Three-dimensional target tracking method under radar pitch angle missing condition based on measurement conversion

Abstract

The invention discloses a three-dimensional target tracking method under a radar pitch angle missing condition based on measurement conversion. The method comprises the following steps: establishing a radar measurement model and a target dynamic model under the pitch angle missing condition; performing one-step prediction on the target state and the mean square error matrix thereof according to the state estimation of the target at the previous moment, the mean square error matrix thereof and the target dynamic model, and calculating sampling points and corresponding weights thereof; spreading sampling points by using a radar measurement model and performing measurement one-step prediction; designing an irrelevant conversion function based on a pseudo pitch angle to calculate irrelevant conversion, performing dimension expansion on original measurement, and calculating a predicted measurement sampling point and performing one-step prediction with dimension expansion measurement by using a Gaussian-Hermitian quadrature rule; and calculating target state estimation at the current moment and a mean square error matrix thereof to obtain a target tracking result at the current moment. According to the invention, the problem of radar three-dimensional target tracking under the condition of pitch angle deficiency can be solved, and the tracking effect is obviously improved compared with a traditional target tracking method.

Description

Technical Field

[0001] The present invention relates to radar three-dimensional target tracking technology, and particularly to a three-dimensional target tracking method for the condition of missing radar elevation angle. Background Art

[0002] Currently, radars that can provide target range measurement, azimuth measurement, and elevation measurement are very common. However, in many application scenarios, there are still situations where the radar cannot provide target elevation measurement, or the elevation measurement error is so large that it cannot be used. During the design process of some radars, in order to achieve a better minimum detectable speed, the design size of the azimuth aperture is usually large. After comprehensively considering the limitations of weight and the carrying platform, the design size of the elevation aperture is small. Such a design makes the elevation measurement error of such radars relatively large.

[0003] Radar is a commonly used sensor in target tracking technology. However, in many current application scenarios, radars that cannot provide target elevation measurement are still widely used, which poses a major challenge to three-dimensional target tracking technology. In existing methods, most of them achieve the tracking of the target in three-dimensional space by using multiple radars with missing elevation measurements or radar networking. Although such methods can effectively track the target, the simultaneous operation of multiple radars will increase the complexity of the system and the data processing pressure. At the same time, in an extremely complex battlefield environment, real-time communication between radars cannot be guaranteed, which may reduce the target tracking accuracy.

[0004] Such problems can be effectively solved by studying how to use a single radar with missing elevation measurement to perform three-dimensional target tracking. Summary of the Invention

[0005] The purpose of the present invention is to solve the problem of high-precision tracking of the target in three-dimensional space under the condition of missing elevation measurement of a single radar. Based on the idea of uncorrelated transformation filtering measurement transformation, the present invention proposes an uncorrelated transformation function based on pseudo-elevation angle and uses it to expand the dimension of the original radar measurement, so as to use the uncorrelated transformation filter to improve the target tracking accuracy. The present invention can be used in the field of three-dimensional target tracking under the condition of missing elevation angle or large elevation angle error of a single radar, and can effectively improve the target tracking accuracy of using a single radar.

[0006] The present invention is realized by the following technical solutions.

[0007] A three-dimensional target tracking method for the condition of missing radar elevation angle based on measurement transformation, comprising:

[0008] Establish a radar measurement model under the condition of missing elevation angle;

[0009] Construct a target dynamic model;

[0010] Using the unscented transformation rule, based on the target state estimate at the previous moment, its mean square error matrix, and the target dynamic model, perform a one-step prediction of the target state and its mean square error matrix;

[0011] The radar receives the measurement at the current moment from the target;

[0012] Using the Gauss-Hermite quadrature rule, calculate the sampling points and their corresponding weights according to the target one-step prediction information;

[0013] According to the sampling points and their corresponding weights, use the radar measurement model to propagate the sampling points and calculate the one-step prediction of the measurement;

[0014] Using the target state one-step prediction and the measurement one-step prediction, design an uncorrelated transformation function based on the pseudo-pitch angle;

[0015] Through the uncorrelated transformation calculated by the uncorrelated transformation function based on the pseudo-pitch angle, expand the dimension of the original measurement. Using the Gauss-Hermite quadrature rule, calculate the predicted measurement sampling points and the expanded measurement one-step prediction; calculate the target state estimate and its mean square error matrix at the current moment, and then obtain the target tracking result at the current moment.

