A method for target position estimation based on limited discontinuous information

Abstract

The invention relates to the field of target position estimation. A target position estimation method based on finite discontinuous information comprises the following steps: step S1, performing state modeling on a missile and a target; step S2, constructing a relative motion model and a measurement model of a missile-target system in a Cartesian system and an improved spherical coordinate system; step S3, respectively designing filters for a dynamic model and a measurement model based on an EKF algorithm and a CKF algorithm; and step S4, constructing a measurement model based on a Gaussian process regression algorithm, and estimating the target position based on target measurement information. The invention is based on a missile-target relative kinematics and a spatial line of sight model, adopts a filtering estimation algorithm, obtains relatively accurate missile-target relative position information from a guidance system observation quantity containing a systematic error and a random error, and provides information for a control law for guidance.

Description

Technical Field

[0001] The invention relates to the field of target position estimation, and in particular to a target position estimation method based on limited discontinuous information. Background Art

[0002] For air-to-air missiles, the relative distance and speed between the missile and the target are of great practical significance for the guidance and tactical performance of the missile. For example, most air-to-air missiles generally use proportional guidance, and for various proportional guidance methods, the relative distance and speed between the missile and the target are very important parameters. For the proximity fuze of air-to-air missiles, it is necessary to know the relative distance between the missile and the target and the arrival time; for infrared-guided air-to-air missiles, the relative distance between the missile and the target is needed to switch the attack point.

[0003] For most air-to-air missiles, due to the use of passive sensors such as infrared-guided air-to-air missiles, or due to tactical needs, the active radar is not turned on during certain periods of time, and the line of sight angle and line of sight angular velocity of these missiles are easy to obtain, which makes passive ranging under bearing only a very important issue. Traditional target recognition and tracking are based on the target information given by the target in the seeker market. When the aircraft undergoes drastic attitude changes, it is easy to lose the target, resulting in a decrease in guidance accuracy or even miss the target. For this reason, the present application proposes a target position estimation method based on limited intermittent information to solve the above problem. Summary of the invention

[0004] The object of the present invention is to provide a method for estimating a target position based on limited discontinuous information to solve the problems raised in the above background technology.

[0005] To achieve the above object, a method for estimating a target position based on limited discontinuous information comprises the following steps:

[0006] Step S1, modeling the missile and the target;

[0007] Step S2, constructing a relative motion model and a measurement model of the projectile-target system in a Cartesian system and an improved spherical coordinate system;

[0008] Step S3, designing filters for the dynamic model and the measurement model based on the EKF and CKF algorithms respectively;

[0009] Step S4: construct a measurement model based on a Gaussian process regression algorithm, and estimate the target position based on the target measurement information.

[0010] Preferably: the relative state vector of the target in step S1 in MSC is defined as,

[0011]

[0012] Preferably: the missile state in step S1 is specifically in the form of:

[0013]

[0014]

[0015]

[0016] F N (7,4)=1 / R n

[0017]

[0018] F N (9,6)=-1,F N It is a system array of 9 basic navigation parameters.

[0019] Preferably: the construction of the dynamic model in step S2 is specifically the state transfer matrix of the CV and CA models is,

[0020]

[0021] The missile is in the time interval [t k-1 ,t k The turning rate of ] is expressed as Notice Indicates CV motion Represents CT motion, and the CT model state transfer matrix is ​​described as follows

[0022]

[0023] Preferably: the initialization of the EKF and CKF algorithms in step S3 is based on the mean and covariance matrix of the given state, and the mean and covariance of the target state in the Cartesian coordinate system satisfy

[0024]

[0025]

[0026] in,

[0027]

[0028] Preferably: in step S3, under the premise of a given distribution of vector φ, the relative target state mean and covariance under MSC are

[0029]

[0030]

[0031] in,

[0032]

[0033] Preferably: the measurement model of step S4 based on the Gaussian process regression algorithm consists of a finite number of Gaussian components f(x i ) constitutes a joint multivariate Gaussian distribution: f(x1),…,f(x n )~N(0,Σ), use the covariance function to obtain the covariance matrix, and select the radial basis covariance function, as shown in the following formula:

[0034]

[0035] In the formula, υ represents the overall measure of prior knowledge, which can optimize the degree of correlation of process variables. represents the variance of the noise that follows the Gaussian distribution, δ ij is the Kronecher operator, ω t Represents the relative importance of each auxiliary variable, and its log-likelihood function is shown as follows:

[0036]

[0037] In the formula is a hyperparameter, c is the unknown covariance matrix corresponding to the training data set, and the derivative of the above formula can be obtained

[0038]

[0039] The optimal hyperparameter θ can be obtained by the conjugate gradient method. For a new test sample point x q , assuming that it and the training sample data belong to the same joint normal distribution, its predicted mean and predicted variance can be obtained:

[0040]

[0041]

[0042] In the above formula, c(x q ) is the covariance vector between the test sample point and each training sample point, c(x q ,x q ) is the covariance value of the test sample point and itself, and C is the covariance matrix of the training sample set.

