Target tracking method based on distributed polynomial set-membership fusion estimation

Abstract

The application provides a target tracking method based on distributed polynomial set-membership fusion estimation. The method models unknown target control input by using bounded noise; a plurality of distance measuring sensors are used to monitor a target to be tracked, distance information from the sensors to the target collected by the sensors is transmitted to a local estimator through a network, and the distance information is encoded into binary strings and then transmitted due to the need of digital transmission; based on the decoded information, a local estimator is designed by using a polynomial set-membership estimation technology, recursive calculation of optimal fully-symmetric polytope parameters in the F radius sense containing the real state of the target is realized, and in addition, higher estimation accuracy can be realized by using high-order partial derivative information of a distance function; a distributed fusion mechanism is used to process each local estimation value and a fully-symmetric polytope containing a local estimation error, so as to generate an optimal global estimation of the target state in the F radius sense of the polytope.

Description

Technical Field

[0001] This invention relates to a target tracking method based on distributed multinomial set member fusion estimation, belonging to the field of state estimation technology. Background Technology

[0002] Existing target tracking techniques based on distributed fusion estimation have the following characteristics:

[0003] 1. The main method used is Kalman filtering and its variants (such as extended Kalman filtering, unscented Kalman filtering and particle filtering) to process the measurement information of each sensor in order to generate a local estimate of the state of the target to be tracked;

[0004] 2. Distributed fusion is achieved by minimizing the global filtering error covariance to generate a global estimate of the target state.

[0005] The above technology has the following shortcomings:

[0006] 1. Measurement information collected by each sensor is often transmitted to the local estimator via remote digital transmission based on a communication network. Existing technology does not fully consider the impact of bit flipping in the codeword during remote digital transmission. Once the local estimator is designed with flipped codewords, the estimation accuracy of the target state may decrease significantly.

[0007] 2. When estimating the target state, only the first and second order partial derivative information of the nonlinear sensor measurement can be used, and higher order partial derivative information cannot be fully utilized. Summary of the Invention

[0008] Technical issues:

[0009] This invention aims to solve the target tracking problem in the following scenario: a moving target on a horizontal plane is sampled by several ranging sensors. The collected measurement information is encoded and transmitted through a communication network to a remote local estimator to generate a local estimate of the target state. Subsequently, each local estimator transmits the generated local estimate information to a fusion center to generate a global estimate of the target state.

[0010] The main objectives are: (1) to design a local set member estimator that can make full use of the higher-order partial derivative information of the distance function by using codewords that may have bit flips, and to realize the recursive calculation of the full symmetric polytope parameters including the target state; (2) to design a distributed fusion estimator to fuse local estimates, thereby achieving a more accurate estimate of the target state.

[0011] Technical solution:

[0012] The target tracking method based on distributed multinomial set fusion estimation includes the following steps:

[0013] Step S1: Establish the state-space model of the tracked target and the transmission model of the signal acquired by the ranging sensor. The state-space model of the tracked target includes state equations and measurement equations, used to characterize the dynamic evolution of the target along the time axis and the known target position information; specifically, it consists of state equations containing bounded noise and measurement equations containing nonlinearity and bounded measurement noise. Details are as follows:

[0014] Consider a target moving on a horizontal surface. According to Newton's second law, its motion can be characterized by the following equation:

[0015]

[0016] Where k represents the kth sampling period; x(k) = [x(k) y(k) v x (k) v y (k)] T Let x(k) and v represent the state vectors of the target. x (k) and y(k), v y (k) represent the target's position and velocity in the horizontal and vertical coordinates, respectively, and the superscript "T" indicates the transpose of a vector or matrix; the initial value of the system state x(0) belongs to the four-dimensional zero vector 0 4×1 A fully symmetric polytope centered at the known fourth-order positive definite diagonal matrix X(0) as the generating matrix <0 4×1 , X(0)>; It is a two-dimensional vector used to represent the control input of the target; it belongs to the category of known two-dimensional vectors. Centered on a known second-order positive definite diagonal matrix W = diag{w (1) ,w (2)}(diag{·} denotes a diagonal matrix, w (1) w (2) (where the diagonal elements of W are the fully symmetric polytopes of the generating matrix) Matrices A and B have the following forms:

[0017]

[0018] In the formula This indicates the sampling period for the target.

