2-D nonlinear system guaranteed probability filtering method and system under full duplex relay network energy collection constraint

Abstract

The invention discloses a 2-D nonlinear system guaranteed probability filtering method and system under full-duplex relay network energy collection constraint, and the method comprises the steps: constructing a state space expression of a 2-D nonlinear system, designing a full-duplex relay network communication mechanism based on a coding and decoding forwarding mechanism, constructing an energy collection constraint model, and carrying out the energy collection constraint of the 2-D nonlinear system. The method comprises the four steps of constructing an augmented system and designing a filter, solving a minimum ellipsoid constraint which meets probability requirements and contains an estimation error and a corresponding optimal filter gain by using a recursive linear matrix inequality, and enabling the minimum ellipsoid constraint and the corresponding optimal filter gain to be more accurate in a long-distance wireless communication network environment by using a stochastic analysis method, a set membership filtering idea and a 2-D mathematical induction method. The filtering method provided by the invention can realize reliable estimation on the 2-D nonlinear system with a guaranteed probability under the influence of random noise.

Description

Technical Field

[0001] The present invention belongs to the technical field of filtering, and mainly relates to a probability-preserving filtering method and system for a 2-D nonlinear system under the constraint of energy harvesting in a full-duplex relay network. Background Art

[0002] Since a 2-D nonlinear system can evolve along two independent directions, it shows unique advantages in complex process modeling and is widely used in engineering fields such as digital image processing, environmental detection systems, and grid sensor networks, having important research value. In signal processing and control engineering, filtering techniques are used for system state estimation to analyze dynamic behavior, which is particularly crucial for 2-D nonlinear systems. Set-membership filtering, as an important method, can estimate the system state in a bounded noise environment, usually using ellipsoidal constraints to characterize the influence of noise to determine the ellipsoidal domain containing the true state. However, in practical applications, not only bounded noise exists, but random noise also widely affects the system, making traditional set-membership filtering difficult to adapt. In addition, due to the unpredictability of equipment failures and signal interference, accurate zero-error state estimation is difficult to achieve in engineering practice. Therefore, a more practical strategy is to adopt a probability guarantee method. For example, in a missile control system, it is necessary to ensure that the error is controlled within a given probability range. However, the current research on 2-D nonlinear systems has not fully considered this requirement, and existing set-membership filtering methods are also difficult to effectively address this problem.

[0003] With the continuous growth of the demand for long-distance wireless transmission in practical applications, relay forwarding has become a key technology to solve this problem. However, in full-duplex relay communication, the interference problem caused by the shadow effect between signals has not been fully concerned. In addition, the transmission process is also affected by bandwidth limitations and relay energy constraints, resulting in signals that may not be completely transmitted to the filter due to insufficient bandwidth, or may not be successfully forwarded by the repeater due to lack of energy, thereby reducing the filtering performance of the 2-D nonlinear system. Current long-distance network filtering technologies mainly focus on traditional simple relay forwarding, and for more complex and efficient full-duplex relay communication, existing methods are still insufficient. At the same time, further research on the filtering problem under bandwidth limitations and energy constraints is also particularly urgent.

[0004] Based on the above analysis, it is necessary to study a probability-preserving filtering method for a 2-D nonlinear system under the constraint of energy harvesting in a full-duplex relay network, thereby improving the relay forwarding efficiency, reducing bandwidth occupation, and characterizing the energy harvesting process. So that accurate and reliable state estimation of the 2-D nonlinear system can be performed with a guaranteed probability. Summary of the Invention

[0005] The present invention precisely addresses the problem of probability - preserving estimation for 2 - D nonlinear systems in long - distance wireless transmission and energy - constrained scenarios in practical engineering, and proposes a probability - preserving filtering method and system for 2 - D nonlinear systems under energy harvesting constraints in a full - duplex relay network. By constructing the state - space expression of the 2 - D nonlinear system, designing a full - duplex relay network communication mechanism based on the encode - decode - forward mechanism, constructing an energy - harvesting constraint model, constructing an augmented system and designing a filter, and using the recursive linear matrix inequality to solve for the minimum ellipsoidal constraint that meets the probability requirements and contains the estimation error and the corresponding optimal filter gain in four steps, and using stochastic analysis methods, set - membership filtering ideas, and 2 - D mathematical induction, the proposed filtering method can achieve reliable estimation of the 2 - D nonlinear system with a guaranteed probability under the influence of random noise in the network environment of long - distance wireless communication.

[0006] To achieve the above object, the technical solution adopted by the present invention is: a probability - preserving filtering method for a 2 - D nonlinear system under energy harvesting constraints in a full - duplex relay network, including the following steps:

[0007] S1. Construct the state - space expression of the 2 - D nonlinear system: The 2 - D nonlinear system is characterized in that its dynamics evolve along two directions, and can more precisely depict the dynamics of complex systems compared with common 1 - D systems. It consists of a state equation containing random nonlinearity and random noise and a measurement equation containing random measurement noise.

