CN110110475A - Extended Kalman filter method based on on-line study fading factor - Google Patents

Extended Kalman filter method based on on-line study fading factor Download PDF

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CN110110475A
CN110110475A CN201910419234.2A CN201910419234A CN110110475A CN 110110475 A CN110110475 A CN 110110475A CN 201910419234 A CN201910419234 A CN 201910419234A CN 110110475 A CN110110475 A CN 110110475A
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traversal
fading factor
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文成林
唐兵
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Hangzhou Dianzi University
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Abstract

The invention discloses a kind of Extended Kalman filter methods based on on-line study fading factor.The present invention first refers to the thought of fading factor in strong tracking, by carrying out a certain amount of ergodic algorithm to fading factor, achievees the effect that update status predication error covariance.And then on-line control gain battle array, to obtain different state estimations, updated state estimation is replaced to the status predication value at current time, and obtain updated observation predicted value, updated observation predicted value is compared with observation, obtain residual information, it takes absolute value to all residual informations, and fading factor corresponding to the least residual after absolute value is extracted, centered on the fading factor, continue the traversal of next stage, finally obtained fading factor is returned after three-level traversal, and using the corresponding filtering estimated value of the fading factor as the filtering estimated value at current time.The method of the present invention has better filtering accuracy, and energy online updating, has certain practicability for Strong tracking filter.