[0016] For the above technical solution, the present invention has a further preferred solution:

[0017] Preferably, using the unscented transformation rule, based on the target state estimate at the previous moment, its mean square error matrix, and the target dynamic model, perform a one-step prediction of the target state and its mean square error matrix, including:

[0018] Use the process noise mean and its covariance matrix to expand the dimension of the target state estimate result and its mean square error matrix at the k-1 moment respectively;

[0019] According to the expanded target state estimate result and its mean square error matrix at the k-1 moment, use the unscented transformation to calculate the sampling points and their corresponding weights;

[0020] Use the target dynamic model to propagate the sampling points to obtain the predicted state sampling points;

[0021] Use the predicted state sampling points and weights to calculate the target state one-step prediction and the mean square error matrix one-step prediction.

[0022] Preferably, using the Gauss-Hermite quadrature rule, calculate the sampling points and their corresponding weights according to the target one-step prediction information, including:

[0023] Obtain the integration points by solving the m-order Hermite polynomial to obtain the corresponding weights;

[0024] By permuting and combining the integration points, the sampling points are obtained based on the one-step prediction of the target state and the one-step prediction of the mean square error matrix.

[0025] Preferably, according to the sampling points and their corresponding weights, the sampling points are propagated using the radar measurement model, and the one-step prediction of the measurement is calculated, including:

[0026] The sampling points are propagated according to the radar measurement model to obtain the predicted measurement sampling points, and the one-step prediction of the measurement is calculated according to the sampling points and their corresponding weights.

[0027] Preferably, using the one-step prediction of the target state and the one-step prediction of the measurement, an uncorrelated transformation function based on the pseudo-pitch angle is designed, including:

[0028] Design the uncorrelated transformation function y k = g(ρ(z k )), where y k is the pseudo-pitch angle at time k, and z k is the independent variable of the uncorrelated transformation function.

[0029] Preferably, the original measurement is dimensionally expanded, and the Gaussian-Hermite quadrature rule is used to calculate the predicted measurement sampling points and the dimensionally expanded one-step prediction of the measurement; the target state estimation and its mean square error matrix at the current time are calculated, that is, the target tracking result at the current time is obtained, including:

[0030] The uncorrelated transformation y k is used to dimensionally expand the original measurement of the radar at the current time to obtain the dimensionally expanded measurement;

[0031] The Gaussian-Hermite quadrature rule is used to calculate the predicted measurement sampling points and the dimensionally expanded one-step prediction of the measurement;

[0032] The target state estimation and its mean square error matrix at the current time are updated, where the target state estimation at the current time is the three-dimensional target tracking result under the condition of missing the radar pitch angle based on the measurement transformation; the mean square error matrix is the target state estimation result, and this matrix reflects the deviation between the estimation result and the true state of the target.

[0033] Due to the above technical solutions adopted by the present invention, it has the following beneficial effects:

[0034] The present invention effectively solves the problems that radar networking is required when using a radar with missing elevation angle measurement for three-dimensional target tracking, and the tracking accuracy is low when using a single radar with missing elevation angle measurement for three-dimensional target tracking. On the one hand, the present invention designs an uncorrelated conversion function based on calculating the pseudo-elevation angle measurement to calculate the uncorrelated conversion regarding the pseudo-elevation angle, thereby effectively solving the problem that radar networking is required when using a single radar with missing elevation angle measurement for target tracking. On the other hand, by using the uncorrelated conversion based on the pseudo-elevation angle to expand the dimension of the original elevation angle missing measurement, it is used to improve the estimation performance of the non-linear structure filter, thereby effectively solving the problem of low accuracy when using a single radar with missing elevation angle measurement for target tracking.