[0008] S2. Design a full - duplex relay network communication mechanism based on the encode - decode - forward mechanism: Based on the measurement equation in step S1, use the encode - decode mechanism to convert the measurement signal into a digital signal and send it to the repeater for decoding and forwarding, thereby reducing the data packet volume and bandwidth occupancy. At the same time, use the full - duplex relay network model to further improve the forwarding efficiency and achieve reliable long - distance wireless communication.

[0009] S3. Construct an energy - harvesting constraint model: Design an energy - harvesting constraint model for the decoded signal after step S2, so that the data forwarding process of the repeater depends on its own energy - harvesting level to accurately depict the problem of limited energy caused by the remote deployment environment of the repeater.

[0010] S4. Construct an augmented system and design a filter: Augment the signal received by the repeater and the system state, and design a linear filter for it.

[0011] S5. Solve for the minimum ellipsoidal constraint that satisfies the probability requirement and includes the estimation error and the corresponding optimal filter gain using the recursive linear matrix inequality: Using the 2-D mathematical induction method, derive the ellipsoidal constraint that includes the estimation error under the given probability guarantee, and obtain the minimum ellipsoidal constraint that includes the system state and the corresponding optimal filter gain by solving the optimization problem formed by the recursive linear matrix inequality.

[0012] As an improvement of the present invention, in the step S1, the state space expression of the constructed 2-D nonlinear system is:

[0013]

[0014] y p,q =C p,q x p,q +v p,q

[0015] where T is a given positive integer; and represent the system state and the measurement output respectively; and C p,q are known time-varying matrices; and represent the process disturbance and the measurement disturbance respectively, and they are zero-mean white noises with covariance matrices satisfying W p,q ≥0 and V p,q >0. The random nonlinear function f(x p,q ,ξ p,q ) has the following properties

[0016]

[0017] where is a zero-mean white noise sequence with covariance ; π s and Π s (s = 1,2,…,t) are known vectors and matrices respectively, t>0 is a given integer; when p = j, δ p,j =1, otherwise δ p,j =0. The initial boundary conditions of the system are uncorrelated white noise variables, satisfying and where and are known vectors, and are known matrices.

[0018] As an improvement of the present invention, in step S2, a full-duplex relay network based on an encoding and decoding forwarding mechanism is constructed, so as to convert the measurement signal into a digital signal and send it to the repeater for decoding and forwarding, thereby reducing the bandwidth occupancy and achieving long-distance transmission. Step S2 includes the following steps:

[0019] S21. For the signal sent by the sensor (which will be specifically introduced in S22), the specific encoding and decoding mechanism adopted is as follows:

[0020] At the encoder end, first quantize the signal , where is the i-th component of the signal (i ∈ {1, 2,..., n y}}). Then, set the quantization interval [-a i , a i )(a i > 0) for each component, and then introduce a scaling factor to make the preprocessed component strictly fall within the interval [-a i , a i ). Define a scalar uniform quantizer for each component

[0021]

[0022] where c is the given maximum quantization level. It can be seen from the quantizer that the coding region [-a i , a i ) of the i-th measurement component is evenly divided into c sub-intervals After quantization, through the index generation function R → [1, c] Z the codeword of can be obtained, denoted as

[0023] When where ε i ∈ {1, 2,..., c} is called the label of the sub-interval . Correspondingly, the codeword of the signal can be expressed as the sequence {ε1, ε2,..., εn y}.

[0024] At the decoder end, after receiving the codeword sequence {ε1, ε2,..., εn y}, for each codeword ε i (i = 1, 2,..., n y ) define the inverse quantization function denoted as

[0025]

[0026] Subsequently, the decoded signal component can be generated by where is the scaling factor used in the encoding process. Define the decoding error The upper bound of the error can be obtained as satisfying

[0027]

[0028] The overall encoded signal can be expressed as

[0029]

[0030] where and

[0031] S22. The constructed full-duplex relay network model is specifically as follows:

[0032] The measurement signal is first sent to the encoder end through the sensor-relay channel with a specific transmission power, and the encoder receives the signal which can be expressed as

[0033]

[0034] where represents the transmission power of the sensor-relay; d sr represents the distance between the sensor and the relay node; represents the random white noise variable of the channel fading coefficient, which satisfies and is the zero-mean white noise with covariance .

[0035] In the full-duplex relay network, the relay can simultaneously receive signals from the decoder and forward them to the filter, thus significantly improving the data transmission efficiency. However, the self-interference phenomenon caused by the shadow effect is also inevitable. Therefore, based on the decoded signal r p,q , the final received signal at the relay can be expressed as

[0036]

[0037] where represents the channel transmission power from the relay to the filter; d rf is the distance between the relay and the filter; is the self-channel random fading coefficient from the relay to the relay, and its statistical characteristics satisfy the expectation and variance The self-interference term sp,q Can be expressed as

[0038]

[0039] To eliminate the negative impact of self-interference, a self-interference compensation signal constructed based on the expected meaning is introduced

[0040]

[0041] As an improvement of the present invention, in the step S3, an energy harvesting constraint model is constructed to characterize the energy change of the repeater during the forwarding process, and the specific expression is:

