Maneuvering target tracking Kalman filtering method based on BP neural network

Abstract

The invention discloses a maneuvering target tracking Kalman filtering method based on a BP neural network. The maneuvering target tracking Kalman filtering method comprises the following steps: setting a section of motion trail of a maneuvering target in a three-dimensional environment, simulating and generating measurement data, establishing a maneuvering target motion model according to a current statistical model, and estimating a target state by using a Kalman filtering algorithm; and BP offline training is carried out by using data obtained by a maneuvering target Kalman filtering tracking algorithm based on the current statistical model, and a compensation value of a Kalman filtering algorithm estimation value is obtained. According to the invention, the BP neural network is utilized to compensate the traditional Kalman filtering algorithm, the problem of large error in the initial tracking stage can be effectively solved, and more accurate target tracking is realized.

Description

Technical Field

[0001] The invention relates to the field of mobile target tracking, and in particular to a mobile target tracking Kalman filtering method based on BP neural network. Background Art

[0002] Mobile target tracking has important applications in both military and civilian fields. In the field of national defense, it can be used for ballistic missile defense, air and space early warning, fire control, interception guidance and low-altitude penetration. In the civilian field, it is used for traffic control, robot road planning and tracking of civilian driving vehicles.

[0003] After establishing a motion model that conforms to the motion law of the maneuvering target, the noise contained in the observation data is filtered out by the filtering algorithm to obtain motion data that is more in line with the tracking target. However, the lack of prior knowledge, idealized processing of noise, initialization and other issues have led to room for optimization of the target tracking algorithm. For the maneuvering target tracking algorithm, the current technology mainly proposes improvements from two aspects. First, adaptive improvements are made to the maneuvering frequency and acceleration in the current statistical model: for example, the exponential function is used to make real-time corrections to the extreme value of acceleration in the current statistical model; a method for adaptive adjustment of the two-segment function of the acceleration variance is proposed in combination with the characteristics of the ascending half-normal fuzzy distribution function; the maneuvering frequency is adaptively changed by estimating the target state error, so that the tracking algorithm is closer to the actual state of the target; the acceleration extreme value is adjusted by using the new information characteristics, and an adaptive maneuvering frequency expression is derived by using the acceleration information of three consecutive moments. The second is to make improvements to the error covariance matrix in the filtering algorithm: for example, use the filtering residual to adjust the prediction covariance, and correct the filtering result of the previous moment when a large deviation occurs in the filtering result; through online learning of the residual, new information and filtering gain matrix between the target state prediction value and the optimal estimate, the size of the target maneuver term and the adaptive adjustment factor of the process noise covariance matrix are obtained, and the optimal estimate and motion model are adjusted in real time.

[0004] In the state estimation of maneuvering targets, maneuvering frequency, maximum acceleration, process noise, and idealization of measurement noise are all reasons that lead to large target tracking errors. The traditional Kalman filter algorithm based on the current statistical model can converge quickly and track maneuvering targets well, but the initial position and covariance matrix are unknown, which can easily lead to large initial errors in tracking maneuvering targets. Summary of the invention

[0005] The purpose of the present invention is to provide a Kalman filter method for tracking a maneuvering target based on a BP neural network, which estimates and compensates the traditional Kalman filter algorithm to achieve better target estimation.

[0006] The technical solution to achieve the purpose of the present invention is as follows: In the first aspect, the present invention provides a Kalman filtering method for tracking a maneuvering target based on a BP neural network, comprising:

[0007] According to the current statistical model, a motion model of the maneuvering target is established, a motion trajectory of the maneuvering target is set in a three-dimensional environment, measurement data is simulated and generated, and the target state is estimated using the Kalman filter algorithm;

[0008] The data obtained by the Kalman filter tracking algorithm is used to perform BP offline training to obtain the compensation value of the Kalman filter algorithm estimation value.

[0009] In a second aspect, the present invention provides a computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the method described in the first aspect when executing the program.

[0010] In a third aspect, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method described in the first aspect.

[0011] In a fourth aspect, the present invention provides a computer program product, comprising a computer program, which implements the steps of the method described in the first aspect when executed by a processor.