[0019] The target to be tracked is monitored in real time using N ranging sensors, where the measurement equation of the j-th sensor can be expressed as:

[0020] z j (k)=g j (x(k))+v j (k) (3)

[0021] Where z j(k) represents the measurement output of the j-th ranging sensor. It is a bounded positive scalar whose upper bound is a known scalar. Indicates the maximum range that it can be measured; g j (·) represents the following distance function:

[0022]

[0023] In the formula ( x j , y j ) represents the sensor's coordinates on the horizontal plane; v j (k) represents the measurement noise of the j-th sensor, which belongs to the interval [-V j V j ](V j (For known positive constants).

[0024] For j∈{1, 2, ..., N}, the measurement output z collected by the j-th ranging sensor is transmitted at the sensor end. j (k) is encoded as a length of L j binary string in The bits representing the binary string are all taken from the set {0, 1}. The following is the result... The specific method. Because... There must exist a non-negative integer γ. j (k) makes the following equation hold:

[0025]

[0026] Let c j (k) represents the relationship between z j (k) The decimal number corresponding to the codeword obtained after encoding is calculated as follows: When At that time, c j (k)=γ j (k);

[0027] And when At that time, c j (k)=γ j (k)+1,

[0028] in After obtaining c j After (k), the string can be obtained by converting it to binary.

[0029] String The data is transmitted to the local estimator via a communication network. Due to factors such as channel noise, one or more bits of the string may be flipped during transmission. For the t-th bit...j t binary bits j ∈{1, 2, ..., L j}), using variables Characterizing the flipping of binary bits:

[0030]

[0031] At this point, the codeword received by the j-th local estimator can be represented as:

[0032] Step S2: Construct a local estimator and recursively calculate the fully symmetric multicell containing the local estimation error.

[0033] To estimate the target state, the codewords received by the j-th local estimator are... Decoding yields the decoded signal d. j (k) is as follows:

[0034]

[0035] To fully utilize the distance function g j The higher-order partial derivative information of (·) estimates the target state, and transforms the zeroth order of the target state to v. j rank (ν) j (Given a positive integer to characterize the order of the higher-order partial derivatives used) Kronecker power augmentation yields a vector. (Using superscript square brackets "[·]" to denote the Kronecker power of a vector or matrix), this invention estimates... The estimated value of the target state x(k) is obtained in this way. Specifically, it is based on the decoded signal d. j (k), construct the following local estimator:

[0036]

[0037] in, and They represent The predicted and estimated values ​​are generated through iterative calculations, with the initial values ​​for the iterations derived from... Here it is.

[0038]

[0039] Vector c(l, 0) (l in set {1, 2, ..., v) j The value is taken from}

[0040] x [l] (0)∈<c(l,0),X(l,0)> (10)

[0041] Given. In equation (10), x[l] (0) represents the l-th power of the vector x(0),<c(l,0),X(l,0)> Indicates that x is included [l] A fully symmetric polytope of x(0) ∈ <0, which can be determined based on the known information x(0) ∈ <0. 4×1 The calculation is performed on x(0)>, and in applications it can be represented as based on x(0)∈<0. 4×1 The calculated value containing x is X(0)> [l] The smallest interval vector of (0).

[0042] The matrix in equation (8) The calculation is as follows:

[0043]

[0044] In the formula, for l = 0, 1, ..., v j q = 0, 1, ..., v j , The calculation is as follows:

[0045]

[0046] Where p! represents the factorial of a positive integer p, and matrices M(l, s, 4) and M(p, q, 4) are calculated recursively by the following formula:

[0047]

[0048] Where I represents an identity matrix with appropriate dimensions, for example Indicates 4 l An identity matrix of order G; matrix G(ls) satisfies the following recurrence relation:

[0049]

[0050] The initial value G(1) of the recursion is a 16th order square matrix, and its transpose matrix G T (1) Line number The elements of the column are given by the following formula.

[0051]

[0052] In the formula and They represent division by 4 respectively. The remainder and the integer part.