[0042] Since the relay device is usually deployed in a remote area far from the city center to achieve long-distance signal transmission. This deployment method may cause the relay to face the problem of energy limitation, and further lead to signal forwarding failure due to insufficient energy. Therefore, a binary random variable γ p,q is introduced to describe the state of successful or failed relay forwarding

[0043]

[0044] where z p,q represents the current energy level of the relay, and ρ p,q is the unit energy required for signal forwarding. This model shows that the current energy z p,q level of the relay directly determines the success or failure of signal transmission: when γ p,q =1, that is, when the energy is sufficient, the signal can be successfully transmitted to the filter; while γ p,q =0 indicates that the transmission fails due to insufficient energy. In the channel from the relay to the filter, it is assumed that the value of ρ p,q is closely related to the transmit power and can be specifically expressed as Let the value range of the current energy level z p,q be the set {0, 1, 2,..., S}, where S≥ρ p,q represents the maximum energy storage unit of the relay, then the dynamic evolution of z p,q can be described as

[0045] z p,q+1 =min{z p,q +χ p,q -γ p,q ρ p,q , S}

[0046] Its initial boundary condition is z p,0 =z0∈[0, S] Z (p∈T), the random white noise variable χ p,q represents the natural energy harvesting efficiency at the position (p, q), and its probability distribution satisfies:

[0047] P{χ p,q = n} = φ n , n = 0, 1, 2, …, S

[0048] where 0 ≤ φ n ≤ 1, Combined with the energy harvesting constraint, the signal transmitted by the relay, which is the final signal received by the filter, can be expressed as

[0049]

[0050] where is the random fading coefficient of the relay-to-filter channel, and its statistical characteristics satisfy and is the transmission noise, which is white noise with zero mean and its covariance satisfies

[0051] In addition, the value of γ p,q is highly correlated with the current energy level z p,q and its statistical characteristics are

[0052]

[0053] where and the element

[0054]

[0055] As an improvement of the present invention, in step S4, an augmented system is constructed and a filter is designed, specifically:

[0056] By defining variables and the following augmented system can be obtained

[0057]

[0058] where

[0059]

[0060] and there is and Based on the augmented state the final received signal of the filter can be written in the following form

[0061]

[0062] where

[0063]

[0064] For the augmented system and the received signal A filter can be constructed as follows through a full-duplex relay network with energy harvesting constraints

[0065]

[0066] where is the estimate of the system state with the initial boundary conditions and where and (p, q ∈ T) are known variables satisfying and (l = 1, 2) are gain matrices of appropriate dimensions to be determined

[0067] As an improvement of the present invention, in step S5, a recursive linear matrix inequality is used to solve the minimum ellipsoidal constraint that satisfies the probability requirement and includes the estimation error and the corresponding optimal filter gain. Step S5 includes the following steps

[0068] S51. Set the initial boundary conditions of the augmented system and the filter

[0069]

[0070] which are satisfied for all p, q ∈ T, where R p,0 and R 0,q are known positive definite matrices of appropriate dimensions

[0071] S52. Combining the definitions of matrices Θ (1) , Ψ p,q and vector in step S4, derive matrix

[0072]

[0073] where and Then decompose matrix Λ p,q , and into

[0074]

[0075] where and are the p,q th and th The th, and the th eigenvalue, and are the corresponding eigenvectors.

[0076] S53. Construct a recursive linear matrix inequality to solve the ellipsoidal constraint including the estimation error and the corresponding filter gain that satisfy the probability requirement. Let and in step S52, where p ∈ (0, 1) is the expected probability parameter. For a given positive scalar sequence (h = 1, 2, …, 9), if there exist positive scalar sequences (s = 1, 2, …, t), non - negative scalar sequences matrix sequences and positive definite matrix sequences {R p+1,q+1} p,q∈T such that the following recursive linear matrix inequality has a feasible solution, then the relation holds for all p, q ∈ T:

[0077]

[0078] where

[0079]

[0080] and there is

[0081]

[0082] In addition,

[0083]

[0084] Among them, G p,q is an orthogonal factor of the matrix R p,q , that is,

[0085] S54. Solve the optimization problem to minimize the ellipsoidal constraint including the estimation error and obtain the optimal filter gain:

[0086]

[0087] subject to the conditions in S53

[0088] Then the minimum ellipsoidal constraint can be achieved at the given probability p, where

[0089]

[0090] and complete the gain parameter setting of the optimal filter.

[0091] To achieve the above object, the technical solution adopted by the present invention is also:

[0092] A probability-preserving filtering system for a 2-D nonlinear system under energy harvesting constraints in a full-duplex relay network, including:

[0093] A state space expression construction module for a 2-D nonlinear system: used to construct the state space expression of the 2-D nonlinear system, where the 2-D nonlinear system is composed of a state equation containing random nonlinearity and random noise and a measurement equation containing random measurement noise;

[0094] A full-duplex relay network communication mechanism design module based on the encoding and decoding forwarding mechanism: used to convert the measurement signal into a digital signal based on the measurement equation by using the encoding and decoding mechanism and send it to the repeater for decoding and forwarding, thereby reducing the data packet volume and bandwidth occupancy; at the same time, further improve the forwarding efficiency by using the full-duplex relay network model to achieve reliable long-distance wireless communication;

