CN109388063A - Adaptive Kalman filter composite control method - Google Patents
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Abstract
A kind of adaptive Kalman filter composite control method provided by the invention, current motion state value is obtained first, it is further adjusted by parameter and carries out state revision, obtain adaptive prediction and the estimation of moving target information, finally by the state estimation value of feedback subsequent time, feedforward and the complex controll of feedback of control method are carried out.The composite control method, it is adjusted based on current kinetic model and parameter, obtain correction motion model, to also can be realized high-precision complex controll in the case where observation information noise jamming, it overcomes traditional composite control method and subsequent resolving mainly is carried out to angle information using the method for test the speed observation and coding, promote the limited problem of precision；Further, the present invention introduces the real-time amendment of motion model in closed loop control process, overcomes deviation accumulation effect, further improves the precision of control method.
Description
Technical Field
The invention relates to the technical field of Kalman filtering, in particular to a composite control method for adaptive Kalman filtering.
Background
With the rapid development of the photoelectric technology, the current photoelectric control technology is widely applied to the fields of target tracking, photoelectric measurement and control and the like, wherein the control precision and the real-time performance of the system are the core of the system application, most of the current researches realize the precise control of the system based on the optimization of the position control gain, and the prior information of the system is required to be precisely known by the method. However, in the case of dynamic time variation, signal interference is increased and tracking accuracy is deteriorated due to the introduction of observation noise. With the rapid application and popularization of the photoelectric technology in various fields, the requirement on photoelectric control precision is greatly improved at present, and the control conditions are increasingly harsh, so that the traditional method is difficult to meet the requirement of a modern photoelectric control system on the precision. The traditional photoelectric control system mainly comprises two parameters of position and speed, a principle control block diagram shown in figure 1 is mostly adopted, and the position information of a target cannot be directly fed back, so that the missing of the target miss information is generally adopted, but the position information of space still lacks, especially the missing of angle space information, so that the angular speed and the angular acceleration cannot be obtained, and the composite control cannot be realized.
In order to solve the problem, researchers innovatively provide a concept of composite control of the photoelectric system, and the precision under stable control is greatly improved by a method of eliminating speed and acceleration lag errors, so that the method becomes one of the main methods for improving the control performance of the photoelectric system at present. The composite control method requires the acquisition of the angular velocity value of a target, and realizes the composite control efficiency of a feedforward loop and a feedback loop, and the traditional composite control method mainly utilizes a velocity measurement observation and coding method to carry out subsequent calculation on the angular information, so that the improvement precision is limited. Especially, under the condition that observation noise exists, the control precision of the device is difficult to meet the requirement of modern photoelectric control on precision.
Disclosure of Invention
On the basis, it is necessary to provide a self-adaptive kalman filter composite control method aiming at the problem that the conventional composite control method mainly utilizes a velocity measurement observation and coding method to perform subsequent calculation on angle information and the improvement precision is limited.
The invention provides a self-adaptive Kalman filtering composite control method, which comprises the following steps:
a data acquisition step, namely acquiring a current motion model and a current motion state estimation value of a moving target at the current moment;
a prediction step, calculating a current prediction motion state value and a current prediction error variance matrix according to a current motion model and the current motion state estimation value;
residual error information sequence detection, namely calculating a current residual error information sequence and a current coefficient regulating factor according to the current prediction motion state value and the current prediction error variance matrix;
parameter adjustment, namely calculating a current random maneuvering frequency and a current acceleration residual variance value according to the current residual and the current coefficient adjustment factor;
a model correction step, namely correcting a transfer matrix and a process noise variance matrix according to the current residual error, the current random maneuvering frequency and the current acceleration residual variance value to obtain a corrected prediction error variance matrix;
a prediction correction step, namely obtaining a predicted motion state value at the next moment according to the corrected prediction error variance matrix;
an observation updating step, wherein observation updating is carried out according to the current motion state observation value, the prediction correction error variance matrix and the predicted motion state value at the next moment, and a motion state estimation value at the next moment is obtained;
and circularly feeding back the motion state estimation value at the next moment to the data acquisition step, and performing real-time composite control according to the motion state estimation value at the next moment.
