Fully symmetric polytope set-membership state estimation method based on coding and quantization mechanism

Abstract

The application discloses a full-symmetrical polyhedral set-membership state estimation method based on coding and quantization mechanism, which comprises the following steps: a corresponding linear repetitive process system model is established; an augmented technology is applied to convert a time-varying linear multi-rate system model into a corresponding time-varying linear single-rate system model; the range of uncertainty factors such as disturbance and measurement noise in the system is expressed by a full-symmetrical polyhedron; a coding mechanism is introduced in the information transmission process of two types of sensors with different sampling rates, and the quantization effect is considered; the properties of the full-symmetrical polyhedron are used to design an estimator for the system, and the estimation value is obtained; and finally, the optimal full-symmetrical polyhedron in the F norm sense is obtained through the design of the parameters of the estimator. The application can process the information transmission security problem under a 2D system, introduces the coding mechanism to reduce the network communication burden, and solves the set-membership state estimation problem considering the coding mechanism under the linear repetitive process.

Description

Technical Field

[0001] This invention belongs to the field of information technology and relates to a method for estimating the state of a fully symmetric multicellular set based on encoding / decoding and quantization mechanisms. Specifically, it relates to a method for estimating the state of a fully symmetric multicellular set by introducing encoding / decoding and quantization mechanisms in a linear repetitive process. Background Technology

[0002] State estimation is a popular data denoising and trajectory tracking technique, widely used in practical applications such as search and rescue, navigation, border patrol, and traffic detection. The fundamental goal of state estimation is to reconstruct the state of a system that is difficult to access through sensory measurements. Broadly speaking, existing estimation methods can be divided into point state estimation and set membership estimation. Set membership estimation, in particular, constructs a compact set that covers the actual system state, and this method performs exceptionally well in analyzing unknown but bounded perturbations. Previous literature has reported numerous results related to set membership estimation. Ellipsoidal sets, polygonal sets, and intervals are widely used; in addition, fully symmetric polytopic set membership estimation based on one-dimensional systems utilizes Minkowski sum operations and order reduction techniques, thus exhibiting considerable performance.

[0003] However, existing methods for estimating the set membership of fully symmetric multicellular structures have limited results for two-dimensional systems and mostly consider time-invariant systems. Furthermore, current methods are typically designed for single-rate systems where the sampling rates of the system and the sensor are the same, but it is difficult to sample the system and the sensor at a consistent rate in many practical applications. Finally, the consideration of quantization effects in existing methods for estimating the set membership of fully symmetric multicellular structures has not been adequately addressed. Summary of the Invention

[0004] The purpose of this invention is to address the shortcomings of existing technologies by providing a fully symmetric multicellular set member state estimation method based on encoding / decoding and quantization mechanisms. This method can solve the multi-rate problem in linear repetitive processes under unknown but bounded external disturbances and measurement noise, ensuring the security and low power consumption of the communication transmission process.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] In a first aspect, the present invention provides a method for estimating the state of a fully symmetric multicell set based on encoding / decoding and quantization mechanisms, comprising the following steps:

[0007] Step (1): Establish a time-varying linear multi-rate system model under a linear repetitive process;

[0008] Step (2): Apply augmentation techniques to convert the time-varying linear multi-rate system model into the corresponding time-varying linear single-rate system model;

[0009] Step (3): Introduce encoding / decoding and quantization mechanisms into the converted time-varying linear single-rate system model to save limited communication resources and protect transmission security.

[0010] Step (4): Design a fully symmetric polytopic set member state estimator based on encoding / decoding and quantization mechanisms to obtain a parameterized fully symmetric polytopic estimation set containing the true state of the system;

[0011] Step (5): Optimize the parameters of the fully symmetric polytope member state estimator to obtain the fully symmetric polytope estimation set that is minimized in the sense of F norm.

[0012] In a second aspect, the present invention provides an electronic device including a processor and a memory, the memory storing machine-executable instructions executable by the processor, the processor executing the machine-executable instructions to implement the above-described method.

[0013] Thirdly, the present invention provides a machine-readable storage medium storing machine-executable instructions that, when invoked and executed by a processor, cause the processor to implement the above-described method.

