Estimation method of continuous-discrete maximum correlation entropy distributed cubature kalman filter

Abstract

The embodiment of the application provides an estimation method of continuous-discrete maximum correlation entropy distributed cubature Kalman filtering, which comprises the following steps: establishing a continuous-discrete target tracking model in a multi-sensor network; based on a maximum correlation entropy criterion, a 1.5-order ITO Taylor expansion, a cubic cubature rule, an average consensus method and a minimum mean square error criterion, calculation is performed to obtain a continuous-discrete maximum correlation entropy distributed cubature Kalman filtering method; and for the continuous-discrete target tracking model, target tracking is performed according to the continuous-discrete maximum correlation entropy distributed cubature Kalman filtering method to obtain accurate target state information. The method can accurately estimate the parameters of an aircraft target and improve reliability.

Description

Technical Field

[0001] This invention relates to the technical field of aircraft target tracking, and more specifically to an estimation method for continuous-discrete maximum correlation entropy distributed capillary Kalman filtering. Background Technology

[0002] In multi-sensor networks, target tracking involves obtaining the target's range and azimuth from sensors to further estimate the target's state. Target tracking based on range and azimuth is widely used in passive target tracking. Traditional target tracking algorithms, such as extended / unscented / volume Kalman filtering, typically establish both the target's process and measurement equations in discrete form and only consider target state estimation under Gaussian noise.

[0003] In practice, the target tracking model is a continuous-discrete nonlinear model. The process equations are time-continuous, in the form of ITO-type stochastic differential equations, and can accurately describe the system operation. The measurement equations are discrete, constructed by the digital sensors used. Furthermore, the influence of environmental noise on the system means that the measurement noise is usually non-Gaussian. Therefore, using traditional target tracking algorithms has the following disadvantages: (1) The continuous process equations need to be discretized, increasing discretization error; (2) The discretization step size is the same as the sampling step size, narrowing the application scope; (3) When the measurement noise is non-Gaussian, it is impossible to obtain state estimation results that meet the conditions. Summary of the Invention

[0004] The purpose of this invention is to provide an estimation method for continuous-discrete maximum correlation entropy distributed capillary Kalman filtering, which can accurately estimate the parameters of aircraft targets and improve reliability.

[0005] This invention provides an estimation method for continuous-discrete maximum correlation entropy distributed capacitive Kalman filtering, the estimation method of which includes:

[0006] Establish a continuous-discrete target tracking model in a multi-sensor network;

[0007] Based on the maximum correlation entropy criterion, 1.5-order ITO Taylor expansion, cubic volume rule, average consensus method and minimum mean square error criterion, a continuous-discrete maximum correlation entropy distributed capacitive Kalman filter method is calculated to obtain the method.

[0008] For the continuous-discrete target tracking model, target tracking is performed according to the continuous-discrete maximum correlation entropy distributed commensurate Kalman filter method to obtain accurate target state information.

[0009] Preferably, establishing the continuous-discrete target tracking model in a multi-sensor network includes:

[0010] In multi-sensor networks, a continuous-discrete nonlinear system under non-Gaussian noise is represented as:

[0011] dx(t)=f(x(t))dt+Gdβ(t) (1)

[0012]

[0013] Where x(t)∈R n It is the estimated state vector, f:R n →R n It is a differentiable nonlinear function, β(t) is an n-dimensional standard Brownian motion independent of the state vector, G∈R n×n Given a time-invariant diffusion matrix, For node i at sampling time t k The measured value when =kT, T = t k -t k-1 The sampling period is It is a known measurement function. The mean is not equal to 0, and the covariance is... Non-Gaussian noise;

[0014] The system equations are:

[0015]

[0016] G=diag([σ1σ2σ1σ2σ3]);

[0017] β(t)=[β1(t)β2(t)β3(t)β4(t)β5(t)] T ;

[0018] Among them, the state variables of the aircraft Where x(t), y(t) and Let be the position and velocity of the aircraft in the coordinate system x and y axes, respectively, and w(t) represent the rate of turn;

[0019] The aircraft's distance r and azimuth θ are determined by multiple sensors at sampling time t. k =kT was measured, and the measurement equation is:

[0020]

[0021] In the formula, Indicates the position coordinates of sensor node i; For measurement noise with a mixed Gaussian distribution,