[0095] An energy harvesting constraint model construction module: used to design an energy harvesting constraint model for the decoded signal, so that the data forwarding process of the repeater depends on its own energy harvesting level to accurately describe the problem of limited energy caused by the remote deployment environment of the repeater;

[0096] An augmented system and filter construction and design module: used to augment the signal received by the repeater and the system state and design a linear filter for it;

[0097] A minimum ellipsoid constraint and corresponding optimal filter gain solving module: use the recursive linear matrix inequality to solve the minimum ellipsoid constraint and corresponding optimal filter gain that meet the probability requirements and contain the estimation error. Specifically, use the 2-D mathematical induction method to derive the ellipsoid constraint containing the estimation error under the given probability guarantee, and obtain the minimum ellipsoid constraint containing the system state and the corresponding optimal filter gain by solving the optimization problem composed of the recursive linear matrix inequality.

[0098] In addition, the present invention also includes a computer storage medium, on which a computer program is stored, and when the computer program is executed by a processor, the steps of the above method are realized.

[0099] The present invention also includes an electronic device, including a memory and one or more processors, where the memory is used to store one or more programs; when the one or more programs are executed by the one or more processors, the above method is realized.

[0100] Compared with the prior art, the beneficial effects of the present invention are as follows: The present invention provides a method and system for guaranteed probability filtering of a 2-D nonlinear system under energy harvesting constraints in a full-duplex relay network. When establishing the 2-D state space model for the proposed method, random nonlinearity is added to the system state, making its dynamic behavior more complex and general; when designing the communication mechanism of the full-duplex relay network based on the encode-decode and forward mechanism, focusing on the bandwidth-limited problem, the packet volume is reduced by using encoding and decoding technologies, and at the same time, the full-duplex relay technology is applied to data forwarding, greatly improving the transmission efficiency; when constructing the energy harvesting constraint model, considering that repeaters are usually deployed in remote areas and energy limited due to insufficient power supply, an energy constraint model is used to characterize the energy change of the repeater, making the result more practical; when constructing the augmented system and designing the filter, the shadow effect problem caused by the full-duplex relay is solved; when using the recursive linear matrix inequality to solve the minimum ellipsoidal constraint that meets the probability requirements and includes the estimation error and the corresponding optimal filter gain, the 2-D mathematical induction method is used to strictly ensure that the system state at each moment is included in the ellipsoidal constraint centered on the estimated value, and the optimal filter gain parameter is obtained by minimizing the ellipsoidal constraint. BRIEF DESCRIPTION OF THE DRAWINGS

[0101] Figure 1 is a flowchart of the steps of the method of the present invention;

[0102] Figure 2 is the state component and its corresponding estimated value in the embodiment of the present invention;

[0103] Figure 3 is the state component and its corresponding estimated value in the embodiment of the present invention;

[0104] Figure 4 is the dynamic characteristic diagram of the estimation error component in the embodiment of the present invention;

[0105] Figure 5 is the dynamic characteristic diagram of the estimation error component in the embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0106] The present invention will be further illustrated below in conjunction with the drawings and specific embodiments. It should be understood that the following specific embodiments are only used to illustrate the present invention and not to limit the scope of the present invention.

[0107] Embodiment

[0108] A method for guaranteed probability filtering of a 2-D nonlinear system under energy harvesting constraints in a full-duplex relay network, asFigure 1 As shown, it includes the following steps:

[0109] Step S1: The state - space expression of the constructed 2 - D nonlinear system.

[0110]

[0111] y p,q = C p,q x p,q + v p,q

[0112] where T is a given positive integer; and represent the system state and the measurement output respectively; (l = 1,2) and C p,q are known time - varying matrices; and represent the process disturbance and the measurement disturbance respectively, and they are zero - mean white noises with covariance matrices satisfying W p,q ≥ 0 and V p,q > 0. The random nonlinear function f(x p,q ,ξ p,q ) has the following properties

[0113]

[0114] where is a zero - mean white - noise sequence with covariance ; π s and Π s (s = 1,2,…,t) are known vectors and matrices respectively, t > 0 is a given integer; when p = j, δ p,j = 1, otherwise δ p,j = 0. The initial boundary conditions of the system are uncorrelated white - noise variables, satisfying and where and are known vectors, and are known matrices.

[0115] Step S2: Design a full - duplex relay network communication mechanism based on the encode - decode - forward mechanism.

[0116] First, at the encoder side, the signal is quantized, where is the i - th component of the signal (i ∈ {1,2,…,n y}). Then, a quantization interval [-a i ,ai )(a i ) > 0), and then introduce a scaling factor to make the preprocessed component strictly fall within the interval [-a i , a i . For each component define a scalar uniform quantizer

[0117]

[0118] where c is the given maximum quantization level. From the quantizer, it can be seen that the coding region [-a i , a i ) of the i-th measured component is evenly divided into c subintervals After quantization, through the index generation function R → [1, c] Z we can obtain the codeword of

[0119] When where ε i ∈ {1, 2,..., c} is called the label of the subinterval . Correspondingly, the codeword of the signal can be expressed as the sequence {ε1, ε2,..., εn y}.