Description

Extended Kalman filter method based on on-line study fading factor
Technical field
The invention belongs to the target tracking domain of nonlinear system, in particular to model parameter during a kind of system modelling There is deviation or because system running environment causes to can be used in target following there are the target velocity of dynamic deviation tracking field The data processing of optimization aim speed tracing.
Background technique
With science and technology progress and development, linear filtering theory be widely used in target following, information processing and In the application fields such as fault diagnosis.Wherein, the filtering mode headed by Kalman filter space flight and aviation, Financial Management, The fields such as unmanned plane are all made that outstanding contribution.But it is uncertain with the increase of system modelling complexity and running environment Property, cause the research of nonlinear system to have become instantly extremely urgent problem.Therefore, in order to Kalman filter is answered For nonlinear system, it is necessary to carry out some improvement to it.
Bucy, Sunahara et al. are proposed and are had studied Extended Kalman filter (Extended Kalman Filter, letter Claim EKF), kalman filtering theory is further applicable to non-linear field.The basic thought of EKF is that nonlinear system is linear Change, then carries out Kalman filtering, therefore EKF is a kind of suboptimal filtering.No mark Kalman then abandoned to nonlinear function into The traditional method of row linearisation, is handled one-step prediction equation using Unscented transform using Kalman linear filtering frame The non-linear problem of transmission of mean value and covariance.So that the statistic of nonlinear Distribution has higher computational accuracy, effectively gram The defect that the estimated accuracy for having taken Kalman filter is low, stability is poor.In addition, there are also volume Kalman filtering (CKF), particles to filter The methods of wave (PF), the filtering based on characteristic function are applied to nonlinear system.
In addition, Zhou Donghua et al. on the basis of EKF, constructs a kind of extension of nonlinear system regiment commander suboptimum fading factor Kalman filtering (SFEKF) automatically adjusts one-step prediction error covariance by introducing fading factor, realizes strong tracking function Can, improve estimated accuracy.But problem is, the acquisition of prior information is often more difficult, and how Suo Huoqu prior information is No credible, whether the selection for weakening the factor is proper, these reasons often limit the effect of Strong tracking filter.
Summary of the invention
The shortcomings that in order to overcome the SFEKF prior art, the purpose of the present invention is to provide one kind be applied to target velocity with The Extended Kalman filter method of the on-line study fading factor of track passes through design one based on the thought of fading factor in SFEKF Kind traverses the mode of fading factor step by step, realizes the speed tracing in nonlinear system to target.
To achieve the goals above, the technical solution adopted by the present invention is that:
The present invention includes the following steps:
(1) design a model parameter:
The propulsion system model of patrol boat is as follows:
In above formula, integer k >=0 is time index, and x is system mode vector, indicates the speed of patrol foot, and y is to pass Sensor observation indicates the speed of the patrol boat as measured by sensor；W (k) is system noise, and v (k+1) is measurement noise；
(2) status predication value, observation predicted value, observation predicted value, residual information, state is calculated under EKF frame to turn Move matrix, observing matrix:
(2a) calculates corresponding status predication value according to above-mentioned model
(2b) calculates corresponding observation predicted value according to (2a)
(2c) calculates residual information γ (k+1) according to (2b)；
(2d) calculates first-order linear state equation, solving state transfer matrix
(2e) calculates first-order linear observational equation, solves observing matrix
(3) it gives level-one and traverses initial range, level-one traversal is carried out to fading factor λ (k+1), is found out updated multiple State estimation
(3a) determines level-one traversal rule；
(3b) by level-one traverse in include all fading factors be added in P (k+1 | k), obtain updated
(3c) calculates updated gain battle array according to (2e), (3b)
(3d) calculates updated state estimation according to (2a), (2c) and (3c)
(4) least residual information is calculatedAnd it finds and is best suited for current time
(4a) will be obtained in (3d)Instead of in (2a)It finds out after being updated in (2b) 's
(4b) is as obtained in (2c) and (4a)It updatesIt calculatesMiddle absolute value is most SmallIt is found out using feedback corresponding
(5) withAs traversal center, traversal range is reduced using traversal thought step by step, continues second level traversal, All steps in repetition (3), (4), find out corresponding
(6) withAs traversal center, traversal range is reduced using traversal thought step by step, continues three-level traversal, All steps in repetition (3), (4), find out correspondingAnd it calculates and is best suited for the filtering at current time and estimates Evaluation
Target following model is inserted in expanded Kalman filtration algorithm by the present invention first, by SFEKF to status predication The thought of fading factor is added in error covariance, fading factor therein is traversed step by step, and utilizes and traverses step by step The residual information online adaptive generated afterwards ground adjustment state estimated value, to be preferably applied for target following.
Compared with prior art, the invention has the following advantages that
(1) residual information of changing over of the invention is merely able to detect the status of the filtering accuracy at a moment, then The filtering estimated value precision at current time is examined using the residual information at current time.
(2) the invention proposes a kind of methods based on on-line study fading factor, so that obtained by each fading factor It can be detected by the residual information at current time to state estimation, by the screening to residual information, can be made each The value of secondary traversal fading factor can be higher than the precision at a upper moment, realizes the function of on-line study.
(3) present invention incorporates the thoughts traversed step by step, and the time for traversing fading factor is greatly shortened.
Detailed description of the invention
Fig. 1 is fading factor traversing graph step by step；
Fig. 2 is state variable analogous diagram；
Fig. 3 is state error analogous diagram.
Specific embodiment
Below in conjunction with attached drawing, the invention will be further described.The present invention the following steps are included:
System model is arranged in step 1, and the propulsion system model of a patrol boat is as follows:
System state equation:
X (k+1)=f (k, x (k))+w (k) (1)
Observational equation:
Y (k+1)=h (k+1, x (k+1))+v (k+1) (2)
