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

Abstract

The invention discloses a set membership fusion estimation method and system for a multi-sensor system based on FlexRay protocol scheduling, and the method comprises the steps: building a state space model of the multi-sensor system, building an input signal model of an estimator under FlexRay protocol scheduling, calculating the parameters of the estimator, and carrying out the recursive calculation of a holosymmetric polytope containing the real state of the system. By means of fusion estimation and set membership estimation technologies, high-precision state estimation is provided for a multi-sensor system under FlexRay protocol scheduling, estimation errors at all moments can be ensured to be consistent and bounded by means of parameters of an estimator designed by the method, and therefore a good estimation effect is achieved.

Description

Technical Field

[0001] The invention belongs to the technical field of state estimation, and mainly relates to a collective fusion estimation method and system for a multi-sensor system under FlexRay protocol scheduling. Background Art

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

[0003] Set membership estimation is a state estimation technique for systems in bounded noise environments. This technique recursively calculates the set containing the true value of the system state and optimizes the size of the resulting set to achieve better estimation results. Although the statistical properties of noise cannot be obtained in many applications, they can usually be treated as bounded quantities. Therefore, these noises can be processed with the help of set membership estimation techniques to 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 this case, the network protocol needs to be used to schedule the order in which each sensor accesses the network. The FlexRay protocol is a communication protocol widely used in fields such as automotive in-vehicle networks. It is a hybrid protocol that switches between static and dynamic protocols. Therefore, compared with static or dynamic protocols, the scheduling of this protocol is more flexible.

[0005] According to the above analysis, it is of great practical significance to develop a set membership fusion estimation method for multi-sensor systems under FlexRay protocol scheduling. The existing set membership fusion estimation technology for multi-sensor systems under FlexRay protocol scheduling mainly gives a set containing the true state of the system by recursively solving linear matrix inequalities. This method, 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 of the invention

[0006] The present invention is aimed at the problem of low accuracy of set membership fusion estimation of a multi-sensor system under FlexRay protocol scheduling in the prior art, and proposes a set membership fusion estimation method and system for a multi-sensor system under FlexRay protocol scheduling. Through four steps of establishing a state space model of the multi-sensor system, establishing an input signal model of an estimator under FlexRay protocol scheduling, calculating estimator parameters and recursively calculating a fully symmetric polyhedron containing the real state of the system, fusion estimation and set membership estimation technology are used to provide high-precision state estimation for the multi-sensor system under FlexRay protocol scheduling. The estimator parameters designed by the present invention can ensure that the estimation error at each moment is consistently bounded, thereby achieving better estimation effect.

[0007] In order to achieve the above object, the technical solution adopted by the present invention is: a collective fusion estimation method for a multi-sensor system under FlexRay protocol scheduling, comprising the following steps:

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

[0009] S2. Establish the input signal model of the estimator under FlexRay protocol scheduling: The estimator adopts the zero-order hold mechanism. At time q, when the jth sensor obtains the right to access the network, the input signal of the estimator That is the measurement signal y at that moment j (q), when the jth sensor does not have access to the network, the input signal of the estimator Using the signal at the previous moment, the input signal of the estimator at time q can be expressed as

[0010]

[0011] in, 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. Calculate estimator parameters: For each node Its corresponding estimator parameters are Use the following formula to calculate

[0013]

[0014] The superscript "-1" indicates the inverse of the matrix. and By simultaneously solving a series of The relevant linear matrix inequalities are obtained:

[0015]

[0016] Among them, several pairs

[0017]

[0018] Characterize the scheduling of the FlexRay protocol;

[0019] S4. Recursively calculate the fully symmetric polytope containing the true state of the system: by calculating the augmented vector The fully symmetric polytope of gives an estimate of the system state x(q).

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

[0021]

[0022] Where q represents the sampling time, represents the set of positive integers; represents the state vector of the system, represents n-dimensional Euclidean space, n is a positive integer; the initial value x(1) of the system state belongs to a known fully symmetric polytope; w(q) represents r-dimensional unknown bounded process noise, which belongs to a known fully symmetric polytope <0, W>, and 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] in, represents the measured output of the jth sensor, Indicates m j dimensional Euclidean space, m j Indicates the dimension of the measurement; C j is a known constant matrix; υ j (q) is the bounded measurement noise.