[0043] Compared with the prior art, the present invention has the following beneficial effects:

[0044] The invention firstly carries out state modeling of a missile and a target; then analyzes the observability of the target under the condition of single missile pure angle tracking, and explains the filter divergence problem caused by the unobservability of the target in a Cartesian system; then constructs a relative motion model and a measurement model of the missile-target system in a Cartesian system and an improved spherical coordinate system; then provides a filter initialization method, and designs filters based on EKF and CKF algorithms respectively for the designed dynamic model and measurement model; then verifies through simulation the filter non-convergence caused by the unobservability of the representation method in a Cartesian coordinate system in the pure angle tracking problem and the filter convergence achieved by missile maneuvering in an improved spherical coordinate system; finally, when the target measurement information is lost, a measurement construction based on a Gaussian process regression algorithm is provided, and then the effectiveness of the proposed filtering algorithm and soft measurement method is explained through simulation and joint simulation. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 It is a flow chart of the Gaussian process regression algorithm of the present invention;

[0046] Figure 2 For the simulation distance estimation and prediction comparison of the present invention;

[0047] Figure 3 For the simulation azimuth estimation and prediction comparison of the present invention;

[0048] Figure 4 For the simulation elevation angle estimation and prediction comparison of the present invention;

[0049] Figure 5 For the simulation dr / r estimation and prediction comparison of the present invention;

[0050] Figure 6 For the simulation estimation and prediction comparison of the present invention;

[0051] Figure 7 The simulation elevation angle rate estimation and prediction comparison of the present invention;

[0052] Figure 8 For the simulation position error estimation and prediction comparison of the present invention;

[0053] Fig. 9 This is the RMSE comparison of the simulation state quantity prediction of the present invention. DETAILED DESCRIPTION

[0054] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the implementation regulations described are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0055] Example

[0056] See also Figure 1-Figure 9 , FIG. 1 is a preferred embodiment of the present invention, a method for estimating a target position based on limited discontinuous information, comprising the following steps:

[0057] Step S1, modeling the missile and the target;

[0058] Step S2, constructing a relative motion model and a measurement model of the projectile-target system in a Cartesian system and an improved spherical coordinate system;

[0059] Step S3, designing filters for the dynamic model and the measurement model based on the EKF and CKF algorithms respectively;

[0060] Step S4: construct a measurement model based on a Gaussian process regression algorithm, and estimate the target position based on the target measurement information.

[0061] In this embodiment, for a given target, the Z axis of the sensor coordinate system is along the line of sight. Using the azimuth and elevation angles of the target, the rotation transformation matrix from the T coordinate system to the S coordinate system is defined as

[0062]

[0063] Here the azimuth angle β∈[0,2π], the elevation angle ε∈[-π / 2,π / 2], the states of the target and the missile can be expressed in the Cartesian coordinate system as

[0064]

[0065] and

[0066]

[0067] Then the relative state vector in the T coordinate system can be expressed as

[0068] x=x t -x o (4)

[0069] make represents the relative state vector in the T coordinate system. Then the relative state vector can be written as

[0070]

[0071] Let r T represents the distance vector from the target to the sensor in the T coordinate system, then r T Defined as

[0072] rT =[xyz] T =[x t -x o y t -y o z t -z o ] T (6)

[0073] The distance is defined as follows:

[0074]

[0075] The distance vector can be expressed in terms of distance, azimuth and elevation as

[0076]

[0077] The horizontal distance can be expressed as

[0078]

[0079] Following the Stallard convention, ω is used as a component of MSC, where

[0080]

[0081] Let ζ(t) represent the logarithm of the distance r(t), then

[0082] ζ(t)=ln r(t) (11)

[0083] but

[0084] r(t)=exp[ζ(t)] (12)

[0085] Differentiating ζ(t) with respect to time, we have

[0086]

[0087] Then the relative state vector of the target in MSC is defined as

[0088]

[0089] Furthermore, the navigation output parameters of the inertial navigation system: 3 inertial navigation platform error angles, 3 velocity errors and 3 position errors, and the 9 state quantities of the inertial instrument extension include 2 states of each gyro extension, 1 state of each accelerometer extension, and 3 axial error models. The navigation output parameters of the inertial navigation system and the state quantities of the inertial instrument extension are combined, and 1 state quantity of the atmospheric first-order Markov error is added. The 19-dimensional system state equation is obtained as follows:

[0090]

[0091] The state vector X is defined as follows:

[0092]

[0093] In the formula is the platform error angle; ε rx ,ε ry ,ε rz is the first-order Markov drift error of the gyro; is the accelerometer zero bias; δh p is the atmospheric measurement error.