[0120] At the decoder end, after receiving the codeword sequence {ε1, ε2,..., εn y}, for each codeword ε i (i = 1, 2,..., n y ) define the inverse quantization function expressed as

[0121]

[0122] Then, the decoded signal component can be generated by where is the scaling factor used in the encoding process. Define the decoding error and we can obtain that the upper bound of the error satisfies

[0123]

[0124] The overall encoded signal can be expressed as

[0125]

[0126] where and

[0127] Then, the measurement signal is first sent to the encoder end through the sensor-relay channel at a specific transmission power, and the encoder receives the signal which can be expressed as

[0128]

[0129] where represents the transmission power of the sensor-relay; d sr represents the distance between the sensor and the relay node; is a random white noise variable representing the channel fading coefficient, which satisfies and is the covariance of zero-mean white noise.

[0130] In addition, in a full-duplex relay network, the relay can simultaneously receive signals from the decoder and forward them to the filter, thus significantly improving the data transmission efficiency. However, the self-interference phenomenon caused by the shadow effect is also inevitable. Therefore, based on the decoded signal r p,q , the final received signal at the relay can be expressed as

[0131]

[0132] where represents the channel transmission power from the relay to the filter; d rf is the distance between the relay and the filter; is the self-channel random fading coefficient from the relay to the relay, and its statistical properties satisfy the expectation and the variance The self-interference term s p,q can be expressed as

[0133]

[0134] To eliminate the negative impact of self-interference, a self-interference compensation signal constructed based on the expected meaning is introduced

[0135]

[0136] Step S3: Construct an energy harvesting constraint model.

[0137] Since relay devices are usually deployed in remote areas far from the city center to achieve long-distance signal transmission. This deployment method may cause the relay to face the problem of energy limitation, and thus the signal forwarding may fail due to insufficient energy. Therefore, a binary random variable γ p,q is introduced to describe the state of successful or failed relay forwarding

[0138]

[0139] where z p,q represents the current energy level of the relay, and ρ p,q is the unit energy consumed for signal forwarding. This model shows that the current energy z p,q level of the relay directly determines the success or failure of signal transmission: when γ p,q = 1, that is, when the energy is sufficient, the signal can be successfully transmitted to the filter; while γ p,q = 0 indicates that the transmission fails due to insufficient energy. In the channel from the relay to the filter, it is assumed that the value of ρ p,q is closely related to the transmit power and can be specifically expressed as Let the value range of the current energy level z p,q be the set {0, 1, 2, …, S}, where S ≥ ρ p,q represents the maximum energy storage unit of the relay, then the dynamic evolution of z p,q can be described as

[0140] z p,q+1 = min{z p,q + χ p,q - γ p,q ρ p,q , S}

[0141] Its initial boundary condition is z p,0 = z0 ∈ [0, S] Z (p ∈ T), the random white noise variable χ p,q represents the natural energy harvesting efficiency at the position (p, q), and its probability distribution satisfies:

[0142] P{χ p,q = n} = φ n , n = 0, 1, 2, …, S

[0143] where 0 ≤ φ n ≤ 1, Combined with the energy harvesting constraint condition, the signal sent by the relay, that is, the final signal received by the filter, can be expressed as

[0144]

[0145] where is the random fading coefficient of the channel from the relay to the filter, and its statistical characteristics satisfy and is the transmission noise, which is white noise with zero mean and the covariance satisfies

[0146] In addition, γ p,qThe value of p,q is highly correlated with the current energy level z, and its statistical characteristics are

[0147]

[0148] where and the elements therein

[0149]

[0150] Step S4: Construct an augmented system and design a filter.

[0151] By defining variables and the following augmented system can be obtained

[0152]

[0153] where

[0154]

[0155] and there is and Based on the augmented state the filter finally receives the signal which can be written in the following form

[0156]

[0157] where

[0158]

[0159] For the augmented system and the received signal through a full-duplex relay network with an energy harvesting constraint, the filter can be constructed as follows

[0160]

[0161] where is the estimate of the system state and the initial boundary conditions are and where and (p,q∈T) are known variables satisfying and (l = 1,2) are dimensionally appropriate gain matrices to be determined.

[0162] Step S5: Use the recursive linear matrix inequality to solve the minimum ellipsoidal constraint that satisfies the probability requirement and contains the estimation error and the corresponding optimal filter gain.

[0163] First, set the initial boundary conditions of the augmented system and the filter

[0164]

[0165] It holds for all p, q ∈ T, where R p,0 and R 0,q are known positive definite matrices of appropriate dimensions.

[0166] Then, combined with the definitions of the matrices Θ (1) , Ψ p,q and the vector in step S4, derive the matrix

[0167]

[0168] where and Next, decompose the matrices Λ p,q , and into

[0169]

[0170] where and are the p,q -th, -th, and -th eigenvalues of the matrices Λ , and respectively, and and are the corresponding eigenvectors.