[0012] Compared with the existing group target tracking method, the present invention has the following significant advantages: the method takes into account the problem of large initial target tracking errors that are not considered by the existing target tracking method, adds intelligent adaptive tracking, and can generate network models suitable for different application scenarios by changing the neural network structure and training the data, and can achieve optimization effects, and the optimization effects are obvious. The present invention uses the BP neural network to compensate the traditional Kalman filter algorithm, which can effectively solve the problem of large initial tracking errors and achieve more accurate target tracking.

[0013] Experiments in a three-dimensional environment show that the algorithm can effectively reduce the position, velocity, and acceleration estimation errors in each dimension and improve the tracking accuracy of maneuvering targets. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 Schematic diagram of the target-observation station location.

[0015] Figure 2 This is the BP network structure diagram.

[0016] Figure 3 is the structure diagram of the jth neuron node.

[0017] Figure 4 This is the flow chart of BP neural network algorithm.

[0018] Figure 5 This is the structure diagram of the optimized KF filtering algorithm.

[0019] Figure 6 Schematic diagram of position tracking error in X, Y, and Z directions.

[0020] Figure 7 Schematic diagram of velocity tracking error in X, Y, and Z directions. DETAILED DESCRIPTION

[0021] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0022] The present invention proposes a Kalman filter method for maneuvering target tracking based on BP neural network optimization, which specifically includes the following steps:

[0023] Step 1: Use the current statistical model to describe the motion model of the maneuvering target in three dimensions, establish a measurement model, set a motion trajectory in a three-dimensional environment, and simulate and generate measurement data;

[0024] Based on the Singer model, the current statistical model uses non-zero mean and modified Rayleigh distribution to characterize the maneuvering acceleration characteristics, which can more realistically reflect the changes in the target maneuvering range and intensity.

[0025] The random maneuver acceleration conforms to the first-order time-dependent process on the time axis, that is:

[0026]

[0027] Where x(t) is the target position information; is the target acceleration; is the current mean value of maneuvering acceleration, which is a constant in each sampling period; a(t) is zero-mean colored acceleration noise; is the speed of change of zero-mean colored acceleration noise; α is the maneuvering parameter; w(t) has a mean of 0 and a variance of Gaussian white noise, where is the target acceleration variance.

[0028] make We can get:

[0029]

[0030] Write the above two equations as state equations to get the current statistical model of the maneuvering target:

[0031]

[0032] Assuming the sampling period is T, through the typical discrete processing method, the discrete state equation is:

[0033]

[0034] Where X(k+1 / k+1) is the optimal estimated state vector of the target at time k+1; X(k / k) is the optimal estimated state of the target at time k; W(k) is the discrete time white noise sequence; the state vector The three elements represent position, velocity, and acceleration respectively.

[0035] State transition matrix Process Input Matrix

[0036] W(k) is a discrete-time white noise sequence, and E(W(k)W T (k+j))=0, Variance Matrix in,

[0037]

[0038] q 21 =q 12 (10)

[0039]

[0040] q 31 =q 13 (13)

[0041] q 32 =q 23 (14)

[0042]

[0043] Considering the three-dimensional space, the maneuvering target gradually approaches the observation station, such as Figure 1 As shown, taking the observation station as the origin, the current statistical model state equation and observation equation are established as follows:

[0044]

[0045] Z k+1 =HX k +V k (17)

[0046] in, is the state vector of the target at time k, and the vector elements represent the position, velocity, acceleration in the X direction, the position, velocity, acceleration in the Y direction, and the position, velocity, acceleration in the Z direction; Φ = (Φ1(k+1 / k), 0, 0; 0, Φ1(k+1 / k), 0; 0, 0, Φ1(k+1 / k)) is the system state transfer matrix; U = (U1, 0, 0; 0, U1, 0; 0, 0, U1) is the system input matrix; Wk The mean is 0 and the covariance matrix is Gaussian noise, where is the acceleration variance in the x-axis direction, is the acceleration variance in the y-axis direction, is the acceleration variance in the z-axis direction; Z k+1 is the measurement value at time k+1; H is the observation matrix; V k is the Gaussian noise at time k.