In one embodiment, the acceleration parameter a (t) of the moving object is as shown in the formulaA zero-mean first-order model is shown in which,is the average of the accelerations which are,is a random quantity of acceleration; random amount of the accelerationIs in the form of a time dependent function.
In one embodiment, the time-dependent function is of the formWherein α is a random maneuvering frequency,is the acceleration parameter variance value.
In one embodiment, in the predicting step, the current predicted motion state value isThe current prediction error variance matrix is
In one embodiment, in the step of detecting the residual information sequence, the current residual information sequence isThe current coefficient adjustment factor is
In one embodiment, in the parameter adjusting step, the current random maneuver frequency is αk＝λkα；
The current acceleration residual variance value isWherein, ck＝λkc。
In one embodiment, in the state modification step, the modified prediction error variance matrix isWherein, in order to be the modified transition matrix,the variance matrix is the modified process noise.
In one embodiment, in the observation updating step, the modified predicted motion state valueThe modified error variance matrixWherein,
in one embodiment, the estimate of the state of motion at the next time instant comprises an estimate of angular velocity.
The self-adaptive Kalman filtering composite control method comprises the steps of firstly obtaining a current motion state value, further carrying out state correction through parameter adjustment, obtaining self-adaptive prediction and estimation of motion target information, and finally carrying out feedforward and feedback composite control of the control method through feeding back a motion state estimation value at the next moment. The composite control method obtains the correction motion model based on the current motion model and parameter adjustment, thereby realizing high-precision composite control under the condition of noise interference of observation information, and overcoming the problem that the traditional composite control method mainly utilizes a speed measurement observation and coding method to carry out subsequent calculation on angle information, and the improvement precision is limited; furthermore, the invention introduces real-time correction of the motion model in the closed-loop control process, overcomes the error accumulation effect and further improves the precision of the control method.
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In order to more clearly illustrate the embodiments of the present application or technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments described in the present invention, and other drawings can be obtained by those skilled in the art according to the drawings.
FIG. 1 is a schematic block diagram of a conventional Kalman filtering composite control method;
FIG. 2 is a schematic block diagram of the adaptive Kalman filtering composite control method of the present invention;
FIG. 3 is a schematic flow chart of the adaptive Kalman filtering composite control method of the present invention;
FIG. 4 is a schematic diagram of the method of FIG. 3;
FIG. 5 is a schematic diagram of a target motion trajectory according to an embodiment of the present invention;
fig. 6 is a tracking error curve obtained by using the method of the present invention, the Extended Kalman Filter (EKF) method, and the unscented kalman filter method for the moving object according to the first embodiment.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below by way of embodiments with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
The principle of the adaptive Kalman filtering composite control method is shown in FIG. 2, position data is obtained and analyzed according to off-target observation data and relevant instrument information, time alignment analysis is carried out on the basis of considering observation information delay, a motion model is corrected in real time based on adaptive Kalman filtering in composite control, a motion state estimation value is fed back to the composite control, and the composite control of the adaptive Kalman filtering is realized.
Referring to fig. 3 and 4, an adaptive kalman filter composite control method according to an embodiment of the present invention includes the following steps:
a data acquisition step, namely acquiring a current motion model and a current motion state estimation value of a moving target at the current moment;
a prediction step, calculating a current prediction motion state value and a current prediction error variance matrix according to a current motion model and a current motion state estimation value;
residual error information sequence detection, namely calculating a current residual error information sequence and a current coefficient regulating factor according to the current predicted motion state value and the current predicted error variance matrix;
parameter adjustment, namely calculating a current random maneuvering frequency and a current acceleration residual variance value according to a current residual and a current coefficient adjustment factor;
a model correction step, namely correcting the transfer matrix and the process noise variance matrix according to the current residual error, the current random maneuvering frequency and the current acceleration residual variance value to obtain a corrected prediction error variance matrix;
a prediction correction step, namely obtaining a predicted motion state value at the next moment according to the corrected prediction error variance matrix;
an observation updating step, wherein observation updating is carried out according to the current motion state observation value, the prediction correction error variance matrix and the predicted motion state value at the next moment, and the motion state estimation value at the next moment is obtained;
and circularly feeding back the motion state estimation value at the next moment to the data acquisition step, and performing real-time composite control according to the motion state estimation value at the next moment.