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

[0027] When the system is scheduled by the RR protocol at time q, the number of sensors connected to the network σ(q) is:

[0028] σ(q)=mod(q-1,N)+1

[0029] Where mod(q-1, N) means q-1 modulo N;

[0030] When the system is scheduled by the TOD protocol at time q, the number of sensors connected to the network σ(q) is calculated as follows:

[0031]

[0032] In the formula, for j∈{l+1,l+2,…,N}, we have

[0033]

[0034]

[0035] That is, the number of sensors connected to the network at time q is such that the quadratic function χ j (q) The largest sensor number j, if there are two sensors corresponding to the quadratic function χ j (q) are equal, then the authority is given to the sensor with the smaller number. As another improvement of the present invention, when the set γ j When (q) is an empty set, In the formula Indicates measurement y j The square of the weighted 2-norm of (q), Indicates the added weight; when the set When not empty, In the formula Representing a collection The maximum value of the elements of ; represents the set of times when the jth sensor (j∈{l+1, l+2,…,N}) measures access to the network before time q. When the jth sensor’s measurement has never obtained access to the network, the set is an empty set, i.e.

[0036] As another improvement of the present invention, in step S3, the estimator parameter The calculation method is:

[0037]

[0038] in and To ensure the solution of the matrix inequality for the steady-state performance of the system, the superscript “-1” indicates the inverse of the matrix.

[0039] As another improvement of the present invention, the step S4 specifically includes the following steps:

[0040] by Indicates that at time q The fully symmetric polytope of is set to the initial value of the iteration:

[0041]

[0042]

[0043] Center Point The calculation method is:

[0044]

[0045] Its shape matrix is:

[0046]

[0047] In the formula

[0048] get Afterwards, polytope Each point in is an augmented system state Estimates.

[0049] In order to achieve the above purpose, the present invention also adopts a technical solution: a collective fusion estimation system of a multi-sensor system under FlexRay protocol scheduling, including a computer program, which implements the steps of any of the above methods when executed by a processor.

[0050] Compared with the prior art, the present invention has the following beneficial effects: the present invention provides a set membership fusion estimation method and system for a multi-sensor system under FlexRay protocol scheduling, adopts dynamic equations to describe a linear multi-sensor system, so that the proposed method has wider applicability; adopts the FlexRay protocol to schedule the transmission of each measurement output of the multi-sensor system to an estimator, which can effectively avoid data conflicts in the process; the input signal of the estimator under FlexRay protocol scheduling adopts fusion estimation technology and set membership estimation technology, and gives the recursive relationship of the center point and the generating matrix of a fully symmetric polyhedron containing the real state of the multi-sensor system in the form of a matrix equation, which reduces the algorithm complexity of the estimation algorithm, so that the proposed estimation algorithm is suitable for the case of online estimation; in addition, the present invention designs estimator parameters that can ensure that the estimation error at each moment is consistently bounded by solving a series of matrix inequalities offline, thereby achieving better estimation effect. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 It is a flow chart of a method for collective fusion estimation of a multi-sensor system under FlexRay protocol scheduling in an embodiment of the present invention;

[0052] Figure 2 It is a schematic diagram for comparing the true value of the fourth state variable of the system in the test example of the present invention and the estimated value obtained by using the estimation method of the present invention;

[0053] Figure 3 is the sensor number connected to the network at each time under the FlexRay protocol scheduling in the test example of the present invention;

[0054] Figure 4 Schematic diagram of the F-radius of a fully symmetric polytope containing the true state of the system in the test example of the present invention. DETAILED DESCRIPTION

[0055] The present invention will be further explained below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the following specific embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention.

