CN109031276A - Adaptive iteration volume kalman filter method in target following with forgetting factor - Google Patents
Adaptive iteration volume kalman filter method in target following with forgetting factor Download PDFInfo
- Publication number
- CN109031276A CN109031276A CN201710436120.XA CN201710436120A CN109031276A CN 109031276 A CN109031276 A CN 109031276A CN 201710436120 A CN201710436120 A CN 201710436120A CN 109031276 A CN109031276 A CN 109031276A
- Authority
- CN
- China
- Prior art keywords
- value
- volume
- volume point
- forgetting factor
- point
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
Classifications
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
- G01S13/66—Radar-tracking systems; Analogous systems
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
- G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
Landscapes
- Engineering & Computer Science (AREA)
- Radar, Positioning & Navigation (AREA)
- Remote Sensing (AREA)
- Computer Networks & Wireless Communication (AREA)
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Filters That Use Time-Delay Elements (AREA)
Abstract
The invention discloses the adaptive iteration volume kalman filter methods in target following with forgetting factor, this method analyzes a kind of citation form-filtering of Target state estimator in target following, novelty proposes the method that forgetting factor is combined with adaptive iteration volume Kalman filtering, both the effect of forgetting factor can have been played, reduce influence of the historical data to filter result, filtering algorithm precision itself can be improved again and handle the ability of nonlinear problem, will finally realize in target following and target is accurately estimated.
Description
Technical field
The invention belongs to target tracking domains, and in particular to the adaptive iteration volume in target following with forgetting factor
Kalman filter method.
Background technique
After there is first radar tracking station SCR-28, target following technology is increasingly becoming on military and civilian
Popular one of research field.Wax first proposed the basic conception of target following, and subsequent target following research is theoretically
Start formally to be established.The seventies, Kalman propose Kalman filtering algorithm, and later Kalman filtering algorithm starts
It is related to the field of target following, the technology of target following is further developed.Target following is actually to target-like
The problem of state tracking filter, the estimation that dbjective state is carried out by the target measuring value that sensor has obtained.Target following
Technology is always the basic research project in military and civilian field, and the technology of target following exists derived from military needs
Military affairs are widely used.For example, defence, air target tracking and the attack of cannon class and guided missile class Ballistic Target, sea
Bank monitoring system and airborne early-warning system.Also have urgent demand and important role at civilian aspect, for example, ground and
Control, electron medicine and GPS navigation system of air traffic etc..Kalman filtering algorithm is the filter being most widely used at present
Wave method has obtained preferable application communication, Navigation, Guidance and Control etc. are multi-field.
The problem of target following itself is a filtering when process noise and measures the Gauss white noise that noise is all zero-mean
When sound, and system equation be it is linear when, then Kalman filter at this time is linear non-skew minimum variance es-timation device.But
It is that system is often nonlinear in reality, in order to accurately describe many practical problems, for the non-linear of state equation
With the nonlinear feature of measurement equation, it has to nonlinear model is established, with the expansion of nonlinear filtering application field
Exhibition, actual environment it is more complicated and changeable, Target Tracking System shows more different features, as noise correlation and
The non-Gaussian system etc. of noise cannot be resolved for these existing non-linear filtering methods of complication system feature, need into
One step is perfect.Therefore, it finds significantly more efficient filtering algorithm and has become many experts to solve the filtering problem of nonlinear system
One of research hotspot of scholar.