[0047] The current statistical model assumes that when a target is maneuvering at a certain acceleration, the acceleration value at the next moment is limited and can only be within the neighborhood of the current acceleration. One-step prediction Considered as the current acceleration at the instant of KT, that is, the mean value of the subsequent maneuvering acceleration:

[0048]

[0049] The acceleration mean adaptive algorithm is obtained:

[0050]

[0051] Φ2(T)=[Φ0(T),0,0;0,Φ0(T),0;0,0,Φ0(T)](21)

[0052] However, it should be noted that the Φ1(k+1 / k) used in the motion equation describing the maneuvering target is different from the Φ2(T) used in the filtering algorithm.

[0053] According to the relationship between the estimated acceleration and the mean of the state noise, we can get:

[0054]

[0055] Among them, a max is the maximum acceleration value set, a -max is the set minimum acceleration value. and The value of can be obtained similarly.

[0056] Assuming the measurement matrix V k is the measurement noise sequence, assuming it is Gaussian noise with a mean of 0 and a covariance of R k .

[0057] Step 2: Construct a Kalman filter algorithm to estimate the target state.

[0058] Kalman filtering is a recursive algorithm, the idea is to use the optimal estimate at time k Starting from the state vector at time k+1 Make predictions and use the observed value Z k Correct the predicted value to obtain the optimal state estimate at time k+1 The specific steps of the algorithm are as follows:

[0059] 1. Determine the linear discrete system model:

[0060]

[0061] Z k =HX k +V k (twenty four)

[0062] E(W k )=0,E(W k W l T )=Q k δ kl (25)

[0063] E(V k )=0,E(V k V l T )=R k δ kl (26)

[0064] E(W k V l T )=0 (27)

[0065] Where W k ,V k are mutually independent noise sequences, k,l=0,1,...n, n is the system order, if k,l are equal, δ kl =1, if not equal, then δ kl =0.

[0066] 2. State quantity and covariance initialization:

[0067]

[0068] In the formula, x0 represents the true initial value, represents the initial estimate, and P0 is the initial covariance matrix.

[0069] 3. Obtain the state prediction value from the state prediction equation:

[0070]

[0071] 4. Forecast error covariance matrix calculation:

[0072]

[0073] 5. Kalman gain calculation:

[0074]

[0075] Where K∈[0,1] represents the ratio of model prediction error to measurement error in the process of optimal state estimation. When K=0, the prediction error is 0, and the optimal estimated state value depends entirely on the prediction value; when K=1, the measurement error is 0, and the optimal estimated state value depends entirely on the measurement value.

[0076] 6. Obtain the optimal estimate of the state from the observed variables:

[0077]

[0078] 7. Update covariance:

[0079]

[0080] Step 3: Use the data obtained by the Kalman filter algorithm to train the BP neural network offline until the minimum loss criterion or number of iterations is met.

[0081] The BP neural network calculates the partial derivative of the loss function with respect to the weights and bias items of each layer, also known as the gradient, and uses this value to update the initial weights and bias items until the loss function reaches the minimum value or the set number of iterations is completed, thereby calculating the optimal parameters in the neural network.

[0082] 3.1BP Neural Network Structure

[0083] Through offline training of BP neural network, the structure of BP neural network is determined; BP neural network is a multi-layer one-way propagation network, which consists of an input layer, one or more hidden layers, and an output layer. The neurons in each layer only receive input from the neurons in the previous layer. The latter layer has no signal feedback to the former layer, and there is no connection between neurons in the same layer. Its network structure is as follows: Figure 2 As shown, n1, n2, and n3 represent the number of neurons in the input layer, hidden layer, and output layer respectively; the structural model of a single neuron is as follows Figure 3 As shown in the figure, The output of the neuron is the sum of the product of the input and the weight and the bias, and then the output α is obtained by the activation function f(·) j , the activation function usually chooses the Sigmoid function:

[0084]

[0085] The BP neural network algorithm includes forward propagation and error back propagation. Forward propagation is calculated through the sequence of "input layer - hidden layer - output layer"; in the back propagation, the error is calculated layer by layer through "output layer - hidden layer - input layer", and the weights of each layer are modified until the error standard is met.