In above formula, integer k >=0 is time index, and x is system mode vector, indicates the speed of patrol foot, and y is to pass Sensor observation indicates the speed of the patrol boat as measured by sensor.System noise w (k) and measurement noise v (k+1) be Q and The white noise of R, and there is following statistical property.
E { w (k) }=E { v (k) }=0 (3)
E{w(k)wT(j) }=Q (k) (4)
E{v(k)vT(j) }=R (k) (5)
E{w(k)vT(j) }=0 (6)
Original state x (0) is the stochastic variable of Gaussian Profile, and meets statistical property:
E { x (0) }=x0 (7)
E{[x(0)-x0][x(0)-x0]T}=P0 (8)
And there are x (0) and w (k), v (k) statistical iteration.
Step 2 calculates error co-variance matrix P (k+1k) under EKF frame, and the specific implementation process of the step is as follows:
(2a) calculates corresponding status predication value according to target following model
In above formula,For the state estimation at k moment.
(2b) calculates corresponding observation predicted value according to (2a)
(2c) calculates residual information γ (k+1) according to (2b)
(2d) calculates first-order linear state equation, solving state transfer matrix
(2e) calculates first-order linear observational equation, solves observing matrix
Step 3 gives level-one traversal initial range, carries out level-one traversal to fading factor λ (k+1), finds out updated more A state estimation
(3a) determines level-one traversal rule
Traversing in the present embodiment step by step takes the form of mathematic(al) representation to describe, wherein λ(i)(k+1) i (i in > 0, and be positive integer) indicate that the i-stage of k+1 moment fading factor λ (k+1) traverses, sum (λ(i)(k+1)) the k+1 moment the is indicated All fading factors for including in i grades of traversals.If i=1, λ(1)(k+1) it indicates to carry out level-one traversal, sum to fading factor (λ(1)(k+1)) all fading factors for including in level-one traversal are indicated.
If λ(1)(k+1) section for traversing value is [1, n] (n is the upper bound), is divided into m parts, then two adjacent fading factors Between spacing beThen have:
(3b) by level-one traverse in include all fading factors be added in P (k+1 | k), obtain updated
It willIt brings the k+1 moment into, can obtain:
(3c) calculates updated gain battle array according to (2e), (3b)
(3d) calculates updated state estimation according to (2a), (2c) and (3c)
Step 4 calculates least residual informationAnd it finds and is best suited for current time
(4a) will be obtained in (3d)Instead of in (2a)It finds out updated in (2b)
(4b) is as obtained in (2c) and (4a)It updatesIt calculatesMiddle absolute value is most SmallIt is found out using feedback corresponding
Wherein,Indicate that absolute value numerical value is one the smallest in all residual errors generated after level-one traversal.According toAnd then it feeds back to obtain by subscript j=min corresponding
Step (5) withAs traversal center, traversal range is reduced using traversal thought step by step, continues second level time It goes through, repeats step (3), (4), find out corresponding
Secondary filter resulting fading factor after being traversed with level-oneCentered on, withFor the section of second level traversal, m parts are equally divided into, then between two adjacent fading factors Spacing isMatching test (14) is it is found that at this time:
In the formula of knowingIt traverses, can acquire referring to level-one Accordingly
(6) withAs traversal center, traversal range is reduced using traversal thought step by step, continues three-level traversal, All steps in repetition (3), (4), find out correspondingAnd it calculates and is best suited for the filtering at current time and estimates Evaluation
Three-level filtering resulting fading factor after being traversed with second levelCentered on, withFor the section of three-level traversal, m parts are equally divided into, then between two adjacent fading factors Spacing isFormula (14) is analogous to it is found that at this time:
Known to
It is traversed referring to level-one, according toAnd then it feeds back to obtain by subscript j=min correspondingI.e. It can acquire corresponding
It enables again?.
In Figure of description 1,Indicate the fading factor for being best suited for current time obtained after i grades of traversals,Indicate the beginning and end of i grades of traversal value intervals,It indicates to traverse the data point being not in contact with i+1 grades,Indicate the beginning and end of i+1 grades of traversal values.
Effect of the invention can be further illustrated by following test and simulation result:
The propulsion system model of one patrol boat is as follows:
System state equation are as follows:
Observational equation are as follows:
Parameter indicates resistance suffered by a hull, and b is the power of ship engine, and x is the speed of foot, parameter a and b Normal value be a respectively0=1.3 and b0=8, it be 0 covariance is the white of Q=[0.0001] that Modelling of Dynamic System noise, which is mean value, Noise sequence has a sensor to be observed state variable, and it be 0 covariance is [0.01] R=that observation noise, which is mean value, Gaussian sequence；System initialization x (0)=1, P (0 | 0)=1.
The range for the fading factor level-one traversal that the present invention provides is [1,100], and traversal is divided into 10 parts every time.Below Relevant parameter, which is arranged, makes the propulsion system model of patrol boat dynamic deviation occur:
Emulate the moment 0<k≤40 K=50 50≤k≤60 60<k<85 85≤k<100
Parameter a A (k)=1.1 A (k)=1.4 A (k)=1 A (k)=1.2 A (k)=1
Parameter b B (k)=7.8 B (k)=8 B (k)=8.1 B (k)=8.1 B (k)=8.2
Analysis of experimental results
In Figure of description, the Strong tracking filter method with fading factor is " SFEKF " when note emulates, and note is based on online The Extended Kalman filter method for learning fading factor is " TEKF ", and state variable analogous diagram and shape is set forth in Fig. 2 and Fig. 3 State error analogous diagram.Wherein, Fig. 2 state value is that timing indicates to accelerate from starting point toward destination forward direction, expression when state value is negative Inversely accelerate from destination toward starting point.
It is as follows to record data:
Filtering mode SFEKF TEKF
Mean square error 0.1062 0.0631
Pass through experiment simulation, it can be seen that two kinds of filtering modes in Fig. 2 suffer from preferably for tracking mode value Tracking effect.
But for Fig. 3, it can be seen that the tracking effect of TEKF is better than SFKEF, this is because TEKF energy online updating is gradually Disappear the factor, and examines filtering estimated value corresponding to each fading factor fine or not using the residual information at each moment, Preferentially retain, continues the on-line study of next stage.The mode of this on-line study passes through the algorithm traversed step by step and makes The value of each fading factor can reach better speed tracing effect more suitable for current time.But for SFEKF For, although the thought for introducing fading factor to be carved with a fading factor when each to the prediction error at current time Covariance is updated, but needs just obtain good filter effect when prior information value is proper, and gradually There is the phenomenon that being unsatisfactory for orthogonality principle during the factor that disappears value, SFEKF is caused to be degenerated to EKF.Therefore, above-mentioned experiment Show that the speed tracing effect of TEKF is better than SFKEF.