[0053] f is a vector-valued function f [s] This represents the s-th power of Cronecker for f; Represents the Kronecker product of matrices. This represents the gradient operator of a nonlinear function with respect to a vector x(k). This represents the p-th Kronecker power of the gradient operator of vector x(k) and the function f. [s] The matrix-valued function of x(k) obtained after performing the Kronecker product. Indicates that the input is The value of the matrix-valued function mentioned above at that time, Calculated by the following formula

[0054]

[0055] w(ls) is derived from

[0056] w [l] (k)∈<w(l),W(l)> (15)

[0057] Given. In equation (16), w(k) = B w (k), w (k) is a two-dimensional bounded signal, belonging to a fully symmetric polytopic <0 2×1 , W>;w [l] (k) represents the l-th power of the Kronecker vector w(k).<w(l),W(l)> Indicates that w [l] The fully symmetric polytope of (k) can be determined according to w(k) = B. w (k) and w (k)∈<0 2×1 , W> is used for calculation, and in applications it can be represented as containing w [l] The smallest interval vector of (k); in particular, w(0) = 1.

[0058] The matrix in equation (8) The calculation is as follows:

[0059]

[0060] Where, for q = 0, 1, ..., v j ,have

[0061]

[0062] In the formula This represents the p-th Kronecker power of the gradient operator of vector x(k) and the distance function g. j (k) The matrix-valued function obtained after performing the Kronecker product. Indicates that the input is The function value of the matrix-valued function mentioned above. Calculated by the following formula:

[0063]

[0064] Code words The estimator gain for the binary bits without flipping is given by the following form:

[0065]

[0066] Where K j (k) represents the parameters of the local estimator to be designed.

[0067] make and They represent The one-step prediction error and local estimation error, in addition, let and They respectively represent the inclusion of é j (k) and Fully symmetrical multicellular Their generating matrices and The following recurrence relation is satisfied:

[0068]

[0069] in

[0070]

[0071] For l = 1, 2, ..., v j ,

[0072]

[0073] ||*|| ∞ Denotes the infinite norm of the matrix "*". p represents the p-th power of the infinity norm of the matrix "*"; When ls≠0, W(ls) is given by (15), and in particular, W(0)=0; The calculation is as follows:

[0074]

[0075] In the formula Right now Let x be a scalar function In fully symmetrical multicellular The maximum value when taking the value inside.

[0076] Step S3: Establish a method for detecting anomalies in the input signal of the local estimator, and design the parameters of the local estimator based on the detection results.

[0077] For the input signal d of the local estimatorj (k), determine

[0078]

[0079] Whether it is true or not, in the formula When equation (24) does not hold, i.e. d j (k) When it does not belong to the fully symmetric polytope in equation (24), the codeword received by the j-th local estimator is... At least one bit has been flipped, and the estimator can be updated according to Equation (8).

[0080] When equation (24) holds, the estimator parameters are calculated using the following formula:

[0081]

[0082] In the formula

[0083]

[0084] The estimator parameters calculated by equation (25) can guarantee that they include local estimation errors. Fully symmetrical multicellular Minimize the F-radius to ensure estimation performance.

[0085] Step S4: Design fusion weights to achieve fusion of local estimates and obtain a global estimate of the target state.

[0086] After obtaining local estimates Then, using equation (13), local estimates of the N target states x(k) can be obtained. Weighted sum of these local estimates As a global estimate, where Ψ1(k), Ψ2(k), ..., Ψ N (k) represents the fusion weights, where the global estimation error satisfies...

[0087]

[0088] in

[0089] The following fusion weights are used:

[0090]

[0091] This ensures that the F-radius of the fully symmetric polycell containing the global estimation error in equation (26) is better than the F-radius of any local fully symmetric polycell, thereby further improving the estimation accuracy of the target state.