[0014] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0015] This invention effectively controls the scale of matrix calculation by augmenting the corresponding outputs of different types of sensors at each time moment, resulting in a smaller computational burden. This overcomes the problem of high computational burden caused by the use of boosting techniques in the conversion of multi-rate to single-rate problems in the prior art.

[0016] This invention provides a fully symmetric polytope set member state estimation method based on encoding / decoding and quantization mechanisms under unknown but bounded noise constraints, obtaining a fully symmetric polytope containing the true values ​​of the target state. Furthermore, through parameter optimization, the minimum fully symmetric polytope estimation set under the norm rule can be obtained, thus ensuring excellent estimation accuracy. The center of the minimum fully symmetric polytope estimation set is selected as the point estimate of the state, achieving state estimation and effectively solving the multi-rate sensor problem and information transmission security problem, saving communication resources while ensuring the security of transmitted information. Attached Figure Description

[0017] Figure 1 This is a schematic diagram of the process of the present invention.

[0018] Figure 2 The system state variable when s=15 and its estimates Illustration of upper and lower bounds.

[0019] Figure 3The system state variables for the entire linear repetitive process and its estimates Illustration of upper and lower bounds.

[0020] Figure 4 The system state variables for the entire linear repetitive process and its estimates Illustration of upper and lower bounds. Detailed Implementation

[0021] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0022] like Figure 1 As shown, this invention provides a method for estimating the state of a fully symmetric multicellular set based on encoding / decoding and quantization mechanisms, comprising the following steps:

[0023] Step (1): Establish a time-varying linear multi-rate system model under a linear repetitive process.

[0024] The time length of the time-varying linear multi-rate system model under the linear repetitive process is: The model is as follows:

[0025]

[0026] Where s is the channel index and k is the time index. This represents the system state vector at time k on the s-th channel. Represents n x Euclidean space of 3D; Let represent the channel profile vector at time k on the s-th channel. Represents n y Euclidean space of 3D; This represents an unknown but bounded system perturbation. Represents n ω Euclidean space of 3D; Given a time-varying real matrix, i = 1, 2; that is: This represents the system state vector at time k+1 on the (s+1)th channel. This represents the system state vector at time k on the (s+1)th channel. Given a time-varying real matrix, This represents the channel profile vector at time k on the s-th channel;

[0027] The system is observed using a multi-rate sampling sensor, and the equation is expressed as:

[0028]

[0029] in This represents the output received by the type I sensor at time k on the s-th channel, where the sampling time of the type I sensor is... Represents n z Euclidean space of 3D; This represents the output received by the Type II sensor at time k on the s-th channel. The sampling times of the Type II sensor are 0, α, ..., rα; α is an integer greater than 1, r is a multiple, and rα is a multiple not exceeding 1. The largest integer; This represents unknown but bounded measurement noise. express Euclidean space of 3D; This represents unknown but bounded measurement noise. express Euclidean space of 3D; Given a known time-varying real matrix. Type I sensors generally refer to high sampling rate sensors, capable of sampling signals at a high frequency, suitable for scenarios requiring the capture of rapidly changing signals. Type II sensors, on the other hand, generally refer to low sampling rate sensors, with a relatively low sampling frequency, more suitable for monitoring slowly changing physical quantities, and can reduce data storage and processing costs while meeting monitoring requirements.

[0030] Step (2): Apply augmentation techniques to convert the time-varying linear multi-rate system model into the corresponding time-varying linear single-rate system model.

[0031] Step (2) is completed by augmenting the two types of sensors, making the system a single-rate system:

[0032]

[0033] in This represents the output of the s-th channel at time k. is n z Euclidean space of 3D; This represents the output received by the type I sensor at time k on the s-th channel. Let represent the output received by the Type II sensor at time k on the s-th channel, and mod(k, α) represent the remainder of k with respect to α at the current time.

[0034] make in express We have a dimensional Euclidean space, where T denotes the transpose; therefore, we can obtain the following augmented system representation:

[0035]

[0036] z(s,k)=Dγ(s,k) (s,k)x(s,k)+H γ(s,k) (s,k)v(s,k)

[0037]

[0038] in This indicates the operating status of the two types of sensors at time k;

[0039] For the initial states x(s,0) and x(0,k) of the system, the system disturbance ω(s,k) and the measurement noise v(s,k) are contained in the following fully symmetric polytope:

[0040] Where X0 and P0 are known vectors and matrices, respectively. and They are of order n ω and n v The identity matrix.