Claims (1)

1. the Extended Kalman filter method based on on-line study fading factor, it is characterised in that this method comprises the following steps:
(1) design a model parameter:
The propulsion system model of patrol boat is as follows:
In above formula, integer k >=0 is time index, and x is system mode vector, indicates the speed of patrol foot, y is sensor Observation indicates the speed of the patrol boat as measured by sensor；W (k) is system noise, and v (k+1) is measurement noise；
(2) status predication value, observation predicted value, observation predicted value, residual information, state transfer square are calculated under EKF frame Battle array, observing matrix:
(2a) calculates corresponding status predication value according to above-mentioned model
(2b) calculates corresponding observation predicted value according to (2a)
(2c) calculates residual information γ (k+1) according to (2b)；
(2d) calculates first-order linear state equation, solving state transfer matrix
(2e) calculates first-order linear observational equation, solves observing matrix
(3) it gives level-one and traverses initial range, level-one traversal is carried out to fading factor λ (k+1), finds out updated multiple states Estimated value
(3a) determines level-one traversal rule；
(3b) by level-one traverse in include all fading factors be added in P (k+1 | k), obtain updated
(3c) calculates updated gain battle array according to (2e), (3b)
(3d) calculates updated state estimation according to (2a), (2c) and (3c)
(4) least residual information is calculatedAnd it finds and is best suited for current time
(4a) will be obtained in (3d)Instead of in (2a)It finds out updated in (2b)
(4b) is as obtained in (2c) and (4a)It updatesIt calculatesMiddle absolute value is the smallestIt is found out using feedback corresponding
(5) withAs traversal center, traversal range is reduced using traversal thought step by step, continues second level traversal, repeats (3), all steps in (4), find out corresponding
(6) withAs traversal center, traversal range is reduced using traversal thought step by step, continues three-level traversal, repeats (3), all steps in (4), find out correspondingAnd calculate the filtering estimated value for being best suited for current time
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CN113314131A (en) * 2021-05-07 2021-08-27 武汉大学 Multistep audio object coding and decoding method based on two-stage filtering
CN114018250A (en) * 2021-10-18 2022-02-08 杭州鸿泉物联网技术股份有限公司 Inertial navigation method, electronic device, storage medium, and computer program product

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Publication number Priority date Publication date Assignee Title
CN111273084A (en) * 2020-02-24 2020-06-12 广东电网有限责任公司广州供电局 Adaptive strong tracking unscented Kalman filtering synchronous phasor parameter estimation method
CN111273084B (en) * 2020-02-24 2022-03-04 广东电网有限责任公司广州供电局 Adaptive strong tracking unscented Kalman filtering synchronous phasor parameter estimation method
CN113314131A (en) * 2021-05-07 2021-08-27 武汉大学 Multistep audio object coding and decoding method based on two-stage filtering
CN113314131B (en) * 2021-05-07 2022-08-09 武汉大学 Multistep audio object coding and decoding method based on two-stage filtering
CN114018250A (en) * 2021-10-18 2022-02-08 杭州鸿泉物联网技术股份有限公司 Inertial navigation method, electronic device, storage medium, and computer program product
CN114018250B (en) * 2021-10-18 2024-05-03 杭州鸿泉物联网技术股份有限公司 Inertial navigation method, electronic device, storage medium and computer program product

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