Preferably, the motion state estimate comprises an angular velocity estimate.
The composite control method of the embodiment first obtains the current motion state value, further performs state correction through parameter adjustment, obtains adaptive prediction and estimation of motion target information, and finally performs feedforward and feedback composite control of the control method through feeding back the motion state estimation value at the next moment. The composite control method obtains the correction motion model based on the current motion model and parameter adjustment, thereby realizing high-precision composite control under the condition of noise interference of observation information, and overcoming the problem that the traditional composite control method mainly utilizes a speed measurement observation and coding method to carry out subsequent calculation on angle information, and the improvement precision is limited; furthermore, the invention introduces real-time correction of the motion model in the closed-loop control process, overcomes the error accumulation effect and further improves the precision of the control method.
The motion model of the present invention, that is, the current motion model, is a statistical model, and is a model applied more in the field of maneuvering target tracking, and the basic idea thereof is mainly to consider that the motion target has higher consistency in time, and the change of parameters is kept in the limited neighborhood range of the current model parameters, so optionally, the acceleration parameter a (t) of the motion target is expressed as a zero-mean first-order model as shown in formula (1):
wherein,is the average of the accelerations which are,is a random quantity of acceleration; random amount of accelerationIs in the form of a time dependent function.
Further optionally, the time-dependent function has the form shown in equation (2):
wherein α is a random maneuvering frequency,is the acceleration parameter variance value.
In the section of the embodiments of the invention, the variance value of the acceleration parameterThe rayleigh distribution calculation used is as shown in equation (3):
as can be seen from the formula (2), the motion model parameters adopted by the invention mainly comprise the random maneuvering frequency α and the acceleration parameter variance valueVariance value of acceleration parameterCan also be understood as an extreme variable a of the acceleration±max. The invention adopts a residual error information sequence gammakAnd performing feedback control on the real-time change condition of the target, and adjusting and optimizing maneuvering parameters.
In the framework of a Kalman filtering method, when an actual motion model of a moving target is matched with a theoretical model of a framework, residual error information meets the characteristics shown in the formula (4):
when the actual motion model is mismatched with the theoretical model, the current predicted motion state value predicted according to the theoretical modelDrift bias occurs and the residual sequence no longer satisfies the property shown in equation (4), in which case the current prediction error variance matrix can be expressed as shown in equation (5) as:
state transition matrix phi due to moving objectsk|k-1Sum process noise variance matrix QkIs related to the parameters of the motion model, therefore, the invention establishes the actual statistical characteristics of the residual error sequence and the current prediction error variance matrix Pk|k-1The relationship (2) adjusts the motion model parameters in real time, and the specific construction process is shown in the formulas (6), (7), (8) and (9):
wherein,for statistical properties, σ ≦ 0 ≦ 1 is a forgetting factor, λkFor adjusting the factor, the parameters are adjusted as shown in formula (10)Shown in the figure:
αk＝λkα (10)
meanwhile, the acceleration mean value is expressed as a predicted value at the current moment, namely as shown in formula (11):
meanwhile, the acceleration extreme value is expressed as a proportional form of the mean value, namely as shown in formula (12):
in the equation (12), c is a proportionality coefficient, and usually takes a small empirical value under the condition of weak state change, and when the state change is large, a time-varying adjustment method is adopted as shown in equation (13):
ck＝λkc (13)
in formula (13), λkThe coefficient adjustment factor in the case of a state mutation.
In the data acquisition step, the current motion model and the current motion state estimation value are acquired.