[0035] The present invention comprehensively and completely explores the problem of using a radar with missing elevation angle measurement for three-dimensional target tracking, and effectively solves the problems that radar networking is required when using a radar with missing elevation angle measurement for three-dimensional target tracking and the low accuracy when using a single radar with missing elevation angle measurement for three-dimensional target tracking. The method of the present invention is simple, the physical meaning of the features is clear, it has good real-time performance, and has high reliability and robustness, providing an effective implementation path for realizing three-dimensional target tracking using a single radar with missing elevation angle measurement.

[0036] To make the above objects, features, and advantages of the present invention more obvious and understandable, the following specifically gives preferred embodiments and, in conjunction with the accompanying drawings, the detailed description is as follows. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] The drawings described herein are used to provide a further understanding of the present invention, form a part of this application, and do not constitute an improper limitation to the present invention. In the drawings:

[0038] Figure 1 It is a flowchart of a three-dimensional target tracking method under the condition of missing radar elevation angle based on measurement conversion;

[0039] Figure 2 It is a schematic diagram of a radar measurement model under the condition of missing elevation angle;

[0040] Figure 3 It is a schematic diagram of the relative motion between an aircraft carrying a sensor and a target in a simulation scenario;

[0041] Figure 4 It is a comparison chart of RMSE of position estimation results between the radar three-dimensional target tracking method under the condition of missing elevation angle based on measurement conversion proposed by the present invention and the traditional target tracking method;

[0042] Figure 5 It is a comparison chart of RMSE of speed estimation results between the radar three-dimensional target tracking method under the condition of missing elevation angle based on measurement conversion proposed by the present invention and the traditional target tracking method. Detailed implementation manners

[0043] The present invention will be described in detail below in conjunction with the accompanying drawings and specific embodiments. The illustrative embodiments and descriptions of the present invention herein are used to explain the present invention, but are not intended to limit the present invention.

[0044] A three-dimensional target tracking method based on measurement conversion under the condition of missing radar elevation angle provided by the present invention has an implementation process as Figure 1 shown, including the following steps:

[0045] S101: Establish a radar measurement model.

[0046] In this embodiment, establishing a radar measurement model is used, on the one hand, to describe the measurement model of a radar with missing elevation angle measurement, and on the other hand, to provide a calculation basis for the one-step prediction of the measurement required for the uncorrelated conversion filter.

[0047] The specific method for establishing the radar measurement model is as follows:

[0048] 11) The radar measurement components under the condition of missing elevation angle include the distance r and the azimuth angle The schematic diagram of the radar measurement model is as Figure 2 shown, and the measurement model is

[0049]

[0050] In the formula, x k is the target state at time k, is the position of the radar at time k; (x k , y k , z k ) is the position of the target at time k; r k is the distance measurement between the target and the radar at time k; is the azimuth measurement at time k; h k (·) is the measurement function; is the measurement noise subject to Gaussian distribution, where,

[0051] S102: Construct a target dynamic model.

[0052] In this embodiment, establishing a target dynamic model is used, on the one hand, to describe the motion characteristics of the target to be tracked, and on the other hand, to provide a calculation basis for the one-step prediction of the target state required for the uncorrelated conversion filter.

[0053] The constructed target dynamic model is:

[0054] x k = f k-1 (x k-1 , wk-1 )

[0055] Wherein, x k is the target motion state at time k; x k-1 is the target motion state at time k-1; f k-1 (·) is the state transition function; w k-1 is the process noise at time k-1, where

[0056] f k-1 (·) needs to be set according to the actual motion of the target. If the target is in uniform linear motion, then f k-1 (·) is as follows:

[0057] x k = f k-1 (x k-1 , w k-1 ) = F k-1 x k-1 + G k-1 w k-1

[0058] Wherein, F k-1 is the state transition matrix; G k-1 is the process noise transition matrix; F k-1 and G k-1 are as follows:

[0059]

[0060] In the above formula, T is the sampling period.

