Multi-rate system event fusion estimation method under complex condition

Abstract

The invention provides a multi-rate system event fusion estimation method under a complex condition, and relates to the technical field of automatic control, and the technical key points are as follows: constructing a state equation of an MRS and a measurement equation of sensor nodes: converting the MRS into an SRS, and performing sampling period unification on each sensor node in an interval to obtain the state equation and the measurement equation of the SRS; designing a local recursive filter, receiving a measured value based on an event triggering mechanism, calculating an upper bound of a filtering error covariance, and deducing a recursive relationship through an inequality technology; filter parameters are designed, and the upper bound of the filtering error covariance is minimized in a recursive mode; and fusing the estimation results of the local filters by using a CI fusion method to obtain global fusion estimation and fusion covariance. Even if the method is influenced by random nonlinearity, sensor degradation and event triggering, the sampling values of different sensors in the multi-rate system can still be fused and estimated quickly and efficiently.

Description

Technical Field

[0001] The present invention relates to the technical field of automatic control, and particularly to an event fusion estimation method for a multi-rate system under complex conditions. Background Art

[0002] The problem of information fusion has been widely applied in fields such as navigation and positioning systems, power systems, computer vision, and bioinformatics. In a multi-sensor environment, centralized fusion and distributed fusion are two basic fusion architectures. Centralized fusion directly utilizes a large amount of measurement data and can obtain a globally optimal estimate, but it may lead to huge communication and computational burdens. In distributed fusion, local estimates are first obtained and then fused at the fusion center. However, in some practical applications, due to the huge computational burden, unknown forms of cross-covariance, or the complexity of calculating cross-covariance, it is difficult to obtain cross-covariance. Therefore, to address these drawbacks, a covariance intersection (CI) fusion scheme is introduced based on convex optimization theory.

[0003] In networked control systems, especially large-scale networked systems, sensors are usually deployed in a distributed manner. Most practical engineering systems are multi-rate systems (MRS), and due to limited communication capabilities and energy storage, it is almost impractical for sensors to continuously transmit data to the estimation center. To solve this problem, an event-triggered mechanism (ETM) is introduced, which can save energy costs and communication bandwidth, thus effectively reducing unnecessary transmissions.

[0004] In most filtering and control systems, sensors are always considered to be fault-free and able to accurately transmit information. However, in engineering systems, sensor degradation phenomena often occur mainly due to various factors such as sensor aging, component failures, and network congestion. If not properly handled, sensor degradation will have a significant impact on system performance.

[0005] Due to the existence of stochastic nonlinearity, sensor degradation, and ETM, it is almost impossible to derive the minimum filtering error covariance in the Kalman filtering framework. In addition, due to the influence caused by the asynchronous sampling characteristics of each sensor, it brings great difficulties to the design of the filter. A new filtering method has been proposed in the existing methods to handle MRS, and a recursive filter has been designed to ensure that the filtering error covariance is within an acceptable range. However, due to the existence of unknown cross-covariance, this method still cannot handle more complex phenomena. Summary of the Invention

[0006] The objective of the present invention is to solve the problem that in the existing technology, due to the existence of stochastic nonlinearity, sensor degradation, and ETM, it is almost impossible to derive the minimum filtering error covariance in the Kalman filtering framework.

[0007] To achieve the above object, the present invention adopts the following technical solutions:

[0008] A method for multi-rate system event fusion estimation in complex situations, comprising the following steps:

[0009] S1: Construct the state equation of the MRS and the measurement equation of the sensor nodes:

[0010] The state equation is a discrete-time linear equation:

[0011] x (k+1)T = Ax kT + Bw kT

[0012] In the above formula, T>0 is the system sampling period, is the state vector at the sampling time kT, is the zero-mean process noise with variance R kT >0, and A and B are known time-invariant matrices with appropriate dimensions;

[0013] The measurement equation of the i-th sensor node is:

[0014]