Further, in the prediction step, the current prediction motion state value and the current prediction error variance matrix are calculated with reference to equations (14) and (15) based on the current motion model and the current motion state estimation value:
Pk|k-1＝Φk|k-1Pk-1|k-1ΦTk|k-1+Qk(15)
further optionally, in the step of detecting the residual information sequence, the method for calculating the current residual information sequence and the current coefficient adjustment factor according to the current predicted motion state value and the current prediction error variance matrix is as shown in equations (16) and (17):
further, the current random maneuvering frequency and the current acceleration residual variance value are calculated according to the current residual and the current coefficient adjustment factor by referring to the formulas (18), (19) and (20), so that the adjustment of the model parameters is realized:
αk＝λkα (18)
ck＝λkc (19)
further correcting the motion model based on the adjusted parameters, executing a model correction step, and correcting a transfer matrix and a process noise variance matrix at the next moment according to the current residual error, the current random maneuvering frequency and the current acceleration residual variance value to obtain a corrected motion model at the next moment;
modified transition matrixAs shown in equation (21):
modified process noise variance matrixAs shown in equation (22):
further, the prediction error variance matrix is correctedAs shown in equation (23):
and further executing a prediction correction step, and obtaining a predicted motion state value at the next moment according to the corrected prediction error variance matrix.
After the prediction correction step, executing an observation updating step, and carrying out observation updating according to the current motion state observation value, the prediction correction error variance matrix and the predicted motion state value at the next moment, wherein the observation updating method is shown in formulas (24), (25) and (26) to obtain the motion state estimation value at the next moment;
further, in order to illustrate the specific control effect of the method under the condition that the motion model is not accurately constructed, the motion model shown in the formula (27) is adopted to carry out a composite control tracking simulation comparative analysis experiment. In a contrast analysis experiment, a second-order constant velocity motion model (CV) and a third-order Constant Acceleration (CA) linear motion model are respectively adopted to mix and construct a motion state of a target, theoretical adaptive modeling is carried out by adopting the method, motion parameters (position, velocity and acceleration) of the target are taken as state variables of a system, and system noise is assumed to be uncorrelated white Gaussian noise. In order to simulate and analyze the nonlinear characteristics of the tracking system, a discrete system model of a polar coordinate mode constructed in simulation is shown as formula (27).
In equation (27), the distance r, the azimuth angle α, and the pitch angle e constitute an observed value Z of the system.
In the simulation contrastive analysis experiment, the observation noise is expressed as varianceThe data is generated by a system constructed by Matlab software, the total time degree of the collected data is 10 seconds, and the sampling period T is 0.007.
For the convenience of comparison analysis, the method is compared with an Extended Kalman Filter (EKF) and an Unscented Kalman Filter (UKF) which are commonly used for tracking an optoelectronic nonlinear system. For the sake of fairness, the current statistical models with the same initial parameters are used for different filtering methods.
Referring to fig. 5 and fig. 6 of the present invention, fig. 5 is a trace for closed-loop control tracking in simulation, and fig. 6 is a tracking result of different methods. As can be seen from FIG. 6, the method of the present invention is superior to EKF and UKF methods, and the main reason is that the present invention introduces real-time correction of model errors in the closed-loop control process, thereby overcoming the error accumulation effect. The EKF and UKF methods have error accumulation effect, so that the tracking error is larger. Meanwhile, because the EKF adopts linear approximation processing of second-order truncation to a nonlinear system, the EKF has influence of stage errors and is only suitable for a weak nonlinear system, but a photoelectric tracking control system has a conversion processing process of polar coordinates and Cartesian coordinates, so that the EKF has strong nonlinearity, and the UKF has no truncation errors due to the fact that a Sigma point propagates a third-order characteristic, so that the tracking accuracy is higher than that of an EKF algorithm, but the tracking effect is poorer than that of the EKF algorithm due to the existence of model accumulated errors.
Further, as can be seen from fig. 4, the method of the present invention maintains a higher tracking accuracy in the tracking of the optoelectronic nonlinear system, and in order to further illustrate the stability and reliability of the method of the present invention, the contents of the comparative analysis experiment are randomly and repeatedly processed, 40 times of repeated experiments are respectively performed, and the average value is calculated, and the specific results are shown in table 1.
TABLE 1 comparison of tracking Performance of different methods
As can be seen from Table 1, the method of the invention maintains higher tracking accuracy and stability, and compared with the method without modifying the traditional model parameters, the overall tracking accuracy is greatly improved, wherein the distance tracking accuracy is improved by 75.2% compared with EKF, and is improved by 54.4% compared with UKF.
