CN110119588B - On-line optimization design method based on extended Kalman filtering state estimation value - Google Patents
On-line optimization design method based on extended Kalman filtering state estimation value Download PDFInfo
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Abstract
The invention discloses an online optimization design method based on an extended Kalman filtering state estimation value. And then obtaining an updated observation predicted value, comparing the updated observation predicted value with the observed value, obtaining a residual information array, checking a state estimated value which is most suitable for the current moment after updating by utilizing residual information, and taking the state estimated value as a state estimated value of the current moment. By the method, the influence of the dynamic model deviation on system tracking can be reduced to a certain extent, the problem of insufficient precision of the extended Kalman filtering when the model deviation occurs in the system is solved, the method can be well applied to the field of nonlinear systems, and the method has certain robustness.
Description
Technical Field
The invention belongs to the field of target tracking of nonlinear systems, and particularly relates to the field of target speed tracking of model parameters in the system modeling process or dynamic deviation caused by a system operation environment, which can be used for data processing of optimizing target speed tracking in target tracking.
Background
With the progress and development of science and technology, the linear filtering theory is widely applied to the application fields of target tracking, information processing, fault diagnosis and the like. The filtering mode, including the Kalman filter, makes outstanding contributions in the fields of aerospace, financial management, unmanned aerial vehicles and the like. However, as the complexity of system modeling increases and the uncertainty of the operating environment, research leading to nonlinear systems has become an ongoing problem. Therefore, in order to apply the kalman filter to the nonlinear system, some improvement must be made. Bucy, sunahara et al proposed and studied extended Kalman filtering (Extended Kalman Filter, EKF for short) to further apply Kalman filtering theory to the non-linear domain. The basic idea of EKF is to linearize a nonlinear system and then perform kalman filtering, so EKF is a suboptimal filtering. The unscented Kalman eliminates the traditional method of linearizing nonlinear functions, adopts a Kalman linear filtering framework, and uses unscented transformation to solve the nonlinear transmission problem of mean and covariance for a one-step prediction equation. The statistics of nonlinear distribution has higher calculation precision, and the defects of low estimation precision and poor stability of Kalman filtering are effectively overcome. In addition, there are also methods such as bulk kalman filter (CKF), particle Filter (PF), and filter based on a characteristic function applied to a nonlinear system.
However, the most important reason for the low extended kalman accuracy is often from four parts, first, the model is simplified. For more complex systems, higher dimensional state variables, even infinitely variable, are often required to accurately describe their behavior. This is a great inconvenience for the reconstruction of the system state. Therefore, a model-simplified approach is generally used, where fewer state variables are used to describe the main features of the system, and some less important factors of the actual system are ignored. I.e. there is a so-called unmodeled dynamics. These unmodeled dynamics may be excited under certain special conditions, resulting in a large mismatch between the model and the actual system. Second, noise statistics are inaccurate. I.e. the noise statistics of the built model is significantly different from the statistics of the actual process noise. The statistical properties of the modeled noise are generally too ideal. In the running process of the actual system, the actual system may be affected by random factors such as strong electromagnetic interference, so that the statistical characteristics of the actual system are greatly changed. Third, modeling the statistical characteristics of the actual system initial state is inaccurate. Fourth, parameters of the actual system change. Due to aging, damage and other reasons of the components of the actual system, parameters of the system change (slowly change or suddenly change), so that the original model is not matched with the actual system.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention aims to provide an algorithm for taking the value of a filtering estimated value, which is used for carrying out online optimization on the filtering estimated value by adding a corresponding sampling point factor to a state estimated value and realizing the speed tracking of a target in a nonlinear system by virtue of online dynamic compensation.
