Method and system for set-membership fusion estimation of multi-sensor system under flexray protocol scheduling

Abstract

The application discloses a kind of based on the scheduling of FlexRay protocol multi-sensor system's set member fusion estimation method and system, through establishing the state space model of multi-sensor system, establishing the input signal model of estimator under the scheduling of FlexRay protocol, calculating estimator parameter and recursively calculating four steps of full symmetric polytope containing system real state, using fusion estimation and set member estimation technology, for the multi-sensor system under the scheduling of FlexRay protocol provides high-precision state estimation, the estimator parameter designed in the application can guarantee that the estimation error of each time is consistent bounded, to realize better estimation effect.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of state estimation, and mainly relates to a set member fusion estimation method and system for a multi-sensor system under FlexRay protocol scheduling. BACKGROUND

[0002] Fusion estimation is a state estimation technique for multi-sensor systems, which aims to appropriately use the measurement information from multiple sensors to provide the optimal estimation of the system state in a certain sense.

[0003] Set member estimation is a state estimation technique for systems in a bounded noise environment. This technique recursively calculates a set containing the true value of the system state, and optimizes the size of the resulting set to obtain better estimation results. Although the statistical properties of noise cannot be obtained in many application scenarios, they can usually be treated as bounded quantities, so set member estimation techniques can be used to process these noises and complete the fusion estimation of multi-sensor systems.

[0004] With the development of network technology, more and more fusion estimation tasks are implemented through communication networks. Due to the limitation of network bandwidth, if all sensors access the network to transmit data at the same time, data conflicts may occur, in which case network protocols are needed to schedule the order in which sensors access the network. FlexRay protocol is a widely used communication protocol in the field of automotive vehicle-mounted networks, etc. It is a hybrid protocol that switches between static and dynamic protocols, so its scheduling is more flexible than that of static or dynamic protocols.

[0005] According to the above analysis, it is of great practical significance to develop a set member fusion estimation method for a multi-sensor system under FlexRay protocol scheduling. Existing set member fusion estimation techniques for a multi-sensor system under FlexRay protocol scheduling mainly give a set containing the true state of the system by recursively solving linear matrix inequalities. This approach, especially when the system dimension is large, will bring a heavy computational burden. In addition, the existing method cannot guarantee the steady-state performance of the estimation, and there is a possibility of estimation error divergence. SUMMARY

[0006] The present application is just in view of the problem of low precision of the consensus fusion estimation of the multi-sensor system under the FlexRay protocol scheduling in the prior art, and provides a consensus fusion estimation method and system of the multi-sensor system under the FlexRay protocol scheduling, which comprises the following four steps: establishing a state space model of the multi-sensor system, establishing an input signal model of the estimator under the FlexRay protocol scheduling, calculating the estimator parameters and recursively calculating a full symmetric polytope containing the real state of the system, and using the fusion estimation and consensus estimation technologies to provide high-precision state estimation for the multi-sensor system under the FlexRay protocol scheduling. The estimator parameters designed in the present application can ensure that the estimation error at each time is uniformly bounded, thereby achieving good estimation effect.

[0007] In order to achieve the above-mentioned purpose, the technical scheme adopted by the present application is as follows: a consensus fusion estimation method of a multi-sensor system under a FlexRay protocol scheduling, comprising the following steps:

[0008] S1, establishing a state space model of the multi-sensor system: the state space model comprises a state equation and a measurement equation, wherein the state equation is a first-order linear difference equation set, which is used to describe the evolution relationship between the internal state variables of the system; the measurement equation is an algebraic equation, which is used to describe the relationship between the measurement output of each sensor and the state of the system;

[0009] S2, establishing an input signal model of the estimator under the FlexRay protocol scheduling: the zero-order hold mechanism is adopted at the estimator end, and at time q, when the jth sensor obtains the access right of the network, the input signal of the estimator is which is the measurement signal y j (q) at this time, and when the jth sensor does not obtain the access right of the network, the input signal of the estimator is which is the signal at the last time, and the input signal of the estimator at time q can be expressed as

[0010]

[0011] wherein, represents the augmented vector of each input signal of the estimator at time q, and the superscript "T" represents the transpose of the vector;

[0012] S3, calculating the estimator parameters: for each node its corresponding estimator parameter is calculated by using the following formula

[0013]

[0014] wherein the superscript "-1" represents the inverse of the matrix, and by simultaneously solving a series of pairs of numbers The related linear matrix inequality is obtained:

[0015]

[0016] where the pair of numbers

[0017]

[0018] The scheduling of FlexRay protocol is described.

