Recursive filtering design method and device of complex network based on energy collection and decode-and-forward relay

Abstract

The invention discloses a recursive filtering design method and device of a complex network based on energy collection and decode-forward relay. The method comprises the following steps: establishing a mathematical model of a non-linear time-varying complex network with random coupling; designing a recursive filter by adopting a decoding and forwarding relay strategy based on an energy harvesting technology, and determining to-be-designed parameters of the filter; calculating a one-step prediction error and a filtering error of the state variable, and determining a prediction error covariance and a filtering error covariance based on the one-step prediction error and the filtering error; considering a prediction error covariance and an estimation error covariance, and adopting two groups of matrix difference equations to determine an upper bound of a filtering error covariance; and designing parameters of the recursive filter by adopting a matching method, thereby obtaining the recursive filter. The method solves the problem that the existing filtering method cannot process the nonlinear complex network with the energy collection technology and the decoding and forwarding relay at the same time, and can be applied to the filtering field with the energy collection technology and the decoding and forwarding relay.

Description

Technical Field

[0001] The present invention relates to the technical field of recursive filtering, and in particular to a recursive filtering design method and device based on a complex network of energy collection and decoding forwarding relay. Background Art

[0002] Complex networks consist of a large number of interconnected nodes, and the edges between these nodes represent interactions, relationships or connections. Due to the wide application of complex networks in many fields such as sensor networks, social networks, and power grids, their dynamic analysis problems have attracted special research attention. To date, there have been a variety of effective methods to solve the problems of stability, synchronization, consistency, and state estimation of complex dynamic networks. Accordingly, in order to provide the expected estimation of the state of nodes in complex dynamic networks under different requirements / constraints, several effective filtering strategies have been developed. Due to the possible existence of harsh network environments and serious interference from other external factors, it is of great significance to discuss the dynamic topology when analyzing the behavior of complex networks. For complex networks with variable connection structures, the filtering problem is a research hotspot with important practical significance.

[0003] Sensors may have limited communication range in practice, which makes it impossible to directly pass information from the sensor to the remote estimator because the distance between the two is too far. Deploying a relay between the sensor and the remote estimator (using a relay to receive and process signals from the source and send the signal to the destination) is considered as an alternative to deal with this situation. Among them, decode-and-forward relay means that the relay decodes the signal from the source node and then re-encodes the signal according to the rules and sends it to the destination. It is well known that the operation of sensors and repeaters requires a lot of power, which is provided by batteries. When the battery energy is exhausted, in some special cases, the battery cannot be removed or replaced, so they are negative for frequently transmitting measurement data. To deal with the energy problem of sensors, traditional battery-powered sensors or repeaters can be replaced with sensors or repeaters equipped with energy harvesters. For sensors or repeaters equipped with energy harvesters, many advanced research results have been applied to estimation problems. However, unlike battery-powered sensors with fixed total energy constraints, the energy of sensors equipped with energy harvesters is related to the energy consumed in the previous transmission and is affected by the external environment. Based on this, the present application proposes a recursive filtering design method for a complex network of decoding and forwarding relays based on energy harvesting technology. Summary of the invention

[0004] The purpose of the present invention is to provide a recursive filtering design method and device for complex networks based on energy collection and decoding forwarding relay, so as to solve the problem that the existing filtering methods cannot simultaneously process nonlinear complex networks with energy collection technology and decoding forwarding relay.

[0005] The technical solution to achieve the purpose of the present invention is:

[0006] A recursive filter design method for a complex network based on energy harvesting and decoding and forwarding relay includes the following steps:

[0007] Step 1: Establish a mathematical model of a nonlinear time-varying complex network with random coupling;

[0008] Step 2: Based on the mathematical model, a decoding and forwarding relay strategy based on energy harvesting technology is adopted to design a recursive filter and determine the parameters of the filter to be designed;

[0009] Step 3: Based on the mathematical model and the recursive filter, a one-step prediction error and a filtering error of the state variable are calculated, and a prediction error covariance and a filtering error covariance are determined based on the one-step prediction error and the filtering error;

[0010] Step 4, considering the prediction error covariance and the estimation error covariance, two sets of matrix difference equations are used to determine the upper bound of the filtering error covariance;

[0011] Step 5: Based on the upper bound of the filtering error covariance, the parameters of the recursive filter are designed using the matching method to obtain the recursive filter.

[0012] Furthermore, the mathematical model of the nonlinear time-varying complex network described in step 1 is:

[0013]

[0014] in and Represent the state variable and measurement output of the i-th node respectively; is the internal coupling matrix; Γ represents the external coupling configuration matrix of the network; and denote zero-mean noise, and and f(·) represents a nonlinear function; and is a known coefficient matrix; and Respectively represent n-dimensional Euclidean space and m×n real matrix set; represents the mathematical expectation, and N is the number of sensors / repeaters.

