CN113536707A - Aircraft seeker radome error slope estimation and compensation method based on Gaussian process regression - Google Patents
Aircraft seeker radome error slope estimation and compensation method based on Gaussian process regression Download PDFInfo
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Abstract
The invention discloses an aircraft seeker radome error slope estimation and compensation method based on Gaussian process regression, which is characterized in that an aircraft dynamics model is established for an aircraft guidance system which is only subjected to line-of-sight angle measurement and is influenced by radome errors, each state in a guidance process is estimated by using an interactive multi-model filtering method, a mapping relation between an aircraft visual angle and a radome error angle is established based on the Gaussian process regression model, an analytic expression form of the radome error slope is obtained based on a derivative of the Gaussian process model, and the analytic expression form is finally used for the compensation of the radome errors of the aircraft seeker, so that the guidance performance is effectively improved.
Description
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
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
A geometric diagram of an aircraft seeker with radome error is shown in fig. 1. Can establish a system dynamics model as
Wherein
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,
for the kinetic equation, it was constructed as follows
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,
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
Wherein v iskN (0, R) is measurement noise, h (x)k；ρθ,k) To be a measurement equation
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.
For each error slope parameter value
Establishing corresponding dynamic and measurement model
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
Wherein
And Pk|kIs the k stepThe estimated mean and covariance of the time,
and
for the estimated value obtained by the ith local filter,
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)
Computing an estimated view angle
As follows
Calculating and estimating antenna housing error angle
As follows
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
Considering arbitrary perspective input
The corresponding required predicted error angle of the antenna housing is
Establishing
And λr,jGaussian process prior distribution between
Wherein
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,
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
Wherein
(32) Calculating radome error slope
The obtained posterior distribution of the Gaussian process is subjected to derivation to obtain any input
The error slope of the radome is
Wherein
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)
Based on the relationship between the measured line-of-sight angular rate and the actual line-of-sight angular rate
Obtaining a corrected line-of-sight angular rate of
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)
Calculating to obtain a corrected aircraft actual guidance instruction in discrete time
Wherein
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
Wherein (X)M,YM) And (X)T,YT) Is the initial position of the aircraft with respect to the target,
and
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
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
Where n-3 is the number of guessed models, the transition probability matrix for the Markov chain is as follows
In addition, process noise wkHas a covariance matrix Q of
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. An aircraft seeker radome 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 dynamic model and a measurement model of the aircraft influenced by the error of the radome of the seeker;
(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.
2. The method for estimating and compensating the error slope of the radome of the aircraft seeker based on the gaussian process regression as recited in claim 1, wherein: 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 line-of-sight angle measured by a guidance head of the aircraft is influenced by a guidance head antenna housing to generate a certain deviation, namely an antenna housing error angle, and the expression of the error angle is an antenna housing error angle
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
Can establish an aircraft guidance dynamic model as
Wherein
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,
as a kinetic squareThe process is constructed as follows
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,
the estimated value of the error slope of the antenna housing is obtained.
(12) Establishing an aircraft guidance measurement model
The aircraft only has a target line-of-sight angle measured value, and the aircraft guidance measurement model is established by considering the influence of an antenna housing error angle as follows:
wherein v iskN (0, R) is measurement noise, h (x)k；ρθ,k) To be a measurement equation
3. The method for estimating and compensating the error slope of the radome of the aircraft seeker based on the gaussian process regression as recited in claim 1, wherein: the step (2) comprises the following steps:
(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.
For each error slope parameter value
Establishing corresponding dynamic and measurement model
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
Wherein
And Pk|kAs the estimated mean and covariance at step k,
and
for the estimated value obtained by the ith local filter,
and the model probability corresponding to the ith local model.
(24) Calculating estimated view angle and radome error
According to the multi-model filtering estimation result obtained in the step (23)
Computing an estimated view angle
As follows
Calculating and estimating antenna housing error angle
As follows
4. The method for estimating and compensating the error slope of the radome of the aircraft seeker based on the gaussian process regression as recited in claim 1, wherein: the step (3) comprises the following steps:
(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
Considering arbitrary perspective input
The corresponding required predicted error angle of the antenna housing is
Establishing
And λr,jGaussian process prior distribution between
Wherein
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,
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
Wherein
(32) Calculating radome error slope
The obtained posterior distribution of the Gaussian process is subjected to derivation to obtain any input
The error slope of the radome is
Wherein
。
5. The method for estimating and compensating the error slope of the radome of the aircraft seeker based on the gaussian process regression as recited in claim 1, wherein: the step (4) comprises the following steps:
(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)
Based on the relationship between the measured line-of-sight angular rate and the actual line-of-sight angular rate
Obtaining a corrected line-of-sight angular rate of
(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)
Calculating to obtain a corrected aircraft actual guidance instruction in discrete time
Wherein
And 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 |
|---|
| KELIN LU等: "Gaussian process-based Bayesian non-linear filtering for online target tracking", IET RADAR SONAR NAVIG, vol. 14, no. 3, pages 448 - 458, XP006089200, DOI: 10.1049/iet-rsn.2019.0495 * |
| 许海深: "导弹导引头天线罩误差斜率补偿研究", 中国优秀硕士学位论文全文数据库（电子期刊）, no. 1, pages 032 - 190 * |
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