[0019] S4, recursively calculating the full-symmetric polytope containing the real state of the system: the estimated value of the system state x(q) is given by calculating the full-symmetric polytope containing the augmented vector .

[0020] As an improvement of the present application, in the state space model of the step S1 multi-sensor system, the state equation is:

[0021]

[0022] where q represents a sampling time, represents a set of positive integers; represents a state vector of the system, represents an n-dimensional Euclidean space, n is a positive integer; the initial value x(1) of the system state belongs to a known full-symmetric polytope; w(q) represents an r-dimensional unknown bounded process noise, which belongs to a known full-symmetric polytope <0, W>, W represents the shape matrix of the polytope <0, W>;

[0023] The measurement equation of the jth sensor is:

[0024] y j (q)=C j x(q)+υ j (q), j=1, 2, …, N

[0025] wherein, represents the measurement output of the jth sensor, represents an m j -dimensional Euclidean space, m j represents the dimension of the measurement; C j is a known constant matrix; υ j (q) is a bounded measurement noise.

[0026] As another improvement of the present application, in step S2, based on the FlexRay protocol, only one sensor's measurement is allowed to access the network at each sampling time q to be transmitted to the remote estimator, the first l sensors of the multi-sensor system are scheduled by the RR protocol, and the measurements of the last N-l sensors are scheduled by the TOD protocol, the set of sampling times of the system scheduled by the RR protocol and the TOD protocol at the t+1th time can be respectively represented as and

[0027] When the system is scheduled by the RR protocol at time q, the sensor number σ(q) accessing the network is:

[0028] σ(q) = mod(q-1, N) + 1

[0029] where mod(q-1, N) represents the remainder of q-1 divided by N;

[0030] When the system is scheduled by the TOD protocol at time q, the sensor number σ(q) accessing the network is calculated as follows

[0031]

[0032] where for j ∈ {l+1, l+2, …, N}, there is

[0033]

[0034]

[0035] That is, at time q, the sensor number σ(q) accessing the network is the sensor number j that makes the quadratic function χ j (q) the largest, and if there are two sensors corresponding to the equal quadratic function χ j (q), the permission is given to the sensor with the smaller number. As another improvement of the present application, when the set γ j (q) is empty, where represents the square of the weighted 2-norm of the measurement y j (q), represents the added weight; when the set γ is not empty, where represents the maximum value of the elements of the set γ ; represents the set of times at which the measurement of the jth sensor (j ∈ {l+1, l+2, …, N}) accesses the network before time q, and when the measurement of the jth sensor has never obtained the permission to access the network, the set is an empty set, i.e.

[0036] As a further improvement of the present application, in the step S3, the estimator parameters are calculated as follows:

[0037]

[0038] where and are the solutions of the matrix inequalities ensuring the stability of the system, and the superscript "-1" denotes the inverse of the matrix.

[0039] As a further improvement of the present application, the step S4 specifically comprises the following steps:

[0040] where denotes the zonotope containing at time q, and the iteration initial value is set as:

[0041]

[0042]

[0043] The central point is calculated as:

[0044]

[0045] and the shape matrix is:

[0046]

[0047] where

[0048] After obtaining , each point in the zonotope is the estimation of the augmented system state .

[0049] In order to achieve the above object, the present application further adopts the technical scheme of: a set member fusion estimation system of a multi-sensor system under FlexRay protocol scheduling, comprising a computer program, the computer program is executed by a processor to realize the steps of the method as described above.