In order to achieve the above purpose, the technical scheme adopted by the invention is as follows:
the invention comprises the following steps:
(1) The design model parameters, a propulsion system model of a patrol vessel are as follows:
in the above formula, the integer k is more than or equal to 0 and is a time index, x is a system state vector, represents the running speed of the patrol ship, y is a sensor observation value, represents the speed of the patrol ship measured by a sensor, w (k) is system noise and v (k+1) is measurement noise;
(2) Calculating state estimation value under EKF framework
(2a) Calculating corresponding state predicted values according to the target tracking model
(2b) According to (2 a), the corresponding observed predicted value is calculated
(2c) Calculating residual information gamma (k+1) according to (2 b);
(2d) Calculating a first-order linearization state equation and solving a state transition matrix
(2e) Calculating a first-order linearization observation equation and solving an observation matrix
(2f) Calculating a state prediction error covariance P (k+ 1|k) according to (2 d);
(2g) Calculating a gain matrix K (k+1) according to the steps (2 e) and (2 f);
(2h) Calculating state estimation values according to (2 a), (2 c) and (2 g)
(3) Obtained by EKF framesAs the center of the first-level traversal, by increasing the sampling point factor, the methodPerforming first-level traversal:
(3a) Traversing the rule step by step;
(3b) Sampling points in an initial sampling intervalAdded to->In (1) up to update->Is effective in (1);
(4) Using updatedFinding the center of the second-level traversal:
(4a) Using updatedCalculating updated->
(4b) Calculating updated residual information from (2 b) and (4 a)
(4c) According toResidual information with the smallest absolute value in the sequence is obtained to obtain corresponding +.>
(5) And (3) repeating all the steps in the steps (3) and (4), completing the secondary traversal, and outputting a state estimation value corresponding to the residual error with the minimum absolute value as the state estimation value at the current moment.
Compared with the prior art, the invention has the following advantages:
(1) The invention creates a mode for updating the filtering estimated value only, and can realize the optimization of the state estimated value obtained by various nonlinear filtering algorithms in theory.
(2) The invention combines the thought of step-by-step traversal, and greatly shortens the time for traversing the sampling point factors.
(3) The method can greatly improve the precision.
Drawings
FIG. 1 is a state variable simulation diagram;
fig. 2 is a state error simulation diagram.
Detailed Description
Embodiments of the present invention are described in detail below with reference to the drawings and examples.
According to the invention, a target speed tracking model is sleeved into an extended Kalman filtering algorithm, the state estimation value is updated by adding a sampling point factor to the state estimation value, the state estimation value is used for replacing a state prediction value, residual information generated by updating is detected in real time, the state estimation value is continuously regulated, and the state variable most suitable for the current moment is used for compensating the dynamic deviation of the system, so that the method is better applied to target tracking.
The invention relates to an online sampling design method based on an extended Kalman filtering state estimation value, which is applied to target speed tracking, and comprises the following steps:
step 1, a system model is set, and a propulsion system model of a patrol ship is as follows:
system state equation:
x(k+1)＝f(k,x(k))+w(k) (1)
observation equation:
y(k+1)＝h(k+1,x(k+1))+v(k+1) (2)
in the above formula, the integer k is equal to or greater than 0 and is a time index, x is a system state vector and represents the speed of the patrol ship, and y is a sensor observation value and represents the speed of the patrol ship measured by the sensor. The system noise w (k) and the measurement noise v (k+1) are Q and R white noise, and have the following statistical characteristics.
E{w(k)}＝E{v(k)}＝0 (3)
E{w(k)w T (j)}＝Q(k) (4)
E{v(k)v T (j)}＝R(k) (5)
E{w(k)v T (j)}＝0 (6)
The initial state x (0) is a random variable of gaussian distribution, and satisfies statistical characteristics:
E{x(0)}＝x 0 (7)
E{[x(0)-x 0 ][x(0)-x 0 ] T }＝P 0 (8)
and x (0) is statistically independent of w (k), v (k).
Step 2, calculating a state estimation value under an EKF framework
The specific implementation process of the step is as follows:
(2a) Calculating corresponding state predicted values according to the target tracking model
In the above-mentioned method, the step of,the state estimate at time k.