[0041] Step (3) Introduce encoding / decoding and quantization mechanisms into the converted time-varying linear single-rate system model to save limited communication resources and protect transmission security.

[0042] The encoding mechanism and quantization are as follows:

[0043]

[0044] in Represents the encoder's internal state vector. Represents n χ Euclidean space of 3D; This represents the encoder output. Represents n ψ Euclidean space of 3D; The time-varying matrix is ​​known; The uniform quantization operator can be represented as:

[0045]

[0046] in τ is the given quantization level. This represents the floor operator.

[0047] Furthermore, the decoding mechanism is as follows:

[0048]

[0049] in This represents the decoder's output, which is also the final output. Represents n z Euclidean space of 3D.

[0050] Furthermore, consider the errors introduced by the quantization mechanism and encoding / decoding. It can be obtained in It is quantization error. express An identity matrix of dimension 1.

[0051] Step (4): Design a fully symmetric polytopic set member state estimator based on encoding / decoding and quantization mechanisms to obtain a parameterized fully symmetric polytopic estimation set containing the true state of the system.

[0052] Based on the mechanism described in step (3), the fully symmetric multicell containing the real state obtained in step (4) through the order reduction technique is shown below. p (·) The fully symmetric polytope obtained can keep the order of the operators from not exceeding a given threshold p, specifically as follows:

[0053]

[0054] In the formula Represents the center and intermediate parameters of a fully symmetric multicellular structure. This represents a one-step estimate of the state; the generating matrix before order reduction can be represented as: intermediate parameters K(s,k) is the parameter to be designed.

[0055] Based on the obtained fully symmetrical multicellular center It can monitor the system status. Perform range estimation to obtain The upper realm and the lower world as follows:

[0056]

[0057] in rows and matrices intermediate parameters yes The element in the i-th row and j-th column; m(s,k) represents The number of columns.

[0058] Step (5): Optimize the parameters to obtain the full symmetric polytope estimation set that minimizes the F-norm (the parameter matrix K(s,k) that minimizes the full symmetric polytope norm).

[0059] It is calculated using the following formula:

[0060]

[0061] The intermediate parameters can be calculated using the following formulas:

[0062]

[0063] When parameter When the F-norm of the fully symmetric polytope obtained above reaches its minimum value, the fully symmetric polytope containing the system state is at its minimum under the F-norm of its generating matrix.

[0064] The following simulation verification is performed using the method provided by this invention.

[0065] The system parameters are set as follows:

[0066]

[0067] System disturbance Noise measurement

[0068] The sampling rate of the Type II sensor is α = 2, the quantization level is τ = 0.1, and the given matrix is ​​δ(s,k) = 0.9I. The reduction parameter in the lemma is p = 10.

[0069] The initial value of the state is set as follows: The initial state is contained in a fully symmetric multicellular structure. in

[0070] Simulation results are as follows Figure 2-4 As shown: Figure 2 The system state variables are given with a fixed channel s=15. System state variables Estimate System state variables The upper and lower bounds; Figure 3-4 The system state variables for the entire linear repetitive process are given. System variables Estimate And the corresponding upper and lower bounds (i = 1, 2).

[0071] Finally, it should be noted that the above examples are merely specific embodiments of the present invention. Obviously, the present invention is not limited to the above embodiments and many variations are possible. All variations that can be directly derived or conceived by those skilled in the art from the disclosure of this invention should be considered within the scope of protection of this invention.

Claims

1. A full-symmetry polytope set-membership state estimation method based on coding and quantization mechanism, characterized in that, The method comprises the following steps: Step (1), establishing a time-varying linear multi-rate system model under a linear repetitive process; Step (2), converting the time-varying linear multi-rate system model into a corresponding time-varying linear single-rate system model by using an augmentation technique; Step (3), introducing a codec mechanism and a quantization mechanism into the converted time-varying linear single-rate system model; Step (4), designing a full-symmetrical polytope set member state estimator based on the codec mechanism and the quantization mechanism to obtain a parameterized full-symmetrical polytope estimation set containing a real state of the system; wherein the codec mechanism and the quantization mechanism are represented as follows: where s is the channel index and k is the time index; denotes the encoder internal state vector, denotes n χ dimensional Euclidean space; denotes the encoder output, denotes n ψ dimensional Euclidean space; denotes the output at time k on the s-th channel, is n z dimensional Euclidean space; is a known time-varying matrix; denotes the uniform quantization operator, which is given by: wherein T is a given quantization level, denotes the rounding operator; The decoding mechanism is represented as follows: wherein represents the output of the decoder, which is also the final output obtained; Step (5), optimizing parameters to obtain a full-symmetrical polytope estimation set that is minimum in the F norm sense.

