Coding and decoding and quantization mechanism-based holosymmetric polytope set membership state estimation method

Abstract

The invention discloses a holosymmetric polytope set membership state estimation method based on coding and decoding and a quantization mechanism. The method comprises the following steps: establishing a corresponding linear repetition process system model; converting the time-varying linear multi-rate system model into a corresponding time-varying linear single-rate system model by applying an augmentation technology; the range of uncertain factors such as disturbance and measurement noise in the system is expressed by using a holosymmetric polytope; in an information transmission process of two types of sensors with different sampling rates, a coding and decoding mechanism is introduced, and a quantization effect is considered; designing an estimator for the system by using the property of the holosymmetric polytope, and obtaining an estimated value of the estimator; and finally, an optimal holosymmetric polytope in F norm significance is obtained by designing parameters of the estimator. According to the method, the information transmission security problem under the 2D system can be solved, a coding and decoding mechanism is introduced, the network communication burden is relieved, and the problem of set membership state estimation considering the coding and decoding mechanism in the linear repetition process is solved.

Description

Technical Field

[0001] The present invention belongs to the field of information technology, and relates to a method for estimating the state of a fully symmetric polytope set membership based on a coding and decoding mechanism and a quantization mechanism, and specifically relates to a method for estimating the state of a fully symmetric polytope set membership by introducing a coding and decoding mechanism and a quantization mechanism under a linear repetitive process. Background Art

[0002] State estimation is a popular data denoising and trajectory tracking technique, which is widely used in practical applications such as search and rescue, navigation, border patrol, and traffic detection. The basic goal of state estimation is to reconstruct the state of an inaccessible system through sensory measurements. Broadly speaking, existing estimation methods can be divided into point state estimation and set membership estimation. Among them, set membership estimation can construct a compact set covering the actual system state, which has excellent performance in analyzing unknown but bounded disturbances. A large number of results related to set membership estimation have been reported in previous literature. Among them, ellipsoid sets, polygon sets, and intervals are widely used; in addition, the set membership estimation based on the fully symmetric polytope of one-dimensional system utilizes Minkowski sum operations and order reduction techniques, so it has quite good performance.

[0003] However, existing methods for estimating the set membership of fully symmetric polytopes have few relevant results in two-dimensional systems, and most of them consider time-invariant systems. In addition, current methods usually target single-rate systems where the sampling rate of the system and the sensor is the same, but in many practical applications it is difficult to sample the system and the sensor at a consistent rate. Finally, the consideration of quantization effects in existing methods for estimating the set membership of fully symmetric polytopes has not been well addressed. Summary of the invention

[0004] The purpose of the present invention is to address the deficiencies in the prior art and to provide a fully symmetric polyhedral set membership state estimation method based on encoding and decoding and quantization mechanisms, which can solve the multi-rate problem in a linear repetitive process under unknown but bounded external disturbances and measurement noise, thereby ensuring the security and low consumption of the communication transmission process.

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

[0006] In a first aspect, the present invention provides a method for estimating the state of a fully symmetric polytope set based on a coding and quantization mechanism, comprising the following steps:

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

[0008] Step (2), applying augmentation technology to convert the time-varying linear multi-rate system model into a corresponding time-varying linear single-rate system model;

[0009] Step (3), introducing a coding and decoding mechanism and a quantization mechanism into the converted time-varying linear single-rate system model to save limited communication resources and protect transmission security;

[0010] Step (4), designing a fully symmetric polytope set membership state estimator based on the encoding and decoding mechanism and the quantization mechanism, and obtaining a parameterized fully symmetric polytope estimation set containing the true state of the system;

[0011] Step (5), optimize the parameters of the fully symmetric polytope set membership state estimator to obtain the smallest fully symmetric polytope estimation set in terms of the F-norm.

[0012] In a second aspect, the present invention provides an electronic device, comprising a processor and a memory, wherein the memory stores machine executable instructions that can be executed by the processor, and the processor executes the machine executable instructions to implement the above method.

[0013] In a third aspect, the present invention provides a machine-readable storage medium storing machine-executable instructions. When the machine-executable instructions are called and executed by a processor, the machine-executable instructions prompt the processor to implement the above method.

[0014] Compared with the prior art, the present invention has the following beneficial effects:

[0015] The present invention can effectively control the scale of matrix calculation by obtaining the corresponding outputs of different types of sensors at each moment and then performing augmentation, with a small calculation burden, thus overcoming the problem of heavy calculation burden caused by using lifting technology in the prior art in converting multi-rate to single-rate problems.

[0016] The present invention provides a fully symmetric polytope set membership state estimation method based on a coding and decoding mechanism and a quantization mechanism under the constraint of unknown but bounded noise, and obtains a fully symmetric polytope containing the true value of the target state; and through parameter optimization, the smallest fully symmetric polytope estimation set under the norm rule can be obtained, thereby ensuring excellent estimation accuracy. The center of the smallest fully symmetric polytope estimation set is selected as the point estimation of the state to achieve the estimation of the state, effectively solving the multi-rate sensor problem and the information transmission security problem, saving communication resources while ensuring the security of transmitted information. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0018] Figure 2 When s=15, the system state variable and its estimation Schematic diagram of the upper and lower bound results.

