CN113536707A - A method for estimating and compensating error slope of aircraft seeker radome based on Gaussian process regression - Google Patents

A method for estimating and compensating error slope of aircraft seeker radome based on Gaussian process regression Download PDF

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CN113536707A
CN113536707A CN202110828849.8A CN202110828849A CN113536707A CN 113536707 A CN113536707 A CN 113536707A CN 202110828849 A CN202110828849 A CN 202110828849A CN 113536707 A CN113536707 A CN 113536707A
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陆科林
符启恩
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Abstract

本发明公开了一种基于高斯过程回归的飞行器导引头天线罩误差斜率估计与补偿方法，针对仅有视线角测量的受天线罩误差影响的飞行器制导系统，建立了飞行器动力学模型，使用交互式多模型滤波方法对制导过程中各状态进行估计，基于高斯过程回归模型建立飞行器视角和天线罩误差角之间的映射关系，并基于高斯过程模型的导数得到天线罩误差斜率的解析表达形式，最后用于飞行器导引头天线罩误差的补偿，从而有效提高了制导性能。

Figure 202110828849

The invention discloses a method for estimating and compensating the error slope of an aircraft seeker radome based on Gaussian process regression. Aiming at the aircraft guidance system affected by the radome error only measured by the line of sight angle, an aircraft dynamics model is established, and an interactive The multi-model filtering method is used to estimate each state in the guidance process, and the mapping relationship between the aircraft viewing angle and the radome error angle is established based on the Gaussian process regression model, and the analytical expression of the radome error slope is obtained based on the derivative of the Gaussian process model. Finally, it is used to compensate the error of the radome of the aircraft seeker, thereby effectively improving the guidance performance.

Figure 202110828849

Description

Aircraft seeker radome error slope estimation and compensation method based on Gaussian process regression
Technical Field
The invention relates to the field of aircraft guidance, in particular to an aircraft seeker radome error slope estimation and compensation method based on Gaussian process regression.
Background
In aircraft guidance missions, radomes are often used to protect aircraft seeker antennas from air currents while reducing aerodynamic drag on aircraft flight. However, the radome refracts electromagnetic wave signals entering the seeker, so that the line-of-sight angle measurement obtained by the seeker deviates, parasitic loops are generated in the aircraft guidance system, and the guidance system is unstable. The method for reducing the influence of errors brought by the antenna housing is mainly divided into three categories, the first category is a hardware-based compensation method, namely, the process processing is carried out by the method of inner profile surface grinding and the like when the antenna housing is manufactured; the second type is that the error angle and the error slope of the antenna housing are directly measured and directly compensated during guidance; the last type is estimation and compensation of the error of the antenna housing on the algorithm level, and the traditional method comprises compensation by using a jitter signal and a low-pass filter, online measurement compensation based on Kalman filtering and multi-model filtering methods, compensation of the error angle of the antenna housing based on a neural network and the like. In recent years, the research on the antenna housing error compensation algorithm is further promoted by the development of technologies such as machine learning and adaptive filtering.
A Loop-Shaping method based on the Radome error compensation method is disclosed in "Loop-Shaping Approach to Mitigate antenna errors in Home issues", which is disclosed in Journal of guidelines, Control, and Dynamics (Klein, I.and Russak, I.,2017.Loop-Shaping Approach to mit antenna errors in homes, Journal of guidelines, Control, and Dynamics,40(7), pp.1789-1795.) to reduce the influence of Radome errors and improve the stability margin of the system by adding a phase lead compensation Loop between the Guidance law and the flight Control system in the Guidance Loop. Time-Varying radar Slope Estimation for Passive antenna cancellation-Ship mismatches, IEEE 58 Conference on Decision and Control (CDC) (Ra, w.s., Ahn, s., Lee, y.and whisg, i.h.,2019, Decumber. Time-Varying radar Slope Estimation for Passive antenna cancellation-Ship mismatches. in 2019 IEEE 58 Conference on Decision and Control (CDC) (pp.4940-4945) discloses a method for compensating for antenna cover errors based on a dither signal and a Time Varying kalman filter, wherein a bandpass filter is used to extract the influence of the dither signal on the line angle, and the Estimation and compensation of errors are combined with filtering. An antenna housing aiming error compensation method based on an EKF technology is disclosed in the systematic simulation science newspaper (Zhou di yearn, Li Junlong, Yuanyuqi, a radar seeker antenna housing slope error real-time estimation method [ J ]. modern defense technology 2020,48(05):1-9.) and an antenna housing error compensation method based on an extended Kalman filter is disclosed, the antenna housing error slope is established as a system state, and estimation is carried out by using an extended Kalman filtering algorithm, so that further compensation is carried out. However, the method based on the traditional filtering and control theory needs to accurately model the system model, the error of the model can generate great influence on the guidance effect, and an accurate dynamic model is often difficult to obtain in practice.