[0022] Preferably, the method for calculating the continuous-discrete maximum correlation entropy distributed capacitive Kalman filter based on the maximum correlation entropy criterion, 1.5-order ITO Taylor expansion, cubic volume rule, average consensus method, and minimum mean square error criterion includes:

[0023] Step 1.1: m-step time update

[0024] Given a state dimension of n, a sampling interval of T, m discretization iterations, a discretization step size of δ = T / m, and the current iteration number of k, the state vector, covariance matrix, and kernel width of sensor node i at time k-1 are known and are respectively... With σ1 = 1 and b = 0, initialize the state mean and covariance of sensor node i as follows:

[0025] 1) To Performing Cholesky decomposition yields

[0026] 2) Calculate the volume points (a = 1, 2, ..., 2n) Volume point ξ a for: e a This represents the a-th column in the identity matrix e;

[0027] 3) Calculate the volume point of propagation.

[0028] 4) Calculate the predicted state vector value

[0029] 5) Calculate the prediction error covariance matrix

[0030]

[0031] In the formula,

[0032] 6) Repeat steps 1)-5), and each time b is executed, b = b + 1; when b = m, m steps of update are completed, and t is obtained. k+1 =Updated values ​​of the state vector and covariance matrix at time kT+mδ and That is, measurement update

[0033] Step 1.2: Measurement Update

[0034] 1) Obtained by m-step time updates The results were obtained by performing the Cholesky decomposition.

[0035] 2) Calculate the volume points (a = 1, 2, ..., 2n)

[0036] 3) Calculate the volume point of propagation.

[0037] 4) Calculate the predicted measurement value

[0038] 5) Calculate the cross-covariance matrix In the formula,

[0039]

[0040] 6) Calculate the new information covariance matrix

[0041] 7) Calculate the pseudo-measurement matrix

[0042] 8) Calculate the noise variance of the innovation measurement.

[0043] 9) Calculate the kernel width σ k =max(e / 3,σ k-1 ), where

[0044] 10) Calculate the Kalman gain In the formula

[0045] 11) Calculate the state update value using the fixed-point iteration method.

[0046] 12) Calculate the updated value of the error covariance matrix.

[0047] Step 1.3: Consistency Filtering

[0048] Initialize the state vector and covariance matrix of sensor node i

[0049] 1) L-step weighted average consensus

[0050] a. To the neighboring nodes j∈C of sensor node i i {i} disseminating information and one's own measure;

[0051] b. Received from neighboring nodes After summing the degrees, calculate the weights of itself and its neighboring nodes;

[0052] c. According to the formula Japanese style

[0053] A weighted average consensus is achieved using the state vector and covariance matrix, where the consensus weights are... It can be determined by the commonly used Metropolis weighting rules:

[0054]

[0055] Where, d i This represents the degree of sensor node i, i.e., the number of adjacent sensors;

[0056] d. Repeat step ac L times to obtain the average consensus. and

[0057] 2) Update the state vector and error covariance matrix of sensor node i after average consensus.

[0058] Preferably, step 1 involves expanding the stochastic differential equation into a 1.5th order ITO Taylor series, resulting in the following formula:

[0059] x(t+δ)=f d (x(t),t)+GW1+(Lf(x(t),t))W2 (4)

[0060] In the above formula, δ=T / m, f d (x(t), t) is a noise-free function:

[0061]

[0062] L0 and L j (j=1,...,n) are two differential operators:

[0063]

[0064]

[0065] Among them, L j f i (i,j=1,...,n) represents the (i,j)th element of Lf;

[0066] W1 and W2 are multidimensional Gaussian random variables generated by the following formula:

[0067]

[0068]

[0069] In the formula, u1 and u2 are independent standard Gaussian random vectors.

[0070] Preferably, the cubic volume rule for calculating the Gaussian weighted integral in step 1 is as follows:

[0071]

[0072] In the above formula, Volume point ξ i for:

[0073]

[0074] In the formula, e i Let the i-th column of the identity matrix e be represented as:

[0075]

[0076] Preferably, the average consensus method in step 1 is as follows:

[0077]

[0078]

[0079] In the formula, Called an information pair, it is the matrix updated by sensor node i in the l-th consensus iteration. As l→∞, each sensor's... They all tend to the same value, 0 < ε < 1 / Δ max Let Δ be the uniformity gain, where Δ max This represents the maximum degree of a node in the graph. Consensus Matrix The (i,j)th element in the array.

