CN113536707B - Aircraft seeker antenna cover error slope estimation and compensation method based on Gaussian process regression - Google Patents
Aircraft seeker antenna cover error slope estimation and compensation method based on Gaussian process regression Download PDFInfo
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Abstract
The invention discloses an aircraft seeker antenna cover error slope estimation and compensation method based on Gaussian process regression, which aims at an aircraft guidance system which is only measured by a sight angle and is influenced by antenna cover errors, establishes an aircraft dynamics model, estimates each state in the guidance process by using an interactive multi-model filtering method, establishes a mapping relation between an aircraft visual angle and the antenna cover error angle based on the Gaussian process regression model, obtains an analysis expression form of the antenna cover error slope based on the derivative of the Gaussian process model, and is finally used for compensating the aircraft seeker antenna cover errors, thereby effectively improving the guidance performance.
Description
Technical Field
The invention relates to the field of aircraft guidance, in particular to an aircraft seeker antenna cover error slope estimation and compensation method based on Gaussian process regression.
Background
During aircraft guidance tasks, radomes are often used to protect aircraft seeker antennas from airflow while reducing aerodynamic drag of the aircraft flight. However, the radome refracts electromagnetic wave signals entering the seeker, so that the line-of-sight angle measurement obtained by the seeker is deviated, and a parasitic loop is generated in the aircraft guidance system, and the guidance system is unstable. The method for reducing the influence of errors brought by the radome is mainly divided into three types, wherein the first type is a compensation method based on hardware, namely, the method comprises the steps of carrying out technological processing through methods such as inner profile surface grinding and the like when the radome is manufactured; the second type is to directly measure the error angle and the error slope of the antenna housing, and directly compensate the error angle and the error slope during guidance; the last category is to estimate and compensate the error of the radome at the algorithm layer, the traditional method comprises the steps of compensating by using a jitter signal and a low-pass filter, compensating on-line measurement based on a Kalman filtering and multi-model filtering method, compensating the error angle of the radome based on a neural network, and the like. In recent years, the development of techniques such as machine learning and adaptive filtering has further promoted the research of radome error compensation algorithms.
Loop-Shaping Approach to Mitigate Radome Effects in Homing Missiles, in Journal of Guidance, control, and Dynamics (Klein, I.and Rusnak, I.2017. Loop-shaping approach to mitigate radome effects in homing industries. Journal of guides, control, and Dynamics,40 (7), pp.1789-1795.) discloses a radome error compensation method based on a Loop shaping method, which reduces the influence of radome errors by adding a phase lead compensation Loop between a Guidance law and a flight Control system in a manufacturing Loop, and improves the stability margin of the system. Time-Varying Radome Slope Estimation for Passive Homing Anti-clip Missiles, described in conference IEEE 58th Conference on Decision and Control (CDC) (Ra, W.S., ahn, S., lee, Y.and Whang, I.H.,2019,December.Time-Varying Radome Slope Estimation for Passive Homing Anti-clip Missiles.In 2019 IEEE 58th Conference on Decision and Control (CDC) (pp.4940-4945) IEEE.) discloses a radome error compensation method based on dither signals and Time-varying Kalman filters, wherein the influence of the dither signals on the angle of view is extracted using a bandpass filter, and the radome error is estimated and compensated in combination with Kalman filtering. A radome aiming error compensation method based on EKF technology is disclosed in System simulation report (Zhou Di, li Junlong, yuan Yuqi) a real-time estimation method for radome slope error of a radar seeker [ J ]. Modern defense technology, 2020,48 (05): 1-9.), and a radome error compensation method based on an extended Kalman filter is disclosed, wherein the radome error slope is established as a system state, and the estimation is performed by using an extended Kalman filtering algorithm, so that the further compensation is performed. However, the method based on the traditional filtering and control theory needs to accurately model a system model, errors of the model can greatly influence the guidance effect, and an accurate dynamics model is often difficult to obtain in practice.