Gauss proposed the optimal filter method based on minimum variance earliest in 1809, least squares filtering, due to
The statistical property of signal is required no knowledge about, so being still widely used at present.The 40's of 20th century, wiener propose wiener filter
Wave has established the basis of optimal filter theory, it will be handled observation currently and previously, computationally intensive, and only
Stationary process can be handled, practical application is not easy to.The 70's, Kalman propose Kalman filtering algorithm, using linear system
Equation inputs observation data by system, the algorithm of optimal estimation is carried out to system mode.Later period is due to every field logarithm
According to the demand of processing, the method for Kalman filtering is widely used.At the same time, kalman filter method is applied to
The field of target following, the technology of target following start to be concerned by people and further study.In practice, it answers
With standard Kalman filtering algorithm, there are limitations, linear Gaussian system are suitable only for, when state equation and measurement equation
When being all linear, and process noise and noise is measured when being all the white Gaussian noise of zero-mean, Kalman filtering algorithm
It is only optimal algorithm for estimating.However the system in reality is often nonlinear, in order to accurately describe much actually to ask
Topic, for the nonlinear feature of the non-linear and measurement equation of state equation, it has to nonlinear model is established, so
When facing nonlinear system problem, a large amount of scholar begins one's study nonlinear filtering algorithm, and there has been proposed the non-of suboptimum
Linear filtering algorithm solves this problem, mainly includes Extended Kalman filter (EKF) algorithm, Unscented kalman filtering
(UKF) algorithm, volume Kalman filtering algorithm (CKF) and particle filter (PF) algorithm etc..
Summary of the invention
In view of the deficiencies of the prior art, the present invention proposes the adaptive iteration volumes in target following with forgetting factor
Kalman filter method.
Adaptive iteration volume kalman filter method in target following provided by the invention with forgetting factor, including
Following steps:
Step 1: establishing model for goal systems, it includes two equations, state equation and observational equation, respectively such as
Shown in lower:
In formula, f ()-system nonlinear state function；
H ()-system nonlinear measurement function；
xkSystem n ties up state vector；
zkSystem m ties up observed quantity.
Assuming that process noise wk-1With measurement noise vkIt independently of each other, be mean value is zero, covariance is respectively Qk-1And Rk's
White Gaussian noise.
Initialization:
Step 2: the time updates
1) volume point X is calculatedJ, k-1And the volume point X propagated through nonlinear state equationJ, k
XJ, k=f (XJ, k-1) (4)
In formula: ξjIndicate volume point,Remember that n dimension unit vector is e=[1,0,0..., 0]T, use [1]
It indicates to carry out fully intermeshing to the element of e and changes the point set that the symbol of element generates, [1]jIndicate point concentrate [1] arrange for j-th to
Amount；Such as when 2 dimension, then it indicates following set:
Sk-1=chol (Pk-1), the Cholesky decomposition of chol () representing matrix.
2) predictive estimation value is calculatedWith prediction variance
In formula:
Step 3: delivery value Z of the volume point through measurement equation is calculatedJ, kAnd measured value
ZJ, k=h (XJ, k) (7)
Wherein λ is forgetting factor, λ=max { 1, trace (N in step 2k)/trace(Mk), effect be in order to
The length of restriction filter, the weight for allowing the legacy data in filter value to account for become smaller, and new data weight becomes larger, and then make estimation more
It is accurate to add.
Step 4: judge whether iteration
Calculate prediction measured valueWith actual observed value zk, volume point delivery value ZJ, kWith actual observed value zkFitness
Function f1And f2, the degree of deviation that the volume point of sampling and target are really estimated is determined according to fitness function ratio ρ, thus adaptive
It should determine whether to be iterated resampling.Specific step is as follows.
1) fitness function is defined
Predict the fitness function f of measured value and actual observed value1For
The fitness function f of volume point delivery value and actual observed value2For
Fitness function ratio ρ are as follows:
Wherein: zkFor actual observed value；To predict measured value；ZJ, kFor volume point delivery value；RkFor observation noise side
Difference.
2) whether Criterion of Iterative
If ρ < 1, the effective approaching to reality estimation of the volume point of sampling is indicated, then without iteration；If ρ > 1, indicate into
Row iteration, return step two, according to predictive estimation valueWith prediction covarianceAs initial value, above step is repeated.
Step 5: it measures and updates
1) new breath variance P is calculatedzzWith covariance Pxz
2) gain K is calculatedk
Kk=Pzz(Pzz)-1 (11)
3) state of computing system updatesP is updated with covariancek
Further, in the step 2, the time updates: 1) calculating volume point XJ, k-1And through nonlinear state side
The volume point X that journey is propagatedJ, k, obtained using 3 rank spherical surfaces-radial direction volume criterion；2) predictive estimation value is calculatedWith prediction varianceThe weight that forgetting factor λ allows the legacy data in filter value to account for wherein is added in prediction variance to become smaller, new data weight becomes
Greatly, and then keep estimation more accurate.