[0015] In the above formula, l i >0 is an integer, is the measurement vector at the sampling time kl i T, C i is a matrix with appropriate dimensions, is the zero-mean measurement noise with variance , represents the influence of the sensor degradation phenomenon on the system, represents the influence of random nonlinearity on the system

[0016] S2: Convert the MRS to SRS. By using the lifting technique and the least common multiple method, the sampling period of each sensor node is unified in the interval [kl i +1, (k + 1)l i to obtain the state equation and measurement equation of the SRS;

[0017] S3: Design a local recursive filter to accept the measurement value based on the event-triggering mechanism and update the state through two stages of prediction and estimation,

[0018] S4: Calculate the upper bound of the filtering error covariance, including the prediction error covariance and the filtering error covariance and deduce its recurrence relationship through inequality techniques;

[0019] S5: Design the filter parameters Minimize the upper bound of the filtering error covariance recursively;

[0020] S6: Use the CI fusion method to fuse the estimation results of each local filter to obtain the global fusion estimation and the fusion covariance.

[0021] Preferably, in the S2, the specific method for converting the MRS to the SRS is as follows:

[0022] For the i-th sensor node, in the interval [kl i +1, (k + 1)l i , expand the state equation by the lifting technique to:

[0023]

[0024] 0 ≤ l ≤ l i -1

[0025] The finally derived state equation and measurement equation of the SRS are:

[0026]

[0027] Preferably, the construction method of the local recursive filter in the S3 is as follows:

[0028]

[0029] In the above formula, and are the prediction and estimation of the state respectively, are the filter parameters to be designed.

[0030] Preferably, the calculation of the upper bound of the filtering error covariance in the S4 satisfies:

[0031]

[0032] In the above formula, ζ 1,k = 1 + ε 1,k + ε 2,k and ε i,k (i = 1, 2, 3, 4, 5) are positive scalars, and the initial value of the FEC is Then is the upper bound of the filtering error covariance, that is

[0033] Preferably, in the S5, the design of the filter parameters is:

[0034] The gain of the filter is determined by the following formula:

[0035]

[0036] where

[0037]

[0038] Preferably, the specific steps of the CI fusion method are as follows:

[0039] Design the set Π k ={i|k = m i,k l i m i,k where m is a positive integer and i ∈ (1, 2, …, M)},

[0040] When this set is not empty, perform fusion on the local part: In the formula, Σ k and are the fusion estimate and the fusion covariance respectively:

[0041]

[0042] In the above formula, u i ≥0, the fusion estimation problem can be formulated as a convex optimization problem to obtain the final fusion covariance:

[0043]

[0044] Compared with the prior art, the present application has the following beneficial effects:

[0045] The present application adopts a multi-rate system event fusion estimation method in complex situations, considering the disadvantages of sensor degradation and random nonlinear problems and the problem that the existing methods cannot obtain the minimum filtering error covariance, introducing an event-triggered mechanism to arrange the transmission sequence to reduce the communication cost, and using the covariance intersection fusion method to fuse the estimations of local filters to obtain the final fusion estimation of the multi-rate system.

[0046] The application of the present application avoids the huge computational burden, the unknown form of cross-covariance or the complexity of calculating cross-covariance, and can quickly and efficiently fuse and estimate the sampling values of different sensors in a multi-rate system in complex situations. The present application can provide reference for engineering implementers and also obtain better estimation results during event fusion estimation, and has great application value. Description of the Drawings

[0047] Figure 1Schematic flowchart of the multi-rate system event fusion estimation method in a complex scenario according to an embodiment of the present invention;

[0048] Figure 2 Simulation experimental diagram of the multi-rate system event fusion estimation method in a complex scenario according to an embodiment of the present invention. Detailed implementation manners

[0049] The present invention will be further described in detail below in conjunction with specific embodiments.