[0094] The system white noise random error vector W is

[0095] W=[ω gx ,ω gy ,ω gz ,ω rx ,ω ry ,ω rz ,ω ax ,ω ay ,ω az ,ω h ] T (16)

[0096] The error coefficient equation G I and the state coefficient equation F I They are

[0097]

[0098] Among them, F S and F M They are

[0099]

[0100]

[0101] F N is a system array of 9 basic navigation parameters, which is determined by the basic error equation of the navigation parameters of the inertial navigation system. Its specific form can be expressed as

[0102]

[0103]

[0104]

[0105] F N (7,4)=1 / R n

[0106]

[0107] F N (9,6)=-1.

[0108] Furthermore, the inertial navigation height h I and pressure altitude h P The difference is used as the observation quantity of the combined Kalman filter. The measurement equation is derived as follows: The height channel information of the inertial navigation system can be expressed as: h I =h t +δh, the altitude channel information given by the atmospheric altimeter can be expressed as: h A =h t -δh p Then, the height channel measurement equation is defined as:

[0109] Z(t)=[h I -h A ]=[δh+δh p ]=H(t)X(t)+V(t) (20)

[0110] In formula (20), H(t) = [0 1×8 1 0 1×9 1] 1×19 , V(t) is the system measurement white noise matrix. Through the above analysis, the dynamic real-time equation of the multi-information fusion integrated navigation system under different measurement conditions can be obtained as follows:

[0111]

[0112] In general, the continuous system needs to be discretized for computer simulation. The discretization sampling time is T, and the dynamic equation of the discretized system is:

[0113]

[0114] If the inertial navigation system error needs to be corrected during the information fusion navigation process, a closed-loop correction system state equation needs to be used, and the control term U needs to be added. k-1 , the dynamic equation of the system is:

[0115]

[0116] in,

[0117]

[0118]

[0119] In addition, the system state noise variance matrix and the system observation noise variance matrix are discretized as follows:

[0120]

[0121] In this embodiment, the target moves at a near-constant speed in three-dimensional space. According to this motion model, the target speed in each dimension will be affected by the random disturbance of Gaussian distribution. In the T coordinate system, the Cartesian coordinate system representation of the target state satisfies the following stochastic differential equation:

[0122]

[0123] Here t (t) is a zero-mean continuous-time Gaussian white noise acceleration with a power spectral density matrix of Q t (t) = diag(q x ,q y ,q z )and

[0124]

[0125]

[0126] Here 03 and I3 represent the 3×3 zero matrix and the identity matrix respectively. Let x o (t) represents the non-random missile state, which satisfies

[0127]

[0128] here is the acceleration of the missile in the T coordinate system. Consider three types of missile maneuvers: constant velocity (CV), constant acceleration (CT) and coordinated turn (CT). On an XY plane parallel to the T coordinate system, the stochastic differential equation of the relative state vector of the target in the T coordinate system is expressed as

[0129] here

[0130]

[0131] Since the measurements are acquired in discrete time, it is desirable to have a discrete time version of the corresponding continuous time dynamic model. This application employs a stochastic difference equation in which t k The state at time t k-1 The state at the time, missile input and random process noise representation, let x k =x(t k ) represents t in the Cartesian coordinate system k The relative state vector of the target at time t, the stochastic discrete difference equation corresponding to the above stochastic differential equation is

[0132]

[0133] Here Δ k =t k -t k-1 is the measurement sampling interval, F(Δ) is the state transition matrix about the time interval Δ,

[0134]

[0135] here represents the Kronecker product. From (3-21), we can see that

[0136] x k =F(Δ k )x k-1 +ω k-1 -u k-1 (35)

[0137]

[0138]

[0139] Using ω t (t), the state transfer matrix F, and the previous k-1 The definition of ω k-1 is a zero-mean Gaussian white integral process noise satisfying the covariance Q(Δ k )