In the step 3, the delivery value Z of the calculating volume point through measurement equationJ, kAnd measured valueI.e. by step 2
Obtained in the volume point propagated of nonlinear state equation obtain delivery value according to formula (7), then by delivery value according to formula
(8) measured value is obtained.
In the step 4, the iteration that judges whether: prediction measured value is calculatedWith actual observed value zkFitness
Function f1, volume point delivery value ZJ, kWith actual observed value zkFitness function f2, further according to the big of fitness function ratio ρ
Small volume point and the degree of deviation really estimated of target to determine sampling, to adaptively determine whether to be iterated to adopt again
Sample indicates the effective approaching to reality estimation of sampled point, then without iteration if ρ < 1；If ρ > 1, expression is iterated.
In the step 5, the measurement updates: 1) calculating new breath variance PzzWith covariance Pxz, see formula (9)；2) it counts
Calculate gain Kk, it is calculated by the resulting new breath variance of formula (9) by formula (10)；3) state of computing system updatesWith
Covariance updates Pk。
Present invention solution current filter arithmetic accuracy is not high enough, to the biggish major issue of target prediction error, that is, provides
One filtering method that forgetting factor and adaptive iteration volume Kalman filtering are combined, reduces the error of prediction,
There is presently no the method that the two is combined presence.Remarkable advantage of the present invention has: can both play the work of forgetting factor
With reducing influence of the historical data to filter result, and filtering algorithm can be improved itself precision and processing nonlinear problem
Ability will finally be realized in target following and accurately be estimated target.
Detailed description of the invention
Fig. 1 is target following basic principle；
Fig. 2 is the flow chart of this method.
Specific embodiment
Following further describes the present invention with reference to the drawings.
The present invention provides the adaptive iteration volume kalman filter method in target following with forgetting factor, such as Fig. 1
Shown, the target following basic principle, object tracking process can not be defined as estimation target at current time (filtering) and not
Carry out the process of (prediction) any moment state.It is provided by the invention it is a kind of in target following with the adaptive of forgetting factor
Iteration volume kalman filter method includes the following steps, and is described in conjunction with attached drawing 2:
Step 1: establishing model for goal systems, it includes two equations, state equation and observational equation, respectively such as
Shown in lower:
In formula, f ()-system nonlinear state function；
H ()-system nonlinear measurement function；
xkSystem n ties up state vector；
zkSystem m ties up observed quantity.
Assuming that process noise wk-1With measurement noise vkIt independently of each other, be mean value is zero, covariance is respectively Qk-1And Rk's
White Gaussian noise.
Initialization:
Step 2: the time updates
1) volume point X is calculatedJ, k-1And the volume point X propagated through nonlinear state equationJ, k
XJ, k=f (XJ, k-1) (4)
In formula: ξjIndicate volume point,Remember that n dimension unit vector is e=[1,0,0..., 0]T, use [1]
It indicates to carry out fully intermeshing to the element of e and changes the point set that the symbol of element generates, [1]jIndicate point concentrate [1] arrange for j-th to
Amount；Such as when 2 dimension, then it indicates following set:
Sk-1=chol (Pk-1), the Cholesky decomposition of chol () representing matrix.
2) predictive estimation value is calculatedWith prediction variance
In formula:
Step 3: calculating delivery value Z of the volume point through measurement equationJ, kAnd measured value
ZJ, k=h (XJ, k) (7)
Wherein λ is forgetting factor, λ=max { 1, trace (N in step 2k)/trace(Mk), effect is to limit
The length of filter processed, the weight for allowing the legacy data in filter value to account for become smaller, and new data weight becomes larger, and then make estimation more
Accurately.
Step 4: judging whether iteration
Calculate prediction measured valueWith actual observed value zk, volume point delivery value ZjkWith actual observed value zkFitness letter
Number f1And f2, the degree of deviation that the volume point of sampling and target are really estimated is determined according to fitness function ratio ρ, thus adaptively
Determine whether to be iterated resampling.Specific step is as follows.