[0171] Then, construct a recursive linear matrix inequality to solve the ellipsoidal constraint that satisfies the probability requirement and contains the estimation error, and the corresponding filter gain. Let and in step S52, where p ∈ (0, 1) is the expected probability parameter. For a given sequence of positive scalars (h = 1, 2, …, 9), if there exist a sequence of positive scalars (s = 1, 2, …, t), a sequence of non-negative scalars a sequence of matrices and a sequence of positive definite matrices {R p+1,q+1} p,q∈T such that the following recursive linear matrix inequality has a feasible solution, then the relation holds for all p, q ∈ T:

[0172]

[0173] wherein

[0174]

[0175] and there is

[0176]

[0177] in addition

[0178]

[0179] Among them, G p,q is an orthogonal factor of matrix R p,q i.e.,

[0180] Finally, solve the optimization problem to minimize the ellipsoidal constraint containing the estimation error and obtain the optimal filter gain:

[0181]

[0182] subject to the conditions in S53

[0183] Then the minimum ellipsoidal constraint can be achieved with a given probability p, where

[0184]

[0185] and complete the setting of the gain parameters of the optimal filter.

[0186] Test example

[0187] To verify the effectiveness of the method proposed by the present invention, the following test experiment is specifically made: Consider a 2-D nonlinear system within a finite time domain p, q ∈ [0, 50] Z The system matrix parameters are as follows:

[0188]

[0189] The random variables w p,q and v p,q are zero-mean white noise sequences, and their covariance matrices are W p,q = 0.0016 and V p,q = 0.0025 respectively. Set the random nonlinear function as:

[0190]

[0191] wherein and (l = 1, 2) respectively represent the vector xp,q and ξ p,q the l-th element of, ξ p,q is a zero-mean white noise sequence with a covariance matrix of the identity matrix. From this expression, its statistical properties can be obtained as t = 1, π s = [0.1 0.2] T , Π s = diag{0.01, 0.04}.

[0192] In a full-duplex relay network adopting the decode-and-forward strategy, the quantization step size a i is set to 2, the maximum quantization level c = 50, and the scaling parameter The statistical characteristic parameters of the transmission power, transmission distance, and channel coefficient of each communication link are set as follows:

[0193]

[0194] The random noise in the channel and are zero-mean sequences, and their covariance matrices are respectively and

[0195] Under the energy harvesting constraint, the maximum energy storage unit of the relay node is set to S = 3, the initial energy z0 = 1, and the probability distribution of the natural energy harvesting efficiency is φ0 = 0.1, φ1 = 0.1, φ2 = 0.4, and φ3 = 0.4. The initial boundary conditions of the system in the range of p, q ∈ [0, 50] are set as:

[0196]

[0197] The expected probability p = 0.8 is set, and the remaining parameters are taken According to the filtering method proposed in the present invention, the optimal filter gain is recursively calculated using MATLAB software and compared with the actual state trajectory.

[0198] Figures 2-3 shows the state components and and their corresponding estimated values and of the evolution process, where and (l = 1, 2) respectively represent the l-th component of the state vector x p,q and the estimated vector of.

[0199] Figures 4-5 presents the dynamic characteristics of the estimation error components and where is the error vector ep,q the l-th component. Among them, the state component and its estimated value (l = 1, 2) satisfy the following bounded constraint relationship:

[0200]

[0201] where represents the l-th row of matrix G p,q . To avoid special cases brought by random parameters, both of these two figures adopt the Monte Carlo method for 30 independent simulations. The data and images together show that although the estimation error component may not be convergent, its value range is always limited within a preset ellipsoidal region under a given probability, which further illustrates the effectiveness of the filtering algorithm proposed in this invention.

[0202] In summary, the method of the present invention discloses a probability-preserving filtering method for a 2-D nonlinear system under energy harvesting constraints in a full-duplex relay network. Aiming at the network constraints of limited transmission distance and limited transmission energy, the present invention constructs a full-duplex relay network communication mechanism based on an encoding and decoding strategy in a 2-D framework. At the same time, to solve the limitations of energy storage and replenishment at the relay end, an energy harvesting constraint mechanism is proposed. By establishing sufficient conditions in the form of recursive linear matrix inequalities, it is ensured that the filtering error is constrained within an ellipsoidal region with a set probability, and an optimization algorithm is further given to minimize this ellipsoidal region, and the optimized filter gain sequence is solved to achieve the optimal estimation goal.

[0203] 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 those of ordinary skill in the art of this technology, without departing from the principle of the present invention, several improvements and refinements can still be made, and these improvements and refinements all fall within the protection scope of the claims of the present invention.