[0015] Furthermore, the step 2 is specifically as follows:

[0016] Step 2.1. Design a model for the evolution of battery charge level over time, i.e., the form of energy harvesting technology;

[0017] Step 2.2, design a decoding and forwarding relay strategy based on the evolution model to obtain the actual measurement value received by the recursive filter;

[0018] Step 2.3: construct a recursive filter based on the actual measurement value received by the recursive filter.

[0019] Furthermore, the evolution model of the battery power level over time is:

[0020]

[0021] The battery power levels of sensor i and repeater i are denoted as Indicates the sensor, Represents a repeater; and Indicates the maximum power level that the batteries of sensor i and repeater i can store; initial power is the characteristic function, abbreviated as when hour, otherwise is an independent and identically distributed random variable representing the amount of energy collected by the battery of sensor / repeater i at time s.

[0022] Furthermore, the actual measurement value received by the recursive filter is:

[0023]

[0024] in, is satisfied and The channel noise, is the output of the decoder.

[0025] Furthermore, the recursive filter is:

[0026]

[0027]

[0028] in and They represent the state variable x at time s+1. s+1 One-step forecasts and estimates of ; is the gain matrix to be designed.

[0029] Furthermore, the one-step prediction error and filtering error are:

[0030]

[0031]

[0032] where e i,s+1|s is the one-step prediction error, e i,s+1|s+1 is the filtering error, Ξ i,s is satisfied The unknown matrix, decoder error is the actual measured value;

[0033] The prediction error covariance and filtering error covariance are:

[0034]

[0035] The parameters are:

[0036]

[0037] Furthermore, the upper bound of the filtering error covariance determined in step 4 is as follows:

[0038] Consider the prediction error covariance and the estimation error covariance, which satisfy the initial value Assume the following two difference equations

[0039]

[0040] Satisfy inequality constraints And solution and Then, we get in,

[0041]

[0042] And 1,s ,σ 2,s ,σ 3,s ,σ 4,s ,σ 5,s ,σ 6,s ,σ 7,s ,γ i,s is a known scaling parameter, is the corresponding reciprocal; A -1 Represents the inverse of the square matrix A.

[0043] Furthermore, the parameters of the recursive filter described in step 5 are:

[0044]

[0045] in,

[0046] A recursive filter design device for a complex network, comprising:

[0047] Model building module, used to build mathematical models of nonlinear time-varying complex networks with random coupling;

[0048] The recursive filter design unit designs the recursive filter based on the mathematical model and adopts the decoding and forwarding relay strategy based on the energy harvesting technology, and determines the parameters of the filter to be designed;

[0049] An error calculation unit calculates a one-step prediction error and a filtering error of a state variable based on a mathematical model and a recursive filter, and determines a prediction error covariance and a filtering error covariance based on the one-step prediction error and the filtering error;

[0050] The upper bound calculation unit of the filter error covariance considers the prediction error covariance and the estimation error covariance and adopts two sets of matrix difference equations to determine the upper bound of the filter error covariance;

[0051] The parameter calculation unit of the filter to be designed designs the parameters of the recursive filter by means of the matching method based on the upper bound of the filter error covariance.

[0052] Compared with the prior art, the present invention has the following significant advantages: (1) a decoding-forwarding-relay strategy is introduced, and a recursive filter is designed based on the decoding-forwarding-relay strategy of the energy harvesting technology to extend the transmission distance of the signal to ensure the filtering performance of the complex network; (2) the energy harvesting technology is applied to both sensors and relays to better reflect the actual engineering scenarios; (3) the system model studied is a type of time-varying nonlinear complex network with random coupling, which solves the problem that the existing filtering method cannot simultaneously process the nonlinear complex network with energy harvesting technology and decoding-forwarding-relay, and can be used in the filtering field with energy harvesting technology and decoding-forwarding-relay. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 It is a flow chart of a recursive filtering design method for a complex network of the present invention.

[0054] Figure 2 1 is a graph of the state components of node 1 and its estimated curve in an embodiment of the present invention.

[0055] Figure 3 1 is a graph showing the state components of node 2 and their estimated curves in an embodiment of the present invention.

[0056] Figure 4 3 is a graph of the state components of node 3 and its estimated curve in an embodiment of the present invention.

[0057] Figure 5 is the energy storage and energy consumption of the battery of sensor i at each moment in the embodiment of the present invention.