In recent years, a radome error estimation and compensation method based on data has been developed. Adaptive Scale Factor Compensation for satellites with satellite vectors, and arXiv (Gaudet, b.,2020.Adaptive Scale Factor Compensation for satellites with satellite vectors Predictive Coding. arXiv Predictive Coding: 2009.00975.) disclose a Predictive Coding method based on a Predictive Coding method, which predicts a radome error angle using a recurrent neural network, adaptively corrects an observation signal, and compensates in an aircraft guidance system. However, the above method has the disadvantage that it requires a large amount of computation and is difficult to implement well in an aircraft guidance mission with a very high real-time requirement.
The Gaussian process is a non-parameterized machine learning model, and compared with a neural network, the posterior covariance obtained in the Gaussian process model prediction can be used as the measurement of the model accuracy, and the model is flexibly applied to model application and has natural advantages. Meanwhile, the data required for training the Gaussian process model is relatively less. A nonlinear filtering method based on Gaussian process is disclosed in IEEE Transactions on Automatic Control (J.Pruher and O.Straka, "Gaussian process motion transform," IEEE Transactions on Automatic Control, vol.63, No.9, pp.2844-2854,2017.), fitting a system dynamics model and a measurement model by using the Gaussian process, performing a statistical moment conversion step in the filtering process based on an identified posterior model of the Gaussian process, and combining a traditional Bayesian filtering framework to be applied to tracking a moving target. However, the method and other control and filtering methods based on the Gaussian process are limited to algorithm improvement, and the combination of the method and the control and filtering method applied to the field of aircraft guidance is not seen.
In the existing error estimation and compensation method for the aircraft guidance antenna housing, a hardware-based method is limited by a process level and needs to be balanced with the protection effect of the antenna housing, and the measurement-based method has high requirements on a sensor for accurately measuring the error of the antenna housing; the methods for compensating at the algorithm level are mostly limited by the accuracy of the system model, and the methods based on data are relatively few and difficult to meet the real-time requirement. At present, no radome error compensation method capable of well applying an unparameterized Bayesian machine learning method such as a Gaussian process model exists.
Disclosure of Invention
The purpose of the invention is as follows: the invention aims to provide an aircraft seeker radome error slope estimation and compensation method based on Gaussian process regression, which is accurate and effective and can carry out online estimation and real-time compensation on seeker radome errors.
The technical scheme is as follows: the invention relates to an aircraft seeker radome error slope estimation and compensation method based on Gaussian process regression, which comprises the following steps:
(1) establishing an aircraft guidance dynamic model and a measurement model influenced by a seeker antenna housing error;
(2) estimating each state in the guidance process of the aircraft based on an interactive multi-model filtering method;
(3) based on a Gaussian process regression method, establishing a mapping relation between an aircraft view angle and an antenna housing error angle, and obtaining an antenna housing error slope;
(4) and compensating the error slope of the antenna housing in the process of manufacturing and guiding based on the established Gaussian process regression model.
Further, the step (1) includes the steps of:
(11) establishing an aircraft guidance dynamics model
The aircraft guidance task is guided by using a proportional guidance method, and a first-order flight control system is configured. The target line-of-sight angle measured by the seeker of the aircraft can generate certain deviation under the influence of the seeker radome, namely a radome error angle, and the expression of the error angle is
Figure BDA0003174750030000035
Figure BDA0003174750030000031
Wherein λ isrIs the radome error angle, thetasIs the angle of view, λ is the target line of view angle, θMIs the projectile attitude angle.