[0092] Compared with existing technologies, the present invention has the following advantages: It uses bounded noise to characterize the unknown control input of the target to be tracked, making it more convenient to establish the target's motion model; it employs a multinomial set-membership estimation technique to design a local estimator, which can fully utilize the higher-order partial derivative information of the distance function in nonlinear measurements to improve the estimation accuracy of the target state when recursively calculating the local estimate of the target state and the fully symmetric polytopic parameters containing the local estimation error; and it uses a distributed fusion mechanism to suppress the influence of potential binary bit flips in the codewords received by the local estimator and the influence of measurement noise, thereby ensuring that the global estimation accuracy of the target state is better than the local estimation accuracy. Attached Figure Description

[0093] Figure 1 This is a flowchart of the steps of the present invention;

[0094] Figure 2 The actual codewords of the three sensors in the test example of this invention The corresponding decimal number and the codeword received by the local estimator under the influence of binary bit flipping. The decimal number corresponding to (j = 1, 2, 3);

[0095] Figure 3 This is a screenshot of the detection results for codeword flipping.

[0096] Figure 4 The true location of the target is given, along with the location estimates generated by the three local estimators and the fusion estimator. Figure 5 The order of the partial derivative of the distance function used, v j The F-radius of a fully symmetric polytope containing global estimation errors That is, the generating matrix of a fully symmetric polytope that includes the global estimation error. The relationship between the F-norm and the F-norm. Detailed Implementation

[0097] The present invention will be further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that the following specific embodiments are for illustrative purposes only and are not intended to limit the scope of the present invention.

[0098] Example

[0099] Target tracking methods based on distributed multinomial set fusion estimation, such as Figure 1 As shown, it includes the following steps:

[0100] Step S1: Establish the state space model of the tracked target and the transmission model of the signal collected by the ranging sensor.

[0101] Consider a target moving on a horizontal surface. According to Newton's second law, its motion can be characterized by the following equation:

[0102]

[0103] Where k represents the kth sampling period; x(k) = [x(k) y(k) v x (k) v y (k)] T Let x(k) and v represent the state vectors of the target. x (k) and y(k), v y (k) represent the target's position and velocity in the horizontal and vertical coordinates, respectively, and the superscript "T" indicates the transpose of a vector or matrix; the initial value of the system state x(0) belongs to the four-dimensional zero vector 0 4×1 A fully symmetric polytope centered at the known fourth-order positive definite diagonal matrix X(0) as the generating matrix <0 4×1 , X(0)>; It is a two-dimensional vector used to represent the control input of the target; it belongs to the category of known two-dimensional vectors. Centered on a known second-order positive definite diagonal matrix W = diag{w (1) w (2)}(diag{·} denotes a diagonal matrix, w (1) w (2) (where the diagonal elements of W are the fully symmetric polytopes of the generating matrix) Matrices A and B have the following forms:

[0104]

[0105] In the formula This indicates the sampling period for the target.

[0106] The target to be tracked is monitored in real time using N ranging sensors, where the measurement equation of the j-th sensor can be expressed as:

[0107] z j (k)=g j (x(k))+v j (k) (3)

[0108] Where z j (k) represents the measurement output of the j-th ranging sensor. It is a bounded positive scalar whose upper bound is a known scalar. Indicates the maximum range that it can be measured; g j (·) represents the following distance function:

[0109]

[0110] In the formula ( x i , y i) represents the sensor's coordinates on the horizontal plane; v j (k) represents the measurement noise of the j-th sensor, which belongs to the interval [-V j V j ](V j (For known positive constants).

[0111] For j∈{1, 2, ..., N}, the measurement output z collected by the j-th ranging sensor is transmitted at the sensor end. j (k) is encoded as a length of L j binary string in The bits representing the binary string are all taken from the set {0, 1}. The following is the result... The specific method. Because... There must exist a non-negative integer γ. j (k) makes the following equation hold:

[0112]

[0113] Let c j (k) represents the relationship between z j (k) The decimal number corresponding to the codeword obtained after encoding is calculated as follows: When At that time, c j (k)=γ j (k);

[0114] And when At that time, c j (k)=γ j (k)+1,

[0115] in After obtaining c j After (k), the string can be obtained by converting it to binary.