[0019] Figure 3is the system state variable of the entire linear repetitive process and its estimation Schematic diagram of the upper and lower bound results.

[0020] Figure 4 is the system state variable of the entire linear repetitive process and its estimation Schematic diagram of the upper and lower bound results. DETAILED DESCRIPTION

[0021] The present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0022] like Figure 1 As shown, the present invention provides a method for estimating the state of a fully symmetric polytope set based on a coding and quantization mechanism, comprising the following steps:

[0023] Step (1), establishing 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] Among them, s is the channel index, k is the time index, represents the system state vector at time k on the sth channel, Indicates n x dimensional Euclidean space; represents the channel profile vector at time k on the sth channel, Indicates n y dimensional Euclidean space; represents an unknown but bounded system perturbation, Indicates n ω dimensional Euclidean space; is a known time-varying real matrix, i=1,2; that is: represents the system state vector at time k+1 on the s+1th channel, represents the system state vector at time k on the s+1th channel, is a known time-varying real matrix, represents the channel profile vector at time k on the sth channel;

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

[0028]

[0029] in represents the output received by the type I sensor at time k on the sth channel, and the sampling time of the type I sensor is Indicates n z dimensional Euclidean space; represents the output received by the type II sensor at time k on the sth channel, where the sampling time of the type II sensor is 0, α, …, rα; α is an integer greater than 1, r is a multiple, and rα is not more than The largest integer of ; represents the unknown but bounded measurement noise, express dimensional Euclidean space; represents the unknown but bounded measurement noise, express dimensional Euclidean space; is a known time-varying real matrix. Type I sensors generally refer to high sampling rate sensors, which can sample signals at a higher frequency and are suitable for scenarios where fast-changing signals need to be captured. Type II sensors generally refer to low sampling rate sensors, which have a relatively low sampling frequency and are more suitable for monitoring physical quantities that change slowly. They can meet monitoring needs while reducing the cost of data storage and processing.

[0030] Step (2), applying augmentation technology, converting the time-varying linear multi-rate system model into a corresponding time-varying linear single-rate system model.

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

[0032]

[0033] in represents the output of the sth channel at time k, Yes 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 type II sensor at time k on the sth channel, mod(k,α) represents the modulus of α at the current time k;

[0034] make in express dimensional Euclidean space, T represents transpose; therefore, the following augmented system representation can be obtained:

[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 Indicates the working status of the two types of sensors at time k;

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

[0040] Where X 0 and P 0 are known vectors and matrices, and They are respectively of order n ω and n v The identity matrix of .

[0041] Step (3) introduces a coding and decoding mechanism and a quantization mechanism 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:

[0043]

[0044] in represents the internal state vector of the encoder, Indicates n χ dimensional Euclidean space; represents the output of the encoder, Indicates n ψ dimensional Euclidean space; is a known time-varying matrix; represents the uniform quantization operator, which can be expressed as:

[0045]

[0046] in τ is a given quantization level, Represents the rounding operator.

[0047] Furthermore, the decoding mechanism is:

[0048]

[0049] in Represents the output of the decoder, which is also the final output. Indicates n zdimensional Euclidean space.

[0050] Furthermore, consider the errors caused by the quantization mechanism and encoding and decoding Can get in is the quantization error, express dimensional identity matrix.

[0051] Step (4): design a fully symmetric polytope set membership state estimator based on the encoding and decoding mechanism and the quantization mechanism to obtain a parameterized fully symmetric polytope estimation set containing the true state of the system.

[0052] Based on the mechanism described in step (3), step (4) obtains a fully symmetric polytope containing the true state through order reduction technology. The order reduction technology↓ p (·) can keep the order of the operator from exceeding the given threshold p, and the obtained fully symmetric polytope is:

[0053]

[0054] In the formula Represents the center of the fully symmetric polytope, the intermediate parameter Represents a one-step estimate of the state; the generating matrix before reduction can be expressed as: Intermediate parameters K(s,k) is the parameter to be designed.

[0055] According to the obtained fully symmetric polytope center System status Perform range estimation and obtain The upper bound of With the lower bound as follows:

[0056]

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

[0058] Step (5), optimize the parameters to obtain the smallest estimated set of fully symmetric polytopes in terms of the F-norm (the parameter matrix K(s, k) that minimizes the norm of the fully symmetric polytopes).

[0059] Calculated by the following formula:

[0060]

[0061] Among them, the intermediate parameters can be calculated using the following formulas:

[0062]

[0063] When the parameter When , the F norm of the above-obtained fully symmetric polytope reaches its minimum value. At this time, in terms of the F norm of its generating matrix, the fully symmetric polytope containing the system state is the smallest.

[0064] The method provided by the present invention is used for simulation verification below.

[0065] The system parameters are set as follows:

[0066]

[0067] System disturbance Measurement noise

[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 p in the lemma is p=10.