Defining the radome error slope as
Figure BDA0003174750030000032
A geometric diagram of an aircraft seeker with radome error is shown in fig. 1. Can establish a system dynamics model as
Figure BDA0003174750030000033
Wherein
Figure BDA0003174750030000034
Is the system state, R is the distance between the aircraft and the target, γMIs the aircraft flight path angle, AMIn order to be the actual guidance instruction of the aircraft,
Figure BDA0003174750030000041
for the kinetic equation, it was constructed as follows
Figure BDA0003174750030000042
Figure BDA0003174750030000043
Figure BDA0003174750030000044
Figure BDA0003174750030000045
Wherein VMFor aircraft speed, N is the proportional guidance factor, τ is the autopilot time constant, TαIs the time constant of the rate of change of heading,
Figure BDA0003174750030000046
the estimated value of the error slope of the antenna housing is obtained. The aircraft guidance loop including the dynamics model is shown in fig. 2.
(12) Establishing an aircraft guidance measurement model
The aircraft only has a target line-of-sight angle measured value, and a measurement model is established by considering the influence of an error angle of the antenna housing
Figure BDA0003174750030000047
Wherein v iskN (0, R) is measurement noise, h (x)k；ρθ,k) To be a measurement equation
Figure BDA0003174750030000048
Further, the step (2) comprises the steps of:
(21) discretized system dynamics model
Discretizing the aircraft guidance dynamic model established in the step (1) based on a four-order Runge Kutta method, namely discretizing the aircraft guidance dynamic model
xk+1＝φ(xk；Δt,ρθ,k)+wk
Wherein wkN (0, Q) is the process noise, representing the discretization error, and Q is its covariance matrix.
(22) Setting local filtering model
Building multiple local filtering models using a set of preset radome error slope values, i.e.
Figure BDA0003174750030000049
For each error slope parameter value
Figure BDA00031747500300000410
Establishing corresponding dynamic and measurement model
Figure BDA0003174750030000051
Figure BDA0003174750030000052
And carrying out filtering estimation on each model by using an unscented Kalman filtering algorithm.
(23) Hybrid local estimation results
Calculating a mixed estimation mean and covariance as estimation results of the multi-model filtering method based on the local model filtering results obtained in the step (22), that is
Figure BDA0003174750030000053
Figure BDA0003174750030000054
Wherein
Figure BDA0003174750030000055
And Pk|kIs the k stepThe estimated mean and covariance of the time,
Figure BDA0003174750030000056
and
Figure BDA0003174750030000057
for the estimated value obtained by the ith local filter,
Figure BDA0003174750030000058
and the model probability corresponding to the ith local model. A schematic diagram of the interactive multi-model filtering method is shown in fig. 3.
(24) Calculating estimated view angle and radome error
According to the multi-model filtering estimation result obtained in the step (23)
Figure BDA0003174750030000059
Computing an estimated view angle
Figure BDA00031747500300000510
As follows
Figure BDA00031747500300000511
Calculating and estimating antenna housing error angle
Figure BDA00031747500300000512
As follows
Figure BDA00031747500300000513
Further, the step (3) includes the steps of:
(31) establishing a Gaussian process regression model from a visual angle to an antenna housing error angle
Using vr,i～N(0,rr,i) Representing the estimation error between the estimated antenna housing error angle and the actual antenna housing error angle in the ith step to obtain the relation between the estimated antenna housing error angle and the estimated visual angle
Figure BDA00031747500300000514
Figure BDA00031747500300000515
Considering arbitrary perspective input
Figure BDA00031747500300000516
The corresponding required predicted error angle of the antenna housing is
Figure BDA00031747500300000517
Establishing
Figure BDA00031747500300000518
And λr,jGaussian process prior distribution between
Figure BDA0003174750030000061
Wherein
Figure BDA0003174750030000062
Is a prior mean, K is a covariance matrix, formed by a covariance function K (x)1,x2) The components of the composition are as follows,
Figure BDA0003174750030000063
based on training data of the estimated radome error angle and the estimated view angle, the posterior distribution of the radome error angle to be predicted can be obtained
Figure BDA0003174750030000064
Wherein
Figure BDA0003174750030000065
Figure BDA0003174750030000066
(32) Calculating radome error slope
The obtained posterior distribution of the Gaussian process is subjected to derivation to obtain any input
Figure BDA0003174750030000067
The error slope of the radome is
Figure BDA0003174750030000068
Wherein
Figure BDA0003174750030000069
Further, the step (4) comprises the steps of:
(41) calculating a corrected line-of-sight angular rate
Constructing a corrected line-of-sight angular rate according to the estimated radome error slope obtained in the step (3)
Figure BDA00031747500300000610
Based on the relationship between the measured line-of-sight angular rate and the actual line-of-sight angular rate
Figure BDA00031747500300000611
Obtaining a corrected line-of-sight angular rate of
Figure BDA00031747500300000612
The aircraft guidance loop after line-of-sight angular rate correction is shown in FIG. 4.