[0061] S103: Adopt the unscented transformation rule, and based on the target state estimate at the previous moment, its mean square error matrix and the target dynamic model, perform one-step prediction of the target state and its mean square error matrix.

[0062] In this embodiment, for one-step prediction of the target motion state and its mean square error matrix, based on the target state estimate at the previous moment, its mean square error matrix and the target dynamic model, calculate the one-step prediction of the target state and the one-step prediction of its mean square error matrix required for the uncorrelated transformation filter.

[0063] The specific method of one-step prediction is as follows:

[0064] 31) Use the process noise mean 0 and its covariance matrix Q k-1 to expand the dimensions of the target state estimation result at time k-1 and its mean square error matrix P k-1 respectively, as follows:

[0065]

[0066] According to and calculate the sampling points using unscented transformation and their corresponding weights as shown in the following formula:

[0067]

[0068] where N is the number of sampling points, N = 2n + 1; n is the dimension of is the upper triangular matrix after Cholesky decomposition; i identifies the i-th column of the matrix; take λ = 3 - n, α = 1, β = 0.

[0069] 32) Propagate the sampling points using the target dynamic model to obtain the predicted state sampling points, as shown below:

[0070]

[0071] where is the first n x terms of is the last n w terms of x n k-1 is the dimension of state x w n k-1 is the dimension of process noise w The corresponding weights of the predicted sampling points are the same as and

[0072] 33) Calculate the one-step prediction of the target state and the one-step prediction of the mean square error matrix as shown in the following formula:

[0073]

[0074]

[0075] where P k|k-1 is the one-step prediction of the target state mean square error matrix, and are the weights calculated by unscented transformation, i represents the i-th sampling point or the i-th weight, N is the total number of sampling points and weights, is the predicted state sampling point, is the one-step prediction of the target state.

[0076] S104: The radar receives the measurement at the current moment from the target.

[0077] S105: Using the Gauss-Hermite quadrature rule, calculate the sampling points and weights according to the one-step prediction information of the target.

[0078] In this embodiment, the Gauss-Hermite quadrature rule is used to calculate the sampling points and weights, providing necessary information for subsequent calculation of the one-step prediction of the measurement using the Gauss-Hermite quadrature rule.

[0079] The specific method for calculating the sampling points and weights using the Gauss-Hermite quadrature rule is as follows:

[0080] 51) The first few Hermite polynomials are

[0081]

[0082] Higher-order Hermite polynomials can be obtained through the following recursive method, which is

[0083] H m+1 (x) = xH m (x) - mH m-1 (x)

[0084] Therefore, the m-th order Hermite polynomial can be defined as

[0085]

[0086] By solving the roots of the m-th order Hermite polynomial, the integration points χ i can be obtained, and their corresponding weights are

[0087]

[0088] 52) After obtaining the integration points for each dimension through the Gauss-Hermite quadrature rule, perform permutations and combinations to obtain the integration points in vector form;

[0089] For the Gauss-Hermite quadrature problem in vector form, it can be obtained by permuting and combining the one-dimensional integration points χ i , that is

[0090]

[0091] where n x is the dimension of the vector after expanding the one-step prediction of the state using the mean of the measurement noise for the one-step prediction of the state , that is, the dimension of the vector shown as follows:

[0092]

[0093] The integration points s i correspond to the weights wi For the one-dimensional integration point χ that constitutes it ij The corresponding weight l ij The product is as follows:

[0094]

[0095] 53) Obtain the sampling points according to the one-step prediction of the target state, the one-step prediction of the mean square error matrix, and the integration points As follows:

[0096]

[0097] In the formula, s i Is the i-th sampling point; Is the one-step prediction state And the mean of the measurement noise The vector after dimension expansion; Is the covariance matrix R of the measurement noise used k To expand the one-step prediction P of the mean square error matrix k|k-1 The expanded matrix, The specific form is as follows:

[0098]

[0099] The corresponding weight w i Is exactly s i The corresponding weight.

