CN109388063A - Adaptive Kalman filter composite control method - Google Patents

Abstract

An adaptive Kalman filter composite control method provided by the present invention firstly obtains the current motion state value, further performs state correction through parameter adjustment, obtains adaptive prediction and estimation of moving target information, and finally feeds back the motion state at the next moment. The estimated value is used for composite control of feedforward and feedback of the control method. The composite control method, based on the current motion model and parameter adjustment, obtains a corrected motion model, so that high-precision composite control can be realized even under the condition of noise interference of observation information, which overcomes the traditional composite control method which mainly uses speed measurement observation and coding. The method performs subsequent calculation on the angle information, which improves the problem of limited accuracy; further, the present invention introduces real-time correction of the motion model in the closed-loop control process, overcomes the cumulative effect of errors, and further improves the accuracy of the control method.

Description

Adaptive Kalman Filter Composite Control Method

technical field

The invention relates to the technical field of Kalman filtering, in particular to an adaptive Kalman filtering composite control method.

Background technique

With the rapid development of optoelectronic technology, optoelectronic control technology is widely used in the fields of target tracking and optoelectronic measurement and control. Among them, the control accuracy and real-time performance of the system are the core of the system application. Most of the current research is based on position The optimization of control gain to achieve precise control of the system requires that the prior information of the system be accurately known. However, in the case of dynamic time-varying, due to the introduction of observation noise, the signal interference is enhanced and the tracking accuracy is deteriorated. With the rapid application and promotion of optoelectronic technology in various fields, the current demand for optoelectronic control accuracy has greatly increased, and the control conditions have become increasingly harsh. Therefore, traditional methods are difficult to meet the accuracy requirements of modern optoelectronic control systems. The traditional photoelectric control system mainly includes two parameters, position and speed. Most of them use the principle control block diagram as shown in Figure 1. Since the position information of the target cannot be directly fed back, the target off-target information is generally obtained by brief introduction, but the spatial position information is still lacking. , especially the lack of angular space information, so that the angular velocity and angular acceleration cannot be obtained, and the composite control cannot be realized.

In order to solve this problem, the researchers innovatively proposed the concept of composite control of optoelectronic systems. By eliminating the speed and acceleration lag errors, the accuracy under stable control has been greatly improved, and it has become the main method to improve the control performance of optoelectronic systems. one. The composite control method requires that the angular velocity value of the target can be obtained to realize the composite control efficiency of the feedforward and feedback loops. The traditional composite control method mainly uses the method of velocity measurement and coding to perform the subsequent calculation of the angle information, and the improvement accuracy is limited. Especially in the presence of observation noise, its control accuracy is difficult to meet the accuracy requirements of modern optoelectronic control.

SUMMARY OF THE INVENTION

Based on this, it is necessary to provide an adaptive Kalman filter composite control method to solve the problem that the traditional composite control method mainly uses the method of velocity measurement and coding to solve the angle information, and its improvement accuracy is limited.

An adaptive Kalman filter composite control method provided by the present invention includes the following steps:

The data acquisition step is to acquire the current motion model of the moving target at the current moment and the estimated value of the current motion state;

The predicting step calculates the current predicted motion state value and the current prediction error variance matrix according to the current motion model and the current motion state estimated value;

In the residual information sequence detection step, the current residual information sequence and the current coefficient adjustment factor are calculated according to the current predicted motion state value and the current predicted error variance matrix;

A parameter adjustment step, calculating the current random maneuvering frequency and the current acceleration residual variance value according to the current residual error and the current coefficient adjustment factor;

The model correction step is to modify the transition matrix and the process noise variance matrix according to the current residual error, the current random maneuver frequency and the current acceleration residual variance value to obtain a corrected prediction error variance matrix;

A prediction correction step, obtaining a predicted motion state value at the next moment according to the corrected prediction error variance matrix;

The observation update step is to observe and update 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 obtain the motion state estimated value at the next moment;

The estimated value of the motion state at the next moment is cyclically fed back to the data acquisition step, and real-time composite control is performed according to the estimated value of the motion state at the next moment.