(42) Calculating and correcting actual guidance instruction of aircraft
Based on the estimated value of each state of the guidance system obtained in the step (2)
Figure BDA00031747500300000613
Calculating to obtain a corrected aircraft actual guidance instruction in discrete time
Figure BDA00031747500300000614
Wherein
Figure BDA0003174750030000071
And using the corrected guidance instruction to complete the compensation of the error slope of the antenna housing. An overall schematic of the estimation and compensation of the radome error slope is shown in fig. 5.
Has the advantages that: compared with a method for designing and polishing from a hardware level, the method does not need to rely on a process level and does not need to consider the balance with the radome protection effect, compared with a method for directly measuring the radome error, the method does not need to be provided with such a sensor with strict requirements, and is easier to realize.
Drawings
FIG. 1 is a geometric block diagram of an aircraft seeker;
FIG. 2 is a diagram of an uncompensated aircraft guidance loop using proportional guidance;
FIG. 3 is a schematic diagram of an interactive multi-model filtering algorithm used in the present invention;
FIG. 4 is a diagram of an aircraft guidance loop after line-of-sight angular rate correction;
FIG. 5 is a general schematic diagram of a method for estimating and compensating an error slope of an antenna radome in accordance with the present invention;
FIG. 6 is a schematic diagram of a mean square error estimation of the line-of-sight angle of an aircraft guidance system;
FIG. 7 is a schematic diagram of an aircraft guidance system aircraft relative distance estimation mean square error with a target;
FIG. 8 is a schematic diagram of a mean square error estimation of a flight path angle for an aircraft guidance system;
FIG. 9 is a schematic diagram of an estimated mean square error of an actual guidance instruction for an aircraft guidance system;
FIG. 10 is a schematic diagram of a target view true trajectory and an estimated trajectory for an aircraft guidance system;
FIG. 11 is a schematic diagram of an actual trajectory and an estimated trajectory of an error angle of an antenna housing of an aircraft guidance system;
fig. 12 is a schematic diagram of an error slope true trajectory of an antenna cover and an estimated trajectory based on gaussian process regression;
fig. 13 is a gaussian process regression-based radome error slope estimation mean square error;
FIG. 14 is a graph comparing the final guidance miss distance of the proposed method with other compensation methods;
Detailed Description
The technical scheme of the invention is further described in the following by combining the attached drawings and the detailed description.
Initial values considering the aircraft and target states are as follows
Figure BDA0003174750030000081
Figure BDA0003174750030000082
Wherein (X)M,YM) And (X)T,YT) Is the initial position of the aircraft with respect to the target,
Figure BDA0003174750030000083
and
Figure BDA0003174750030000084
for an initial velocity of the aircraft with the target, the target is assumed to be a fixed target. Obtaining the initial state of the guidance system according to the establishment of the dynamic model in the step (2) as follows
Figure BDA0003174750030000085
The corresponding model parameters are as follows
{VM,N,ρθ,τ,Tα}＝{500m/s,4,0.025°/°,0.1s,1s}
In the interactive multi-model filter, the discretization time interval is set to Δ t 0.001s, and the estimated mean and variance of the initial state are
Figure BDA0003174750030000086
Figure BDA0003174750030000087
Where n-3 is the number of guessed models, the transition probability matrix for the Markov chain is as follows
Figure BDA0003174750030000088
In addition, process noise wkHas a covariance matrix Q of
Figure BDA0003174750030000089
Observation noise vkVariance of (R) 1.74532×10-12rad2Is as follows.
Based on the above settings, the states in the aircraft guidance process are estimated according to the steps (1) to (4) and the method shown in fig. 5, and the radome error slope is estimated and compensated. In the gaussian process regression, the prediction of the radome error angle and the estimation of the radome error slope are performed in two ways, namely prediction by using all historical data (full history) and prediction by using sliding window historical data (sliding window), respectively. Fig. 6-9 show the mean square error of each state estimation of the guidance system, fig. 10-11 show the real track and the estimated track of the target view angle and the antenna housing error angle, fig. 12 shows the real value and the estimated value of the antenna housing error slope, fig. 13 shows the mean square error of the antenna housing error slope estimation, it can be seen that better effect can be obtained by using sliding window data to perform gaussian process prediction, and fig. 14 shows the final guidance miss distance after the gaussian process estimation and compensation method provided by the invention is adopted, and the comparison of the guidance miss distance based on the traditional multi-model filter compensation (IMM) and the extended kalman filter compensation (EKF) is carried out under the condition of no compensation. The result shown in the attached drawing shows that the method provided by the invention can effectively improve the estimation precision of each state of the guidance system, can effectively estimate the error slope of the antenna housing, and can obtain a better guidance effect compared with other compensation methods.