[0080] Preferably, the maximum correlation entropy criterion used in step 1 includes:

[0081] Correlation entropy is used to describe the similarity between two random variables X and Y. Its correlation entropy is defined as: V(X,Y)=E[κ(X,Y)]=∫κ(x,y)dF XY (x,y); where E[·] represents the mathematical expectation, κ[·,·] represents the shift-invariant Messer kernel function, and F XY (x,y) is the joint distribution function of X and Y;

[0082] When the joint density function is difficult to obtain and the dataset only contains a limited amount of data, the correlation entropy can be estimated by averaging the samples: Among them, e(i)=x(i)-y(i), From the joint density function F XY Data sampled from (x,y).

[0083] Preferably, the step of performing target tracking according to the continuous-discrete maximum correlation entropy distributed capacitive Kalman filter method to obtain accurate target state information for the continuous-discrete target tracking model includes:

[0084] Step 2.1: Initialize the state vector, process covariance matrix, measurement noise mean, and measurement noise covariance matrix;

[0085] Step 2.2: Target tracking actual motion trajectory generation. The Euler-Maruyama method of equation (14) is used to numerically solve the stochastic differential equation to simulate the real dynamics of the aircraft. The step size is a fixed value of 0.0005s.

[0086] x(t+δ)=x(t)+δf(x(t),t)+Gw (14)

[0087] To compare the estimation performance of the algorithms, the root mean square error (RMSE) and cumulative root mean square error (ARMSE) of position and velocity are used as performance standards; Equations (17) and (18) are the RMSE and ARMSE of position, and the RMSE and ARMSE of velocity are in the same form as those of position.

[0088]

[0089]

[0090] in, These are the actual coordinates of the aircraft during the nth Monte Carlo simulation. This corresponds to the optimal estimate; N is the total number of simulation samples, and M is the number of Monte Carlo simulations;

[0091] Step 2.3: The continuous-discrete maximum correlation entropy distributed capillary Kalman filter method is used to estimate the state of the target tracking model.

[0092] In addition, the present invention provides a machine-readable storage medium storing instructions for causing a machine to perform the above-described estimation method for continuous-discrete maximum correlation entropy distributed commensurate Kalman filtering.

[0093] Through the above technical solutions

[0094] The continuous-discrete target tracking model established in this invention for multi-sensor networks accurately describes the trajectory of the aircraft's flight through process equations, while the measurement equations are derived from sensor characteristics. The parameters derived from this model are more closely aligned with actual conditions, resulting in significantly improved accuracy.

[0095] The continuous-discrete maximum correlation entropy distributed capacitive Kalman filter algorithm established in this invention transforms the process stochastic differential equations into stochastic difference equations using a 1.5th-order ITO Taylor expansion during the m-step time update process. Then, it employs a cubic capacitive rule to solve for accurate state predictions. The use of m-step time updates solves the problem of solving for state predictions using stochastic differential equations, and allows for very small solution step sizes in the numerical solution, overcoming the dependence on sampling intervals in state estimation.

[0096] The continuous-discrete maximum correlation entropy distributed capacitive Kalman filter algorithm established in this invention introduces the maximum correlation entropy criterion and proposes a new cost function in measurement updates, which can effectively handle non-Gaussian noise problems in measurements. At the same time, a new kernel width selection method is proposed based on measurement innovation error, avoiding repeated experiments to select the kernel width. It has a wide range of applications and is convenient to use.

[0097] The continuous-discrete maximum correlation entropy distributed capacitive Kalman filter algorithm established in this invention does not require a pseudo-measurement matrix in the consensus update. It directly uses the state estimate and covariance matrix estimate of each sensor node when filtering individually, which will not lead to the accumulation of errors in the iteration and improves the estimation accuracy of the algorithm.

[0098] The kernel bandwidth adaptive continuous-discrete maximum correlation entropy distributed capacitive Kalman filter algorithm adopted in this invention, compared with the traditional discrete distributed filtering algorithm, can not only accurately estimate the state of the aircraft under non-Gaussian noise with high estimation accuracy and ease of use, but also can break through the limitation of sampling interval, greatly expanding the application scenarios.

