficient accuracy of state estimation. Summary of the Invention

[0006] To address the shortcomings of the prior art, this invention provides a distributed elastic fusion filtering method based on a generalized inverted pendulum system. This method can effectively handle the fusion filtering problem of a generalized inverted pendulum system under a multi-sensor network, which is affected by colored measurement noise and filter parameter variations. It can objectively fit real-world engineering scenarios, is easy to implement online iterative calculations, and improves the accuracy of state estimation and the performance of the filtering algorithm.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: a distributed elastic fusion filtering method based on a generalized inverted pendulum system, comprising the following steps:

[0008] Step 1: Construct a dynamic model of the generalized inverted pendulum system under a multi-sensor network with colored measurement noise, and derive the measurement output information after the influence of colored measurement noise.

[0009] Step 2: Under the influence of colored measurement noise, the dynamic model of the generalized inverted pendulum system with colored measurement noise constructed in Step 1 is converted into the dynamic model of the non-generalized inverted pendulum system.

[0010] Step 3: Based on the dynamic model of the non-generalized inverted pendulum system transformed in Step 2, and combined with the measurement information of each node, construct a local elastic filter;

[0011] Step 4: Calculate the first... in the multi-sensor network. The node at the th Upper bound of one-step prediction covariance at time step ;

[0012] Step 5: Based on the one-step prediction of the upper bound of covariance obtained in Step 4. In computational multi-sensor networks, the first... The node at the th Correction parameter matrix at time ;

[0013] Step 6: Apply the correction parameter matrix obtained in Step 5. Substituting into the local elastic filter in step three, we obtain the first... The node at the th State filtering at time 1 At the same time, determine the current time. Has the total duration of the sensor network been reached? ,like If so, proceed to the next step. If so, the filtering process ends;

[0014] Step 7: Based on the correction parameter matrix obtained in Step 5 Calculate the first The node at the th Upper bound of the filtered covariance at time step ;

[0015] Step 8: Filter the state obtained in Step 6 The upper bound of the filter covariance obtained in step seven The inverse covariance cross-fusion method is used to calculate the first... Timing fusion filtering and fusion filter error covariance matrix At the same time, let Return to step three and perform iterations until the condition is met. The filtering process ends.

[0016] Furthermore, in step one, the dynamic model of the generalized inverted pendulum system under a multi-sensor network with colored measurement noise is expressed as follows:

[0017]

[0018] In the formula, Let be the generalized matrix of the inverted pendulum system. , , and These are the first generalized inverted pendulum system. The angular position, angular velocity, and DC motor current information at any given time. For the generalized inverted pendulum system in the first The state matrix at time 10:00. , , and These are the first generalized inverted pendulum system. The angular position, angular velocity, and DC motor current information at any given time. For the first The nonlinear variables of the generalized inverted pendulum system at any given time. For the generalized inverted pendulum system in the first The noise matrix at time step, For the generalized inverted pendulum system, the first The mean at time step is zero and the variance is Process noise, For the first The node at the th The measurement output information at time. For the generalized inverted pendulum system in the first The node of the first The measurement matrix at time, For the first The node at the th Colored measurement noise at any given time, , For the first The node at the th The noise matrix at time step, For the first The node at the th Colored measurement noise at any given time, For the first The node at the th The time variance is Zero-mean noise, Sensor node labels, The number of nodes in a multi-sensor network;

[0019] The expression for the measurement output information affected by colored measurement noise is:

[0020]

[0021] In the formula, For the first The node at the th Measurement output information after the influence of colored measurement noise at all times. For the generalized inverted pendulum system in the first The node of the first The measurement matrix at time, , , and These are the first generalized inverted pendulum system. Information on the angular position, angular velocity, and current of the DC motor at any given time.