[0056] Example 1

[0057] The set membership estimation method of multi-sensor system under FlexRay protocol scheduling, such as Figure 1 As shown, the following steps are included:

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

[0059] The state space model of the multi-sensor system includes the state equation and the measurement equation. The state equation is:

[0060]

[0061] Where q represents the sampling time, represents the set of positive integers; represents the state vector of the system, represents n-dimensional Euclidean space, n is a positive integer; the initial value x(1) of the system state belongs to the known fully symmetric polytope, that is, It means that c(1) is the center point and the matrix is the fully symmetric polytope of the shape matrix; w(q) represents the r-dimensional bounded process noise, which satisfies w(q)∈<0, W>, that is, the process noise at each sampling moment belongs to the known fully symmetric polytope w(q)∈<0, W>, where 0 indicates that the center point of the fully symmetric polytope is the zero vector, and W represents the shape matrix of the fully symmetric polytope <0, W>.

[0062] The system is sampled by N sensors, where 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] in, represents the measured output of the jth sensor, m j is a known positive integer, which represents the dimension of the measurement; C j is a known constant matrix; υ j (q) is the bounded measurement noise, which satisfies υ j (q)∈<0,V j >, where <0, V j > is centered at 0 and V j A fully symmetric polytope of the shape matrix.

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

[0066] Under the FlexRay protocol scheduling, at each sampling time q, only one sensor's measurement is allowed to access the network and be transmitted to the remote estimator. Below, σ(q) represents the number of the sensor connected to 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 using the RR (Round-Robin) protocol, and the measurements of the next Nl sensors are scheduled using the TOD (Try-once-discard) protocol. At the initial moment, the measurement of the first sensor is connected to the network. Based on this, the set of sampling times scheduled by the RR protocol and the TOD protocol for the system's t+1th time (t is a natural number) can be expressed as and

[0067] when That is, when the system is scheduled by the RR protocol at time q, the sensor number σ(q) connected to the network is given by the following formula:

[0068] σ(q)=mod(q-1,N)+1 (3)

[0069] Where mod(q-1, N) means q-1 modulo N;

[0070] when That is, when the system is scheduled by the TOD protocol at time q, the sensor number σ(q) connected to the network is calculated as follows:

[0071]

[0072] In the formula, for j∈{l+1,l+2,…,N}, we have

[0073]

[0074] That is, the number of sensors connected to the network at time q is such that the quadratic function χ j (q) The largest sensor number j, if there are two sensors corresponding to the quadratic function χ j (q) are equal, the authority is given to the sensor with the smaller number; the quadratic function X j Calculation and collection of (q) Regarding, specifically, when the set When it is an empty set, In the formula Indicates measurement y j The square of the weighted 2-norm of (q), is a given positive definite matrix, which represents the added weight, and when the set When not empty, In the formula Representing a collection The maximum value of the elements of ; represents the set of times when the jth sensor (j∈{l+1, l+2,…,N}) measures access to the network before time q (excluding q). When the jth sensor’s measurement has never obtained the permission to access the network, the set is an empty set, i.e.

[0075] A zero-order hold mechanism is used at the estimator end, and the input signal from the jth sensor received by the estimator at time q can be expressed as

[0076]

[0077] That is, at time q, when the jth sensor obtains access to the network, the input signal of the estimator That is the measurement signal y at that moment j (q), and when the jth sensor does not have access to the network, the input signal of the estimator Using the signal at the previous moment, that is The initial value of this signal is set to In the formula Indicates m j dimensional zero vector.

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

[0079]

[0080] Where the superscript “T” represents 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

[0083]

[0084] For any

[0085]

[0086] All are established, here the number of pairs It means that at two adjacent sampling moments, the sensor connected to the network at the previous moment is the jth sensor, and the sensor connected to the network at the next moment is the jth sensor. A sensor, and The value set of is the union of three sets (“∪” represents the union of sets), which describes the relationship between the sensor numbers connected to the network at two adjacent sampling times under the FlexRay protocol. In the static RR protocol scheduling, when the jth sensor accesses the network at the previous moment, the sensor number accessing the network at the next moment is must be j+1, which reflects the periodic scheduling characteristics of the RR protocol. It describes the sensor number j that is connected to the network at the previous moment when it takes a value in {l, l+1, ..., N} under the TOD protocol scheduling. The value set of is {l+1, l+2, ..., N}, and the set It reflects the relationship between the sensor numbers connected to the network from the last moment of TOD protocol scheduling to the first moment of RR protocol scheduling.