[0099] Other features and advantages of the embodiments of the present invention will be described in detail in the following detailed description section. Attached Figure Description

[0100] The accompanying drawings are provided to further illustrate embodiments of the present invention and form part of the specification. They are used together with the following detailed description to explain the embodiments of the present invention, but do not constitute a limitation thereof. In the drawings:

[0101] Figure 1 This is a flowchart illustrating the continuous-discrete maximum correlation entropy distributed capacitive Kalman filter method in this invention;

[0102] Figure 2 This is a diagram illustrating the sensor network topology of the present invention;

[0103] Figure 3 This is a flowchart illustrating the target state estimation process of the present invention. Detailed Implementation

[0104] The specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are for illustration and explanation only and are not intended to limit the scope of the present invention.

[0105] Figure 1 The estimation method of the continuous-discrete maximum correlation entropy distributed capacitive Kalman filter of the present invention is carried out according to the following steps:

[0106] Step 1: Establish a continuous-discrete target tracking model in a multi-sensor network

[0107] In multi-sensor networks, for example, Figure 2 Taking the sensor network topology as an example, the state estimation problem of a continuous-discrete nonlinear system under non-Gaussian noise is generally described by the following system stochastic differential equation (SDE) (1) and discrete measurement equation (2):

[0108] dx(t)=f(x(t))dt+Gdβ(t) (1)

[0109]

[0110] In equations (1) and (2), x(t) ∈ R n It is the estimated state vector, f:R n →R n It is a differentiable nonlinear function, β(t) is an n-dimensional standard Brownian motion independent of the state vector, G∈R n×n Given a time-invariant diffusion matrix, For node i at sampling time t k The measured value when =kT, T = t k -t k-1 The sampling period is It is a known measurement function. The mean is not equal to 0, and the covariance is... Non-Gaussian noise.

[0111] In the nonlinear target tracking model, the aircraft turns at a constant rate, and its motion model can be represented by the stochastic differential equation (1). The aircraft's state variables... Where x(t), y(t) and Let be the aircraft's position and velocity along the x and y axes of the coordinate system, respectively, and w(t) represent the rate of turn. System equations: G=diag([σ1σ2σ1σ2σ3]), β(t)=[β1(t)β2(t)β3(t)β4(t)β5(t)] T It is standard Brownian motion.

[0112] The aircraft's distance r and azimuth θ are determined by multiple sensors at sampling time t. k =kT was measured, and the measurement equation is:

[0113]

[0114] In the formula, This represents the position coordinates of sensor node i. For measurement noise with a mixed Gaussian distribution,

[0115] Step 2: Based on the maximum correlation entropy criterion, 1.5th order ITO Taylor expansion, cubic volume rule, average consensus method, and minimum mean square error criterion, a continuous-discrete maximum correlation entropy distributed capacitive Kalman filter method is derived. In specific implementation, since the stochastic differential equation shown in Equation (1) cannot be directly solved analytically, the state estimation problem of each sensor node cannot continue. Therefore, the stochastic differential equation is transformed into a stochastic difference equation using the 1.5th order ITO Taylor expansion shown in Equations (4)-(9). Then, the Gaussian weighted integral in the filtering process is approximated using the cubic volume rule in Equations (10)-(11). Consistency filtering is achieved using the average consensus method in Equations (12)-(13). A new cost function is generated by combining the minimum mean square error criterion and the maximum correlation entropy criterion. Finally, a continuous-discrete maximum correlation entropy distributed capacitive Kalman filter method is derived through a series of numerical approximations.

[0116] Step 2.1: 1.5th order ITO Taylor expansion

[0117] First, the sampling interval T is divided into m (m>1) equal subintervals, and then a 1.5th order ITO Taylor expansion is performed on equation (1). The resulting stochastic difference equation is:

[0118] x(t+δ)=f d (x(t),t)+GW1+(Lf(x(t),t))W2 (4)

[0119] In the above formula, δ=T / m, f d (x(t), t) is a noise-free function:

[0120]

[0121] L0 and L j (j=1,...,n) are two differential operators:

[0122]

[0123]

[0124] Among them, Lj f i (i,j=1,...,n) represents the (i,j)th element of Lf.

[0125] W1 and W2 are multidimensional Gaussian random variables generated by the following formula:

[0126]

[0127]

[0128] In the formula, u1 and u2 are independent standard Gaussian random vectors.