[0022] Furthermore, in step two, the dynamic model of the non-generalized inverted pendulum system is expressed as follows:

[0023]

[0024] In the formula, For the non-generalized inverted pendulum system in the first... The node of the first The state matrix at time 10:00. This is the first intermediate matrix. For the first The node of the first The second intermediate matrix at time t, For the first The node at the th The noise matrix at time step, For the first The nonlinear variables of the non-generalized inverted pendulum system at any given time. For the first The node at the th Measurement output information after the influence of colored measurement noise at all times. For the non-generalized inverted pendulum system in the first... The noise matrix at time step, For the first The node at the th The time variance is Zero-mean noise, in addition, the first intermediate matrix With the second intermediate matrix satisfy , It is an identity matrix.

[0025] Furthermore, in step three, the expression for the local elastic filter is:

[0026]

[0027] In the formula, For the first The node at the th A one-step prediction of time, For the first The node at the th State filtering at any given time. For the first The state filtering of the nth node is in the... The nonlinear variables of the non-generalized inverted pendulum system at any given time. For the first The node at the th State filtering at any given time. For the generalized inverted pendulum system in the first The node of the first The measurement matrix at time, The parameter variation matrix, For the first The node at the th The correction parameter matrix at time step, yes The node at the th Zero-mean noise with a time variance of 1 It is the first The node at the th The perturbation matrix at time t.

[0028] Furthermore, in step four, the first The node at the th The upper bound of the one-step prediction covariance at time t is expressed as:

[0029]

[0030] In the formula, For the first The node at the th The upper bound of the one-step prediction covariance at time t. For the first The known positive first parameter of each node, For the first The node at the th The upper bound of the filtered covariance at time t. Given nonlinear transfer parameters that are known to be greater than zero, Indicates to To trace.

[0031] Furthermore, in step five, the first The node at the th Correction parameter matrix at time The calculation is as follows:

[0032]

[0033] in, The intermediate parameter matrix is ​​represented as follows:

[0034]

[0035] In the formula, and The first The known positive-zero second and third parameters of each node, Representation matrix The maximum value among the eigenvalues.

[0036] Furthermore, in step seven, the first The node at the th The upper bound of the filtered covariance at time t is expressed as:

[0037]

[0038] In the formula, For the first The node at the th The upper bound of the filtered covariance at time t.

[0039] Furthermore, in step eight, the first... Timing fusion filtering and fusion filter error covariance matrix The calculation is as follows:

[0040]

[0041]

[0042] In the formula, Weight coefficients that are greater than zero and satisfy .

[0043] Furthermore, the iterative calculations in steps four through eight follow the following design logic:

[0044] Calculate the minimum upper bound of the filtering covariance for each node, i.e., find... , making ,in For the first The node at the th The filtered covariance at time t, For the first The node at the th Time error, For elements Expectations;

[0045] By minimizing the upper bound of the filter covariance The trace, solve the first Time of the first Correction parameter matrix of each node Then, the fusion filter and the fusion filter error covariance matrix obtained by the inverse covariance cross-fusion method are made so that .

[0046] Compared with the prior art, the beneficial effects of the present invention are:

[0047] 1. The method of this invention simultaneously considers the impact of colored measurement noise and filter parameter changes on the fusion filtering performance. It utilizes distributed elastic fusion filtering, fully considers the effective information of the filter covariance, and implements distributed elastic fusion filtering for the generalized inverted pendulum system under multi-sensor network. It has strong anti-interference capability of the filter and is easy to implement online.

[0048] 2. This invention utilizes the Kalman filtering method, stochastic analysis, and matrix theory to derive a specific expression for the filter covariance by fully leveraging the effective information of the filter covariance. Subsequently, a correction parameter matrix is ​​designed to ensure that the trace of the filter covariance is at its minimum at every moment, significantly improving the state estimation accuracy. Simulation experiments have verified that, compared with the traditional CI fusion method, the average improvement in accuracy of this invention can reach 1.35%. Attached Figure Description

[0049] Figure 1 This is a flowchart of the method of the present invention;

[0050] Figure 2 This embodiment uses a multi-sensor network to track the actual state trajectory of the generalized inverted pendulum system. , Its fusion state filter trajectory , Comparison chart;

[0051] Figure 3 This embodiment uses a multi-sensor network to track the actual state trajectory of the generalized inverted pendulum system. , Its fusion state filter trajectory , Comparison chart;