[0050] Compared with the prior art, the application has the beneficial effects that: the application provides a set member fusion estimation method and system of a multi-sensor system under FlexRay protocol scheduling, a dynamic equation is used to describe a linear multi-sensor system, so that the method has wide applicability; the transmission of each measurement output of the multi-sensor system to the estimator is scheduled by the FlexRay protocol, so that data conflicts in the process can be effectively avoided; the input signal of the estimator under the FlexRay protocol scheduling is scheduled by the fusion estimation technology and the set member estimation technology, the recursive relationship formula of the center point of the totally symmetric polytope containing the real state of the multi-sensor system and the generating matrix is given in the form of a matrix equation, the algorithm complexity of the estimation algorithm is reduced, so that the estimation algorithm is applicable to the online estimation situation; in addition, the application solves a series of matrix inequalities offline to design the estimator parameters capable of guaranteeing that the estimation errors at each time are uniformly bounded, so that a better estimation effect is achieved. BRIEF DESCRIPTION OF DRAWINGS

[0051] Figure 1 A flow chart of the set member fusion estimation method of the multi-sensor system under the FlexRay protocol scheduling in the embodiment of the application;

[0052] Figure 2 A comparison diagram of the true value of the fourth state variable of the system and the estimation value obtained by the estimation method of the application in the test example of the application;

[0053] Figure 3 The number of the sensors accessing the network at each time under the FlexRay protocol scheduling in the test example of the application;

[0054] Figure 4 An F-radius diagram of the totally symmetric polytope containing the real state of the system in the test example of the application. DETAILED DESCRIPTION

[0055] The application will be further illustrated below in combination with the drawings and the specific embodiments, and it should be understood that the following specific embodiments are only used to illustrate the application and are not used to limit the scope of the application.

[0056] Embodiment 1

[0057] The set member estimation method of the multi-sensor system under the FlexRay protocol scheduling, as shown in the figure, comprises the following steps: Figure 1

[0058] Step S1: establishing a state space model of the multi-sensor system.

[0059] The state space model of the multi-sensor system comprises a state equation and a measurement equation, and the state equation is:

[0060] ​

[0061] where q denotes the sampling time, denotes a set of positive integers; denotes the state vector of the system, denotes n-dimensional Euclidean space, n is a positive integer; the initial value x(l) of the system state belongs to a known zonotope, i.e. denotes a zonotope with c(l) as the center point and the matrix as the shape matrix; w(q) denotes r-dimensional bounded process noise, which satisfies w(q)∈<0, W>, i.e. the process noise at each sampling time belongs to a known zonotope w(q)∈<0, W>, where 0 denotes that the center point of the zonotope is a zero vector and W denotes the shape matrix of the zonotope <0, W>.

[0062] The system is sampled by N sensors, wherein the measurement equation of the jth sensor is:

[0063] y j (q)=C j x(q)+υ j (q), j=1, 2, …, N (2)

[0064] wherein, denotes the measurement output of the jth sensor, m j is a known positive integer, which denotes the dimension of the measurement; C j is a known constant matrix; υ j (q) is bounded measurement noise, which satisfies υ j (q)∈<0, V j >, wherein <0, V j > is a zonotope with 0 as the center point and V j as the shape matrix.

[0065] Step S2: establishing the input signal model of the estimator under the FlexRay protocol scheduling.

[0066] Under the FlexRay protocol scheduling, only one sensor is allowed to access the network to transmit the measurement to the remote estimator at each sampling time q, and the following σ(q) denotes the number of the sensor accessing the network at time q. According to the scheduling rules of the FlexRay protocol, the first l (l is a positive integer) sensors of the system are scheduled by the RR (Round-Robin) protocol, and the measurements of the last N-l sensors are scheduled by the TOD (Try-once-discard) protocol. At the initial time, the measurement of the first sensor accesses the network, and accordingly, the set of sampling times of the t+1th (t is a natural number) time when the system is scheduled by the RR protocol and the TOD protocol can be respectively represented as and

[0067] When That is, at time q when the system is scheduled by the RR protocol, the sensor number σ(q) accessing the network is given by

[0068] σ(q) = mod(q - 1, N) + 1 (3)

[0069] where mod(q - 1, N) denotes the remainder of q - 1 divided by N;