The data-based radome error estimation and compensation methods have also been developed in recent years. Adaptive Scale Factor Compensation for Missiles withStrapdown Seekers via Predictive Coding, in arXiv (gauset, b.,2020.Adaptive Scale Factor Compensation for Missiles with Strapdown Seekers via Predictive Coding.arXiv preprint arXiv:2009.00975), discloses a radome error compensation method based on a predictive coding method, wherein a cyclic neural network is used to predict a radome error angle, adaptively correct an observed signal, and compensate in an aircraft guidance system. However, the method has the defect of large calculation amount and is difficult to realize well in the aircraft guidance task with very high real-time requirement.
The Gaussian process is a non-parameterized machine learning model, and compared with a neural network, posterior covariance obtained in Gaussian process model prediction can be used as a measure of model accuracy, is flexibly applied to model application, and has natural advantages. At the same time, relatively little data is required to train the gaussian process model. A nonlinear filtering method based on gaussian process is disclosed in Gaussian process quadrature moment transform, in IEEE Transactions on Automatic Control (j. Pruher and o. Straka, "Gaussian process quadrature moment transform," IEEE Transactions on Automatic Control, vol.63, no.9, pp.2844-2854,2017), a system dynamics model and a measurement model are fitted with a gaussian process, a statistical moment conversion step in the filtering process is performed based on a gaussian process posterior model obtained by recognition, and the method is applied in moving object tracking in combination with a conventional bayesian filtering framework. However, this approach, along with other gaussian process based control and filtering approaches, is limited to algorithmic improvements and is not seen in conjunction with applications in the field of aircraft guidance.
In the existing aircraft guidance radome error estimation and compensation method, the hardware-based method is limited by the process level, the balance between the method and the protection effect of the radome is needed, the radome error is accurately measured based on the measurement method, and the requirements on the sensor are high; the method for compensating at the algorithm level is mostly limited by the accuracy of a system model, and the method based on data is relatively less and is difficult to meet the real-time requirement. No radome error compensation method capable of better applying a non-parameterized bayesian machine learning method such as a gaussian process model exists at present.
Disclosure of Invention
The invention aims to: the invention aims to provide an aircraft pilot head antenna cover error slope estimation and compensation method based on Gaussian process regression, which is accurate and effective and can be used for carrying out online estimation and real-time compensation on pilot head antenna cover errors.
The technical scheme is as follows: the invention relates to an aircraft seeker antenna cover error slope estimation and compensation method based on Gaussian process regression, which comprises the following steps:
(1) Establishing an aircraft guidance dynamics model and a measurement model influenced by the error of the seeker radome;
(2) Estimating each state in the aircraft guidance process based on an interactive multi-model filtering method;
(3) Based on a Gaussian process regression method, establishing a mapping relation between an aircraft visual angle and an antenna housing error angle, and obtaining an antenna housing error slope;
(4) And compensating the error slope of the radome in the manufacturing process 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 uses a proportional guidance method to conduct guidance, and a first-order flight control system is configured. The target sight angle measured by the guide head of the aircraft can be influenced by the guide head antenna housing to generate certain deviation, namely an antenna housing error angle, and the expression of the error angle is that
Wherein lambda is r Is the error angle of the radome, θ s For the viewing angle, λ is the target viewing angle, θ M Is the attitude angle of the projectile body.
Defining the error slope of the radome as
A diagram of the geometry of an aircraft introducer with radome error is shown in fig. 1. Can build a system dynamics model into
Wherein the method comprises the steps ofIn the system state, R is the distance between the aircraft and the target, gamma M For the flight path angle of the aircraft, A M Instruction for the actual guidance of the aircraft, < >>Is a kinetic equation constructed as follows
Wherein V is M For aircraft speed, N is the proportional guide coefficient, τ is the autopilot time constant, T α As a time constant for the rate of change of heading,is the antenna housing error slope estimate. The aircraft guidance circuit including the dynamics model is shown in fig. 2.