[0052] Figure 4 This embodiment uses a multi-sensor network to track the actual state trajectory of the generalized inverted pendulum system. State filtering at each node and fusion state filtering trajectory Comparison chart of mean square errors;

[0053] Figure 5 This embodiment uses a multi-sensor network to track the actual state trajectory of the generalized inverted pendulum system. State filtering at each node and fusion state filtering trajectory Comparison chart of mean square errors;

[0054] Figure 6 This embodiment uses a multi-sensor network to track the actual state trajectory of the generalized inverted pendulum system. State filtering at each node and fusion state filtering trajectory Comparison chart of mean square errors;

[0055] Figure 7 This embodiment uses a multi-sensor network to track the actual state trajectory of the generalized inverted pendulum system. State filtering at each node and fusion state filtering trajectory Comparison chart of mean square errors;

[0056] Figure 8 This is a comparison diagram of the trajectories of the fusion filtering algorithm of the present invention and the CI fusion filtering algorithm under the influence of colored measurement noise and filter parameter changes in the embodiment. Detailed Implementation

[0057] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the invention, not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0058] A distributed elastic fusion filtering method based on a generalized inverted pendulum system, the process of which is combined with Figure 1As shown, firstly, a dynamic model of a generalized inverted pendulum system with colored measurement noise under a multi-sensor network is constructed. Simultaneously, based on the constructed dynamic model, it is transformed into a dynamic model of a non-generalized inverted pendulum system under a multi-sensor network. Based on the measurement information of each node in the multi-sensor network, a local elastic filter is designed to filter the system state. Next, the correction parameter matrix is ​​calculated and substituted into the designed local elastic filter to obtain the local state filtering and the upper bound of the filtering covariance of the generalized inverted pendulum system with colored measurement noise under a multi-sensor network. Finally, this local information is transmitted to the information fusion center, and the optimal fusion filtering process is obtained using the inverse covariance cross-fusion method, specifically including the following steps:

[0059] Step 1: Construct a dynamic model of the generalized inverted pendulum system under a multi-sensor network with colored measurement noise;

[0060] In a multi-sensor network, considering the impact of colored measurement noise on sensor output, the effect of filter parameter variations on the filter, and the structural characteristics of the generalized system, a dynamic model of the generalized inverted pendulum system with colored measurement noise in a multi-sensor network is established, expressed as:

[0061]

[0062] In the formula, Let be the generalized matrix of the inverted pendulum system. , , and These are the first generalized inverted pendulum system. The angular position, angular velocity, and DC motor current information at any given time. For the generalized inverted pendulum system in the first The state matrix at time 10:00. , , and These are the first generalized inverted pendulum system. The angular position, angular velocity, and DC motor current information at any given time. For the first The nonlinear variables of the generalized inverted pendulum system at any given time. For the generalized inverted pendulum system in the first The noise matrix at time step, For the generalized inverted pendulum system, the first The mean at time step is zero and the variance is Process noise, For the first The node at the th The measurement output information at time. For the generalized inverted pendulum system in the first The node of the first The measurement matrix at time, For the first The node at the th Colored measurement noise at any given time, , For the first The node at the th The noise matrix at time step, For the first The node at the th Colored measurement noise at any given time, For the first The node at the th The time variance is Zero-mean noise, Sensor node labels, This represents the number of nodes in a multi-sensor network.

[0063] Under the influence of colored measurement noise, the resulting measurement output information is derived as follows:

[0064]

[0065] In the formula, For the first The node at the th Measurement output information after the influence of colored measurement noise at all times. For the generalized inverted pendulum system in the first The node of the first The measurement matrix at time, , , and These are the first generalized inverted pendulum system. Information on the angular position, angular velocity, and current of the DC motor at any given time.