A photoelectric system composite control technology for accurately robustness under the condition of observing noise interference belongs to one of key research contents in the field of photoelectric target tracking. The invention develops research aiming at the accurate control problem of the photoelectric system under the observation noise interference condition, provides a self-adaptive Kalman filtering composite control method based on self-adaptive correction on the basis of considering model errors, and constructs the self-adaptive correction relation between an information residual sequence and model parameters; the method realizes real-time estimation of the angular velocity, constructs a composite control scheme combining feedback and feedforward based on the estimated angular velocity, verifies the superiority of the method through a comparative analysis experiment, and can realize 40% improvement of the precision while keeping the control stability of the method.
The above-mentioned embodiments only express several embodiments of the present invention, and the description thereof is more specific and detailed, but not construed as limiting the scope of the present invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the inventive concept, which falls within the scope of the present invention. Therefore, the protection scope of the present patent shall be subject to the appended claims.
Claims (9)
1. A composite control method of adaptive Kalman filtering is characterized by comprising the following steps:
a data acquisition step, namely acquiring a current motion model and a current motion state estimation value of a moving target at the current moment;
a prediction step, calculating a current prediction motion state value and a current prediction error variance matrix according to a current motion model and the current motion state estimation value;
residual error information sequence detection, namely calculating a current residual error information sequence and a current coefficient regulating factor according to the current prediction motion state value and the current prediction error variance matrix;
parameter adjustment, namely calculating a current random maneuvering frequency and a current acceleration residual variance value according to the current residual and the current coefficient adjustment factor;
a model correction step, namely correcting a transfer matrix and a process noise variance matrix according to the current residual error, the current random maneuvering frequency and the current acceleration residual variance value to obtain a corrected prediction error variance matrix;
a prediction correction step, namely obtaining a predicted motion state value at the next moment according to the corrected prediction error variance matrix;
an observation updating step, wherein observation updating is carried out according to the current motion state observation value, the prediction correction error variance matrix and the predicted motion state value at the next moment, and a motion state estimation value at the next moment is obtained;
and circularly feeding back the motion state estimation value at the next moment to the data acquisition step, and performing real-time composite control according to the motion state estimation value at the next moment.
2. The adaptive Kalman filtering composite control method according to claim 1, characterized in that the acceleration parameter a (t) of the moving target is as shown in formulaA zero-mean first-order model is shown in which,is the average of the accelerations which are,is a random quantity of acceleration; random amount of the accelerationIs statistically characterized byIn the form of a time dependent function.
3. The adaptive Kalman filtering composite control method of claim 2, wherein the time-dependent function is of the formWherein α is a random maneuvering frequency,is the acceleration parameter variance value.
4. The adaptive Kalman filtering composite control method according to any one of claims 1 to 3, characterized in that in the prediction step, the current prediction motion state value isThe current prediction error variance matrix is
5. The adaptive Kalman filtering composite control method according to any one of claims 1 to 3, characterized in that in the residual information sequence detection step, the current residual information sequence isThe current coefficient adjustment factor is
6. The adaptive Kalman filtering composite control method according to any one of claims 1 to 3Wherein, in the parameter adjusting step, the current random maneuver frequency is αk＝λkα；
The current acceleration residual variance value isWherein, ck＝λkc。
7. The adaptive Kalman filtering composite control method according to any one of claims 1 to 3, characterized in that in the state correction step, the corrected prediction error variance matrix isWherein, in order to be the modified transition matrix,the variance matrix is the modified process noise.
8. The adaptive Kalman filtering composite control method according to any one of claims 1 to 3, characterized in that in the observation updating step, the modified predicted motion state valueThe modified error variance matrixWherein,
9. the adaptive kalman filter composite control method according to any one of claims 1 to 3, wherein the motion state estimation value at the next time includes an angular velocity estimation value.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110569410A (en) * | 2019-08-30 | 2019-12-13 | 广西师范大学 | Distance measurement data processing method and device and computer readable storage medium |
| CN111523076A (en) * | 2020-03-24 | 2020-08-11 | 中国人民解放军军事科学院评估论证研究中心 | Method, device and system for calculating angular acceleration based on Fal function |
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