[0058] Figure 6It is the energy storage and energy consumption of the battery of repeater i at each moment in the embodiment of the present invention.

[0059] Figure 7 It is the upper bound of the mean square error MSE and the filter error covariance trace in the embodiment of the present invention. DETAILED DESCRIPTION

[0060] Combination Figure 1 This project invents a recursive filter design method for complex networks, including the following steps:

[0061] Step 1: Establish a mathematical model of a nonlinear time-varying complex network with random coupling;

[0062] Step 2: Design a recursive filter for the decode-forward relay strategy based on energy harvesting technology;

[0063] Step 3: With the help of two sets of matrix difference equations, the upper bound of the filtering error covariance is given;

[0064] Step 4, obtaining the gain parameters of the filter by using the matching method;

[0065] Step 5: Analyze the relationship between the measured transmission probability and the minimum upper bound from the perspective of monotonicity.

[0066] As a specific implementation, in step 1, a mathematical model of a nonlinear time-varying complex network with random coupling is established, as follows:

[0067] Create a time-varying nonlinear complex network consisting of N nodes with random internal couplings:

[0068]

[0069] in and Represent the state variable and measurement output of the i-th node respectively; is the internal coupling matrix; Γ represents the external coupling configuration matrix of the network; and denote zero-mean noise, and and f(·) represents a nonlinear function; and is a known coefficient matrix; and Respectively represent n-dimensional Euclidean space and m×n real matrix set; represents mathematical expectation.

[0070] As a specific implementation, in step 2, a filter is designed according to a decoding and forwarding relay strategy based on energy harvesting technology, as follows:

[0071] Step 2.1: To power the sensors and repeaters, use energy harvesting techniques in the following form:

[0072] At time s, the sensor and repeaters The battery charge level is recorded as here and represents the maximum power level that the battery of sensor i and repeater i can store; the evolution model of battery power level over time can be expressed as the following recursive equation:

[0073]

[0074] The initial charge is an indicative function, abbreviated as when hour, otherwise also, is an independent and identically distributed random variable representing the amount of energy collected by the battery of sensor / repeater i at time s, and it has the following probability distribution:

[0075]

[0076] in satisfy and The probability of event "A" occurring;

[0077] Step 2.2: Design a decoding and forwarding relay strategy based on energy harvesting technology

[0078] The battery-powered sensor can transmit the measured value it perceives to the repeater, and the actual measured value received by the repeater can be expressed as:

[0079]

[0080] Before transmission, measure the signal Preprocessing is performed according to a specific coding scheme. The coding scheme used is

[0081]

[0082] in θ i,s and ρ i,s-1 Represent the internal state, the output of the encoder, a known scalar, and a known connection matrix respectively. is the quantizer used in the encoder and has the following form:

[0083]

[0084] where l=1,2,…,n y , the quantizer of component l is

[0085]

[0086] Where β is a pre-given quantization parameter;

[0087] The decoding rules are as follows:

[0088]

[0089] in is the output of the decoder;

[0090] make The decoding error is as follows:

[0091]

[0092] The quantization error γ i,s satisfy This means that the decoding error satisfies

[0093]

[0094] Where ||·|| represents the norm of the vector;

[0095] Considering the repeater using energy harvesting technology, the actual measurement received by the filter can be expressed as:

[0096]

[0097] in is satisfied and The channel noise;

[0098] Step 2.3, design the filter:

[0099] According to the measured values ​​actually received by the filter, a filter of the following form can be constructed:

[0100]

[0101] in and They represent the state variable x at time s+1. s+1 One-step forecasts and estimates of ; is the gain matrix to be designed.

[0102] As a specific implementation, in step 2, the random variable ω i,s 、v i,s , τi,s , κ i,s and x i,0 The following constraints are met:

[0103] Random variable ω i,s ,υ i,s , τ i,s , κ i,s and x i,0 They are independent of each other.

[0104] As a specific implementation, in step 3, the probability distribution of battery power levels of the sensor and the repeater is obtained as follows:

[0105] First, the battery level at time s The probability distribution of

[0106] Energy level The recursive probability distribution of satisfy

[0107]

[0108] in

[0109]

[0110] You can The expected value of

[0111]

[0112] As a specific implementation, in step 3, the one-step prediction error and the estimation error are calculated as follows:

[0113] remember is the one-step prediction error, is the filtering error; and Respectively represent the one-step prediction error covariance and filtering error covariance; A T represents the transpose of matrix A;

[0114] From (11), we can see that the one-step prediction error e i,s+1|s It can be written as

[0115]

[0116] Take f(x i,s )exist Taylor expansion is performed at

[0117]