[0116] String The data is transmitted to the local estimator via a communication network. Due to factors such as channel noise, one or more bits of the string may be flipped during transmission. For the t-th bit... j t binary bits j ∈{1, 2, ..., L j}), using variables Characterizing the flipping of binary bits:

[0117]

[0118] At this point, the codeword received by the j-th local estimator can be represented as:

[0119] Step S2: Construct a local estimator and recursively calculate the fully symmetric multicell containing the local estimation error.

[0120] To estimate the target state, the codewords received by the j-th local estimator are... Decoding yields the decoded signal d. j (k) is as follows:

[0121]

[0122] To fully utilize the distance function g j The higher-order partial derivative information of (·) estimates the target state, and transforms the zeroth order of the target state to v. j rank (ν) j (Given a positive integer to characterize the order of the higher-order partial derivatives used) Kronecker power augmentation yields a vector. (Using superscript square brackets "[·]" to denote the Kronecker power of a vector or matrix), this invention estimates... The estimated value of the target state x(k) is obtained in this way. Specifically, it is based on the decoded signal d. j (k), construct the following local estimator:

[0123]

[0124] in, and They represent The predicted and estimated values ​​are generated through iterative calculations, with the initial values ​​for the iterations derived from... Here it is.

[0125]

[0126] Vector c(l, 0) (l in set {1, 2, ..., v) j The value is taken from}

[0127] x[l] (0)∈<c(l,0),X(l,0)> (10)

[0128] Given. In equation (10), x [l] (0) represents the l-th power of the vector x(0),<c(l,0),X(l,0)> Indicates that x is included [l] A fully symmetric polytope of x(0) ∈ <0, which can be determined based on the known information x(0) ∈ <0. 4×1 The calculation is performed on x(0)>, and in applications it can be represented as based on x(0)∈<0. 4×1 The calculated value containing x is X(0)> [l] The smallest interval vector of (0).

[0129] The matrix in equation (8) The calculation is as follows:

[0130]

[0131] In the formula, for l = 0, 1, ..., v j q = 0, 1, ..., v j , The calculation is as follows:

[0132]

[0133] Where p! represents the factorial of a positive integer p, and matrices M(l, s, 4) and M(p, q, 4) are calculated recursively by the following formula:

[0134]

[0135]

[0136] Where I represents an identity matrix with appropriate dimensions, for example Indicates 4 l An identity matrix of order G; matrix G(ls) satisfies the following recurrence relation:

[0137]

[0138] The initial value G(1) of the recursion is a 16th order square matrix, and its transpose matrix G T (1) Line number The elements of the column are given by the following formula.

[0139]

[0140] In the formula and They represent division by 4 respectively. The remainder and the integer part.

[0141] f is a vector-valued function f [s] This represents the s-th power of Cronecker for f; Represents the Kronecker product of matrices. This represents the gradient operator of a nonlinear function with respect to a vector x(k). This represents the p-th Kronecker power of the gradient operator of vector x(k) and the function f. [s] The matrix-valued function of x(k) obtained after performing the Kronecker product. Indicates that the input is The value of the matrix-valued function mentioned above at that time, Calculated by the following formula

[0142]

[0143] w(ls) is derived from

[0144] w [l] (k)∈<w(l),W(l)> (15)

[0145] Given. In equation (16), w(k) = B w (k), w (k) is a two-dimensional bounded signal, belonging to a fully symmetric polytopic <0 2×1 , W>;w [l] (k) represents the l-th power of the Kronecker vector w(k).<w(l),W(l)> Indicates that w [l] The fully symmetric polytope of (k) can be determined according to w(k) = B. w (k) and w (k)∈<0 2×1 , W> is used for calculation, and in applications it can be represented as containing w [l] The smallest interval vector of (k); in particular, w(0) = 1.

[0146] The matrix in equation (8) The calculation is as follows:

[0147]

[0148] Where, for q = 0, 1, ..., v j ,have

[0149]

[0150] In the formula This represents the p-th Kronecker power of the gradient operator of vector x(k) and the distance function g. j (k) The matrix-valued function obtained after performing the Kronecker product. Indicates that the input is The function value of the matrix-valued function mentioned above. Calculated by the following formula:

[0151]

[0152] Code words The estimator gain for the binary bits without flipping is given by the following form:

[0153]

[0154] Where K j (k) represents the parameters of the local estimator to be designed.