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

[0088]

[0089] Where 0 represents the zero matrix, and its subscript gives its dimension, such as Represents n rows zero matrix of columns; represents the sum of the dimensions measured by each sensor in (2); Λ j The following diagonal matrix

[0090]

[0091] Its diagonal elements are Where δ(·) is a binary function, its function value is 1 when its input is 0, and its function value is 0 when the input is non-zero, I represents the identity matrix, and its subscript represents the order of the identity matrix; The calculation is similar to Λ j , just change Λ j The subscript j is replaced by That's it;

[0092] for Estimator parameters Use the following formula to calculate

[0093]

[0094] The superscript “-1” indicates the inverse of the matrix.

[0095] Step S4: Recursively calculate the fully symmetric polytope that contains the true state of the system.

[0096] By calculating the augmented vector The fully symmetric polytope of gives an estimate of the system state x(q).

[0097] by Indicates that at time q The fully symmetric polytope of is given below. The initial value of the iteration is set to

[0098]

[0099] This initial value ensures That is, the state of the augmented system at the initial moment belongs to the fully symmetric polytope

[0100] Next in That is, the state of the augmented system at time q belongs to the known fully symmetric polytope Based on The fully symmetric polytope The calculation method of .

[0101] The center point Calculate by formula (12);

[0102]

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

[0104]

[0105] In the formula

[0106] In got Afterwards, polytope Each point in can be used as an augmented system state In application, the center point can usually be used for convenience. As the state of the augmented system The estimate of the system state x(q) is The estimated first n components of .

[0107] Test Case

[0108] In order to verify the effectiveness of the method proposed in the present invention, the following test experiment is conducted. During the experiment: the experimental step length is 200, and a multi-sensor system with four sensors is used for verification. 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 external process and measurement noise added in the test are as follows:

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

[0114] υ2(q)=0.2sin(0.15q), υ3(q)=0.2sin(0.2q)

[0115] υ4(q)=0.2sin(0.25q)

[0116] Accordingly, the parameters of the fully symmetric polytope including 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 parameters of the polytope containing it are set to:

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

[0123]

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

[0125] Figure 2 The true values ​​of the four state variables of the system (solid lines in the figure) and their estimated values ​​obtained by the estimation method of this patent (dashed lines in the figure) are given. It can be seen that even for unstable systems, the estimated values ​​obtained by the present invention are still relatively accurate.

[0126] Figure 3 The sensor numbers connected to the network at each time under the FlexRay protocol scheduling are given, which shows the orderliness of the access of each sensor node to the network under the protocol scheduling, thus verifying the scheduling effect of the protocol.

[0127] Figure 4 The F-radius of the fully symmetric polytope that contains the true state of the system is given. The figure shows that the calculated F-radius of the polytope is uniformly bounded, which can verify the role of the designed estimator parameters in ensuring the steady-state performance of the estimate.

[0128] In summary, the method of the present invention utilizes technologies such as fusion estimation and set membership estimation 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 a higher effect.

[0129] It should be noted that the above content only illustrates the technical idea of ​​the present invention and cannot be used to limit the protection scope of the present invention. For ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications all fall within the protection scope of the claims of the present invention.

Claims

1. A method for collective fusion estimation of a multi-sensor system under FlexRay protocol scheduling, characterized in that: The steps include: S1. Establish a state space model of a multi-sensor system: The state space model includes a state equation and a measurement equation, wherein the state equation is a set of first-order linear difference equations, which is used to describe the evolution relationship between the internal state variables of the system; the measurement equation is N algebraic equations, where N represents the number of sensors, which is used to describe the relationship between the measurement output of each sensor and the system state; S2. Establish the input signal model of the estimator under FlexRay protocol scheduling: The estimator adopts the zero-order hold mechanism. At time q, when the jth sensor obtains the right to access the network, the input signal of the estimator That is the measurement signal y at that moment j (q), when the jth sensor does not have access to the network, the input signal of the estimator Using the signal at the previous moment, the input signal of the estimator at time q is expressed as: in, represents the augmented vector of each input signal of the estimator at time q, and the superscript "T" represents the transpose of the vector; S3. Calculate estimator parameters: For each node Its corresponding estimator parameters are The following formula is used for calculation: The superscript "-1" indicates the inverse of the matrix. and By simultaneously solving the The relevant linear matrix inequality is obtained: Number pairs Describe the scheduling of the FlexRay protocol, specifically: S4. Recursively calculate the fully symmetric polytope containing the true state of the system: by calculating the augmented vector The fully symmetric polytope of gives an estimate of the system state x(q).