[0118] in o(|e i,s|s |) represents the linearization error and satisfies

[0119]

[0120] in and is a known matrix, Ξ i,s is satisfied The unknown matrix of

[0121] Substituting (16) and (17) into (12), the one-step prediction error e i,s+1|s Can be rewritten as

[0122]

[0123] Estimation error e i,s+1|s+1 It can be written as

[0124]

[0125] As a specific implementation, in step 3, the prediction error covariance and the filtering error covariance are calculated as follows:

[0126] Forecast error covariance x i,s+1|s and the filter error covariance x i,s+1|s+1 It can be written as

[0127]

[0128] in

[0129]

[0130]

[0131] As a specific implementation, in step 3, the upper bound of the filtering error covariance is calculated as follows:

[0132] Consider the prediction error covariance (20) and the estimation error covariance (21), which satisfy the initial value Assume the following two difference equations

[0133]

[0134] Satisfy inequality constraints And solution and Then, we can get in

[0135]

[0136] And1,s ,σ 2,s ,σ 3,s ,σ 4,s ,σ 5,s ,σ 6,s ,σ 7,s ,γ i,s is a known scaling parameter, is the corresponding reciprocal; A -1 Represents the inverse of the square matrix A.

[0137] As a specific implementation, in step 4, the gain parameter of the filter is obtained as follows:

[0138] If the gain matrix satisfy

[0139]

[0140] in Then the upper bound of the filtering error covariance can be guaranteed The minimum value can be obtained in each calculation; in addition, the obtained The minimum value of is given by:

[0141]

[0142] in

[0143]

[0144] As a specific implementation, in step 5, the relationship between the measured transmission probability and the minimum upper bound is analyzed as follows:

[0145] For two given parameters if is increasing, then the minimum upper bound It is decreasing.

[0146] The present invention also provides a recursive filter design device for a complex network, comprising:

[0147] Model building module, used to build mathematical models of nonlinear time-varying complex networks with random coupling;

[0148] The recursive filter design unit designs the recursive filter based on the mathematical model and adopts the decoding and forwarding relay strategy based on the energy harvesting technology, and determines the parameters of the filter to be designed;

[0149] An error calculation unit calculates a one-step prediction error and a filtering error of a state variable based on a mathematical model and a recursive filter, and determines a prediction error covariance and a filtering error covariance based on the one-step prediction error and the filtering error;

[0150] The upper bound calculation unit of the filter error covariance considers the prediction error covariance and the estimation error covariance and adopts two sets of matrix difference equations to determine the upper bound of the filter error covariance;

[0151] The parameter calculation unit of the filter to be designed designs the parameters of the recursive filter by means of the matching method based on the upper bound of the filter error covariance.

[0152] The present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0153] Example

[0154] Recursive filtering of complex networks can be used in practical application scenarios such as power system state estimation, information dissemination in social networks, and navigation and positioning in unmanned systems. In order to further illustrate the effectiveness of the algorithm proposed in this invention, a comparative simulation was performed based on the navigation and positioning scenario in an unmanned system. Consider a complex network with the following parameters:

[0155]

[0156] Linear function f(x i,s )for

[0157]

[0158] in

[0159] Given the initial state variables and The other parameters are chosen as 1,s =σ 2,s =1,σ 3,s =σ 4,s =σ 5,s =σ 6,s =0.1,σ 7,s =0.01, β i =0.1,θ 1,s =θ 2,s =θ 3,s =0.1, and For node i, the zero-mean random variable κ i,s ,ω i,s ,υ i,s and τ i,s Distribution satisfies and Set the maximum battery storage capacity and initial battery power of sensor / repeater i to and

[0160] The simulation results are shown in Figure 2-Figure 7 Specifically, Figure 2-Figure 4 Describes the state x i,s The actual trajectory of (i=1,2,3) and the corresponding filter estimate, Figure 5-Figure 6 represents the energy stored and consumed by sensor / repeater i at each moment, Figure 7 It can be seen that the mean square error of the system state variables is always smaller than the trace of the upper bound of the filter error covariance.

[0161] In summary, the present invention adopts a decode-amplify-forward relay strategy based on energy harvesting technology to solve the recursive state estimation problem of complex networks. In order to enhance the communication reliability, a decode-amplify-forward relay mechanism is adopted for the transmission from sensor to estimator. The energy harvesting technology provides power for the sensor and the repeater. Subsequently, the upper bound of the filter error covariance is ensured and minimized by selecting appropriate filter gain parameters. In addition, the monotonic relationship between the minimum upper bound and the measured transmission probability is revealed.