1) fitness function is defined
Predict the fitness function f of measured value and actual observed value1For
The fitness function f of volume point delivery value and actual observed value2For
Fitness function ratio ρ are as follows:
Wherein: zkFor actual observed value；To predict measured value；ZJ, kFor volume point delivery value；RkFor observation noise side
Difference.
2) whether Criterion of Iterative
If ρ < 1, the effective approaching to reality estimation of the volume point of sampling is indicated, then without iteration；If ρ > 1, indicate into
Row iteration, return step two, according to predictive estimation valueWith prediction covarianceAs initial value, above step is repeated.
Step 5: measuring and update
1) new breath variance P is calculatedzzWith covariance Pxz
2) gain K is calculatedk
Kk=Pzz(Pzz)-1 (11)
3) state of computing system updatesP is updated with covariancek
The above is only the contents of the present invention, oneself, is not intended to restrict the invention, and is come for those skilled in the art
It says, the invention may be variously modified and varied.All within the spirits and principles of the present invention, made any modification, equivalent
Replacement, improvement etc., should all be included in the protection scope of the present invention.
Claims (5)
1. the adaptive iteration volume kalman filter method in target following with forgetting factor, which is characterized in that this method packet
Include following steps:
Step 1: establishing model for goal systems, it includes two equations, state equation and observational equation, the following institute of difference
Show:
In formula, f ()-system nonlinear state function；
H ()-system nonlinear measurement function；
xkSystem n ties up state vector；
zkSystem m ties up observed quantity.
Assuming that process noise wk-1With measurement noise vkIt independently of each other, be mean value is zero, covariance is respectively Qk-1And RkWhite Gaussian
Noise.
Initialization:
Step 2: the time updates
1) volume point X is calculatedJ, k-1And the volume point X propagated through nonlinear state equationJ, k
XJ, k=f (XJ, k-1) (4)
In formula: ξjIndicate volume point,Remember that n dimension unit vector is e=[1,0,0..., 0]T, use [1] expression pair
The element of e carries out fully intermeshing and changes the point set that the symbol of element generates, [1]jIndicate that point concentrates j-th of column vector of [1]；Such as
When 2 dimension, then it indicates following set:
Sk-1=chol (Pk-1), the Cholesky decomposition of chol () representing matrix.
2) predictive estimation value is calculatedWith prediction variance
In formula:
Step 3: delivery value Z of the volume point through measurement equation is calculatedJ, kAnd measured value
ZJ, k=h (XJ, k) (7)
Wherein λ is forgetting factor, λ=max { 1, trace (N in step 2k)/trace(Mk), effect is to limit filter
The length of wave device, the weight for allowing the legacy data in filter value to account for become smaller, and new data weight becomes larger, and then keep estimation more accurate.
Step 4: judge whether iteration
Calculate prediction measured valueWith actual observed value zk, volume point delivery value ZJ, kWith actual observed value zkFitness function f1
And f2, the degree of deviation that the volume point of sampling and target are really estimated is determined according to fitness function ratio ρ, to adaptively determine
Whether resampling is iterated.Specific step is as follows.
1) fitness function is defined
Predict the fitness function f of measured value and actual observed value1For
The fitness function f of volume point delivery value and actual observed value2For
Fitness function ratio ρ are as follows:
Wherein: zkFor actual observed value；To predict measured value；ZJ, kFor volume point delivery value；RkFor observation noise variance.
2) whether Criterion of Iterative
If ρ < 1, the effective approaching to reality estimation of the volume point of sampling is indicated, then without iteration；If ρ > 1, expression changes
Generation, return step two, according to predictive estimation valueWith prediction covarianceAs initial value, above step is repeated.
Step 5: it measures and updates
1) new breath variance P is calculatedzzWith covariance Pxz
2) gain K is calculatedk
Kk=Pzz(Pzz)-1 (11)
3) state of computing system updatesP is updated with covariancek
2. the adaptive iteration volume kalman filter method in target following according to claim 1 with forgetting factor,
It is characterized by: the time updates in the step 2: 1) calculating volume point XJ, k-1And propagated through nonlinear state equation
Volume point XJ, k, obtained using 3 rank spherical surfaces-radial direction volume criterion；2) predictive estimation value is calculatedWith prediction varianceWherein exist
Predict varianceThe weight that middle addition forgetting factor λ allows the legacy data in filter value to account for becomes smaller, and new data weight becomes larger, and then makes
It is more accurate to estimate.