Claims (5)

1.一种基于高斯过程回归的飞行器导引头天线罩误差斜率估计与补偿方法；其特征在于：包括以下步骤：1. an aircraft seeker radome error slope estimation and compensation method based on Gaussian process regression; it is characterized in that: comprise the following steps: (1)建立受导引头天线罩误差影响的飞行器的制导动力学模型和测量模型；(1) Establish the guidance dynamics model and measurement model of the aircraft affected by the seeker radome error; (2)基于交互式多模型滤波方法，对飞行器制导过程中各状态进行估计；(2) Based on the interactive multi-model filtering method, each state in the guidance process of the aircraft is estimated; (3)基于高斯过程回归方法，建立飞行器视角和天线罩误差角之间的映射关系，并得到天线罩误差斜率；(3) Based on the Gaussian process regression method, the mapping relationship between the aircraft viewing angle and the radome error angle is established, and the radome error slope is obtained; (4)基于所建立的高斯过程回归模型，在制导过程中对天线罩误差斜率进行补偿。(4) Based on the established Gaussian process regression model, the radome error slope is compensated during the guidance process. 2.根据权利要求1所述的基于高斯过程回归的飞行器导引头天线罩误差斜率估计与补偿方法，其特征在于：所述步骤(1)包括以下步骤：2. The method for estimating and compensating the error slope of an aircraft seeker radome based on Gaussian process regression according to claim 1, wherein the step (1) comprises the following steps: (11)建立飞行器制导动力学模型(11) Establish a dynamic model of aircraft guidance 将所述飞行器制导任务使用比例导引方法进行制导，配置一阶飞行控制系统，飞行器其导引头测量的目标视线角，会受导引头天线罩的影响而产生一定偏差，即天线罩误差角，所述误差角的表达式为The aircraft guidance task is guided by the proportional guidance method, and a first-order flight control system is configured. The target line-of-sight angle measured by the aircraft's seeker will be affected by the seeker radome and produce a certain deviation, that is, the radome error angle, the expression of the error angle is
Figure FDA0003174750020000011
Figure FDA0003174750020000011
Figure FDA0003174750020000012
Figure FDA0003174750020000012
 其中，λr为天线罩误差角，θs为视角，λ为目标视线角，θM为弹体姿态角。定义天线罩误差斜率为Among them, λ r is the radome error angle, θ s is the viewing angle, λ is the target line of sight angle, and θ M is the missile body attitude angle. Define the radome error slope as
Figure FDA0003174750020000013
Figure FDA0003174750020000013
 可建立飞行器制导动力学模型为The aircraft guidance dynamics model can be established as
Figure FDA0003174750020000014
Figure FDA0003174750020000014
 其中
Figure FDA0003174750020000015
为系统状态，R为飞行器和目标间距离，γM为飞行器飞行路径角，AM为飞行器实际制导指令，
Figure FDA0003174750020000016
为动力学方程，其构建如下in
Figure FDA0003174750020000015
is the system state, R is the distance between the aircraft and the target, γ M is the flight path angle of the aircraft, A M is the actual guidance command of the aircraft,
Figure FDA0003174750020000016
is the kinetic equation, which is constructed as follows
Figure FDA0003174750020000017
Figure FDA0003174750020000017
Figure FDA0003174750020000018
Figure FDA0003174750020000018
Figure FDA0003174750020000019
Figure FDA0003174750020000019
Figure FDA0003174750020000021
Figure FDA0003174750020000021
 其中VM为飞行器速度，N为比例导引系数，τ为自动驾驶仪时间常数，Tα为航向变化率时间常数，
Figure FDA0003174750020000022
Figure FDA0003174750020000023
为天线罩误差斜率估计值。where VM is the speed of the aircraft, N is the proportional steering coefficient, τ is the autopilot time constant, T α is the heading rate time constant,
Figure FDA0003174750020000022
Figure FDA0003174750020000023
is an estimate of the radome error slope. (12)建立飞行器制导测量模型(12) Establish an aircraft guidance measurement model 所述飞行器仅有目标视线角测量值，考虑到天线罩误差角的影响，建立飞行器制导测量模型为：The aircraft only has the measurement value of the target line of sight angle. Considering the influence of the error angle of the radome, the aircraft guidance measurement model is established as follows:
Figure FDA0003174750020000024
Figure FDA0003174750020000024
 其中vk～N(0,R)为测量噪声，h(xk；ρθ,k)为测量方程where v k ～N(0, R) is the measurement noise, h(x k ; ρ θ, k ) is the measurement equation
Figure FDA0003174750020000025
Figure FDA0003174750020000025
 3.根据权利要求1所述的基于高斯过程回归的飞行器导引头天线罩误差斜率估计与补偿方法，其特征在于：所述步骤(2)包括以下步骤：3. The method for estimating and compensating the error slope of an aircraft seeker radome based on Gaussian process regression according to claim 1, wherein the step (2) comprises the following steps: (21)离散化系统动力学模型(21) Discretized system dynamics model 基于四阶龙格库塔法，将所述步骤(1)中建立的飞行器制导动力学模型离散化，即Based on the fourth-order Runge-Kutta method, the aircraft guidance dynamics model established in the step (1) is discretized, namely xk+1＝φ(xk；Δt,ρθ,k)+wk x k+1 = φ(x k ; Δt,ρ θ,k )+w k 其中wk～N(0,Q)为过程噪声，代表离散化误差，Q为其协方差矩阵。where w k ~N(0,Q) is the process noise, representing the discretization error, and Q is its covariance matrix. (22)设定局部滤波模型(22) Set the local filter model 使用一组预设定天线罩误差斜率值来构建多个局部滤波模型，即A set of preset radome error slope values are used to build multiple local filtering models, namely
Figure FDA0003174750020000026
Figure FDA0003174750020000026
 针对每个误差斜率参数值
Figure FDA0003174750020000027
建立对应的动力学与测量模型For each error slope parameter value
Figure FDA0003174750020000027
Establish corresponding kinetic and measurement models
Figure FDA0003174750020000028
Figure FDA0003174750020000028
Figure FDA0003174750020000029
Figure FDA0003174750020000029
 使用无迹卡尔曼滤波算法进行各个模型的滤波估计。The filter estimation of each model is performed using the unscented Kalman filter algorithm. (23)混合局部估计结果(23) Mixed local estimation results 根据所述步骤(22)中得到的各局部模型滤波结果，计算混合估计均值和协方差，作为多模型滤波方法的估计结果，即According to the filtering results of each local model obtained in the step (22), the mixed estimated mean and covariance are calculated as the estimated results of the multi-model filtering method, that is,
Figure FDA0003174750020000031
Figure FDA0003174750020000031
Figure FDA0003174750020000032
Figure FDA0003174750020000032
 其中
Figure FDA0003174750020000033
和Pk|k为第k步时的估计均值和协方差，
Figure FDA0003174750020000034
和
Figure FDA0003174750020000035
为第i个局部滤波器得到的估计值，
Figure FDA0003174750020000036
为第i个局部模型对应的模型概率。in
Figure FDA0003174750020000033
and P k|k are the estimated mean and covariance at step k,
Figure FDA0003174750020000034
and
Figure FDA0003174750020000035
is the estimated value obtained for the ith local filter,
Figure FDA0003174750020000036
is the model probability corresponding to the ith local model. (24)计算估计视角和天线罩误差(24) Calculate the estimated viewing angle and radome errors 根据所述步骤(23)中得到的多模型滤波估计结果
Figure FDA0003174750020000037
计算估计视角
Figure FDA0003174750020000038
如下According to the multi-model filtering estimation result obtained in the step (23)
Figure FDA0003174750020000037
Calculate the estimated angle of view
Figure FDA0003174750020000038
as follows
Figure FDA0003174750020000039
Figure FDA0003174750020000039
 计算估计天线罩误差角
Figure FDA00031747500200000310
如下Calculate the estimated radome error angle
Figure FDA00031747500200000310
as follows
Figure FDA00031747500200000311
Figure FDA00031747500200000311
 4.根据权利要求1所述的基于高斯过程回归的飞行器导引头天线罩误差斜率估计与补偿方法，其特征在于：所述步骤(3)包括以下步骤：4. The method for estimating and compensating the error slope of an aircraft seeker radome based on Gaussian process regression according to claim 1, wherein the step (3) comprises the following steps: (31)建立视角到天线罩误差角的高斯过程回归模型(31) Establish a Gaussian process regression model from the viewing angle to the radome error angle 使用vr,i～N(0,rr,i)表示第i步时估计天线罩误差角和实际天线罩误差角之间的估计误差，得到估计天线罩误差角与估计视角之间的关系Use v r,i ~N(0,r r,i ) to represent the estimated error between the estimated radome error angle and the actual radome error angle at the i-th step, and obtain the relationship between the estimated radome error angle and the estimated viewing angle