In one of the embodiments, the acceleration parameter a(t) of the moving target is as follows The zero-mean first-order model shown, where, is the mean value of acceleration, is a random amount of acceleration; the random amount of said acceleration The statistical properties of are in the form of time-dependent functions.

In one of the embodiments, the time correlation function is in the form of where α is the random maneuvering frequency, is the variance value of the acceleration parameter.

In one of the embodiments, in the predicting step, the current predicted motion state value is The current prediction error variance matrix is

In one embodiment, in the residual information sequence detection step, the current residual information sequence is The current coefficient adjustment factor is

In one embodiment, in the parameter adjustment step, the current random maneuvering frequency is α _k =λ _k α;

The current acceleration residual variance value is where c _k =λ _k c.

In one of the embodiments, in the state modification step, the modified prediction error variance matrix is in, is the modified transition matrix, is the corrected process noise variance matrix.

In one of the embodiments, in the observation update step, the revised predicted motion state value The corrected error variance matrix in,

In one of the embodiments, the estimated value of the motion state at the next moment includes an estimated value of angular velocity.

The above-mentioned adaptive Kalman filter composite control method first obtains the current motion state value, further performs state correction through parameter adjustment, obtains adaptive prediction and estimation of moving target information, and finally controls by feeding back the motion state estimate value at the next moment. Feedforward and feedback composite control of the method. The composite control method, based on the current motion model and parameter adjustment, obtains a corrected motion model, so that high-precision composite control can be realized even under the condition of noise interference of observation information, which overcomes the traditional composite control method which mainly uses speed measurement observation and coding. The method performs subsequent calculation on the angle information, which improves the problem of limited accuracy; further, the present invention introduces real-time correction of the motion model in the closed-loop control process, overcomes the cumulative effect of errors, and further improves the accuracy of the control method.

Description of drawings

In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the accompanying drawings required in the embodiments will be briefly introduced below. Obviously, the accompanying drawings in the following description are only described in the present invention. For some of the embodiments, those of ordinary skill in the art can also obtain other drawings according to these drawings.

Fig. 1 is the principle block diagram of the traditional Kalman filter compound control method;

Fig. 2 is the principle block diagram of the adaptive Kalman filter compound control method of the present invention;

3 is a schematic flowchart of an adaptive Kalman filter composite control method of the present invention;

FIG. 4 is a schematic diagram of the principle of the method shown in FIG. 3;

5 is a schematic diagram of a target motion trajectory according to an embodiment of the present invention;

FIG. 6 shows the tracking error curves obtained by the method of the present invention, the extended Kalman filter (EKF) method and the unscented Kalman filter method respectively for the moving target in the first embodiment.

Detailed ways

In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below through embodiments and in conjunction with the accompanying drawings. It should be understood that the specific embodiments described herein are only used to explain the present invention, but not to limit the present invention.

The principle of the adaptive Kalman filter composite control method of the present invention is shown in FIG. 2 . The position data is acquired and analyzed for the off-target observation data and instrument-related information, and the time alignment is carried out on the basis of considering the delay of the observation information. Analysis, in the composite control, based on the adaptive Kalman filter, the motion model is corrected in real time, and the estimated value of the motion state is fed back to the composite control to realize the composite control of the adaptive Kalman filter.

Please refer to FIG. 3 and FIG. 4 , an adaptive Kalman filter composite control method according to an embodiment of the present invention includes the following steps:

The data acquisition step is to acquire the current motion model of the moving target at the current moment and the estimated value of the current motion state;

The prediction step is to calculate the current predicted motion state value and the current prediction error variance matrix according to the current motion model and the current motion state estimated value;

In the residual information sequence detection step, the current residual information sequence and the current coefficient adjustment factor are calculated according to the current predicted motion state value and the current predicted error variance matrix;

The parameter adjustment step is to calculate the current random maneuvering frequency and the current acceleration residual variance value according to the current residual error and the current coefficient adjustment factor;

The model correction step is to correct the transition matrix and the process noise variance matrix according to the current residual error, the current random maneuver frequency and the current acceleration residual variance value to obtain a corrected prediction error variance matrix;

The prediction correction step is to obtain the predicted motion state value at the next moment according to the corrected prediction error variance matrix;

The observation update step is to perform observation update 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 obtain the motion state estimation value at the next moment;

The estimated value of the motion state at the next moment is cyclically fed back to the data acquisition step, and real-time composite control is performed according to the estimated value of the motion state at the next moment.