[0140] ω k-1 ~N(·;0,Q(Δ k )) (38)

[0141] here

[0142]

[0143] The missile is in the time interval [t k-1 ,t k The turning rate of ] is expressed as Notice Indicates CV motion Represents CT motion. For general missile motion, the input vector u k-1 Given as follows

[0144]

[0145] For the pure angle measurement problem, this application considers three specific missile maneuvers, CV, CA and CT. Because the missile motion assumption is certain, the process noise is not used in the dynamic model of the missile, and the state transfer matrix is ​​sufficient. The state transfer matrix of the CV model has been given above, and the CA is consistent with it. The state transfer matrix of the CT model is described as follows

[0146]

[0147] Note that when tends to zero, Simplified to F(Δ k ) and u k-1 To make it zero, we need to reconstruct a dynamic model for the relative state vector under MSC so that it is equivalent to the relative state vector model obtained under the Cartesian coordinate system. We consider the following two methods. The first method is to discretize a continuous-time model equivalent to the Cartesian system. The second method is to use the discrete-time model obtained for the relative state vector in Cartesian coordinates and the conversion between MSC and Cartesian coordinates.

[0148] (1) The first approach is to discretize the continuous-time dynamics of an MSC. The details are given below: Differentiating r in time gives

[0149]

[0150]

[0151]

[0152] Differentiating the above three equations again, we can get

[0153]

[0154]

[0155]

[0156] The acceleration of the target relative to the missile is defined as follows

[0157]

[0158] Convert the relative acceleration from the T coordinate system to the S coordinate system

[0159]

[0160] From the above formula, we can get

[0161]

[0162]

[0163]

[0164]

[0165] Simplifying (53) we can get

[0166]

[0167] Simplifying the above equation and substituting it into the Y component of (51), we have

[0168]

[0169] Rewriting the above equation using the MSC representation yields

[0170]

[0171] Simplify The expression of

[0172]

[0173] Simplifying the above equation and substituting the X component of (50) into the equation, we have

[0174]

[0175] Representing the above equation using symbols in MSC, we have

[0176]

[0177] Similarly, simplify The expression of

[0178]

[0179] Simplifying the above equation and substituting it into the Z component of (52), we have

[0180]

[0181] Available

[0182]

[0183] Using the expression under MSC, we can get

[0184]

[0185] Same reason

[0186]

[0187] From the definition of MSC, we can know

[0188]

[0189]

[0190] Combining the above results, we can get the stochastic differential equation under MSC

[0191]

[0192] here

[0193]

[0194]

[0195]

[0196] There are two points to note about the above equation:

[0197] The previous continuous motion equation can be described as follows:

[0198]

[0199] here, and are the components of the target acceleration along the radial, horizontal and vertical directions, and is the acceleration of the missile platform along the corresponding direction.

[0200] Furthermore, it can be concluded from the above equation that when neither the target nor the platform is maneuvering, there is no coupling between the first five states and the sixth state, which means that in theory all states except the first state are observable. In practice, to ensure that the fourth state is observable, the line of sight angular velocity must be non-zero. The advantage of implementing target tracking in MSC is that the lack of distance estimation does not reduce the estimation of observable states in the absence of maneuvers. If the target is non-maneuverable, an accurate range estimate can be generated when the platform is maneuvering. The disadvantage of using MSC is that the solution and discretization of the above equation will produce a highly nonlinear dynamic model.

[0201] In this embodiment, the truncated random Taylor series expansion can be used to obtain an approximate discretization of (71). The random Taylor series expansion is obtained by repeatedly applying Ito's lemma, and let ξ k =ξ(t k ) indicates t k The relative state vector under MSC at time instant can be obtained by first-order random Taylor series approximation as follows:

[0202] ξ k ≈a(ξk-1 ,t k-1 ; Δ k )+υ k (72)

[0203] Here k ~N(·;0,C(ξ k-1 ; Δ k ))and

[0204] a(ξ,t;Δ)=ξ+Δf(ξ,t) (73)

[0205] C(ξ;Δ)=ΔG(ξ)diag(q x ,q y ,q z )G T (ξ) (74).

[0206] Furthermore, the above linearization can infinitely approximate the original nonlinear function, which can be achieved simply by increasing the order of the Taylor series expansion. However, in practical applications, this will lead to an increase in the amount of calculation. In order to balance the problem of calculation amount and calculation accuracy, in actual use, multiple low-order approximations can be used as a substitute while reducing the update cycle.