[0129] Step 2.2: Tertiary Volume Rule

[0130]

[0131] In the above formula, Volume point ξ i for:

[0132]

[0133] In the formula, e i Let the i-th column of the identity matrix e be represented as:

[0134] Step 2.3: Average Consensus Method

[0135]

[0136]

[0137] In the formula, Called an information pair, it is the matrix updated by sensor node i in the l-th consensus iteration. As l→∞, each sensor's... They all tend to the same value, 0 < ε < 1 / Δ max Let Δ be the uniformity gain, where Δ max This represents the maximum degree of a node in the graph. Consensus Matrix The (i,j)th element in the array.

[0138] Step 2.4: Maximum Correlation Entropy Criterion

[0139] Correlation entropy can be used to describe the similarity between two random variables X and Y. Its correlation entropy is defined as: V(X,Y)=E[κ(X,Y)]=∫κ(x,y)dF XY (x,y). Where E[·] represents the mathematical expectation, κ[·,·] represents the shift-invariant Messer kernel function, and F XY(x, y) is the joint distribution function of X and Y. The correlation entropy kernel function chosen in this invention is the Gaussian kernel function, defined as: Where e = xy and σ > 0 represents the Gaussian kernel width.

[0140] When the joint density function is difficult to obtain and the dataset only contains a limited amount of data, the correlation entropy can be estimated by sample averaging. Among them, e(i)=x(i)-y(i), From the joint density function F XY Data sampled from (x,y).

[0141] Step 2.5: Derivation of the combined maximum correlation entropy criterion and least squares cost function

[0142] This invention combines the maximum correlation entropy criterion and the least squares cost function to construct a new cost function. Where α and β are adjustment weighting factors, In practical implementation, the pseudo-measurement matrix Measure the updated value of the noise variance matrix

[0143] By minimizing the newly constructed cost function Obtain the state vector The optimal estimate, i.e.

[0144]

[0145] In the formula, the adaptive factor It is a scalar. The components are easily separated during computation, avoiding numerical solution problems. Furthermore, to ensure that the filter converges to a traditional Kalman filter when the Gaussian kernel width approaches infinity, the adjustment factors in this invention are set to α = 1 and β = -2σ. 2 In practice, by substituting the adjustment factor into equation (14) and solving it using a fixed-point iterative algorithm, the updated state value and the updated error covariance matrix value can be obtained:

[0146]

[0147]

[0148] in, It should also be noted that in the fixed-point iteration, due to If it is unknown, then Available To replace, therefore Can be rewritten as

[0149] Step 2.6: Adaptive Kernel Bandwidth Derivation

[0150] In the continuous-discrete maximum correlation entropy distributed capacitive Kalman filter method, the kernel bandwidth σ plays a crucial role, affecting the algorithm's robustness to non-Gaussian measurements. Only by selecting an appropriate kernel bandwidth can the algorithm's estimation performance be guaranteed. This invention proposes an adaptive kernel width adjustment method based on measurement innovation error: σ k =max(e / 3,σ k-1 In the formula, The initial value σ1 = 1.

[0151] Step 2.7: Continuous-Discrete Maximum Correlation Entropy Distributed Cumulative Kalman Filtering Method

[0152] A: m-step time update

[0153] The state vector and covariance matrix of sensor node i at time k-1 are known and are respectively and Let b = 0, and initialize the state mean and covariance of sensor node i as follows: In practice, the assignment operation can be performed using Matlab's "=".

[0154] 1) To Cholesky decomposition yields In practice, the "chol" function in Matlab can be used directly.

[0155] 2) Calculate the volume points (a = 1, 2, ..., 2n) In specific implementation, it can be Copy the matrix multiplied by 1xn, then... Performing addition and subtraction operations avoids the use of "for" loops, thus speeding up the algorithm's execution.

[0156] 3) X i a,b,k-1|k-1 Substitute the values ​​into equation (5) and perform the calculation to obtain the propagation volume point. In practice, a "for" loop can be used to perform the calculation.

[0157] 4) To Weighted summation yields the predicted state vector value. In practice, the "sum" function can be used to perform matrix operations, reducing computational overhead.

[0158] 5) Calculate the prediction error covariance matrix

[0159]

[0160] In the formula, In practice, the "repmat" function can be used to copy. Vector, then Subtract the matrix obtained by copying from the original matrix, and then divide the result by . You can get Compared to using a "for" loop, using the "repmat" function speeds up the algorithm's execution and reduces computational overhead.