(2b) According to (2 a), the corresponding observed predicted value is calculated
(2c) Calculating residual information gamma (k+1) from (2 b)
(2d) Calculating a first-order linearization state equation and solving a state transition matrix
(2e) Calculating a first-order linearization observation equation and solving an observation matrix
(2f) Calculating a state prediction error covariance P (k+ 1|k) from (2 d)
(2g) Calculating a gain matrix K (k+1) according to (2 e) and (2 f)
(2h) Calculating state estimation values according to (2 a), (2 c) and (2 g)
Step 3 obtained with an EKF frameworkAs the center of the first-order traversal, by increasing the sampling point factor, for +.>Performing first-level traversal:
(3a) Traversing rules step by step
The stepwise traversal of the sampling point factor in the present embodiment is described in the form of a mathematical expression, in which the sampling point factor c (i) I (i) in (k+1)>0 and is a positive integer) represents the ith level traversal, sum (c) (i) (k+1)) represents all the sampling point factors included in the i-th level traversal. If i=1, c (1) (k+1) represents a first-order traversal of the sample point factor, sum (c) (1) (k+1)) represents all sample point factors contained in the first-level traversal.
If c (1) The interval taken by the (k+1) traversal is [0, n](n is the upper bound), equally divided into m parts, the spacing between two adjacent sampling point factors isThen there are:
(3b) The sampling point factor in the initial sampling intervalAdded to->In (1) up to update->Is composed of (1) a base and (2) a plurality of base
For convenience of description, the updated first-level traversal filter estimation value is setThe following are provided:
step 4 utilizing the updatedFinding the center of the second-level traversal:
(4a) Using updatedCalculating updated->
(4b) Calculating updated residual information from (2 b) and (4 a)
(4c) According toResidual information with the smallest absolute value in the sequence is obtained to obtain corresponding +.>
Recording deviceThe absolute value of the residual error generated after the first-level traversal is the smallest. According toI.e. can be defined by subscript j 1 =min get->Then the corresponding feedback is obtained by the formula (18)
And 5, repeating all the steps in the step 3 and the step 4, completing the second-level traversal, and outputting a state estimation value corresponding to the residual error with the minimum absolute value as the state estimation value at the current moment.
To be used forAs a traversing center, narrowing the traversing range by utilizing the step-by-step traversing idea, continuing the secondary traversing, repeating the steps (3) and (4), and obtaining the corresponding +.>
The second level is traversed and the first level is traversedFor the center, in->For the two-level traversing interval, equally dividing into m parts, the interval between two adjacent sampling point factors is
The analogy (17) shows that, at this time:
in the known typeWith reference to a first level traversal, can be defined byObtain corresponding->
Reams theAnd (3) obtaining the product.
So far, the online optimization design method based on the extended Kalman filtering state estimation value is completed.
The effect of the invention can be further illustrated by the following simulation results and field tests:
the propulsion system model of a patrol vessel is as follows:
the system state equation is:
the observation equation is:
the parameter represents the resistance of the hull a, b is the power of the ship engine, x is the speed of the ship, and the normal values of the parameters a and b are a respectively 0 =1 and b 0 =8, the dynamic system modeling noise is the sameA value of 0 covariance is q= [0.00001 ]]A sensor observes the state variable, the observed noise is the mean value of 0 covariance r= [0.001 ]]Is a gaussian white noise sequence of (c); system initialization x (0) =1, p (0|0) =1.
The range of the first-level traversal of the sampling point factors is [0,1], and each traversal is equally divided into 10 parts.