[0155] make and They represent The one-step prediction error and local estimation error, in addition, let and They respectively represent the inclusion and Fully symmetrical multicellular Their generating matrices and The following recurrence relation is satisfied:

[0156]

[0157] in

[0158]

[0159] For l = 1, 2, ..., v j ,

[0160]

[0161] ||*|| ∞ Denotes the infinite norm of the matrix "*". p represents the p-th power of the infinity norm of the matrix "*"; When ls≠0, W(ls) is given by (15), and in particular, W(0)=0; The calculation is as follows:

[0162]

[0163] In the formula Right now Let x be a scalar function In fully symmetrical multicellular The maximum value when taking the value inside.

[0164] Step S3: Establish a method for detecting anomalies in the input signal of the local estimator, and design the parameters of the local estimator based on the detection results.

[0165] For the input signal d of the local estimator j (k), determine

[0166]

[0167] Whether it is true or not, in the formula When equation (24) does not hold, i.e. d j (k) When it does not belong to the fully symmetric polytope in equation (24), the codeword received by the j-th local estimator is... At least one bit has been flipped, and the estimator can be updated according to Equation (8).

[0168] When equation (24) holds, the estimator parameters are calculated using the following formula:

[0169]

[0170] In the formula

[0171]

[0172] The estimator parameters calculated by equation (25) can guarantee that they include local estimation errors. Fully symmetrical multicellular Minimize the F-radius to ensure estimation performance.

[0173] Step S4: Design fusion weights to achieve fusion of local estimates and obtain a global estimate of the target state.

[0174] After obtaining local estimates Then, using equation (13), local estimates of the N target states x(k) can be obtained. Weighted sum of these local estimates As a global estimate, where Ψ1(k), Ψ2(k), ..., Ψ N (k) represents the fusion weights, where the global estimation error satisfies...

[0175]

[0176] in

[0177] The following fusion weights are used:

[0178]

[0179] This ensures that the F-radius of the fully symmetric polycell containing the global estimation error in equation (26) is better than the F-radius of any local fully symmetric polycell, thereby further improving the estimation accuracy of the target state.

[0180] Test case

[0181] To verify the effectiveness of the method proposed in this invention, the following test experiment was conducted: Consider a moving target on a plane, with the initial position of the target on the established coordinate plane being x(0) = [-0.1 0.1 -0.1 0.1] T The target's control input is The motion of the target is detected using three ranging sensors with a sampling step size of 200 and a sampling period of 1 / 3 for each sensor. The deployment locations are respectively (x 1, y 1) = (5, 10), ( x 2, y 2) = ( x 3, y 3), the measurement noise of the three sensors (5, -5) is

[0182] (v1(k), v2(k), v3(k)=(0.1cos(0.1k), 0.15sin(0.1k), 0.2cos(0.2k))

[0183] The initial position of the target selected in the test and the relevant parameters of the sensor are as follows:

[0184] X(0)=daig{0.1, 0.1, 0.1, 0.1}

[0185] W=diag{0.3, 0.2}, V1=0.1, V2=0.15, V3=0.2

[0186] The relevant parameters of the binary encoding mechanism are L1 = L2 = L3 = 8. The moment when a binary bit flip occurs in the codeword is: codeword For 50 and 110, code words For 30, 100 and 170, the code words For 20, 50, 130, and 160. Use τ. j (k)(j=1,2,3) characterizes the codewords received by the j-th local estimator. The value indicates whether a binary bit has been flipped. A value of 1 indicates that a flip has been detected, and a value of 0 indicates that a flip has not been detected.

[0187] Figure 2 The actual codewords of the three sensors in the test example of this invention are shown. The decimal number corresponding to (j = 1, 2, 3) and the codeword received by the local estimator under the influence of binary bit flipping. The decimal number corresponding to (j = 1, 2, 3).

[0188] Figure 3 The figure shows the detection results of codeword flipping. As can be seen from the figure, all flipping signals were detected, thus verifying the effectiveness of the proposed detection method.