Preferably, the motion state estimate includes an angular velocity estimate.

The composite control method of this embodiment firstly obtains the current motion state value, further performs state correction through parameter adjustment, obtains adaptive prediction and estimation of the moving target information, and finally feeds back the motion state estimated value at the next moment to carry out the control method. Composite control of feedforward and feedback. The composite control method, based on the current motion model and parameter adjustment, obtains a corrected motion model, so that high-precision composite control can be realized even under the condition of noise interference of observation information, which overcomes the traditional composite control method which mainly uses speed measurement observation and coding. The method performs subsequent calculation on the angle information, which improves the problem of limited accuracy; further, the present invention introduces real-time correction of the motion model in the closed-loop control process, overcomes the cumulative effect of errors, and further improves the accuracy of the control method.

The motion model of the present invention, that is, the current motion model, is a statistical model, which is widely used in the field of maneuvering target tracking. Therefore, optionally, the acceleration parameter a(t) of the moving target is expressed as a first-order model with zero mean as shown in equation (1):

in, is the mean value of acceleration, is a random amount of acceleration; a random amount of acceleration The statistical properties of are in the form of time-dependent functions.

Further optionally, the time correlation function form is shown in formula (2):

where α is the random maneuvering frequency, is the variance value of the acceleration parameter.

In the specific embodiment part of the present invention, the acceleration parameter variance value The Rayleigh distribution used is calculated as shown in formula (3):

It can be seen from formula (2) that the motion model parameters used in the present invention mainly include random maneuvering frequency α and acceleration parameter variance value Acceleration parameter variance value It can also be understood as the extreme value parameter a _±max of the acceleration. The present invention adopts the residual information sequence γ _k to feedback control the real-time change of the target, and adjust and optimize the maneuvering parameters.

In the framework of the Kalman filter method, when the actual motion model of the moving target matches the theoretical model of the frame, the residual information satisfies the characteristics shown in equation (4):

When the actual motion model does not match the theoretical model, the current predicted motion state value predicted by the theoretical model When drift deviation occurs, the residual sequence no longer meets the characteristics shown in Equation (4). In this case, the current prediction error variance matrix can be expressed as Equation (5):

Since the state transition matrix Φ _k|k-1 of the moving target and the process noise variance matrix Q _k are related to the parameters of the motion model, the present invention establishes the actual statistical characteristics of the residual sequence and the current prediction error variance matrix P _k|k- The relationship of ₁ is used to adjust the parameters of the motion model in real time. The specific construction process is shown in formulas (6), (7) (8) (9):

in, is a statistical characteristic, 0≤σ≤1 is the forgetting factor, λ _k is the adjustment factor, and the parameter adjustment is shown in formula (10):

α _k =λ _k α (10)

At the same time, the mean acceleration value is expressed as the predicted value at the current moment, as shown in formula (11):

At the same time, the acceleration extreme value is expressed as the proportional form of the mean value, that is, as shown in formula (12):

In formula (12), c is the proportional coefficient, which usually takes a smaller empirical value when the state changes weakly. When the state changes greatly, the time-varying adjustment method is used as shown in formula (13):

c _k =λ _k c (13)

In formula (13), λ _k is the coefficient adjustment factor in the case of state mutation.

In the data acquisition step, the above-mentioned current motion model and estimated value of the current motion state are acquired.