Figure FDA00031747500200000312
Figure FDA00031747500200000312
Figure FDA00031747500200000313
Figure FDA00031747500200000313
 考虑任意视角输入
Figure FDA00031747500200000314
其对应所需预测的天线罩误差角为
Figure FDA00031747500200000315
建立
Figure FDA00031747500200000316
和λr,j之间的高斯过程先验分布Consider Arbitrary Perspective Input
Figure FDA00031747500200000314
The radome error angle corresponding to the required prediction is
Figure FDA00031747500200000315
Establish
Figure FDA00031747500200000316
Gaussian process prior distribution between and λ r,j
Figure FDA00031747500200000317
Figure FDA00031747500200000317
 其中
Figure FDA00031747500200000318
为先验均值，K为协方差矩阵，由协方差函数k(x1,x2)组成，in
Figure FDA00031747500200000318
is the prior mean, K is the covariance matrix, which consists of the covariance function k(x 1 , x 2 ),
Figure FDA00031747500200000319
Figure FDA00031747500200000319
 基于估计天线罩误差角和估计视角的训练数据，可以得到所需预测的天线罩误差角的后验分布
Figure FDA0003174750020000041
其中Based on the training data of the estimated radome error angle and estimated viewing angle, the posterior distribution of the desired predicted radome error angle can be obtained
Figure FDA0003174750020000041
in
Figure FDA0003174750020000042
Figure FDA0003174750020000042
Figure FDA0003174750020000043
Figure FDA0003174750020000043
 (32)计算天线罩误差斜率(32) Calculate the radome error slope 对所得到的高斯过程后验分布进行求导，可以得到对任意输入
Figure FDA0003174750020000044
其天线罩误差斜率为Derivating the obtained posterior distribution of the Gaussian process, it is possible to obtain for any input
Figure FDA0003174750020000044
Its radome error slope is
Figure FDA0003174750020000045
Figure FDA0003174750020000045
 其中
Figure 1
。in
Figure 1
. 5.根据权利要求1所述的基于高斯过程回归的飞行器导引头天线罩误差斜率估计与补偿方法，其特征在于：所述步骤(4)包括以下步骤：5. The method for estimating and compensating the error slope of an aircraft seeker radome based on Gaussian process regression according to claim 1, wherein the step (4) comprises the following steps: (41)计算修正视线角速率(41) Calculate the corrected line-of-sight angular rate 根据所述步骤(3)中得到的估计天线罩误差斜率，构建修正视线角速率According to the estimated radome error slope obtained in the step (3), the corrected line-of-sight angular rate is constructed
Figure FDA0003174750020000047
Figure FDA0003174750020000047
 根据测量视线角速率和实际视线角速率之间的关系
Figure FDA0003174750020000048
得到修正视线角速率为According to the relationship between the measured line-of-sight angular rate and the actual line-of-sight angular rate
Figure FDA0003174750020000048
The corrected line-of-sight angular rate is obtained as
Figure FDA0003174750020000049
Figure FDA0003174750020000049
 (42)计算修正飞行器实际制导指令(42) Calculate and correct the actual guidance command of the aircraft 基于所述步骤(2)中得到的制导系统各状态估计值
Figure FDA00031747500200000410
计算得到离散时间下的修正飞行器实际制导指令Based on the estimated value of each state of the guidance system obtained in the step (2)
Figure FDA00031747500200000410
Calculate the actual guidance command of the modified aircraft in discrete time
Figure FDA00031747500200000411
Figure FDA00031747500200000411
 其中
Figure FDA00031747500200000412
使用该修正后制导指令，完成天线罩误差斜率的补偿。in
Figure FDA00031747500200000412
Compensation of the radome error slope is completed using the corrected guidance command.
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CN106507895B (en) * 2010-11-29 2014-06-04 中国空空导弹研究院 A kind of seeker antenna cover collimating fault compensation method

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