[0162] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical scheme and inventive concept of the present invention within the technical scope disclosed by the present invention, which should be within the protection scope of the present invention.

Claims

1. A recursive filter design method for a complex network based on energy harvesting and decoding and forwarding relay, characterized in that: The following steps are involved: Step 1: Establish a mathematical model of a nonlinear time-varying complex network with random coupling; Step 2: Based on the mathematical model, a decoding and forwarding relay strategy based on energy harvesting technology is adopted to design a recursive filter and determine the parameters of the filter to be designed; Step 3: Based on the mathematical model and the recursive filter, a one-step prediction error and a filtering error of the state variable are calculated, and a prediction error covariance and a filtering error covariance are determined based on the one-step prediction error and the filtering error; Step 4, considering the prediction error covariance and the estimation error covariance, two sets of matrix difference equations are used to determine the upper bound of the filtering error covariance; Step 5: Based on the upper bound of the filtering error covariance, the parameters of the recursive filter are designed using the matching method to obtain the recursive filter.

2. The recursive filter design method for complex networks according to claim 1, characterized in that: The mathematical model of the nonlinear time-varying complex network described in step 1 is: in and Represent the state variable and measurement output of the i-th node respectively; is the internal coupling matrix; Γ represents the external coupling configuration matrix of the network; and denote zero-mean noise, and and f(·) represents a nonlinear function; and is a known coefficient matrix; and Respectively represent n-dimensional Euclidean space and m×n real matrix set; represents the mathematical expectation, and N is the number of sensors / repeaters.

3. The recursive filter design method for complex networks according to claim 2, characterized in that: The step 2 is specifically as follows: Step 2.

1. Design a model for the evolution of battery charge level over time, i.e., the form of energy harvesting technology; Step 2.2, design a decoding and forwarding relay strategy based on the evolution model to obtain the actual measurement value received by the recursive filter; Step 2.3: construct a recursive filter based on the actual measurement value received by the recursive filter.

4. The recursive filter design method for complex networks according to claim 3, characterized in that: The model for the evolution of the battery charge level over time is: The battery power levels of sensor i and repeater i are denoted as Indicates the sensor, Represents a repeater; and Indicates the maximum power level that the batteries of sensor i and repeater i can store; initial power is the characteristic function, abbreviated as when hour, otherwise is an independent and identically distributed random variable representing the amount of energy collected by the battery of sensor / repeater i at time s.

5. The recursive filter design method for complex networks according to claim 4, characterized in that: The actual measurement value received by the recursive filter is: in, is satisfied and The channel noise, is the output of the decoder.

6. The recursive filter design method for complex networks according to claim 5, characterized in that: The recursive filter is: in and They represent the state variable x at time s+1. s+1 One-step forecasts and estimates of ; is the gain matrix to be designed.

7. The recursive filter design method for complex networks according to claim 6, characterized in that: The one-step prediction error and filtering error are: Among them, e i,s+1|s is the one-step prediction error, e i,s+1|s+1 is the filtering error, Ξ i,s is satisfied The unknown matrix, decoder error is the actual measured value; The prediction error covariance and filtering error covariance are: The parameters are:

8. The recursive filter design method for complex networks according to claim 7, characterized in that: The upper bound of the filtering error covariance determined in step 4 is as follows: Consider the prediction error covariance and the estimation error covariance, which satisfy the initial value Assume the following two difference equations Satisfy inequality constraints And solution and Then, we get in, And 1,s ,σ 2,s ,σ 3,s ,σ 4,s ,σ 5,s ,σ 6,s ,σ 7,s ,γ i,s is a known scaling parameter, is the corresponding reciprocal; A -1 Represents the inverse of the square matrix A.

9. The recursive filter design method for complex networks according to claim 8, characterized in that: The parameters of the recursive filter described in step 5 are: in, 10. A recursive filter design device for a complex network implementing any of the methods described in claims 1-9, characterized in that: include: Model building module, used to build mathematical models of nonlinear time-varying complex networks with random coupling; The recursive filter design unit designs the recursive filter based on the mathematical model and adopts the decoding and forwarding relay strategy based on the energy harvesting technology, and determines the parameters of the filter to be designed; An error calculation unit calculates a one-step prediction error and a filtering error of a state variable based on a mathematical model and a recursive filter, and determines a prediction error covariance and a filtering error covariance based on the one-step prediction error and the filtering error; The upper bound calculation unit of the filter error covariance considers the prediction error covariance and the estimation error covariance and adopts two sets of matrix difference equations to determine the upper bound of the filter error covariance; The parameter calculation unit of the filter to be designed designs the parameters of the recursive filter by means of the matching method based on the upper bound of the filter error covariance.

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