[0070] When That is, at time q when the system is scheduled by the TOD protocol, the sensor number σ(q) accessing the network is given by

[0071]

[0072] where for j ∈ {l + 1, l + 2,..., N}, we have

[0073]

[0074] That is, at time q the sensor number σ(q) accessing the network is the sensor number j for which the quadratic function χ j (q) is maximum, and if there are two sensors for which the quadratic function χ j (q) is equal, the permission is given to the sensor with the smaller number; the computation of the quadratic function χ j (q) is related to the set , specifically, when the set is empty, we have where denotes the square of the weighted 2-norm of the measurement y j (q), is a given positive definite matrix representing the weights added, and when the set is non-empty, we have where denotes the maximum value of the elements of the set ; denotes the set of times at which the jth sensor (j ∈ {l + 1, l + 2,..., N}) has accessed the network before time q (not including q), and when the jth sensor has never accessed the network, this set is empty, i.e.

[0075] At the estimator side, a zero-order hold mechanism is employed, and the input signal received by the estimator from the jth sensor at time q can be represented as

[0076]

[0077] That is, at time q, when the j-th sensor gains access to the network, the input signal of the estimator... That is, the measurement signal y at that moment. j (q), and when the j-th sensor does not have permission to access the network, the input signal of the estimator is... Using the signal from the previous moment, i.e. The initial value of the signal is set to In the formula m j The zero vector of dimension.

[0078] Based on model (6), the input signal of the estimator at time q can be expressed as:

[0079]

[0080] In the formula, the superscript "T" indicates the transpose of the vector.

[0081] Step S3: Calculate the estimator parameters.

[0082] To obtain the estimator parameters, a series of matrix inequalities need to be solved. Specifically, the matrix inequalities need to be satisfied.

[0083]

[0084] For any

[0085]

[0086] All of them are true; here are several pairs. This indicates that at two adjacent sampling times, the sensor connected to the network at the previous time is the j-th sensor, and the sensor connected at the next time is the j-th sensor. One sensor, and The set of values ​​is the union of three sets ("∪" represents the union of sets), which describes the relationship between sensor numbers accessing the network at two adjacent sampling times under the FlexRay protocol, where the set This indicates the sensor number that will join the network in the next time step when the j-th sensor joined the network in the previous time step under the static segment RR protocol scheduling. It must be j+1, which reflects the periodic scheduling characteristic of the RR protocol, set This describes the sensor number that will access the network in the next moment when the sensor number j that accessed the network in the previous moment takes a value in {l, l+1, ..., N} under the TOD protocol scheduling. The set of values ​​for is {l+1, l+2, ..., N}, while the set This reflects the relationship between the sensor numbers accessing the network from the last moment of the TOD protocol scheduling to the first moment of the RR protocol scheduling.

[0087] In the matrix inequality (8), for j e {1, 2,..., N} and positive scalar λ j , positive definite matrix P j , and matrix are variables to be solved, Θ = diag{W, V1, V2,..., V N} is a constant diagonal matrix, and other matrices are calculated as follows

[0088]

[0089] where 0 denotes a zero matrix, and its subscript gives its dimension, e.g. denotes a zero matrix of n rows and m columns; denotes the sum of dimensions of measurements of each sensor in (2); Λ j is a diagonal matrix

[0090]

[0091] whose diagonal elements are where δ(·) is a binary function, whose value is 1 when its input is 0, and 0 when its input is nonzero, and I denotes an identity matrix, whose subscript indicates the order of the identity matrix; The calculation of is similar to Λ j , only the subscript j of Λ j is replaced by ;

[0092] For the estimator parameter , it is calculated as follows

[0093]

[0094] where the superscript "-1" denotes the inverse of a matrix.

[0095] Step S4: recursively calculate the zonotope containing the true state of the system.

[0096] The estimated value of the state x(q) of the system is given by calculating the zonotope containing the augmented vector .