[0086] The algorithm steps are as follows:

[0087] 1. Initialize the weights and biases in the network

[0088] The parameters from the input layer to the hidden layer are: The parameters from hidden layer to output layer are The input data is x, and the activation functions are f1(·) and f2(·);

[0089] 2. Data transfer from input layer to hidden layer

[0090] net1=(w (1) ) T x+b (1) (36)

[0091] α=f1(net1) (37)

[0092] In the formula

[0093] 3. Data transfer from hidden layer to output layer

[0094] net2=(w (2) ) T α+b (2) (38)

[0095] y=f2(net2) (39)

[0096] In the formula α=f1(net1),

[0097] 4. Set the loss function

[0098]

[0099] In the formula, y i is the true output of the network, is the expected output of the network, and E is the error performance indicator function of the neural network.

[0100] 5. According to the loss function, calculate the error terms of the output unit and the hidden unit

[0101] Output unit error terms:

[0102]

[0103] Hidden unit error term:

[0104]

[0105] 6. Update the weights and biases in the network

[0106] Output unit parameter update:

[0107]

[0108] Hidden unit parameter update:

[0109]

[0110] Where η is the learning rate, η∈[0,1].

[0111] In summary, the BP neural network algorithm flow chart is as follows Figure 4 shown.

[0112] 3.2 BP neural network optimized KF

[0113] Applying the trained BP neural network to the Kalman filter algorithm to obtain the compensation value of the Kalman filter algorithm estimation value can achieve the effect of optimizing the Kalman filter algorithm tracking.

[0114] according to The deformation can be obtained:

[0115]

[0116] The above expression shows that the estimation effect of the KF filtering algorithm on the target state is the difference between the state prediction value and the optimal estimate value. Gain value K, the difference between the measured value and the measured predicted value The three variables are used as the input values ​​of the BP neural network, 0 is the expected output of the BP neural network, and when the neural network is trained, the difference between the true value and the Kalman filter estimate is As the output value. The output value of the trained BP neural network Δx k After compensating to the optimal estimate of the KF filtering algorithm, the optimal estimate after BP neural network optimization is obtained.

[0117] The optimized KF filtering algorithm structure diagram is as follows: Figure 5 shown.

[0118] The present invention adopts a single hidden layer neural network, uses 70% of the data set obtained by the Kalman filtering algorithm based on the current statistical model as a training set, 15% as a validation set, and 15% as a test set, sets the maximum number of network iterations to 1000, the learning rate η=0.01, and selects the LM algorithm and the trainlm training function for system training.

[0119] Example

[0120] When the enemy's UAV reconnaissance aircraft approaches our airspace, our radar sensors in the air sense it and feed back information, so we can track and attack the UAV reconnaissance aircraft.

[0121] The quality of state estimation is described by the root mean square error RMSE:

[0122]

[0123] Where N is the number of Monte Carlo simulations, which is set to 100; i represents the i-th simulation; X i Indicates the true value of a certain state of the target during the i-th simulation; Represents the estimated value of the target state corresponding to the i-th simulation.

[0124] Simulation environment settings: Assume that the maneuvering target is moving in a linear motion with variable acceleration, and the acceleration change rate is 0.1m / s 3 , the initial state in the filtering algorithm is set to [5000; 0; -50; 4000; 0; -50; 4500; 0; -50], the initial covariance matrix is ​​the unit matrix, the sampling period T = 0.1, and the inverse of the maneuvering time constant The maximum acceleration is a max =20m / s 2 , the minimum acceleration is a -max =-a max , the standard deviation of distance observation noise is 40m.

[0125] Firstly, a motion trajectory of a maneuvering target in a three-dimensional environment is set, and then the measurement data is simulated and generated. The motion model of the maneuvering target is established according to the "current" statistical model, and the target state is estimated using the Kalman filter algorithm. The data obtained by the Kalman filter tracking algorithm of the maneuvering target based on the current statistical model is used for BP offline training to obtain the compensation value of the Kalman filter algorithm estimation value, and the tracking performance of the two algorithms is compared under the same simulation setting.

[0126] The target tracking simulation results are shown in the figure Figure 6 , Figure 7 shown.

[0127] Results analysis: In the early stage of tracking, the estimation error of the Kalman filter tracking algorithm optimized by the BP neural network is much smaller than that of the traditional Kalman filter algorithm. After a period of oscillation, the error tends to be stable. In the later stage of position tracking stabilization, the error of the BPCSKF algorithm becomes smaller, and the error in the later stage of speed tracking is roughly the same. It can be seen that the BPCSKF algorithm can effectively solve the problem of large error in the early stage of tracking.