(12) Establishing an aircraft guidance measurement model
The aircraft only has target sight angle measurement value, and a measurement model is established by considering the influence of the error angle of the radome
Wherein v is k N (0, R) is the measurement noise, h (x) k ；ρ θ,k ) For measuring equation
Further, the step (2) includes the steps of:
(21) Discretized system dynamics model
Discretizing the aircraft guidance dynamics model established in the step (1) based on a fourth-order Dragon-Gregory tower method, namely
x k+1 ＝φ(x k ；Δt,ρ θ,k )+w k
Wherein w is k N (0, Q) is the process noise, representing the discretization error, and Q is its covariance matrix.
(22) Setting local filtering model
Constructing a plurality of local filtering models using a set of preset radome error slope values, i.e.
For each error slope parameter valueEstablishing corresponding powerLearning and measuring model
The unscented kalman filter algorithm is used to perform the filter estimation for each model.
(23) Mixing local estimation results
Calculating a mixed estimation mean and covariance as estimation results of the multi-model filtering method according to the filtering results of the local models obtained in the step (22), namely
Wherein the method comprises the steps ofAnd P k|k For the estimated mean and covariance at the kth step, +.>And->Estimated value for the i-th local filter, is +.>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 an estimated viewing angle and radome error
Based on the multi-model filter estimation result obtained in the step (23)
Calculating an estimated viewing angle->The following are listed below
Calculating an estimated radome error angleThe following are listed below
Further, the step (3) includes the steps of:
(31) Establishing a Gaussian process regression model from the viewing angle to the radome error angle
Using v r,i ～N(0,r r,i ) Representing the estimated error between the estimated radome error angle and the actual radome error angle at the ith step, and obtaining the relation between the estimated radome error angle and the estimated viewing angle
Consider arbitrary perspective inputThe antenna housing error angle corresponding to the required prediction is +.>Build->And lambda (lambda) r,j Gaussian process prior distribution between
Wherein the method comprises the steps ofFor a priori mean, K is the covariance matrix, which is calculated by the covariance function K (x 1 ,x 2 ) The composition of the composite material comprises the components,
based on the 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 obtainedWherein the method comprises the steps of
(32) Calculating error slope of radome
Deriving the obtained Gaussian process posterior distribution to obtain arbitrary inputThe error slope of the antenna housing is as follows
Wherein the method comprises the steps of
Further, the step (4) includes the steps of:
(41) Calculating a corrected gaze angular rate
Constructing a corrected line-of-sight angular rate according to the estimated radome error slope obtained in the step (3)
Based on the relationship between the measured angular rate of view and the actual angular rate of viewObtaining a corrected line of sight angular rate of
The corrected view angle rate aircraft guidance circuit is shown in fig. 4.
(42) Calculating and correcting actual guidance instruction of aircraft
Based on the estimated values of each state of the guidance system obtained in the step (2)Calculating to obtain actual guidance instruction of corrected aircraft under discrete time
Wherein the method comprises the steps ofUsingAnd the corrected guidance instruction completes the compensation of the error slope of the antenna housing. The overall schematic of the estimation and compensation of the radome error slope is shown in fig. 5.
The beneficial effects are that: compared with a method for designing and polishing from a hardware level, the aircraft seeker antenna cover error slope estimation and compensation method based on Gaussian process regression does not need to depend on a process level, does not need to consider balance with the antenna cover protection effect, is easier to realize compared with a method for directly measuring the antenna cover error, does not need to be provided with a sensor with severe requirements, reduces dependence on accurate modeling compared with an estimation and compensation method based on a traditional control and filtering algorithm, can adaptively estimate each state of a system under the condition that the antenna cover error slope is unknown, and further improves the estimation precision of the antenna cover error slope by using Gaussian process model derivation technology, so that a better compensation effect is achieved.