Further in the prediction step, calculate the current predicted motion state value and the current prediction error variance matrix with reference to formulas (14) and (15) according to the current motion model and the current motion state estimated value:

P _k|k-1 =Φ _k|k-1 P _k-1|k-1 ΦT _k|k-1 +Q _k (15)

Further optionally, in the residual information sequence detection step, 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 predicted error variance matrix is shown in formulas (16) and (17) :

Further, according to the current residual and the current coefficient adjustment factor, the current random maneuver frequency and the current acceleration residual variance value are calculated with reference to formulas (18), (19), (20) to realize the adjustment of the model parameters:

α _k =λ _k α (18)

c _k =λ _k c (19)

Further modify the motion model based on the adjusted parameters, perform the model modification step, and modify the transition matrix and process noise variance matrix at the next moment according to the current residual, the current random maneuver frequency and the current acceleration residual variance value to obtain the next moment. The revised motion model of ;

Modified transition matrix As shown in formula (21):

Modified Process Noise Variance Matrix As shown in formula (22):

Then, the corrected prediction error variance matrix As shown in formula (23):

The prediction modification step is further performed, and the predicted motion state value at the next moment is obtained according to the modified prediction error variance matrix.

After the prediction correction step, the observation update step is performed, and the observation update is performed according to the current motion state observation value, the prediction correction error variance matrix, and the predicted motion state value at the next moment. The observation update method is as follows: (24), (25), ( 26), obtain the estimated value of the motion state at the next moment;

Further, in order to illustrate the specific control effect of the method of the present invention in the case of inaccurate construction of the motion model, the motion model as shown in formula (27) is used to conduct a composite control tracking simulation comparative analysis experiment. In the comparative analysis experiment, the second-order constant velocity motion model (CV) and the third-order constant acceleration (CA) linear motion model are respectively used to construct the motion state of the target, and the method of the present invention is used to carry out theoretical adaptive modeling, taking the target's motion state. The motion parameters (position, velocity, acceleration) are used as state variables of the system, and the system noise is assumed to be uncorrelated Gaussian white noise. In order to simulate and analyze the nonlinear characteristics of the tracking system, the discrete system model of the polar coordinate mode constructed in the simulation is shown in equation (27).

In formula (27), the distance r, the azimuth angle α and the elevation angle e constitute the observation value Z of the system.

In the simulation comparative analysis experiment, the observation noise is expressed as variance The data is generated by a system constructed by Matlab software, the total time level of the collected data is 10 seconds, and the sampling period T=0.007.

For the convenience of comparative analysis, the methods of Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF), which are commonly used in optoelectronic nonlinear system tracking, are compared. For the sake of fairness, different filtering methods use the current statistical model with the same initial parameters.

Please refer to FIG. 5 and FIG. 6 of the present invention, FIG. 5 is the trajectory used for closed-loop control tracking in the simulation, and FIG. 6 is the tracking results of different methods. As can be seen from FIG. 6 , the method of the present invention is superior to the EKF and UKF methods. The analysis shows that the main reason is that the present invention introduces real-time correction of model errors in the closed-loop control process, which overcomes the cumulative effect of errors. However, the EKF and UKF methods have the error accumulation effect, so the tracking error is larger. At the same time, because the EKF adopts the second-order truncation linear approximation processing for the nonlinear system, there is the influence of stage error, and it is only suitable for weak nonlinear systems, but the photoelectric tracking control system has the transformation process of polar coordinates and Cartesian coordinates, so it has Strong nonlinearity, and UKF has no truncation error due to the use of the third-order characteristics of Sigma point propagation. Therefore, the tracking accuracy is higher than that of the EKF algorithm, but also due to the existence of model cumulative errors, the tracking effect is better than this. The method of invention is poor.

Further, it can be concluded from Fig. 4 that the method of the present invention maintains a high tracking accuracy in the tracking of the optoelectronic nonlinear system. Repeat the treatment, carry out 40 repeated experiments respectively, and calculate the mean value. The specific results are shown in Table 1.