[0128] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features may be replaced by equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A Kalman filter method for maneuvering target tracking based on BP neural network optimization, characterized in that: include: According to the current statistical model, a motion model of the maneuvering target is established, a motion trajectory of the maneuvering target is set in a three-dimensional environment, measurement data is simulated and generated, and the target state is estimated using the Kalman filter algorithm; The data obtained by the Kalman filter tracking algorithm is used to perform BP offline training to obtain the compensation value of the Kalman filter algorithm estimation value.

2. The Kalman filter method for maneuvering target tracking based on BP neural network optimization according to claim 1 is characterized in that: The current statistical model is used to describe the motion model of the maneuvering target in three dimensions, a measurement model is established, a motion trajectory in a three-dimensional environment is set, and measurement data is simulated and generated, as follows: The random maneuver acceleration conforms to the first-order time-dependent process on the time axis, that is: Where x(t) is the target position information; is the target acceleration; is the current mean value of maneuvering acceleration, which is a constant in each sampling period; a(t) is zero-mean colored acceleration noise; is the speed of change of zero-mean colored acceleration noise; α is the maneuvering parameter; w(t) has a mean of 0 and a variance of Gaussian white noise, where is the target acceleration variance; make We can get: Write the above two equations as state equations to get the current statistical model of the maneuvering target: Assuming the sampling period is T, through discretization, the discrete state equation is: Where X(k+1 / k+1) is the optimal estimated state vector of the target at time k+1; X(k / k) is the optimal estimated state of the target at time k; W(k) is the discrete time white noise sequence; the state vector The three elements represent position, velocity, and acceleration respectively; the state transfer matrix Process Input Matrix W(k) is a discrete-time white noise sequence, and E(W(k)W T (k+j))=0, Variance Matrix in, q 21 =q 12 (10) q 31 =q 13 (13) q 32 =q 23 (14) Considering the three-dimensional space, the maneuvering target gradually approaches the observation station. Taking the observation station as the origin, the current statistical model state equation and observation equation are established as follows: Z k+1 =HX k +V k (17) in, is the state vector of the target at time k, and the vector elements represent the position, velocity, acceleration in the X direction, the position, velocity, acceleration in the Y direction, and the position, velocity, acceleration in the Z direction; Φ = (Φ1(k+1 / k), 0, 0; 0, Φ1(k+1 / k), 0; 0, 0, Φ1(k+1 / k)) is the system state transfer matrix; U = (U1, 0, 0; 0, U1, 0; 0, 0, U1) is the system input matrix; W k The mean is 0 and the covariance matrix is Gaussian noise, is the acceleration variance in the x-axis direction, is the acceleration variance in the y-axis direction, is the acceleration variance in the z-axis direction; Z k+1 is the measurement value at time k+1; H is the observation matrix; V k is Gaussian noise at time k; The current statistical model assumes that when the target is maneuvering at a certain acceleration, the acceleration value at the next moment is limited and can only be within the neighborhood of the current acceleration; therefore, One-step prediction Considered as the current acceleration at the instant of KT, that is, the mean value of the subsequent maneuvering acceleration: The acceleration mean adaptive algorithm is obtained: Φ2(T)=[Φ0(T),0,0;0,Φ0(T),0;0,0,Φ0(T)](21) The Φ1(k+1 / k) used in the motion equations describing the maneuvering target is different from the Φ2(T) used in the filtering algorithm; According to the relationship between the estimated acceleration and the mean value of the state noise, we can get: Among them, a max is the maximum acceleration value set, a -max is the minimum acceleration value set, and The value of can be obtained in the same way; Assuming the measurement matrix V k is the measurement noise sequence, assuming it is Gaussian noise with a mean of 0 and a covariance of R k .