Drawings
FIG. 1 is a geometric block diagram of an aircraft introducer;
FIG. 2 is a diagram of an uncompensated aircraft guidance circuit 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 view of an aircraft guidance circuit after correction of the angular rate of view;
FIG. 5 is a general schematic diagram of a method for estimating and compensating the error slope of a radome according to the present invention;
FIG. 6 is a schematic view of an aircraft guidance system angle estimation mean square error;
FIG. 7 is a schematic diagram of an aircraft guidance system aircraft relative distance estimation mean square error from a target;
FIG. 8 is a schematic representation of an aircraft guidance system flight path angle estimate mean square error;
FIG. 9 is a schematic diagram of an actual guidance command estimation mean square error for an aircraft guidance system;
FIG. 10 is a schematic diagram of a real trajectory and estimated trajectory of an aircraft guidance system target view;
FIG. 11 is a schematic diagram of an actual trajectory versus an estimated trajectory for an aircraft guidance system radome error angle;
FIG. 12 is a diagram of a true trajectory of the radome error slope and an estimated trajectory based on Gaussian process regression;
FIG. 13 is a graph of a radome error slope estimate mean square error based on Gaussian process regression;
FIG. 14 is a graph comparing final guidance miss distance for the proposed method with other compensation methods;
Detailed Description
The technical scheme of the invention is further described below with reference to the accompanying drawings and the specific embodiments.
The initial values for the aircraft and target conditions are considered as follows
Wherein (X) M ,Y M ) And (X) T ,Y T ) For the initial position of the aircraft and the target,and->For the initial speed of the aircraft and the target, the target is assumed to be a fixed target. According to the establishment of the dynamics model in the step (2), the initial state of the guidance system is obtained as follows
The corresponding model parameters are as follows
{V M ,N,ρ θ ,τ,T α }＝{500m/s,4,0.025°/°,0.1s,1s}
In the interactive multimode filter, the discretization time interval is set to Δt=0.001 s, and the estimated mean and variance of the initial state is
Where n=3 is the number of guessed models, the transition probability matrix of the markov chain is as follows
In addition, process noise w k Is the covariance matrix Q of (1)
Observation noise v k Variance r= 1.7453 2 ×10 -12 rad 2 Is the following.
Based on the above settings, the states during the guidance of the aircraft are estimated according to the methods shown in steps (1) - (4) and fig. 5, and the radome error slope is estimated and compensated. In gaussian process regression, the prediction of the radome error angle and the estimation of the radome error slope are performed in two ways, namely, using all the historical data (full history) and using sliding window historical data (sliding window). Fig. 6-9 show mean square error of estimation of each state of the guidance system, fig. 10-11 show true track and estimation track of target view angle and error angle of antenna housing, fig. 12 shows true value and estimation value of error slope of antenna housing, fig. 13 shows mean square error of error slope estimation of antenna housing, it can be seen that better effect can be obtained by using sliding window data to conduct gaussian process prediction, fig. 14 shows final guidance miss-target amount after adopting the gaussian process estimation and compensation method provided by the invention, and comparison of guidance miss-target amount based on multi-model filter compensation (IMM) and extended kalman filter compensation (EKF) in the prior art without compensation. As can be seen from the results shown in the drawings, 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 radome, and can obtain better guidance effect compared with other compensation methods.
Claims (1)
1. An aircraft seeker antenna cover error slope estimation and compensation method based on Gaussian process regression; the method is characterized in that: the method comprises the following steps:
(1) Establishing a guidance dynamics model and a measurement model of the aircraft affected by the pilot head radome error;
(2) Estimating each state in the aircraft guidance process based on an interactive multi-model filtering method;
(3) Based on a Gaussian process regression method, establishing a mapping relation between an aircraft visual angle and an antenna housing error angle, and obtaining an antenna housing error slope;
(4) Based on the established Gaussian process regression model, compensating the error slope of the radome in the manufacturing process;
the step (1) comprises the following steps:
(11) Establishing an aircraft guidance dynamics model
The aircraft guidance task is guided by using a proportional guidance method, a first-order flight control system is configured, a target sight angle measured by a guide head of the aircraft can be influenced by a guide head radome to generate certain deviation, namely a radome error angle, and the expression of the error angle is that
Wherein lambda is r Is the error angle of the radome, θ s For the viewing angle, λ is the target viewing angle, θ M Is an elastomer attitude angle; defining the error slope of the radome as
Can establish an aircraft guidance dynamics model as
Wherein the method comprises the steps ofIn the system state, R is the distance between the aircraft and the target, gamma M For the flight path angle of the aircraft, A M Instruction for the actual guidance of the aircraft, < >>Is a kinetic equation constructed as follows
Wherein V is M For aircraft speed, N is the proportional guide coefficient, τ is the autopilot time constant, T α As a time constant for the rate of change of heading,an estimated value of error slope of the antenna housing;
(12) Establishing an aircraft guidance measurement model
The aircraft only has a target sight angle measurement value, and the aircraft guidance measurement model is established by considering the influence of the error angle of the antenna housing as follows:
wherein v is k N (0, R) is the measurement noise, h (x) k ；ρ θ,k ) For measuring equation
The step (2) comprises the following steps:
(21) Discretized system dynamics model
Discretizing the aircraft guidance dynamics model established in the step (1) based on a fourth-order Dragon-Gregory tower method, namely
x k+1 ＝φ(x k ；△t,ρ θ,k )+w k
Wherein w is k -N (0, Q) is process noise, representing discretization error, Q is covariance matrix thereof;
(22) Setting local filtering model
Constructing a plurality of local filtering models using a set of preset radome error slope values, i.e.