[0100] S106: Propagate the sampling points using the radar measurement model and perform one-step measurement prediction.

[0101] In this embodiment, the sampling points are propagated using the radar measurement model, and combined with the corresponding weights of the sampling points. According to the Gauss-Hermite quadrature rule, the one-step measurement prediction can be calculated. The one-step measurement prediction is one of the information required for the non-correlated transformation filter.

[0102] The method for propagating the sampling points using the radar measurement model to perform one-step measurement prediction is as follows:

[0103] 61) Use the radar measurement model h k (x k ,v k ) to propagate the sampling points, and the predicted measurement sampling points are obtained as follows:

[0104]

[0105] In the formula, Is The first n x Items, Is The last nv items, where n x is the dimension, n v is the measurement noise v k the dimension, h k (·) is the measurement function.

[0106] The predicted measurement sampling points The corresponding weight w i and the sampling points have the same corresponding weight.

[0107] 62) Calculate the one-step measurement prediction as follows through the predicted measurement sampling points and the corresponding weights of the sampling points:

[0108]

[0109] In the formula, N 2 is the number of sampling points, is the predicted measurement sampling point, w i is the weight.

[0110] S107: Design an uncorrelated conversion function based on the pseudo-pitch angle.

[0111] In this embodiment, an uncorrelated conversion function based on the pseudo-pitch angle is designed. In the subsequent uncorrelated conversion filtering step, the original measurement is dimension-expanded using the uncorrelated conversion based on the pseudo-pitch angle, which can improve the estimation performance of the original filter.

[0112] Design the uncorrelated conversion function based on the pseudo-pitch angle as follows:

[0113] y k = g(ρ(z k ))

[0114]

[0115] In the above formula, y k is the uncorrelated conversion based on the pseudo-pitch angle at time k, is the preliminary estimated target motion state, z k is the target measurement received by the radar at time k, K k is the gain matrix, which describes the utilization rate of the measurement information;

[0116] where, P xz and P z are as follows:

[0117]

[0118] S108: Calculate the decorrelation transformation through a decorrelation transformation function based on the pseudo-pitch angle, expand the dimension of the original measurement, and use the Gauss-Hermite quadrature rule to calculate the predicted measurement sampling points and the one-step prediction of the expanded measurement; calculate the target state estimation and its mean square error matrix at the current moment, and update the target state estimation result.

[0119] In this embodiment, based on the calculation results of the above steps and the decorrelation transformation filtering theory, estimate the motion state and its mean square error matrix of the target at the current moment.

[0120] Update the target state estimation result, and the specific method is as follows:

[0121] 81) Use the decorrelation transformation obtained in the previous step to expand the dimension of the original measurement to obtain the expanded measurement.

[0122] Adopt the decorrelation transformation y based on the pseudo-pitch angle k for the radar original measurement z k to expand the dimension and obtain the expanded measurement as shown in the following formula:

[0123]

[0124] 82) Use the Gauss-Hermite quadrature rule to calculate the relevant first and second moments required for estimation.

[0125] Among them, the specific process of calculating the relevant first and second moments required for estimation in step 82) is as follows:

[0126] 821) Calculate the one-step prediction of the expanded measurement as shown in the following formula:

[0127]

[0128] In the formula, is the predicted measurement sampling point after dimension expansion, as shown below:

[0129]

[0130] In the formula, is the predicted measurement sampling point, is the predicted decorrelation transformation sampling point;

[0131] The calculation is as follows:

[0132]

[0133] Among them, can be calculated through the following formula:

[0134]