[0207] The following is an accurate dynamic model based on coordinate transformation. represents the transformation from the relative Cartesian coordinate system to the MSC, represents its inverse transformation, then

[0208]

[0209]

[0210] in

[0211]

[0212]

[0213] Based on x k The recursive expression of

[0214]

[0215] where ω k-1 and u k-1 This is consistent with the previous definition. However, the analytical expression of the above expression is difficult to obtain and due to the inclusion of noise ω in the dynamic model k-1 , which makes the filtering algorithm slightly complicated when performing numerical calculations.

[0216] In this embodiment, the initialization is based on the measurement z1 at time t1 and the prior information of the relative distance and target speed. The target state at time t1 can be completely represented by the vector φ = [β, ε, r, s, α, γ] T Definition, where β is the azimuth, ε is the elevation, r is the distance, s is the speed, α is the azimuth component of the heading, and γ is the height component of the heading. Given the measurement z1 and the prior information of the distance and target speed, the distribution of φ satisfies

[0217]

[0218] here

[0219]

[0220]

[0221] The initialization of the EKF and CKF algorithms requires the state mean and covariance matrix. According to the distribution of the vector φ given above, the mean and covariance of the target state in the Cartesian coordinate system can be obtained to satisfy

[0222]

[0223]

[0224] here

[0225]

[0226] In general, most two-dimensional and three-dimensional pure angle tracking problems can achieve acceptable initial values ​​using the linear approximation of the above integral.

[0227] Given the distribution of the vector φ, the relative target state mean and covariance under MSC are

[0228]

[0229]

[0230] here

[0231]

[0232] For the mean and expected integral calculations, except for the distance r, all other quantities are known. The integral of the distance r can be implemented by numerical calculation using Monte Carlo.

[0233] In this embodiment, the existing measurement reconstruction methods are all based on soft measurement, and most of the soft measurement methods are a regression analysis method. First, a large amount of data is collected, and a regression model between difficult-to-measure variables and easy-to-measure variables is established offline. Then, the regression model is applied to the online real-time estimation, that is, the easy-to-measure variables are substituted into the regression model to estimate the difficult-to-measure variables. Commonly used soft measurement methods include principal component regression, least squares regression, partial least squares regression method, neural network method, support vector machine, etc. Since the state variables and noise measurement values ​​need to be modeled in this application, the Gaussian Process Regression method is adopted. The GPR algorithm, as a soft measurement modeling method developed from Bayesian statistical theory, has a good processing effect on small data, nonlinear, high dimensional and other related problems. In addition, it also has the advantages of few model parameters, fast parameter estimation, and output with probabilistic meaning.

[0234] The GPR model is a non-parametric probability model based on Bayesian statistical theory. For any given input, GPR can be used to obtain a Gaussian distribution of the corresponding output. Given a training sample set input X = {x i |x i ∈R m} i＝1,…,n And output Y = {y i ∈R} i＝1,…,n , in general, the relationship between input and output is as follows:

[0235] y=f(x)+ε (89)

[0236] In the formula, f(x) is the unknown function relationship, ε is the mean value of 0, and the variance is Gaussian noise, the Gaussian process regression model is composed of a finite number of Gaussian components f(x i ) constitutes a joint multivariate Gaussian distribution: f(x1),…,f(x n )~N(0,Σ), the covariance matrix can be obtained by using the covariance function. This paper selects the radial basis covariance function, as shown in the following formula:

[0237]

[0238] In the formula, υ represents the overall measure of prior knowledge, which can optimize the degree of correlation of process variables. represents the variance of the noise that follows the Gaussian distribution, δ ij is the Kronecher operator, ω t Represents the relative importance of each auxiliary variable, and its log-likelihood function is shown as follows:

[0239]

[0240] In the formula is a hyperparameter, and c is the unknown covariance matrix corresponding to the training data set. Derivative of the above formula yields

[0241]

[0242] The optimal hyperparameter θ can be obtained by the conjugate gradient method.

[0243] Among them, for the new test sample point x q , assuming that it and the training sample data belong to the same joint normal distribution, its predicted mean and predicted variance can be obtained:

[0244]

[0245]

[0246] In the above formula, c(x q ) is the covariance vector between the test sample point and each training sample point, c(x q ,x q ) is the covariance value of the test sample point and itself, C is the covariance matrix of the training sample set, and finally the root mean square error index is used to evaluate the performance of the soft sensor method. The specific calculation formula is shown in the following formula:

[0247]

[0248] Where y q is the true value, is the corresponding estimated value, and h is the number of test data points.