[0189] Figure 4 The figure shows the true location of the target and the location estimates generated by the three local estimators and the fusion estimator. As can be seen from the figure, the accuracy of the fusion estimation is higher than that of the local estimation.

[0190] Figure 5The order of the partial derivative of the distance function used, v j For the F-radius of a fully symmetric polytope containing global estimation errors That is, the generating matrix of a fully symmetric polytope that includes the global estimation error. The influence of the F-norm (as shown in the figure) varies with the order ν of the partial derivative used. j The increase in ...

[0191] In summary, this invention discloses a target tracking method based on distributed multinomial set-membership fusion estimation. This method uses bounded noise to model the unknown target control input, then employs multinomial set-membership estimation to design a local estimator, achieving recursive calculation of the optimal fully symmetric polytope parameters in the F-radius sense, incorporating the target's true state. Furthermore, this technique achieves high estimation accuracy by utilizing higher-order partial derivatives of the distance function. In addition, a distributed fusion mechanism is used to process each local estimate and the fully symmetric polytope containing local estimation errors, providing the optimal global estimate of the target state in the F-radius sense of the polytope.

[0192] It should be noted that the above content merely illustrates the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. For those skilled in the art, various improvements and modifications can be made without departing from the principle of the present invention, and all such improvements and modifications fall within the scope of protection of the claims of the present invention.

Claims

1. A target tracking method based on distributed multinomial set fusion estimation, characterized in that, Includes the following steps: Step S1: Establish the state space model of the tracking target and the transmission model of the signal collected by the ranging sensor: The state space model of the tracking target includes state equations and measurement equations, which are used to characterize the dynamic evolution of the target along the time axis and the known target position information; specifically, it consists of state equations containing bounded noise and measurement equations containing nonlinearity and bounded measurement noise. Step S2: Construct a local estimator and recursively calculate the fully symmetric multicell containing the local estimation error; Step S3: Establish a method for detecting anomalies in the input signal of the local estimator, and design the parameters of the local estimator based on the detection results; Step S4: Design fusion weights to fuse local estimates and obtain a global estimate of the target state; Step S1 specifically includes: Consider a target moving on a horizontal surface. According to Newton's second law, its motion is characterized by the following equation: (1) in Indicates the first One sampling period; The state vector representing the target. and Representing the target's position and velocity in the horizontal and vertical axes respectively, superscript Represents the transpose of a vector or matrix; initial values ​​of the system state. Belongs to the zero vector of four dimensions Centered on a known fourth-order positive definite diagonal matrix To generate a fully symmetric multicell of the matrix ; It is a two-dimensional vector used to represent the control input of the target; it belongs to the category of known two-dimensional vectors. Centered on a known second-order positive definite diagonal matrix To generate a fully symmetric multicell of the matrix ,in Represents a diagonal matrix. for Diagonal elements; matrix It has the following form: (2) In the formula Indicates the sampling period for the target; use A ranging sensor monitors the target to be tracked in real time, among which the first... The measurement equations for each sensor are expressed as follows: (3) in For the first The measurement output of a ranging sensor is a bounded positive scalar, whose upper bound is a known scalar. , indicating the maximum range that it can measure; The distance function is expressed as follows: (4) In the formula This indicates the sensor's coordinates on the horizontal plane; Indicates the first The measurement noise of each sensor, which belongs to the interval , For known positive constants; for At the sensor end, the first Measurement output collected by a distance measuring sensor The encoding is of length 1000. binary string ,in The bits representing binary strings are all from a set Take the value from; get The specific method is as follows: due to There must exist non-negative integers. This makes the following equation true: (5) make Indicates to The decimal number corresponding to the encoded codeword is calculated as follows: When hour, ; And when hour, , in ; after obtaining Then, you can obtain the string by converting it to binary. ; String The string is transmitted to the local estimator via a communication network; since one or more bits of the string may be flipped during transmission, for the first... binary bits Using variables Characterizing the flipping of binary bits: (6) At this time, the The codewords received by a local estimator can be represented as .