[0066] Step 2: Convert the dynamic model of the generalized inverted pendulum system into the dynamic model of the non-generalized inverted pendulum system;

[0067] Under the influence of colored measurement noise, the dynamic model of the generalized inverted pendulum system with colored measurement noise constructed in step one is transformed into the dynamic model of the non-generalized inverted pendulum system under the multi-sensor network, with the expression being:

[0068]

[0069] In the formula, For the non-generalized inverted pendulum system in the first... The node of the first The state matrix at time 10:00. This is the first intermediate matrix. For the first The node of the first The second intermediate matrix at time t, For the first The node at the th The noise matrix at time step, For the first The nonlinear variables of the non-generalized inverted pendulum system at any given time. For the first The node at the th Measurement output information after the influence of colored measurement noise at all times. For the non-generalized inverted pendulum system in the first... The noise matrix at time step, For the first The node at the th The time variance is Zero-mean noise, in addition, the first intermediate matrix With the second intermediate matrix satisfy , It is an identity matrix.

[0070] Step 3: Based on the dynamic model of the transformed non-generalized inverted pendulum system, design a local elastic filter;

[0071] Based on the dynamic model of the non-generalized inverted pendulum system under the multi-sensor network in step two, and combining the measurement information of each node, a local elastic filter is constructed. The filter expression is:

[0072]

[0073] In the formula, For the first The node at the th A one-step prediction of time, For the first The node at the th State filtering at any given time. For the first The state filtering of the nth node is in the... The nonlinear variables of the non-generalized inverted pendulum system at any given time. For the first The node at the th State filtering at any given time. For the generalized inverted pendulum system in the first The node of the first The measurement matrix at time, The parameter variation matrix, For the first The node at the th The correction parameter matrix at time step, yes The node at the th Zero-mean noise with a time variance of 1 It is the first The node at the th The perturbation matrix at time t.

[0074] Step 4: Calculate the... Upper bound of one-step prediction covariance for each node;

[0075] The following formula is used to calculate the first sensor in a multi-sensor network. The node at the th The upper bound of the one-step prediction covariance at time t is expressed as:

[0076]

[0077] In the formula, For the first The node at the th The upper bound of the one-step prediction covariance at time t. For the first The known positive first parameter of each node, For the first The node at the th The upper bound of the filtered covariance at time t. Given nonlinear transfer parameters that are known to be greater than zero, Indicates to To trace.

[0078] Step 5: Calculate the... The node at the th The correction parameter matrix at time step;

[0079] Based on the result obtained in step four The node at the th Upper bound of one-step prediction covariance at time step In computational multi-sensor networks, the first... The node at the th Correction parameter matrix at time The calculation is as follows:

[0080]

[0081] in, The intermediate parameter matrix is ​​represented as follows:

[0082]

[0083] In the formula, and The first The known positive-zero second and third parameters of each node, Representation matrix The maximum value among the eigenvalues.

[0084] Step Six: Local State Filtering Calculation and Iterative Judgment;

[0085] Based on the result obtained in step five The node at the th Correction parameter matrix at time Substituting this into the local elastic filter in step three, we obtain the first... The node at the th State filtering at time 1 This achieves local state filtering for a generalized inverted pendulum system under a multi-sensor network with colored measurement noise.

[0086] At the same time, determine the current moment. Has the total duration of the sensor network been reached? ,like If so, proceed to the next step. If the filtering process ends, the filtering process is terminated.

[0087] Step 7: Calculate the... Upper bound of the filtering covariance of each node;

[0088] Based on the result obtained in step five The node at the th Correction parameter matrix at time Calculate the first The node at the th The upper bound of the filtered covariance at time t is expressed as:

[0089]

[0090] In the formula, For the first The node at the th The upper bound of the filtered covariance at time t.

[0091] Step 8: Distributed fusion filtering calculation;

[0092] Based on the result obtained in step six The node at the th State filtering at time 1 and the result obtained in step seven The node at the th Upper bound of the filtered covariance at time step The inverse covariance cross-fusion method is used to calculate the first... Timing fusion filtering and fusion filter error covariance matrix The calculation is as follows:

[0093]

[0094]

[0095] In the formula, Weight coefficients that are greater than zero and satisfy ;

[0096] At the same time, Return to step three and perform iterations until the condition is met. The filtering process ends.