[0161] 6) Repeat steps 1)-5), and each time b is executed, b = b + 1. When b = m, m updates are complete, and t is obtained. k+1 =Updated values ​​of the state vector and covariance matrix at time kT+mδ and That is, measurement update and In practice, you can use the "for" loop in Maltab to repeatedly execute 1)-5), and use "=" to perform assignment operations.

[0162] B: Measurement Update

[0163] 1) Obtained by m-step time updates The results were obtained by performing the Cholesky decomposition. In practice, the "chol" function in Matlab can be used directly.

[0164] 2) Calculate the volume points (a = 1, 2, ..., 2n) In specific implementation, it can be Copy the matrix multiplied by 1xn, then... Performing addition and subtraction operations avoids the use of "for" loops, thus speeding up the algorithm's execution.

[0165] 3) Calculate the volume point of propagation using the measurement equation. In practice, a "for" loop can be used to perform the calculation.

[0166] 4) Weighted summation of the propagation volume points yields the measurement prediction value. In practice, the "sum" function can be used to perform matrix operations, reducing computational overhead.

[0167] 5) Calculate the cross-covariance matrix

[0168] In the formula,

[0169] In practice, the "repmat" function can be used to reduce computational overhead.

[0170] 6) Calculate the new information covariance matrix In specific implementation, the information obtained in step 5) can be utilized. Perform the operation.

[0171] 7) Calculate the pseudo-measurement matrix In practice, " / " represents right division of a matrix, and A / B is equivalent to A*inv(B). Using " / " for calculation can enhance the accuracy of the result and speed up the calculation.

[0172] 8) Calculate the updated value of the measurement noise variance matrix.

[0173] 9) Calculate the kernel width σ k =max(e / 3,σ k-1 ), where

[0174] 10) Calculate the Kalman gain In the formula

[0175] 11) Calculate the state update value using the fixed-point iteration method.

[0176] 12) Calculate the updated value of the error covariance matrix.

[0177]

[0178] C: Consistency Filtering

[0179] Initialize the state vector and covariance matrix of sensor node i In practice, the assignment operation can be performed using the "=" operator in Matlab.

[0180] 1) L-step weighted average consensus

[0181] a. To the neighboring nodes j∈C of sensor node i i {i} disseminating information And one's own measure.

[0182] b. Received from neighboring nodes After summing the degrees, calculate the weights of itself and its neighboring nodes.

[0183] c. Achieve weighted average consensus of the state vector and covariance matrix according to equations (12) and (13). Where, consensus weights... It can be determined by the commonly used Metropolis weighting rules:

[0184]

[0185] Where, d iThis represents the degree of sensor node i, i.e., the number of adjacent sensors.

[0186] d. Repeat step ac L times to obtain the average consensus. and In practice, a "for" loop can be used to execute the operation.

[0187] 2) Update the state vector and error covariance matrix of sensor node i after average consensus. In practice, the assignment operation can be performed using the "=" operator in Matlab.

[0188] Step 3: For the target tracking problem described in Step 1, the continuous-discrete maximum correlation entropy distributed capacitive Kalman filter method proposed in Step 2 is applied to perform target tracking and obtain accurate target state information. Specifically, as follows... Figure 3 As shown.

[0189] Step 3.1: Initialize the state vector, process covariance matrix, measurement noise mean, and measurement noise covariance matrix. In practice, the assignment operation is performed using "=".

[0190] Step 3.2: Target tracking actual motion trajectory generation. In specific implementation, the Euler-Maruyama method of equation (17) is used to numerically solve the stochastic differential equation (1) to simulate the real dynamics of the aircraft. The step size is a fixed value of 0.0005s.

[0191] x(t+δ)=x(t)+δf(x(t),t)+Gw (17)

[0192] To compare the estimation performance of the algorithms, the root mean square error (RMSE) and cumulative root mean square error (ARMSE) of position and velocity are used as performance standards. Equations (18) and (19) are the RMSE and ARMSE of position, and the RMSE and ARMSE of velocity are in the same form as those of position.

[0193]

[0194]

[0195] in, These are the actual coordinates of the aircraft during the nth Monte Carlo simulation. This is the corresponding optimal estimate. N is the total number of simulation samples, and M is the number of Monte Carlo simulations.