Claims

1. A probability-preserving filtering method for a 2-D nonlinear system under energy harvesting constraints in a full-duplex relay network, characterized in that, It includes the following steps: S1. Construct the state-space expression of a 2-D nonlinear system: The 2-D nonlinear system evolves dynamically in two directions and can more accurately characterize the dynamics of complex systems. It consists of a state equation containing stochastic nonlinearity and stochastic noise and a measurement equation containing stochastic measurement noise. S2. Design a full-duplex relay network communication mechanism based on the encode-decode-forward mechanism: Based on the measurement equation in step S1, use the encode-decode mechanism to convert the measurement signal into a digital signal and send it to the repeater for decoding and forwarding, thereby reducing the packet volume and bandwidth occupancy. At the same time, use the full-duplex relay network model to further improve the forwarding efficiency and achieve reliable long-distance wireless communication. S3. Construct an energy harvesting constraint model: Design an energy harvesting constraint model for the decoded signal after step S2, so that the data forwarding process of the repeater depends on its own energy harvesting level to accurately characterize the problem of limited energy caused by the remote deployment environment of the repeater. S4. Construct an augmented system and design a filter: Augment the signal received by the repeater and the system state, and design a linear filter for it. S5. Use the recursive linear matrix inequality to solve the minimum ellipsoidal constraint satisfying the probability requirement and containing the estimation error and the corresponding optimal filter gain: Use the 2-D mathematical induction method to derive the ellipsoidal constraint containing the estimation error under a given probability guarantee, and solve the optimization problem composed of recursive linear matrix inequalities to obtain the minimum ellipsoidal constraint containing the system state and the corresponding optimal filter gain.

2. The probability-preserving filtering method for a 2-D nonlinear system under energy harvesting constraints in a full-duplex relay network according to claim 1, wherein: In step S1, the constructed state-space expression of the 2-D nonlinear system is: y p,q = C p,q x p,q + v p,q where T is a given positive integer; and represent the system state and measurement output, respectively; and C p,q are known time-varying matrices; and represent the process disturbance and measurement disturbance, respectively, which are zero-mean white noises with covariance matrices satisfying W p,q ≥ 0 and V p,q > 0; the random nonlinear function f(x p,q , ξ p,q ) has the following properties f(0, ξ p,q ) = 0, where is a zero-mean white noise sequence with covariance ; π s and Π s (s = 1, 2, …, t) are known vectors and matrices respectively, t > 0 is a given integer; when p = j, δ p,j = 1, otherwise δ p,j = 0; the initial boundary conditions of the system are uncorrelated white noise variables, satisfying and where and are known vectors, and are known matrices.

3. The probability-preserving filtering method for a 2-D nonlinear system under energy harvesting constraints in a full-duplex relay network according to claim 2, wherein: In step S2, construct a full-duplex relay network based on the encode-decode-forward mechanism, so as to convert the measurement signal into a digital signal and send it to the repeater for decoding and forwarding to reduce the bandwidth occupancy and achieve long-distance transmission. It specifically includes the following steps: S21. For the signal sent by the sensor The specific encoding and decoding mechanism adopted is as follows: At the encoder side, first, the signal is quantized, where is the i-th component of the signal (i ∈ {1, 2, …, n y}); then, a quantization interval [-a i , a i )(a i > 0) is set for each component, and then a scaling factor is introduced to make the preprocessed component strictly fall within the interval [-a i , a i ); for each component a scalar uniform quantizer wherein c is the given maximum quantization level; As can be seen from the quantizer, the coding region [-a i , a i ) of the i-th measurement component is evenly divided into c sub-intervals After quantization, through the index generation function obtain The codeword of, denoted as When where ε i ∈ {1, 2, …, c} is called the label of the sub - interval ; correspondingly, the codeword of the signal is represented as the sequence {ε1, ε2, …, εn y}; At the decoder side, after receiving the codeword sequence {ε1, ε2, …, εn y}, for each codeword ε i (i = 1, 2, …, n y ), define the inverse quantization function denoted as Then, the decoded signal component is generated by where is the scaling factor used in the encoding process; the decoding error is defined such that the upper bound of the error satisfies The overall encoded signal is expressed as Among them and S22. The specifically constructed full-duplex relay network model is: The measurement signal is first sent to the encoder end through the sensor-relay channel at a specific transmission power, and the encoder receives the signal Denoted as Among them represents the transmission power of the sensor - repeater; d sr represents the distance between the sensor and the relay node; represents the random white noise variable of the channel fading coefficient, which satisfies and is the covariance of zero - mean white noise; In the full-duplex relay network, the relay can simultaneously receive signals from the decoder and forward them to the filter, thus significantly improving the data transmission efficiency. However, the self-interference phenomenon caused by the shadow effect is also inevitable. Therefore, based on the decoded signal r p,q , the final received signal at the relay is expressed as Among them represents the channel transmit power relayed to the filter; d rf is the distance between the relay and the filter; is the self-channel random fading coefficient from the relay to the relay, and its statistical characteristics satisfy the expectation and variance The self-interference term s p,q is expressed as To eliminate the negative impact of self-interference, introduce a self-interference compensation signal constructed based on the expected meaning 4. The method for probability-preserving filtering of a 2-D nonlinear system under energy harvesting constraints in a full-duplex relay network according to claim 3, wherein: In step S3, construct an energy harvesting constraint model to characterize the energy change of the repeater during the forwarding process, and the specific expression is: Introduce a binary random variable γ p,q to describe the state of successful or failed relay forwarding where z p,q represents the current energy level of the relay, and ρ p,q is the unit energy required for signal forwarding; this model shows that the current energy z p,q level of the relay directly determines the success or failure of signal transmission: when γ p,q = 1, that is, when the energy is sufficient, the signal can be successfully transmitted to the filter; while γ p,q = 0 indicates that the transmission fails due to insufficient energy; in the channel from the relay to the filter, it is assumed that the value of ρ p,q is closely related to the transmit power , specifically expressed as Let the value range of the current energy level z p,q be the set {0, 1, 2, …, S}, where S ≥ ρ p,q represents the maximum energy storage unit of the relay, then the dynamic evolution of z p,q is described as z p,q+1 = min{z p,q + χ p,q - γ p,q ρ p,q , S} Its initial boundary condition is z p,0 = z0 ∈ [0, S] Z (p ∈ T), the random white noise variable χ p,q represents the natural energy harvesting efficiency at the position (p, q), and its probability distribution satisfies: P{χ p,q = n} = φ n , n = 0, 1, 2, …, S where \(0\leqslant\varphi\) n \(\leqslant1\), Combined with the energy harvesting constraint, the signal transmitted by the relay, i.e., the final signal received by the filter, is expressed as wherein is the random fading coefficient relayed to the filter channel, and its statistical characteristics satisfy and is the transmission noise, which is white noise with zero mean and its covariance satisfies In addition, γ p,q takes values that are highly correlated with the current energy level z p,q and its statistical characteristics are wherein and wherein the element 5. The probability-preserving filtering method for a 2-D nonlinear system under energy harvesting constraints in a full-duplex relay network according to claim 4, wherein: In step S4, construct an augmented system and design a filter, specifically: By defining variables and the following augmented system is obtained where and there is and based on the augmented state the filter finally receives the signal written in the following form where For the augmented system and the received signal A filter can be constructed as follows through a full-duplex relay network with an energy harvesting constraint where is the estimation of the system state with the initial boundary conditions being and where and are known variables satisfying and is the gain matrix to be solved with appropriate dimensions.