[0135] 822) Calculate the covariance matrix of the augmented measurement one-step prediction, the one-step prediction of the target state, and the cross-covariance matrix between the one-step prediction of the target state and the one-step prediction of the augmented measurement. The specific calculations are as follows:

[0136]

[0137] 83) Calculate the target state estimate and its mean square error matrix at the current time:

[0138] The final estimate of the target state at the current time is:

[0139]

[0140] In the formula, is the one-step prediction of the target state, is the cross-covariance matrix between the one-step prediction of the target state and the one-step prediction of the augmented measurement, is the covariance matrix of the augmented measurement one-step prediction, is the augmented measurement, is the one-step prediction of the augmented measurement;

[0141] The mean square error matrix P of the target state estimate at the current time k is:

[0142]

[0143] In the formula, P k|k-1 is the one-step prediction of the target state mean square error matrix, is the cross-covariance matrix between the one-step prediction of the target state and the one-step prediction of the augmented measurement, is the covariance matrix of the augmented measurement one-step prediction.

[0144] Among them, is the target state estimate result at the current time, that is, the three-dimensional target tracking result under the condition of missing radar pitch angle based on measurement conversion; P k is the mean square error matrix of the target state estimate result, which reflects the deviation between the estimate result and the true target state.

[0145] The following further illustrates the present invention through specific embodiments.

[0146] S101: Establish a radar measurement model h k (·);

[0147] S102: Construct a target dynamic model x k = f k-1 (x k-1 , w k-1 ) = F k-1 x k-1 + Gk-1 w k-1 , where x k is the target motion state at time k; x k-1 is the target motion state at time k-1; f k-1 (·) is the state transition function; w k-1 is the process noise at time k-1, and the state transition matrix F k-1 and the process noise transition matrix G k-1 are as follows:

[0148]

[0149] In the above formula, the sampling period T = 0.1s.

[0150] S103: Based on the target state estimation information at the previous moment and its mean square error matrix P k-1 , using the state transition function f k-1 (·), perform a one-step prediction to calculate the one-step state prediction and the one-step mean square error matrix prediction P k|k-1 .

[0151] S104: The radar receives the measurement from the target at the current moment, i.e., time k;

[0152] S105: Select the Hermite polynomial order m = 3, and use the Gauss-Hermite quadrature rule to calculate the integration points χ i and their corresponding weights l i . By arranging and combining the one-dimensional integration points X i to obtain the integration points in vector form where n x is the mean of the measurement noise For the one-step state prediction after dimension expansion, the vector The dimension of, the integration point s i The corresponding weight is w i . According to the measurement noise covariance matrix R k For the one-step mean square error matrix prediction P k|k-1 The expanded matrix And the integration point s i , obtain the sampling points The sampling points The weight of is the same as the weight of its corresponding integration point s i , both are w i ;

[0153] S106: Use the radar measurement model h k (·) to propagate the sampling points Obtain the predicted measurement sampling points Predicted measurement sampling points Corresponding weights and sampling points The weights are the same, all being w i . Calculate the one-step measurement prediction as

[0154] S107: Design an uncorrelated conversion function based on the pseudo-pitch angle, and calculate the uncorrelated conversion y at time k k ;

[0155] S108: Calculate the uncorrelated conversion y through the uncorrelated conversion function based on the pseudo-pitch angle k , expand the dimension of the original measurement z k , use the Gauss-Hermite quadrature rule to calculate the predicted measurement sampling points and the one-step prediction of the expanded measurement; calculate the target state estimation at the current moment and its mean square error matrix, and update the target state estimation result.