2. The full symmetric zonotope set-membership state estimation method based on codec and quantization mechanism according to claim 1, characterized in that, The time length of the time-varying linear multi-rate system model under the linear repetitive process is The specific implementation is as follows: where s is the channel index and k is the time index, denotes the system state vector at time k in the s-th channel, denotes the n x dimensional Euclidean space; denotes the channel profile vector at time k in the s-th channel, denotes the n y dimensional Euclidean space; denotes the unknown but bounded system disturbance, denotes the n ω dimensional Euclidean space; is a known time-varying real matrix; The system is observed by using a multi-rate sampling sensor, and the equation is represented as: wherein represents the output received by the kth sensor of type I at the (s+1)th channel, the sampling time of the sensor being represents the output received by the nth sensor of type II at the (s+1)th channel, the sampling time of the sensor being z a d-dimensional Euclidean space; represents the output received by the kth sensor of type II at the (s+1)th channel, the sampling time of the sensor being 0, a,..., r a; a is an integer greater than 1, r is a multiple, and r a is the largest integer not exceeding the number of samples of the sensor; represents the unknown but bounded measurement noise, represents the output received by the kth sensor of type I at the (s+1)th channel, the sampling time of the sensor being a d-dimensional Euclidean space; represents the unknown but bounded measurement noise, represents the output received by the kth sensor of type II at the (s+1)th channel, the sampling time of the sensor being a d-dimensional Euclidean space; is a known time-varying real matrix.

3. The full symmetric zonotope set-membership state estimation method based on codec and quantization mechanism according to claim 2, characterized in that, Step (2) is completed by augmenting the outputs of the two types of sensors, so that the system becomes a single-rate system: wherein represents the output at time k on the s-th channel, is n z dimensional Euclidean space; represents the output received by the I-type sensor at time k on the s-th channel, represents the output received by the II-type sensor at time k on the s-th channel, mod(k, a) represents the current time k modulo a. Let where denotes Euclidean space, T denotes transpose; The following augmented system representation is obtained: z(s, k) = D γ(s,k) (s, k) x(s, k) + H γ(s,k) (s, k) v(s, k) Wherein γ(s, k) represents a working state of the sensor at time k.

4. The full symmetric zonotope set-membership state estimation method based on codec and quantization mechanism according to claim 3, characterized in that, Step (4) by the reduction technique ↓ p (·) the resulting full-symmetry polytope containing the real state, the resulting full-symmetry polytope is specifically: wherein denotes the center of the zonotope, the intermediate parameter denotes a one-step estimate of the state; The generation matrix before order reduction is represented as: Wherein Π(s, k) is an intermediate parameter; K(s, k) is a parameter to be designed.

5. The full symmetric zonotope set-membership state estimation method based on codec and quantization mechanism according to claim 4, characterized in that, According to the obtained central symmetry polyhedron On the system state Perform range estimation, get Upper bound And lower bound wherein the rows and matrices intermediate parameters is the element of the i-th row and j-th column of ; m(s, k) denotes the number of columns of 6. The full symmetric zonotope set-membership state estimation method based on coding and quantization mechanism according to claim 5, characterized in that, The full-symmetrical polytope estimation set that is minimum in the F norm sense is calculated by the following formula: Wherein the intermediate parameters are calculated by the following formulas, respectively: When the parameter the F-norm of the above-obtained holohedral polyhedron reaches a minimum value.

7. An electronic device comprising a processor and a memory, characterized in that The memory stores machine executable instructions capable of being executed by the processor, and the processor executes the machine executable instructions to implement the method according to any one of claims 1-6.

8. A machine-readable storage medium, characterized in that, The machine readable storage medium stores machine executable instructions, and when the machine executable instructions are called and executed by the processor, the machine executable instructions cause the processor to implement the method according to any one of claims 1-6.

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