[0050] Please refer to Figure 1 , a multi-rate system event fusion estimation method in a complex scenario, comprising the following steps:

[0051] S1: Construct a multi-rate system (MRS) equation, define and initialize relevant parameters

[0052] In one embodiment, the discrete system considered by the MRS is shown in Formula (1):

[0053] x (k+1)T = Ax kT + Bw kT (1)

[0054] In the above formula, T>0 is the system sampling period, is the state vector at the sampling time kT, is a zero-mean process noise with variance R kT >0, and A and B are known time-invariant matrices with appropriate dimensions;

[0055] In the case of being affected by sensor degradation and random nonlinearity, the output of the i-th (i = 1, 2, 3... M) sensor node is shown in Formula (2),

[0056]

[0057] In the above formula, l i >0 is an integer, is the measurement vector at the sampling time kl i T, C i is a matrix with an appropriate dimension, is a zero-mean measurement noise with variance , represents the influence of the sensor degradation phenomenon on the system, represents the influence of random nonlinearity on the system.

[0058] S2: Convert the MRS equation into a single-rate (SRS) equation

[0059] In one embodiment, the formulas (1) and (2) of the MRS system in S1 are transformed into the SRS system. For each interval [kl i +1, (k + 1)l i , using the lifting technique and the method of least common multiple, as shown in formula (3):

[0060]

[0061] The final derivation result of the single-rate system of the measurement value of the i-th sensor node is as shown in formula (4),

[0062]

[0063] In the above formulas,

[0064] S3: Design and construct a local recursive filter;

[0065] The construction of the local recursive filter is based on representing the measurement value received from the i-th sensor node at the latest event time point The corresponding local recursive filter is constructed as shown in formula (5),

[0066]

[0067] In the above formulas, and are the prediction and estimation of the state respectively, are the filter parameters to be designed.

[0068] S4: Obtain the upper bound of the filtering error covariance of each local filter;

[0069] Due to the influence of sensor degradation, random nonlinearity, and event-triggering mechanism, it is usually difficult to obtain the exact value of the filtering error covariance; therefore, in this application, the upper bound of the filtering error covariance is found. For the MRS (formula (1)) with the filter (formula (5)), the prediction error covariance and the filtering error covariance can be obtained by definition. The matrices and satisfy the following formulas:

[0070]

[0071]

[0072] In the above formulas, ζ 1,k = 1 + ε1,k +ε 2,k and ε i,k (i = 1, 2, 3, 4, 5) are positive scalars, and the initial value of FEC is Then is the upper bound of the filtering error covariance, that is

[0073] S5: Design appropriate filter parameters to recursively minimize the upper bound of the filtering error covariance;

[0074] The filter parameters for minimizing the upper bound of the filter error covariance are shown in Equation (8):

[0075]

[0076] In the above formula and are shown in Equations (9) and (10) respectively,

[0077]

[0078] Based on the above formula, the finally minimized upper bound of the filter error covariance is shown in Equation (11):

[0079]

[0080] S6: Use the covariance intersection (CI) fusion method to fuse the local estimates to obtain the fused estimate and the fused covariance.

[0081] Due to the influence of sensor degradation, random nonlinearity, and event-triggering mechanism, it is difficult to derive the cross-covariance of the sensor nodes. In this application, the CI method is used for fusion, and the specific steps are as follows:

[0082] Set the set Π k ={i|k = m i,k l i m i,k are positive integers, i ∈ (1, 2,..., M)}. When this set is not empty, fuse the local: In the formula, Σ k and are the fused estimate and the fused covariance respectively, as shown in Equations (12) and (13), where u i ≥0, and the fused estimation problem can be formulated as a convex optimization problem, as shown in Equation (14), and the final fused covariance is obtained therefrom.

[0083]

[0084] The simulation results are as Figure 2As shown Figure 2 (a) The first sub - figure depicts the actual state and the estimate with a sampling rate of 2T, the second sub - figure depicts the actual state and the estimate with a sampling rate of 3T, and the third sub - figure depicts the actual state and the fused estimate; Figure 2 (b) depicts the estimate of the second state component; Figure 2 (c) In the first sub - figure, the mean - square error and the upper bound with a sampling rate of 2T are plotted, in the second sub - figure, the mean - square error and the upper bound with a sampling rate of 3T are plotted, and in the third sub - figure, the mean - square error and the upper bound of the fusion are plotted. The experimental results show that the fused estimate effect is significantly better than the estimate before fusion.