[0196] Step 3.3: The continuous-discrete maximum correlation entropy distributed capacitive Kalman filter method is used to estimate the state of the target tracking model in Step 1. In practice, the state estimation process is implemented through the Matlab program in Step 2.

[0197] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0198] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0199] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0200] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0201] In a typical configuration, a computing device includes one or more processors (CPU), input / output interfaces, network interfaces, and memory.

[0202] Memory may include non-persistent memory in computer-readable media, such as random access memory (RAM) and / or non-volatile memory, such as read-only memory (ROM) or flash RAM. Memory is an example of computer-readable media.

[0203] Computer-readable media includes both permanent and non-permanent, removable and non-removable media that can store information using any method or technology. Information can be computer-readable instructions, data structures, modules of programs, or other data. Examples of computer storage media include, but are not limited to, phase-change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, CD-ROM, digital versatile optical disc (DVD) or other optical storage, magnetic tape, magnetic magnetic disk storage or other magnetic storage devices, or any other non-transferable medium that can be used to store information accessible by a computing device. As defined herein, computer-readable media does not include transient computer-readable media, such as modulated data signals and carrier waves.

[0204] It should also be noted that the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element.

[0205] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0206] The above are merely embodiments of this application and are not intended to limit the scope of this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of the claims of this application.

Claims

1. An estimation method for continuous-discrete maximum correlation entropy distributed capacitive Kalman filtering, characterized in that, The estimation method for the continuous-discrete maximum correlation entropy distributed capacitive Kalman filter includes: Establish a continuous-discrete target tracking model in a multi-sensor network; Based on the maximum correlation entropy criterion, 1.5-order ITO Taylor expansion, cubic volume rule, average consensus method and minimum mean square error criterion, a continuous-discrete maximum correlation entropy distributed capacitive Kalman filter method is calculated to obtain the method. For the continuous-discrete target tracking model, target tracking is performed according to the continuous-discrete maximum correlation entropy distributed commensurate Kalman filter method to obtain accurate target state information; The method for calculating continuous-discrete maximum correlation entropy distributed capacitive Kalman filtering based on the maximum correlation entropy criterion, 1.5-order ITO Taylor expansion, cubic volume rule, average consensus method, and minimum mean square error criterion includes: Step 1: m-step time update The state dimension is set to n, the sampling interval to T, the number of discretizations to m, and the discretization step size to be... The current iteration number is k, and the state vector, covariance matrix, and kernel width of sensor node i at time k-1 are known and are respectively... , and ,make The initial state mean and covariance of sensor node i are respectively... , ; 1) To Performing Cholesky decomposition yields , ; 2) Calculate the volume point ( ) Volume point for: , Represents the identity matrix The first in List; 3) Calculate the volume point of propagation. ; 4) Calculate the predicted state vector value ; 5) Calculate the prediction error covariance matrix. ； In the formula, ; 6) Repeat steps 1)-5), and each time, ;when When m steps of the update are completed, the result is... Updated values ​​of the state vector and covariance matrix at time step and That is, measurement update and ; Step 2: Measurement Update 1) Obtained by m-step time updates The results were obtained by performing the Cholesky decomposition. , ; 2) Calculate the volume point ( ) ; 3) Calculate the volume point of propagation. ; 4) Calculate the predicted measurement value ; 5) Calculate the cross-covariance matrix In the formula, , ； 6) Calculate the new information covariance matrix ; 7) Calculate the pseudo-measurement matrix ; 8) Calculate the noise variance of the innovation measurement. ; 9) Calculate kernel width In the formula ; 10) Calculate the Kalman gain. , In the formula ; 11) Calculate the state update value using the fixed-point iteration method. ; 12) Calculate the updated value of the error covariance matrix. ; Step 3: Consistency Filtering Initialize the state vector and covariance matrix of sensor node i , ; 1) Step-by-step weighted average consensus a. To the neighboring nodes of sensor node i disseminating information , and one's own measure; b. Received from neighboring nodes , After summing the degrees, calculate the weights of itself and its neighboring nodes; c. According to the formula Japanese style Achieve weighted average consensus based on the state vector and covariance matrix; where, consensus weight It can be determined by the commonly used Metropolis weighting rules: ； in, This represents the degree of sensor node i, i.e., the number of adjacent sensors; d. Repeat step ac Next, after obtaining the average consensus and ; 2) Update the state vector and error covariance matrix of sensor node i after average consensus. , ; Step 1 involves expanding the 1.5th order ITO Taylor stochastic differential equation, resulting in the following formula: (4) In the above formula, , For noise-free functions: (5) and ( ) are two differential operators: (6) (7) in, ( )express No. One element; and Let be a multidimensional Gaussian random variable generated by the following formula: (8) (9) In the formula, and They are mutually independent standard Gaussian random vectors; The cubic volume rule for calculating the Gaussian weighted integral in step 1 is as follows: (10) In the above formula, Volume point for: (11) In the formula, Represents the identity matrix The first in List, It can be represented as: 。 2. The estimation method for continuous-discrete maximum correlation entropy distributed capacitive Kalman filtering according to claim 1, characterized in that, The establishment of the continuous-discrete target tracking model in the multi-sensor network includes: In multi-sensor networks, a continuous-discrete nonlinear system under non-Gaussian noise is represented as: (1) (2) in, It is the estimated state vector. It is a differentiable nonlinear function. It is an n-dimensional standard Brownian motion independent of the state vector. Given a time-invariant diffusion matrix, For node i at sampling time The measured value at that time The sampling period is It is a known measurement function. The mean is not equal to 0, and the covariance is... Non-Gaussian noise; The system equations are: ； ； ； In the formula, the state variable of the aircraft ; , and , These represent the aircraft's position and velocity along the x and y axes of the coordinate system, respectively. Indicates the turning rate; Distance of the aircraft Azimuth Multiple sensors at sampling time The measurement was obtained, and the measurement equation is: (3) In the formula, Indicates the position coordinates of sensor node i; For measurement noise with a mixed Gaussian distribution, .