For each error slope parameter valueEstablishing corresponding dynamics and measurement models
Performing filtering estimation of each model by using an unscented Kalman filtering algorithm;
(23) Mixing local estimation results
Calculating a mixed estimation mean and covariance as estimation results of the multi-model filtering method according to the filtering results of the local models obtained in the step (22), namely
Wherein the method comprises the steps ofAnd P k|k For the estimated mean and covariance at the kth step, +.>And->Estimated value for the i-th local filter, is +.>The model probability corresponding to the ith local model is set;
(24) Calculating an estimated viewing angle and radome error
Based on the multi-model filter estimation result obtained in the step (23)
Calculating an estimated viewing angle->The following are listed below
Calculating an estimated radome error angleThe following are listed below
The step (3) comprises the following steps:
(31) Establishing a Gaussian process regression model from the viewing angle to the radome error angle
Using v r,i ～N(0,r r,i ) Representing the estimated error between the estimated radome error angle and the actual radome error angle at the ith step, and obtaining the relation between the estimated radome error angle and the estimated viewing angle
Consider arbitrary perspective inputThe antenna housing error angle corresponding to the required prediction is +.>Build->And lambda (lambda) r,j Gaussian process prior distribution between
Wherein the method comprises the steps ofFor a priori mean, K is the covariance matrix, which is calculated by the covariance function K (x 1 ,x 2 ) The composition of the composite material comprises the components,
based on the 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 obtainedWherein the method comprises the steps of
(32) Calculating error slope of radome
Deriving the obtained Gaussian process posterior distribution to obtain arbitrary inputThe error slope of the antenna housing is as follows
Wherein the method comprises the steps of
The step (4) comprises the following steps:
(41) Calculating a corrected gaze angular rate
Constructing a corrected line-of-sight angular rate according to the estimated radome error slope obtained in the step (3)
Based on the relationship between the measured angular rate of view and the actual angular rate of viewObtaining a corrected line of sight angular rate of
(42) Calculating and correcting actual guidance instruction of aircraft
Based on the estimated values of each state of the guidance system obtained in the step (2)Calculating to obtain actual guidance instruction of corrected aircraft under discrete time
Wherein the method comprises the steps ofAnd using the corrected guidance instruction to complete the compensation of the error slope of the antenna housing.
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Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US3940767A (en) * | 1955-01-21 | 1976-02-24 | Hughes Aircraft Company | Electronic radome-error compensation system |
| 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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Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US3940767A (en) * | 1955-01-21 | 1976-02-24 | Hughes Aircraft Company | Electronic radome-error compensation system |
| 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 |
Non-Patent Citations (2)
| Title |
|---|
| Gaussian process-based Bayesian non-linear filtering for online target tracking;Kelin Lu等;IET Radar Sonar Navig;第14卷(第3期);第448-458页 * |
| 导弹导引头天线罩误差斜率补偿研究;许海深;中国优秀硕士学位论文全文数据库（电子期刊）(第1期);第C032-190页 * |
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