[0085] The present invention adopts a method for event - fusion estimation of a multi - rate system in complex situations, considering the disadvantages of sensor degradation and random non - linear problems, as well as the problem that the existing methods cannot obtain the minimum filtering error covariance. An event - triggering mechanism is introduced to arrange the transmission sequence to reduce the communication cost. The covariance intersection fusion method is used to fuse the estimates of local filters to obtain the final fusion estimate of the multi - rate system. The application of this method avoids the huge computational burden, the unknown form of cross - covariance or the complexity of calculating cross - covariance, and can quickly and efficiently fuse the sampling values of different sensors in the multi - rate system for fusion estimation. The present invention can provide a reference for engineering implementers and also obtain better estimation results during event - fusion estimation, having great application value.

Claims

1. A method for multi-rate system event fusion estimation in complex situations, characterized in that: S1: Construct the state equation of the MRS and the measurement equation of the sensor nodes: The state equation is a discrete-time linear equation: x (k+1)T = Ax kT + Bw kT In the above formula, T > 0 is the system sampling period, is the state vector at the sampling time kT, is the zero-mean process noise with variance R kT > 0, and A and B are known time-invariant matrices with appropriate dimensions; The measurement equation of the i-th sensor node is: In the above formula, l i > 0 is an integer, is the measurement vector at the sampling time kl i at T, C i is a matrix of appropriate dimension, is the zero-mean measurement noise with variance , represents the impact of the sensor degradation phenomenon on the system, represents the impact of the random nonlinearity on the system S2: Convert the MRS to SRS. By using the lifting technique and the least common multiple method, sample period unification is performed for each sensor node in the interval [kl i +1, (k + 1)l i , and the state equation and measurement equation of the SRS are obtained; S3: Design a local recursive filter to accept measurement values based on an event-triggering mechanism Update the state through two stages of prediction and estimation S4: Calculate the upper bound of the filtering error covariance, including the prediction error covariance and the filtering error covariance and derive its recurrence relation through inequality techniques; S5: Design filter parameters Minimize an upper bound of the filtering error covariance in a recursive manner; S6: Use the CI fusion method to fuse the estimation results of each local filter to obtain the global fusion estimation and the fusion covariance.

2. The method for multi-rate system event fusion estimation in a complex situation according to claim 1, wherein: In the above S2, the specific method for converting the MRS into the SRS is: For the i-th sensor node, within the interval [kl i +1, (k + 1)l i , the state equation is extended by the lifting technique to: 0≤l≤l i -1 The finally derived state equation and measurement equation of the SRS are:

3. A method for multi-rate system event fusion estimation in complex situations according to claim 2, characterized in that: The construction method of the local recursive filter in the above S3 is as follows: In the above formula, and are the prediction and estimation of the state respectively, and are the filter parameters to be designed.

4. A method for multi-rate system event fusion estimation in complex situations according to claim 3, characterized in that: The calculation of the upper bound of the filtering error covariance in the above S4 satisfies: In the above formula, ζ 1,k = 1 + ε 1,k + ε 2,k and ε i,k (i = 1, 2, 3, 4, 5) are positive scalars, and the initial value of FEC is Then is the upper bound of the filtering error covariance, that is 5. A method for estimating multi-rate system event fusion in complex situations according to claim 4, characterized in that: In the above S5, the design of the filter parameters is: Gain of the filter is determined by the following formula: Among them 6. A method for multi-rate system event fusion estimation in complex situations according to claim 5, characterized in that: The specific steps of the CI fusion method are: Design set Π k = {i|k = m i,k l i , m i,k are positive integers, i ∈ (1, 2, …, M)}. When this set is not empty, perform local fusion: In the formula, Σ k and are the fusion estimate and the fusion covariance respectively: In the above formula, The fusion estimation problem can be formulated as a convex optimization problem to obtain the final fusion covariance:

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