3. The estimation method for continuous-discrete maximum correlation entropy distributed commensurate Kalman filtering according to claim 1, characterized in that, The average consensus method in step 3 is as follows: (12) (13) In the formula, This is called an information pair, which is a sensor node. No. The matrix updated in each consensus iteration At that time, each sensor They all tend to the same value. For the consistency gain, where This represents the maximum degree of a node in the graph. Consensus Matrix The first in One element, .

4. The estimation method for continuous-discrete maximum correlation entropy distributed capacitive Kalman filtering according to claim 1, characterized in that, The maximum correlation entropy criterion used in step 2 includes: Correlation entropy is used to describe the similarity between two random variables X and Y. Its correlation entropy is defined as: ;in Represents the mathematical expectation. This represents a shift-invariant Messer type kernel function. Let X be the joint distribution function of Y; When the joint density function is difficult to obtain and the dataset only contains a limited amount of data, the correlation entropy can be estimated by averaging the samples: ;in, , From the joint density function Data sampled from the middle.

5. The estimation method for continuous-discrete maximum correlation entropy distributed commensurate Kalman filtering according to claim 1, characterized in that, For the continuous-discrete target tracking model, target tracking is performed according to the continuous-discrete maximum correlation entropy distributed capacitive Kalman filter method to obtain accurate target state information, including: Step 1: Initialize the state vector, process covariance matrix, measurement noise mean, and measurement noise covariance matrix; Step 2: The actual motion trajectory of the target is generated. The stochastic differential equation is numerically solved using the Euler-Maruyama method of equation (14) to simulate the real dynamics of the aircraft. The step size is a fixed value of 0.0005 s. (14) To compare the estimation performance of the algorithms, the root mean square error (RMSE) and cumulative root mean square error (ARMSE) of position and velocity are used as performance standards; Equations (15) and (16) are the RMSE and ARMSE of position, and the RMSE and ARMSE of velocity are in the same form as those of position. (15) (16) in, These are the actual coordinates of the aircraft during the nth Monte Carlo simulation. This is the corresponding optimal estimate; This represents the total number of samples in the simulation. Number of Monte Carlo simulations; Step 3: Use the continuous-discrete maximum correlation entropy distributed capillary Kalman filter method to estimate the state of the target tracking model.

6. A machine-readable storage medium, characterized in that, The machine-readable storage medium stores instructions for causing the machine to perform the estimation method of the continuous-discrete maximum correlation entropy distributed commensurate Kalman filter as described in any one of claims 1-5.

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