2. The method for collective fusion estimation of a multi-sensor system under FlexRay protocol scheduling as claimed in claim 1, characterized in that: In the state space model of the multi-sensor system in step S1, the state equation is: Where q represents the sampling time, represents the set of positive integers; represents the state vector of the system, represents n-dimensional Euclidean space, n is a positive integer; the initial value x(1) of the system state belongs to a known fully symmetric polytope; w(q) represents r-dimensional unknown bounded process noise, which belongs to a known fully symmetric polytope <0, W>, W represents 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 in, represents the measured output of the jth sensor, Indicates m j dimensional Euclidean space, m j Indicates the dimension of measurement; C j is a known constant matrix; v j (q) is the bounded measurement noise.

3. The method for collective fusion estimation of a multi-sensor system under FlexRay protocol scheduling as claimed in claim 2, characterized in that: In step S2, based on the FlexRay protocol, at each sampling time q, only one sensor's measurement is allowed to access the network and be transmitted to the remote estimator. The first l sensors of the multi-sensor system are scheduled using the RR protocol, and the measurements of the next Nl sensors are scheduled using the TOD protocol. The set of sampling times at which the system is scheduled by the RR protocol and the TOD protocol for the t+1th time can be expressed as S(t)={tN+1, tN+2, ..., tN+1} and When the system is scheduled by the RR protocol at time q, the number of sensors connected to the network σ(q) is: σ(q)=mod(q-1,N)+1 Where mod(q-1, N) means q-1 modulo N; When the system is scheduled by the TOD protocol at time q, the number of sensors connected to the network σ(q) is calculated as follows: In the formula, for j∈{l+1,l+2,...,N}, we have That is, the number of sensors connected to the network at time q is such that the quadratic function χ j (q) The largest sensor number j, if there are two sensors corresponding to the quadratic function χ j (q) are equal, the sensor with the smaller number is given the authority.

4. The method for collective fusion estimation of a multi-sensor system under FlexRay protocol scheduling as claimed in claim 3, characterized in that: When the collection j When (q) is an empty set, In the formula Indicates measurement y j The square of the weighted 2-norm of (q), Q j Represents the added weight; when the set γ j (q) is not empty, In the formula Represents the set γ j The maximum value of the elements of (q); γ j (q) represents the set of times when the jth sensor's measurements access the network before time q, j∈{l+1,l+2,...,N}; when the jth sensor's measurements have never obtained access to the network, the set is an empty set, i.e.

5. The method for collective fusion estimation of a multi-sensor system under FlexRay protocol scheduling as claimed in claim 1, characterized in that: In step S3, the remaining parameters of the matrix inequality are specifically: for j∈{1, 2, ..., N} and Positive scalar λ j , positive definite matrix P j , and matrix are all variables to be determined, matrix Θ, and They are all related to the multi-sensor system parameters under consideration, and 0 represents a zero matrix.

6. The method for collective fusion estimation of a multi-sensor system under FlexRay protocol scheduling as claimed in claim 4 or 5, characterized in that: The step S4 specifically includes the following steps: by Indicates that at time q The fully symmetric polytope of is set to the initial value of the iteration: Center Point The calculation method is: Its shape matrix is: In the formula get Afterwards, polytope Each point in is an augmented system state Estimates.

7. A collective fusion estimation system for a multi-sensor system under FlexRay protocol scheduling, including a computer program, characterized in that: When the computer program is executed by a processor, the steps of any of the above methods are implemented.

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