3. The Kalman filter algorithm for maneuvering target tracking based on BP neural network optimization according to claim 2 is characterized in that: Construct a Kalman filter algorithm to estimate the target state, as follows: Determine the linear discrete system model: Z k =HX k +V k (24) E(W k )=0,E(W k W l T )=Q k δ kl (25) E(V k )=0,E(V k V l T )=R k δ kl (26) E(W k V l T )0 (27) Where W k ,V k are mutually independent noise sequences, k,l=0,1,...n, n is the system order, if k,l are equal, δ kl =1, if not equal, then δ kl =0; State quantity and covariance initialization: In the formula, x0 represents the true initial value, represents the initial estimate, P0 is the initial covariance matrix; The state prediction value is obtained from the state prediction equation: Forecast error covariance matrix calculation: Kalman gain calculation: Where K∈[0,1] represents the ratio of model prediction error to measurement error in the process of optimal state estimation. When K=0, the prediction error is 0, and the optimal estimated state value depends entirely on the prediction value; when K=1, the measurement error is 0, and the optimal estimated state value depends entirely on the measurement value. The optimal estimate of the state is obtained from the observed variables: Update the covariance:

4. The Kalman filter algorithm for maneuvering target tracking based on BP neural network optimization according to claim 1 is characterized in that: The BP neural network is trained offline using the data obtained by the Kalman filter algorithm until the minimum loss criterion or the number of iterations is met; the BP neural network calculates the partial derivatives of the loss function with respect to the weights and bias items of each layer, and uses the values ​​to update the initial weights and bias items until the loss function reaches the minimum value or the set number of iterations is completed, thereby calculating the optimal parameters in the neural network.

5. The Kalman filter algorithm for maneuvering target tracking based on BP neural network optimization according to claim 4 is characterized in that: The structure of the BP neural network is determined by offline training of the BP neural network. The BP neural network consists of an input layer, one or more hidden layers, and an output layer. The neurons in each layer only receive input from the neurons in the previous layer. The latter layer has no signal feedback to the former layer. There is no connection between neurons in the same layer. The output of the neuron is the sum of the product of the input and the weight and the bias, and then the output α is obtained through the activation function f(·). j , the activation function selects the Sigmoid function: The BP neural network algorithm includes forward propagation and error back propagation; forward propagation is calculated through the sequence of "input layer - hidden layer - output layer"; during back propagation, the error is calculated layer by layer through "output layer - hidden layer - input layer", and the weights of each layer are modified until the error standard can be met; the specific steps of the algorithm are as follows: 1) Initialize the weights and biases in the network The parameters from the input layer to the hidden layer are: The parameters from hidden layer to output layer are The input data is x, and the activation functions are f1(·) and f2(·); 2) Data transfer from input layer to hidden layer net1=(w (1) ) T x+b (1) (36) α=f1(net1) (37) In the formula 3) Data transfer from hidden layer to output layer net2=(w (2) ) T a+b (2) (38) y=f2(net2)(39) In the formula 4) Set the loss function In the formula, y i is the true output of the network, is the expected output of the network, E is the error performance index function of the neural network, and n3 is the number of neurons in the output layer; 5) According to the loss function, calculate the error terms of the output unit and the hidden unit Output unit error terms: is the derivative of the loss function with respect to the output unit weights, is the inverse of the loss function with respect to the output unit bias; Hidden unit error term: is the derivative of the loss function with respect to the hidden unit weights, is the derivative of the loss function with respect to the bias of the hidden unit; 6) Update the weights and biases in the network Output unit parameter update: Hidden unit parameter update: Where η is the learning rate, η∈[0,1].

6. The Kalman filter method for maneuvering target tracking based on BP neural network optimization according to claim 5 is characterized in that: Apply the trained BP neural network to the Kalman filter algorithm to obtain the compensation value of the Kalman filter algorithm estimation value; according to The deformation can be obtained: The above expression shows that the estimation effect of the KF filtering algorithm on the target state is the difference between the state prediction value and the optimal estimate value. Gain value K, the difference between the measured value and the measured predicted value The three variables are used as the input values ​​of the BP neural network, 0 is the expected output of the BP neural network, and when the neural network is trained, the difference between the true value and the Kalman filter estimate is As output value; The output value Δx of the trained BP neural network k After compensating to the optimal estimate of the KF filtering algorithm, the optimal estimate after BP neural network optimization is obtained.

7. A computer device comprising a memory, a processor and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the program, the steps of the method described in any one of claims 1 to 6 are implemented.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the steps of any method described in claims 1-6 are implemented.

9. A computer program product, comprising a computer program, characterized in that When the computer program is executed by a processor, the steps of the method described in any one of claims 1 to 6 are implemented.

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