[0069] The initial value of the state is set to: The initial state is contained in the fully symmetric polytope in

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

[0071] Finally, it should be noted that the above examples are only specific embodiments of the present invention. Obviously, the present invention is not limited to the above examples, and many variations are possible. All variations that can be directly derived or associated with the content disclosed by a person skilled in the art should be considered as the protection scope of the present invention.

Claims

1. A method for estimating the state of a fully symmetric polytope set based on a coding and quantization mechanism, characterized in that: The following steps are involved: Step (1), establishing a time-varying linear multi-rate system model under a linear repetitive process; Step (2), applying augmentation technology to convert the time-varying linear multi-rate system model into a corresponding time-varying linear single-rate system model; Step (3), introducing a coding and decoding mechanism and a quantization mechanism into the converted time-varying linear single-rate system model; Step (4), designing a fully symmetric polytope set membership state estimator based on the encoding and decoding mechanism and the quantization mechanism, and obtaining a parameterized fully symmetric polytope estimation set containing the true state of the system; Step (5), optimize the parameters to obtain the smallest estimated set of fully symmetric polytopes in terms of the F-norm.

2. The method for estimating the state of a fully symmetric polytope set based on a coding 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 details are as follows: Among them, s is the channel index, k is the time index, represents the system state vector at time k on the sth channel, Indicates n x dimensional Euclidean space; represents the channel profile vector at time k on the sth channel, Indicates n y dimensional Euclidean space; represents an unknown but bounded system perturbation, Indicates n ω dimensional Euclidean space; is a known time-varying real matrix; The system is observed using a multi-rate sampling sensor, and the equation is expressed as: in represents the output received by the type I sensor at time k on the s+1th channel, and the sampling time of the type I sensor is Indicates n z dimensional Euclidean space; represents the output received by the type II sensor at time αk on the s+1th channel, where the sampling time of the type II sensor is 0, α, …, rα; α is an integer greater than 1, r is a multiple, and rα is not more than The largest integer of ; represents the unknown but bounded measurement noise, express dimensional Euclidean space; represents the unknown but bounded measurement noise, express dimensional Euclidean space; is a known time-varying real matrix.

3. The method for estimating the state of a fully symmetric polytope set based on a coding and quantization mechanism according to claim 1, characterized in that: Step (2) is completed by augmenting the outputs of the two types of sensors, making the system a single-rate system: in represents the output of the sth channel at time k, Yes 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 type II sensor at time k on the sth channel, mod(k,α) represents the modulus of α at the current time k; make in represents n-dimensional Euclidean space, T represents transposition; The following augmented system representation is obtained: Where γ(s,k) represents the working state of the sensor at time k.

4. The method for estimating the state of a fully symmetric polytope set based on a coding and quantization mechanism according to claim 1, characterized in that: In step (3), the encoding mechanism and quantization mechanism are expressed as follows: in represents the internal state vector of the encoder, Indicates n χ dimensional Euclidean space; represents the output of the encoder, Indicates n ψ dimensional Euclidean space; is a known time-varying matrix; represents the uniform quantization operator, which is expressed as: in τ is a given quantization level, Represents the rounding operator.

5. The method for estimating the state of a fully symmetric polytope set based on a coding and quantization mechanism according to claim 4, characterized in that: In step (3), the decoding mechanism is expressed as follows: in Represents the output of the decoder, which is also the final output.

6. The method for estimating the state of a fully symmetric polytope set based on a coding and quantization mechanism according to claim 1, characterized in that: Step (4) obtains a fully symmetric polytope containing the true state through the order reduction technique. The obtained fully symmetric polytope is specifically: in Represents the center of the fully symmetric polytope, the intermediate parameter represents a one-step estimate of the state; The generated matrix before reduction is expressed as: Where Π(s, k) is an intermediate parameter; K(s, k) is a parameter to be designed.

7. The method for estimating state of a fully symmetric polytope set based on a coding and quantization mechanism according to claim 1, characterized in that: According to the obtained fully symmetric polytope center System status Perform range estimation and obtain The upper bound of With the lower bound in The rows and matrices of Intermediate parameters yes The element in the i-th row and j-th column of ; m(s,k) represents The number of columns.

8. The method for estimating the state of a fully symmetric polytope set based on a coding and quantization mechanism according to claim 1, characterized in that: The smallest fully symmetric polytope estimation set in the sense of F norm is calculated by the following formula: Among them, the intermediate parameters can be calculated using the following formulas: When the parameter When , the F norm of the fully symmetric polytope obtained above reaches the minimum value.

9. An electronic device comprising a processor and a memory, characterized in that: The memory stores machine executable instructions that can be executed by the processor, and the processor executes the machine executable instructions to implement the method according to any one of claims 1 to 8.

10. A machine-readable storage medium, characterized in that: The machine-readable storage medium stores machine-executable instructions. When the machine-executable instructions are called and executed by a processor, the machine-executable instructions prompt the processor to implement the method as described in any one of claims 1 to 8.

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