[0097] The theory behind the iterative calculations in steps four through eight above is as follows:

[0098] Calculate the minimum upper bound of the filtering covariance for each node, i.e., find... , making ,in For the first The node at the th The filtered covariance at time t, For the first The node at the th Time error, For elements The expectation.

[0099] Since the filter covariance contains uncertainties, its exact result cannot be obtained. Therefore, minimizing the upper bound of the filter covariance is necessary. The traces can be obtained from the first Time of the first Correction parameter matrix of each node Then, the inverse covariance cross-fusion method was used to obtain the result at the 1st... Timing fusion filtering and fusion filter error covariance matrix , making .

[0100] Example

[0101] This embodiment focuses on a generalized inverted pendulum system with colored measurement noise in a multi-sensor network, and uses the method of this invention for simulation, wherein:

[0102] The relevant parameters of the generalized inverted pendulum system are given below:

[0103]

[0104]

[0105]

[0106]

[0107] Other initial values ​​for the simulation are selected as follows:

[0108] The initial state is a zero-mean Gaussian variable, whose Sampling period The process noise and the variance of the measurement noise of the four sensors are respectively... , , , , , , , , .

[0109] This embodiment introduces the average boost ratio to evaluate the performance of the fusion filtering algorithm, which is defined as the boost ratio taking... Average improvement in accuracy compared to ,in, and They were respectively in the second The trace of the upper bound of the covariance of the CI fusion filtering algorithm at time step and the fusion filtering algorithm of this invention.

[0110] The fusion filtering effect is as follows:

[0111] Combination Figures 2-3 It can be seen that, for the generalized inverted pendulum system under a multi-sensor network with color measurement noise, the fusion filtering algorithm of this invention can effectively estimate the state trajectory, which is consistent with the theoretical results of this invention, wherein:

[0112] Figure 2 Demonstrates the use of a multi-sensor network to track the actual state trajectory of a generalized inverted pendulum system. Its fusion state filter trajectory The comparison diagram (see part a in the upper half of the diagram) and the actual state trajectory Its fusion state filter trajectory The comparison diagram is shown in section b of the lower half of the diagram. The actual state trajectory of the multi-sensor network in the th... The first component of the state variable at time t, For the fusion filtering trajectory of the multi-sensor network in the first... The first component of the fused state filter variable at time t. The actual state trajectory of the multi-sensor network in the th... The second component of the state variable at time t, For the fusion filtering trajectory of the multi-sensor network in the first... The second component of the fusion state filter variable at time step;

[0113] Figure 3 Demonstrates the use of a multi-sensor network to track the actual state trajectory of a generalized inverted pendulum system. Its fusion state filter trajectory The comparison diagram (see part a in the upper half of the diagram) and the actual state trajectory Its fusion state filter trajectory The comparison diagram is shown in section b of the lower half of the diagram. The actual state trajectory of the multi-sensor network in the th... The third component of the state variable at time t, For the fusion filtering trajectory of the multi-sensor network in the first... The third component of the fused state filter variable at time step [time]. The actual state trajectory of the multi-sensor network in the th... The fourth component of the state variable at time t, For the fusion filtering trajectory of the multi-sensor network in the first... The fourth component of the fusion state filter variable at time t.

[0114] Combination Figures 4-7 It can be seen that, for each sensor, the trajectory of the mean square error of the elastic fusion filter always remains below the mean square error of the filter for each sensor, verifying the correctness of the present invention, wherein:

[0115] Figure 4 Demonstrates the use of a multi-sensor network to track the actual state trajectory of a generalized inverted pendulum system. State filtering at each node and fusion state filtering trajectory Comparison chart of mean square errors For the first The node at the th The first component of the state filter variable at time t;

[0116] Figure 5 Demonstrates the use of a multi-sensor network to track the actual state trajectory of a generalized inverted pendulum system. State filtering at each node and fusion state filtering trajectory Comparison chart of mean square errors. For the first The node at the th The second component of the state-filtered variable at time t;

[0117] Figure 6 Demonstrates the use of a multi-sensor network to track the actual state trajectory of a generalized inverted pendulum system. State filtering at each node and fusion state filtering trajectory Comparison chart of mean square errors. For the first The node at the th The third component of the state filter variable at time t;

[0118] Figure 7 Demonstrates the use of a multi-sensor network to track the actual state trajectory of a generalized inverted pendulum system. State filtering at each node and fusion state filtering trajectory Comparison chart of mean square errors. For the first The node at the th The fourth component of the state filter variable at time t.