The corresponding parameters are set below so that dynamic errors occur in the propulsion system model of the patrol ship:
| simulation time | 0<k≤40 | 40<k<50 | 50≤k≤60 | 60<k<85 | 85≤k<100 |
| Parameter a | a(k)＝1.1 | a(k)＝1.3 | a(k)＝1.4 | a(k)＝1.2 | a(k)＝1.3 |
| Parameter b | b(k)＝7.8 | b(k)＝8.1 | b(k)＝7.9 | b(k)＝8.0 | b(k)＝8.1 |
Analysis of experimental results
The method for recording the band extension Kalman filtering during simulation is 'EKF', the method for recording the on-line sampling design based on the extended Kalman filtering state estimation value is 'EKF+', and a state variable simulation diagram and a state error simulation diagram are respectively given in FIG. 1 and FIG. 2.
The recorded data are as follows:
| filtering mode | EKF | EKF+ |
| Mean square error | 0.6475 | 0.0095 |
Through experimental simulation, the method has the advantages that after the method is added, the precision of EKF filtering is higher by one order, because the method can update the state estimation value on line, utilize the residual information of each moment to check the quality of the filtering estimation value corresponding to each sampling point factor, keep preferentially, and continue on-line learning of the next stage, the mode of on-line learning sampling points enables the value of each state estimation value to be more suitable for the current moment through a step-by-step traversal algorithm, thereby achieving better speed tracking effect, relieving dynamic deviation caused by external environment to the system structure, and carrying out corresponding dynamic compensation, thereby achieving better filtering effect. Thus, the above experiments demonstrate the effectiveness of the inventive method of this patent.
Claims (1)
1. The online optimization design method based on the extended Kalman filtering state estimation value is applied to target speed tracking and comprises the following steps:
(1) The model parameters are designed, and a propulsion system model of the patrol ship is set as follows:
in the above formula, the integer k is more than or equal to 0 and is a time index, x is a system state vector, represents the running speed of the patrol ship, y is a sensor observation value, represents the speed of the patrol ship measured by a sensor, w (k) is system noise and v (k+1) is measurement noise;
(2) Calculating state estimation value under EKF framework
(2a) Calculating corresponding state predicted values according to the target tracking model
(2b) According to (2 a), the corresponding observed predicted value is calculated
(2c) Calculating residual information gamma (k+1) according to (2 b);
(2d) Calculating a first-order linearization state equation and solving a state transition matrix
(2e) Calculating a first-order linearization observation equation and solving an observation matrix
(2f) Calculating a state prediction error covariance P (k+ 1|k) according to (2 d);
(2g) Calculating a gain matrix K (k+1) according to the steps (2 e) and (2 f);
(2h) Calculating state estimation values according to (2 a), (2 c) and (2 g)
(3) Obtained by EKF framesAs the center of the first-level traversal, by increasing the sampling point factor, the methodPerforming first-level traversal:
(3a) Traversing the rule step by step;
the progressive traversal of the sampling point factors is described by a mathematical expression, wherein the sampling point factors c (i) I in (k+1) represents an ith level traversal, sum (c) (i) (k+1)) represents all sampling point factors included in the i-th level traversal;
if i=1, c (1) (k+1) represents a first-order traversal of the sample point factor, sum (c) (1) (k+1)) represents all sampling point factors contained in the first-level traversal;
(3b) Sampling points in an initial sampling intervalAdded to->In (1) up to update->Wherein j is 2 ＝1,2,···,m；
(4) Using updatedFinding the center of the second-level traversal:
(4a) Using updatedCalculating updated->
(4b) Calculating updated residual information from (2 b) and (4 a)
(4c) According toResidual information with the smallest absolute value in the sequence is obtained to obtain corresponding +.>
(5) Repeating all steps (3) and (4), completing the second-level traversal, and outputting a state estimation value corresponding to the residual error with the minimum absolute value as the state estimation value at the current moment;
to be used forAs a traversing center, narrowing the traversing range by utilizing the step-by-step traversing idea, continuing the secondary traversing, repeating the steps (3) and (4), and obtaining the corresponding +.>
The second level is traversed and the first level is traversedCentered on/>The interval of the second-level traversal is equally divided into m parts.
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