[0156] Figure 3 The simulation scenario shown includes an aircraft equipped with a single radar with missing pitch angle measurement and a target aircraft, and the simulation duration is 100 seconds. At the beginning of the simulation, the aircraft equipped with the radar with missing pitch angle measurement moves at a constant velocity (Constant Velocity, CV) with a speed of (20 m / s, 0 m / s, 0 m / s) in the horizontal plane from the position of (0 m, 150 m, 25 m); from the 30th second to the 70th second of the simulation, the aircraft successively makes constant turn rate (Constant Turn rate, CT) motion, CV motion and CT motion to increase the aircraft altitude; after the 70th second of the simulation, the aircraft continues to make CV motion. The target aircraft moves at a constant velocity with a speed of (0 m / s, -20 m / s, 0 m / s) from the position of (2000 m, 100 m, 30 m) since the start of the simulation, and the process noise covariance matrix Q = diag[1 1 1]×10 -6 (m / s 2 ) 2 . During the simulation process, the radar sampling period T = 0.1 s is set, and the measurement noise wherein,

[0157] Figure 4 The root mean square error is used to compare the traditional target tracking method and the target tracking method based on measurement conversion proposed by the present invention. The accuracy of the position tracking results is mainly compared, and the traditional target tracking methods selected are the extended Kalman filter and the unscented filter. Figure 4 Shows the root mean square error of the target position tracking results after 100 Monte Carlo experiments of the traditional target tracking method and the method proposed by the present invention in Figure 3 the scenario shown. FromFigure 4 It can be clearly seen that when the method of the present invention is used to perform three-dimensional tracking on a target under the condition of using a single radar with missing pitch angle measurement, the target tracking position accuracy is much higher than that of the traditional method.

[0158] Figure 5 The root mean square error is used to compare the traditional target tracking method and the target tracking method based on measurement transformation proposed by the present invention. The accuracy of the speed tracking results is mainly compared, and the selected traditional target tracking methods are extended Kalman filter and unscented filter. Figure 5 shows the root mean square error of the target speed tracking results after 100 Monte Carlo experiments for the traditional target tracking method and the method proposed by the present invention in the Figure 3 scenario shown. It can be clearly seen from Figure 5 that when the method of the present invention is used to perform three-dimensional tracking on a target under the condition of using a single radar with missing pitch angle measurement, the target tracking speed accuracy is much higher than that of the traditional method.

Claims

1. A three-dimensional target tracking method based on measurement conversion under the condition of missing radar pitch angle, characterized in that: include: Establish radar measurement model and target dynamic model under the condition of missing pitch angle; Adopting the unscented transformation rule, the target state and its mean square error matrix are predicted in one step according to the target state estimation and its mean square error matrix at the previous moment and the target dynamic model; The radar receives current moment measurements from the target; The Gauss-Hermitian quadrature rule is used to calculate the sampling points and their corresponding weights according to the target one-step prediction information; According to the sampling points and their corresponding weights, the radar measurement model is used to propagate the sampling points and perform one-step measurement prediction; By using the one-step prediction of target state and the one-step prediction of measurement, an uncorrelated transfer function based on pseudo pitch angle is designed. The uncorrelated transformation is calculated by the uncorrelated transformation function based on the pseudo pitch angle, the original measurement is expanded, and the predicted measurement sampling points and the expanded measurement one-step prediction are calculated by using the Gauss-Hermite quadrature rule; Calculate the target state estimation and its mean square error matrix at the current moment, and get the target tracking result at the current moment.

2. The three-dimensional target tracking method according to claim 1, characterized in that: The radar measurement model under the condition of missing pitch angle is established as follows: In the formula, x k is the target state at time k; is the position of the radar at time k; (x k ,y k ,z k ) is the target location at time k; r k is the distance measurement between the target and the radar at time k; is the azimuth measurement at time k; h k (·) is the measurement function; v k is the measurement noise that obeys Gaussian distribution.

3. The three-dimensional target tracking method according to claim 1, characterized in that: The target dynamic model is: x k =f k-1 (x k-1 ,w k-1 ) In the formula, x k-1 is the target motion state at time k-1; f k-1 (·) is the state transition function; w k-1 is the process noise at time k-1.