[0097] Let denote the zonotope containing at time q, and the recursive calculation method thereof is given as follows. Set the initial iteration value as

[0098]

[0099] ​The initial value can ensure i.e. the augmented system state at initial time belongs to the fully symmetric polytope

[0100] Next, at i.e. the augmented system state at time q belongs to the known fully symmetric polytope The calculation method of the fully symmetric polytope containing is given.

[0101] The center point of the fully symmetric polytope is calculated by formula (12);

[0102]

[0103] The shape matrix is calculated by formula (13)

[0104]

[0105] In the formula

[0106] After obtaining , each point in the polytope can be used as an estimate of the augmented system state In application, the center point is usually used as an estimate of the augmented system state , and the estimate of the system state x(q) is the first n components of the estimate of .

[0107] Test example

[0108] In order to verify the effectiveness of the method proposed in the present application, the following test experiment is made. In the experiment, the experimental step is 200, a multi-sensor system with four sensors is used for verification, and the parameters of the system are as follows:

[0109]

[0110] C1 = [0.1 0 0 0], C2 = [0 0 0 0.4]

[0111] C3 = [0 0 0.3 0], C4 = [0.1 0 0.15 0]

[0112] The process and measurement noise of the external environment in the test are as follows:

[0113] w(q) = 0.3cos(0.1q), υ1(q) = 0.2sin(0.1q)

[0114] u2(q) = 0.2sin(0.15q), u3(q) = 0.2sin(0.2q)

[0115] u4(q) = 0.2sin(0.25q)

[0116] Accordingly, the parameters of the zonotope containing the above process and measurement noise are as follows:

[0117] W = 0.3I, V1 = V2 = V3 = V4 = 0.2

[0118] The parameters of the FlexRay protocol are set as

[0119]

[0120] In addition, the parameter λ in the matrix inequality (8) j = 1 (j = 1, 2, 3, 4).

[0121] The initial state x(1) of the system and the zonotope containing it are set as:

[0122] x(1) = [0.3 0.2 0.1 0.2] T

[0123]

[0124] According to the state estimation method proposed in the present application, the estimation value is generated by using MATLAB software, and is compared with the true value of the system state provided by the platform.

[0125] Figure 2 The true values of the four state variables of the system (solid line in the figure) and the estimation values thereof obtained by using the estimation method of the present application (dashed line in the figure) are given, and it can be seen that even for an unstable system, the estimation value obtained by the present application is still relatively accurate.

[0126] Figure 3 The numbers of sensors accessing the network at each time under the FlexRay protocol scheduling are given, and it can be seen that the orderliness of the sensor nodes accessing the network under the protocol scheduling, thereby verifying the scheduling effect of the protocol.

[0127] Figure 4 The F-radius of the zonotope containing the true state of the system is given, and it can be seen from the figure that the F-radius of the calculated zonotope is uniformly bounded, and thereby the effect of the designed estimator parameters on guaranteeing the steady-state performance of the estimation can be verified.

[0128] In conclusion, the method of the present application uses fusion estimation and set membership estimation and other technologies to provide high-precision state estimation for a multi-sensor system under FlexRay protocol scheduling, effectively avoids data conflicts, is suitable for online estimation, and has higher effects.

[0129] It should be noted that the above content only illustrates the technical idea of the present application, and cannot be used to limit the protection scope of the present application. For ordinary skilled persons in the art, a number of improvements and refinements can be made without departing from the principles of the present application, and these improvements and refinements all fall within the protection scope of the claims of the present application.