[0249] Based on the target navigation information obtained by the volumetric Kalman filtering algorithm and the Gaussian process regression algorithm proposed above, the two are combined for joint simulation. It can be seen from the MSC-CKF algorithm that the simulation tends to be stable after 5s, and the tracking curve is basically close to the true value. Therefore, the data of 5-15s is used as the training data of Gaussian process regression, and then the measurement reconstruction is performed based on the system state of 15-17s, and the reconstructed measurement is used for the measurement update step in the filtering algorithm.

[0250] The following simulation gives the true value of the system state and the filter tracking results when the measurement is available, and adds the prediction results of the measurement reconstructed by Gaussian process regression at 15-17s. The initial value of the prediction algorithm here is the filter value obtained based on the real sampling measurement at the end of 14s. The detailed simulation results are shown in Figure 2-Figure 9 shown.

[0251] from Figure 2-Figure 8It can be seen that based on the Gaussian process regression algorithm, when the measurement is lost, the target tracking system is reconstructed based on the previously accumulated measurement information, and the system state is corrected based on the reconstructed measurement information, which can obtain a relatively satisfactory estimation accuracy. Fig. 9 In the , the root mean square errors of the state estimates tend to diverge, but overall, the prediction algorithm based on Gaussian process regression can obtain acceptable estimation accuracy in a short time.

[0252] The above content is a further detailed description of the present invention in combination with specific implementation methods. It cannot be determined that the specific implementation of the present invention is limited to these descriptions. For ordinary technicians in the technical field to which the present invention belongs, some simple deductions or substitutions can be made without departing from the concept of the present invention, which should be regarded as belonging to the scope of protection determined by the claims submitted for the present invention.

Claims

1. A method for estimating target position based on limited discontinuous information, characterized in that: The steps include: Step S1, modeling the missile and the target; Step S2, constructing the relative dynamic model and measurement model of the projectile-target system in the Cartesian system and the improved spherical coordinate system, and reconstructing a dynamic model for the relative state vector under the MSC so that it is equivalent to the relative state vector model obtained in the Cartesian coordinate system; Step S3, designing filters for the relative dynamic model and the measurement model based on the CKF algorithm; Step S4, when the target measurement information is lost, construct a measurement model based on the Gaussian process regression algorithm; and use the reconstructed measurement in the measurement update step of the filtering algorithm to estimate the target position based on the known target measurement information; The relative state vector of the target in step S1 in MSC is defined as 2. A target position estimation method based on limited discontinuous information according to claim 1, characterized in that: The missile status in step S1 is specifically in the form of: F N (9,6)=-1,F N It is a system array of 9 basic navigation parameters.

3. The target position estimation method based on limited discontinuous information according to claim 1, characterized in that: The step S2 constructs a state transfer matrix with respect to the time interval Δ relative to the dynamic model: The CT model state transfer matrix is ​​described as follows 4. The target position estimation method based on limited discontinuous information according to claim 1, characterized in that: The initialization of the EKF and CKF algorithms in step S3 is based on the mean and covariance matrices of the given state, and the mean and covariance of the target state in the Cartesian coordinate system satisfy in, 5. The target position estimation method based on limited discontinuous information according to claim 4, characterized in that: In step S3, under the premise of the distribution of the given vector φ, the relative target state mean and covariance under MSC are in, 6. The target position estimation method based on limited discontinuous information according to claim 1, characterized in that: The measurement model of step S4 based on the Gaussian process regression algorithm consists of a finite number of Gaussian components f(x i ) constitutes a joint multivariate Gaussian distribution: f(x1),…,f(x n )~N(0,Σ), use the covariance function to obtain the covariance matrix, and select the radial basis covariance function, as shown in the following formula: In the formula, υ represents the overall measure of prior knowledge, which can optimize the degree of correlation of process variables. represents the variance of the noise that follows the Gaussian distribution, δ ij is the Kronecher operator, ω t Represents the relative importance of each auxiliary variable, and its log-likelihood function is shown as follows: In the formula is a hyperparameter, C is the unknown covariance matrix corresponding to the training data set, and the derivative of the above formula can be obtained The optimal hyperparameter θ can be obtained by the conjugate gradient method. For a new test sample point x q , assuming that it and the training sample data belong to the same joint normal distribution, its predicted mean and predicted variance can be obtained: In the above formula, c(x q ) is the covariance vector between the test sample point and each training sample point, c(x q ,x q ) is the covariance value of the test sample point and itself, and C is the covariance matrix of the training sample set.

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