4. The three-dimensional target tracking method according to claim 1, characterized in that: Adopting the unscented transformation rule, based on the target state estimation and its mean square error matrix at the previous moment and the target dynamic model, the target state and its mean square error matrix are predicted in one step, including: The process noise mean and its covariance matrix are used to expand the dimension of the target state estimation result and its mean square error matrix at time k-1 respectively; According to the target state estimation result at time k-1 after dimension expansion and its mean square error matrix, the sampling points and their corresponding weights are calculated using unscented transformation; Propagate sampling points using the target dynamic model to obtain predicted state sampling points; Using the predicted state sampling points and weights, the one-step prediction of the target state and the one-step prediction of the mean square error matrix are calculated.

5. The three-dimensional target tracking method according to claim 4, characterized in that: Using the predicted state sampling points and weights, the one-step prediction of the target state and the one-step prediction of the mean square error matrix are calculated as follows: Where P k|k-1 is the target state mean square error matrix for one-step prediction, and is the weight calculated by untraceable transformation, i represents the ith sampling point or the ith weight, N is the total number of sampling points and weights, is the predicted state sampling point, One-step prediction for the target state.

6. The three-dimensional target tracking method according to claim 1, characterized in that: The Gauss-Hermitian quadrature rule is used to calculate the sampling points and their corresponding weights according to the target one-step prediction information, including: By solving the m-order Hermitian polynomial, we can get the integral points and the corresponding weights; By arranging and combining the integral points, the sampling points are obtained according to the one-step prediction of the target state and the one-step prediction of the mean square error matrix. as follows: In the formula, s i is the i-th integral point obtained after permuting and combining the integral points; is the mean value of the measurement noise One-step prediction of the state The vector after expansion; is the measurement noise covariance R k One-step prediction of the mean square error matrix P k|k-1 The matrix after expansion.

7. The three-dimensional target tracking method according to claim 1, characterized in that: Using the radar measurement model to propagate sampling points for one-step measurement prediction, including: Using the radar measurement model to propagate the sampling points, the predicted measurement sampling points are: In the formula, for The first n x Item, n x for The dimension of for The last n v Item, n v is the measured noise v k The dimension, h k (·) is the measurement function; The measurement one-step prediction is Where N2 is the number of sampling points, is the predicted measurement sampling point, w i is the weight.

8. The three-dimensional target tracking method according to claim 1, characterized in that: The uncorrelated transfer function based on the pseudo-pitch angle is as follows: y k =g(ρ(z k )) In the formula, y k is the uncorrelated transformation based on the pseudo pitch angle at time k, z k is the target measurement received by the radar at time k, One-step prediction state for the target, is the initial estimated target motion state, z k is the original radar measurement, K k is the gain matrix.

9. The three-dimensional target tracking method according to claim 1, characterized in that: Expand the original measurement and use the Gauss-Hermitian quadrature rule to calculate the predicted measurement sampling points and the expanded measurement one-step prediction, including: Adopting an uncorrelated transformation y based on pseudo-pitch angle k The original radar measurement z k Perform dimension expansion to obtain dimension expansion measurement Using the Gauss-Hermite quadrature rule, calculate the one-step prediction of the expanded dimension measurement Where N2 is the number of sampling points, w i is the integral point s i The corresponding weights, The measurement sampling points for the prediction after dimension expansion: In the formula, is the predicted measurement sampling point, The uncorrelated transition sampling points for prediction.

10. The three-dimensional target tracking method according to claim 1, characterized in that: The target state estimation at the current moment for: In the formula, One-step prediction for the target state, is the cross-covariance matrix between the one-step prediction of the target state and the one-step prediction of the expanded measurement, To expand the dimension, measure the one-step prediction covariance matrix, To expand the measurement dimension, One-step prediction for dimension expansion measurement; The mean square error matrix P of the target state estimation at the current moment k for: Where P k|k-1 is the target state mean square error matrix for one-step prediction, is the cross-covariance matrix between the one-step prediction of the target state and the one-step prediction of the expanded measurement, One-step prediction covariance matrix for the expanded dimension measure.

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