Claims

1. A method for set-membership fusion estimation of a multi-sensor system under FlexRay protocol scheduling, characterized in that, The method comprises the following steps: S1, establishing a state space model of the multi-sensor system, wherein the state space model comprises state equations and measurement equations, the state equations are a set of first-order linear difference equations, and the measurement equations are N algebraic equations, N representing the number of sensors, and the measurement equations are used to describe the relationship between the measurement output of each sensor and the system state; S2, establishing the input signal model of the estimator under the FlexRay protocol scheduling: the zero-order hold mechanism is adopted at the estimator end, at time q, when the jth sensor obtains the access right of the network, the input signal of the estimator is i.e. the measurement signal y j (q) at this time, when the jth sensor does not obtain the access right of the network, the input signal of the estimator is the signal at the last time is adopted, the input signal of the estimator at time q is expressed as: wherein denotes the augmented vector of the input signals of the estimator at time q, the superscript "T" denotes the transposition of the vector. Based on the FlexRay protocol, only one sensor is allowed to access the network transmission to the remote estimator at each sampling time q, the first l sensors of the multi-sensor system use the RR protocol for scheduling, and the measurement of the last N-l sensors uses the TOD protocol for scheduling, and the set of sampling times of the system scheduled by the RR protocol and the TOD protocol at the t+1 time can be represented as and When the system is scheduled by the RR protocol at time q, the sensor number σ(q) accessing the network is: σ(q) = mod(q-1, N) + 1 Wherein mod(q-1, N) represents q-1 modulo N; When the system is scheduled by the TOD protocol at time q, the calculation of the sensor number σ(q) accessing the network is as follows Wherein, for j ∈ {l+1, l+2,..., N}, there is Y j (q) = {k: 1 < k < q, s(k) = j} i.e. the sensor number σ(q) accessing the network at time q is the sensor number j for which the quadratic function χ j (q) is maximum, and if there are two sensors for which the quadratic function χ j (q) is equal, the right is given to the sensor with the lower number. S3, compute estimator parameters: for each node its corresponding estimator parameters The computation is done using the following formula: where the superscript "-1" denotes the inverse of a matrix, and By simultaneously solving linear matrix inequalities associated with the pairs of numbers one obtains: Number pairs The scheduling of the FlexRay protocol is characterized in that: S4. Recursively compute the zonotope containing the true state of the system: Compute an estimate of the system state x(q) by computing the zonotope containing the augmented vector S4. Recursively compute the zonotope containing the true state of the system: Compute an estimate of the system state x(q) by computing the zonotope containing the augmented vector 2. The method of claim 1, wherein the FlexRay protocol schedule is a schedule of a FlexRay protocol. In the state space model of the multi-sensor system in the step S1, the state equations are: where q denotes the sampling time, denotes the set of positive integers; denotes the state vector of the system, denotes the n-dimensional Euclidean space, n is a positive integer; the initial value x(1) of the system state belongs to a known zonotope; w(q) denotes an unknown bounded process noise of dimension r, which belongs to a known zonotope <0, W>, and W denotes the shape matrix of <0, W>; The measurement equation of the jth sensor is: y j (q) = C j x(q) + v j (q), j = 1, 2,..., N wherein, represents the measurement output of the jth sensor, represents the m j dimensional Euclidean space, m j represents the dimension of the measurement; C j is a known constant matrix; v j (q) is a bounded measurement noise.

3. The method of claim 2, wherein the FlexRay protocol schedule is a schedule of the FlexRay protocol. when the set Y j (q) is empty, where denotes the measurements y j (q) of the weighted 2-norm of, denotes the added weight; when the set Y j (q) is non-empty, where denotes the maximum value of the elements of the set Y j (q) ; Y j (q) denotes the set of the times at which the jth sensor's measurements access the network before time q, j e {l+1, l+2,..., N}; when the jth sensor's measurements never gain access to the network, this set is empty, i.e.

4. The method of claim 1, wherein the FlexRay protocol schedule is a schedule of a FlexRay protocol. The remaining parameters of the matrix inequality in step S3 are specifically: for j∈{1, 2, …, N} and positive scalar λ j positive definite matrix P j , and matrix are variables to be solved, matrix Θ, and are related to the parameters of the multi-sensor system under consideration, and 0 represents a zero matrix.

5. The federated fusion estimation method for multi-sensor system under FlexRay protocol scheduling as claimed in claim 3 or 4, wherein: The step S4 specifically comprises the following steps: In represents the full-symmetric polytope containing at time q, set the iteration initial value as: center point is calculated as; The shape matrix is: In the formulae Obtained After, polytopes Each point in the set is an estimate of the augmented system state .

6. A multi-sensor system's consensus fusion estimation system under FlexRay protocol scheduling, comprising a computer program, characterized in that: The computer program is executed by the processor to realize the steps of the method in any one of claims 1-5.

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