Table 1 Comparison of tracking performance of different methods

It can be seen from Table 1 that the method of the present invention maintains high tracking accuracy and stability. Compared with the method in which the traditional model parameters are not corrected, the overall tracking accuracy is greatly improved, and the distance tracking accuracy is improved compared with EKF. increased by 75.2%, which is 54.4% higher than UKF.

Accurate and robust optoelectronic system composite control technology under observation noise interference is one of the key research contents in the field of optoelectronic target tracking. The present invention conducts research on the problem of precise control of optoelectronic systems in the case of observation noise interference, proposes an adaptive Kalman filter composite control method based on adaptive correction on the basis of considering model errors, and constructs a relationship between the information residual sequence and model parameters. Real-time estimation of the angular velocity is realized, and a composite control scheme combining feedback and feedforward is constructed based on the estimated angular velocity, and the superiority of the method of the present invention is verified through comparative analysis experiments, which can maintain the control of the method. Stable while achieving a 40% improvement in accuracy.

The above-mentioned embodiments only represent several embodiments of the present invention, and the descriptions thereof are specific and detailed, but should not be construed as a limitation on the scope of the patent of the present invention. It should be pointed out that for those of ordinary skill in the art, without departing from the concept of the present invention, several modifications and improvements can also be made, which all belong to the protection scope of the present invention. Therefore, the protection scope of the patent of the present invention should be subject to the appended claims.

Claims (9)

1. an adaptive Kalman filter composite control method, is characterized in that, comprises the following steps: The data acquisition step is to acquire the current motion model of the moving target at the current moment and the estimated value of the current motion state; The predicting step calculates the current predicted motion state value and the current prediction error variance matrix according to the current motion model and the current motion state estimated value; In the residual information sequence detection step, the current residual information sequence and the current coefficient adjustment factor are calculated according to the current predicted motion state value and the current predicted error variance matrix; A parameter adjustment step, calculating the current random maneuvering frequency and the current acceleration residual variance value according to the current residual error and the current coefficient adjustment factor; The model correction step is to modify the transition matrix and the process noise variance matrix according to the current residual error, the current random maneuver frequency and the current acceleration residual variance value to obtain a corrected prediction error variance matrix; A prediction correction step, obtaining a predicted motion state value at the next moment according to the corrected prediction error variance matrix; The observation update step is to observe and update 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 obtain the motion state estimated value at the next moment; The estimated value of the motion state at the next moment is cyclically fed back to the data acquisition step, and real-time composite control is performed according to the estimated value of the motion state at the next moment. 2. The adaptive Kalman filter composite control method according to claim 1, wherein the acceleration parameter a(t) of the moving target is as follows The zero-mean first-order model shown, where, is the mean value of acceleration, is a random amount of acceleration; the random amount of said acceleration The statistical properties of are in the form of time-dependent functions. 3. adaptive Kalman filter composite control method according to claim 2, is characterized in that, described time correlation function form is where α is the random maneuvering frequency, is the variance value of the acceleration parameter. 4. The adaptive Kalman filter composite control method according to any one of claims 1 to 3, characterized in that, in the predicting step, the current predicted motion state value is The current prediction error variance matrix is 5. The adaptive Kalman filter composite control method according to any one of claims 1 to 3, wherein, in the residual information sequence detection step, the current residual information sequence is The current coefficient adjustment factor is 6. The adaptive Kalman filter composite control method according to any one of claims 1 to 3, wherein, in the parameter adjustment step, the current random maneuver frequency is α _k =λ _k α; The current acceleration residual variance value is where c _k =λ _k c. 7. The adaptive Kalman filter composite control method according to any one of claims 1 to 3, wherein in the state modification step, the modified prediction error variance matrix is in, is the modified transition matrix, is the corrected process noise variance matrix. 8. The adaptive Kalman filter composite control method according to any one of claims 1 to 3, characterized in that, in the observation update step, the modified predicted motion state value The corrected error variance matrix in, 9 . The adaptive Kalman filter composite control method according to claim 1 , wherein the estimated value of the motion state at the next moment includes an estimated value of angular velocity. 10 .