2. The target tracking method based on distributed multinomial set-member fusion estimation according to claim 1, characterized in that, Step S2 specifically includes: To estimate the target state, for the th The codewords received by the local estimator Decoding the decoded signal as follows: (7) To fully utilize the distance function The higher-order partial derivative information is used to estimate the target state, and the zeroth-order partial derivative of the target state is reduced to the higher-order partial derivative information. The Kronecker power increases, of which Given a positive integer, we use it to characterize the order of the higher-order partial derivatives used, thus obtaining a vector. , where superscript Represents the Kronecker power of a vector or matrix; By estimation Obtain the target state in this way The estimated value; specifically, based on the decoded signal. Construct the following local estimator: (8) in, and They represent The predicted and estimated values ​​are generated through iterative calculations, with the initial values ​​for the iterations derived from... Here it is. (9) vector Given by equation (10), where In the set Take the value from; (10) In formula (10) Representing vectors of Second Kronecker power, Indicates inclusion A fully symmetrical polytope, which, based on known information Perform calculations and represent them in applications as based on The calculated contents The smallest interval vector; The matrix in equation (8) The calculation is as follows: (11) In the formula, for , , The calculation is as follows: (12) in Represents positive integers factorial, matrix and matrix Calculated recursively by the following formula: in Represents an identity matrix with appropriate dimensions; a matrix The following recurrence relation is satisfied: Initial value of recursion For one A square matrix of order n, its transpose matrix The Line number The elements of the column are given by the following formula. In the formula and They represent remove The remainder and the integer part; Vector-valued functions , express of Second Kronecker power; " represents the Kronecker product of matrices, Represents a nonlinear function with respect to a vector gradient operator, Indicates the vector gradient operator The Kronecker power and functions The information obtained after performing the Kronecker product Matrix-valued functions, Indicates that the input is The value of the matrix-valued function mentioned above at that time, Calculated by the following formula (13) (14) Depend on (15) Given; in equation (16) , It is a two-dimensional bounded signal, belonging to a fully symmetric multicellular structure. ; Representing vectors of Second Kronecker power, Indicates inclusion A fully symmetrical polycellular form, which is based on and Perform calculations and represent it as containing in applications. The smallest interval vector; in particular, ; The matrix in equation (8) The calculation is as follows: (16) Among them, for ,have (17) In the formula Indicates the vector gradient operator Tkrönek power and distance function The matrix-valued function obtained after performing the Kronecker product. Indicates that the input is The function value of the matrix-valued function mentioned above. Calculated by the following formula: (18) Code words The estimator gain for the binary bits without flipping is given by the following form: (19) in The parameters are those of the local estimator to be designed. make and They represent The one-step prediction error and local estimation error, in addition, let and They respectively represent the inclusion and The fully symmetrical multicellular shape, Their generating matrices and The following recurrence relation is satisfied: (20) (21) in (22) for , Representing a matrix The infinite norm of ". Representing a matrix The infinite norm of " Power of; ;when hour, Given by (15), in particular, ; The calculation is as follows: (23) In the formula ,Right now For about vectors scalar functions In fully symmetrical multicellular The maximum value when taking the value inside.

3. The target tracking method based on distributed multinomial set member fusion estimation according to claim 2, characterized in that, Step S3 specifically includes: For the input signal of the local estimator ,judge (24) Whether it is true or not, in the formula When equation (24) does not hold, i.e. When it does not belong to the fully symmetrical polytope in equation (24), then the first... The codewords received by the local estimator At least one bit has been flipped, and the estimator is updated according to Equation (8); When equation (24) holds, the estimator parameters are calculated using the following formula: (25) In the formula The estimator parameters calculated by equation (25) can guarantee that they include local estimation errors. Fully symmetrical multicellular of Minimize the radius to ensure estimation performance.

4. The target tracking method based on distributed multinomial set member fusion estimation according to claim 3, characterized in that, Step S4 specifically includes: After obtaining local estimates Then, using equation (13) we obtain Target state Local estimates Weighted sum of these local estimates As a global estimate, where For weight fusion, the global estimation error at this point satisfies (26) in ; The following fusion weights are used: (27) This ensures that equation (26) contains a fully symmetric polytope containing the global estimation error. The radius is better than that of any locally fully symmetric multicellular form. The radius is used to further improve the accuracy of target state estimation.

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