[0119] Combination Figure 8 As can be seen, the trajectory comparison diagram of the upper bound of the filter covariance trace between the fusion filtering algorithm of the present invention and the CI fusion filtering algorithm under the influence of colored measurement noise and filter parameter changes verifies the effectiveness of the present invention.

[0120] Table 1 shows a partial comparison of the fusion accuracy values ​​between the fusion filtering algorithm of this invention and the CI fusion filtering algorithm. The fusion accuracy value is determined by the values ​​obtained in the first... The trace representation of the upper bound of the fusion filter covariance at time step is shown in Table 1 below:

[0121] Table 1 Comparison of accuracy of fusion filtering algorithms

[0122]

[0123] Based on the above comparison Figures 2-8 According to Table 1, the elastic fusion filtering method of the present invention can effectively estimate the target state and has higher accuracy than the traditional CI fusion filtering algorithm.

[0124] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered illustrative and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of the equivalents of the claims are intended to be included within the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

[0125] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A distributed elastic fusion filtering method based on a generalized inverted pendulum system, characterized in that: Includes the following steps: Step 1: Construct a dynamic model of the generalized inverted pendulum system under a multi-sensor network with colored measurement noise, and derive the measurement output information after the influence of colored measurement noise. Step 2: Under the influence of colored measurement noise, the dynamic model of the generalized inverted pendulum system with colored measurement noise constructed in Step 1 is converted into the dynamic model of the non-generalized inverted pendulum system. Step 3: Based on the dynamic model of the non-generalized inverted pendulum system transformed in Step 2, and combined with the measurement information of each node, construct a local elastic filter; Step 4: Calculate the first... in the multi-sensor network. The node at the th Upper bound of one-step prediction covariance at time step ; Step 5: Based on the one-step prediction of the upper bound of covariance obtained in Step 4. In computational multi-sensor networks, the first... The node at the th Correction parameter matrix at time ; Step 6: Apply the correction parameter matrix obtained in Step 5. Substituting into the local elastic filter in step three, we obtain the first... The node at the th State filtering at time 1 At the same time, determine the current time. Has the total duration of the sensor network been reached? ,like If so, proceed to the next step. If so, the filtering process ends; Step 7: Based on the correction parameter matrix obtained in Step 5 Calculate the first The node at the th Upper bound of the filtered covariance at time 1 ; Step 8: Filter the state obtained in Step 6 The upper bound of the filter covariance obtained in step seven The inverse covariance cross-fusion method is used to calculate the first... Timing fusion filtering and fusion filter error covariance matrix At the same time, let Return to step three and perform iterations until the condition is met. The filtering process ends.

2. The distributed elastic fusion filtering method based on a generalized inverted pendulum system according to claim 1, characterized in that: In step one, the dynamic model of the generalized inverted pendulum system under a multi-sensor network with colored measurement noise is expressed as follows: In the formula, Let be the generalized matrix of the inverted pendulum system. , , and These are the first generalized inverted pendulum system. The angular position, angular velocity, and DC motor current information at any given time. For the generalized inverted pendulum system in the first The state matrix at time 10:

00. , , and These are the first generalized inverted pendulum system. The angular position, angular velocity, and DC motor current information at any given time. For the first The nonlinear variables of the generalized inverted pendulum system at any given time. For the generalized inverted pendulum system in the first The noise matrix at time step, For the generalized inverted pendulum system, the first The mean at time step is zero and the variance is Process noise, For the first The node at the th The measurement output information at time. For the generalized inverted pendulum system in the first The node of the first The measurement matrix at time, For the first The node at the th Colored measurement noise at any given time, , For the first The node at the th The noise matrix at time step, For the first The node at the th Colored measurement noise at any given time, For the first The node at the th The time variance is Zero-mean noise, Sensor node labels, The number of nodes in a multi-sensor network; The expression for the measurement output information affected by colored measurement noise is: In the formula, For the first The node at the th Measurement output information after the influence of colored measurement noise at all times. For the generalized inverted pendulum system in the first The node of the first The measurement matrix at time, , , and These are the first generalized inverted pendulum system. Information on the angular position, angular velocity, and current of the DC motor at any given time.

3. The distributed elastic fusion filtering method based on a generalized inverted pendulum system according to claim 2, characterized in that: In step two, the dynamic model of the non-generalized inverted pendulum system is expressed as follows: In the formula, For the non-generalized inverted pendulum system in the first... The node of the first The state matrix at time 10:

00. This is the first intermediate matrix. For the first The node of the first The second intermediate matrix at time t, For the first The node at the th The noise matrix at time step, For the first The nonlinear variables of the non-generalized inverted pendulum system at any given time. For the first The node at the th Measurement output information after the influence of colored measurement noise at all times. For the non-generalized inverted pendulum system in the first The noise matrix at time step, For the first The node at the th The time variance is Zero-mean noise, in addition, the first intermediate matrix With the second intermediate matrix satisfy , It is an identity matrix.

4. The distributed elastic fusion filtering method based on a generalized inverted pendulum system according to claim 3, characterized in that: In step three, the expression for the local elastic filter is: In the formula, For the first The node at the th A one-step prediction of time, For the first The node at the th State filtering at any given time, For the first The state filtering of the nth node is in the... The nonlinear variables of the non-generalized inverted pendulum system at any given time. For the first The node at the th State filtering at any given time. For the generalized inverted pendulum system in the first The node of the first The measurement matrix at time, The parameter variation matrix, For the first The node at the th The correction parameter matrix at time step, yes The node at the th Zero-mean noise with a time variance of 1 It is the first The node at the th The perturbation matrix at time t.

5. The distributed elastic fusion filtering method based on a generalized inverted pendulum system according to claim 4, characterized in that: In step four, the first The node at the th The upper bound of the one-step prediction covariance at time t is expressed as: In the formula, For the first The node at the th The upper bound of the one-step prediction covariance at time t. For the first The known positive first parameter of each node, For the first The node at the th The upper bound of the filtered covariance at time t. Given nonlinear transfer parameters that are known to be greater than zero, Indicates to To trace.

6. The distributed elastic fusion filtering method based on a generalized inverted pendulum system according to claim 5, characterized in that: In step five, the first The node at the th Correction parameter matrix at time The calculation is as follows: in, The intermediate parameter matrix is ​​represented as follows: In the formula, and The first The known positive-zero second and third parameters of each node, Representation matrix The maximum value among the eigenvalues.

7. The distributed elastic fusion filtering method based on a generalized inverted pendulum system according to claim 6, characterized in that: In step seven, the first The node at the th The upper bound of the filtered covariance at time t is expressed as: In the formula, For the first The node at the th The upper bound of the filtered covariance at time t.

8. The distributed elastic fusion filtering method based on a generalized inverted pendulum system according to claim 7, characterized in that: In step eight, the first Timing fusion filtering and fusion filter error covariance matrix The calculation is as follows: In the formula, Weight coefficients that are greater than zero and satisfy .

9. The distributed elastic fusion filtering method based on a generalized inverted pendulum system according to claim 8, characterized in that: The iterative calculations in steps four through eight follow the following design logic: Calculate the minimum upper bound of the filtering covariance for each node, i.e., find... , making ,in For the first The node at the th The filtered covariance at time t, For the first The node at the th Time error, For elements Expectations; By minimizing the upper bound of the filter covariance The trace, solve the first Time of the first Correction parameter matrix of each node Then, the fusion filter and the fusion filter error covariance matrix obtained by the inverse covariance cross-fusion method are made so that .

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