6. The probability-preserving filtering method for a 2-D nonlinear system under energy harvesting constraints in a full-duplex relay network according to claim 5, wherein: In step S5, use the recursive linear matrix inequality to solve the minimum ellipsoidal constraint satisfying the probability requirement and containing the estimation error and the corresponding optimal filter gain. It specifically includes the following steps: S51. Set the initial boundary conditions of the augmented system and the filter is satisfied for all p, q ∈ T, where R p,0 and R 0,q are known positive definite matrices of appropriate dimensions; S52. Combine with the matrix Θ in step S4 (1) , Ψ p,q and the vector definition, derive the matrix Among them and Then decompose matrix Λ p,q , and into where and are the p,q -th, -th, and -th eigenvalues of the matrices Λ and respectively, and and are the corresponding eigenvectors; S53. Construct a recursive linear matrix inequality to solve the ellipsoidal constraint that satisfies the probability requirement and includes the estimation error, and the corresponding filter gain; let in step S52 and where p ∈ (0, 1) is the expected probability parameter; for a given positive scalar sequence If there exist positive scalar sequences non - negative scalar sequences matrix sequences and positive definite matrix sequences {R p+1,q+1} p,q∈T such that the following recursive linear matrix inequality has a feasible solution, then the relation holds for all p, q ∈ T: where and there is and also Among these, G p,q is an orthogonal factor of matrix R p,q , that is S54. Solve the optimization problem to minimize the ellipsoidal constraint containing the estimation error and obtain the optimal filter gain: subject to the conditions in S53 Then the minimum ellipsoidal constraint is achieved under the given probability p, where and complete the setting of the gain parameters of the optimal filter.

7. A 2-D nonlinear system probability-preserving filtering system under energy harvesting constraints in a full-duplex relay network, characterized in that: The method according to any one of claims 1-6 is adopted, including: A state-space expression construction module for a 2-D nonlinear system: which is used to construct the state-space expression of a 2-D nonlinear system, where the 2-D nonlinear system consists of a state equation containing stochastic nonlinearity and stochastic noise and a measurement equation containing stochastic measurement noise; A full-duplex relay network communication mechanism design module based on the encode-decode-forward mechanism: which is used to, based on the measurement equation, convert the measurement signal into a digital signal by using the encode-decode mechanism and send it to the repeater for decoding and forwarding, thereby reducing the data packet volume and bandwidth occupancy; at the same time, further improving the forwarding efficiency by using the full-duplex relay network model to achieve reliable long-distance wireless communication; An energy harvesting constraint model construction module: which is used to design an energy harvesting constraint model for the decoded signal, such that the data forwarding process of the repeater depends on its own energy harvesting level, so as to accurately characterize the problem of limited energy caused by the remote deployment environment of the repeater; An augmented system and filter construction and design module: which is used to augment the signal received by the repeater and the system state and design a linear filter for it; A minimum ellipsoid constraint and corresponding optimal filter gain solving module: which uses recursive linear matrix inequalities to solve the minimum ellipsoid constraint and corresponding optimal filter gain that meet the probability requirements and contain the estimation error. Specifically, the 2-D mathematical induction method is used to derive the ellipsoid constraint containing the estimation error under a given probability guarantee, and the minimum ellipsoid constraint containing the system state and the corresponding optimal filter gain are obtained by solving the optimization problem composed of recursive linear matrix inequalities.

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