3. the adaptive iteration volume kalman filter method in target following according to claim 1 with forgetting factor,
It is characterized by: in the step 3, the delivery value Z of the calculating volume point through measurement equationJ, kAnd measured valueI.e. by step
The volume point that nonlinear state equation obtained in rapid two is propagated obtains delivery value according to formula (7), then by delivery value according to
Formula (8) obtains measured value.
4. the adaptive iteration volume kalman filter method in target following according to claim 1 with forgetting factor,
It is characterized by: the iteration that judges whether: calculating prediction measured value in the step 4With actual observed value zkAdaptation
Spend function f1, volume point delivery value ZJ, kWith actual observed value zkFitness function f2, further according to the big of fitness function ratio ρ
Small volume point and the degree of deviation really estimated of target to determine sampling, to adaptively determine whether to be iterated to adopt again
Sample indicates the effective approaching to reality estimation of the volume point of sampling, then without iteration if ρ < 1；If ρ > 1, expression changes
Generation.
5. the adaptive iteration volume kalman filter method in target following according to claim 1 with forgetting factor,
It is characterized by: the measurement updates in the step 5: 1) calculating new breath variance PzzWith covariance Pxz, see formula (9)；2)
Calculate gain Kk, it is calculated by the resulting new breath variance of formula (9) by formula (10)；3) state of computing system updates
P is updated with covariancek。
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201710436120.XA CN109031276A (en) | 2017-06-09 | 2017-06-09 | Adaptive iteration volume kalman filter method in target following with forgetting factor |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201710436120.XA CN109031276A (en) | 2017-06-09 | 2017-06-09 | Adaptive iteration volume kalman filter method in target following with forgetting factor |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN109031276A true CN109031276A (en) | 2018-12-18 |
Family
ID=64630043
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201710436120.XA Pending CN109031276A (en) | 2017-06-09 | 2017-06-09 | Adaptive iteration volume kalman filter method in target following with forgetting factor |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN109031276A (en) |
Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109582915A (en) * | 2019-01-28 | 2019-04-05 | 杭州电子科技大学 | The non-linear observability degree adaptive filter method of improvement applied to bearingsonly tracking |
| CN110740127A (en) * | 2019-09-26 | 2020-01-31 | 浙江工业大学 | deviation attack estimation method based on improved adaptive Kalman filtering |
| CN110824432A (en) * | 2019-08-28 | 2020-02-21 | 深圳大学 | Radar clutter suppression method, device and computer readable storage medium |
| CN115529606A (en) * | 2021-06-25 | 2022-12-27 | 中国移动通信集团吉林有限公司 | Parameter updating method and system and electronic equipment |
| CN115902667A (en) * | 2023-02-15 | 2023-04-04 | 广东电网有限责任公司东莞供电局 | Lithium battery SOC estimation method based on weight and volume point self-adaption |
-
2017
- 2017-06-09 CN CN201710436120.XA patent/CN109031276A/en active Pending
Cited By (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109582915A (en) * | 2019-01-28 | 2019-04-05 | 杭州电子科技大学 | The non-linear observability degree adaptive filter method of improvement applied to bearingsonly tracking |
| CN109582915B (en) * | 2019-01-28 | 2023-08-18 | 杭州电子科技大学 | Improved nonlinear observability self-adaptive filtering method applied to pure azimuth tracking |
| CN110824432A (en) * | 2019-08-28 | 2020-02-21 | 深圳大学 | Radar clutter suppression method, device and computer readable storage medium |
| CN110824432B (en) * | 2019-08-28 | 2023-02-28 | 深圳大学 | Radar clutter suppression method, device and computer readable storage medium |
| CN110740127A (en) * | 2019-09-26 | 2020-01-31 | 浙江工业大学 | deviation attack estimation method based on improved adaptive Kalman filtering |
| CN110740127B (en) * | 2019-09-26 | 2022-03-04 | 浙江工业大学 | Improved adaptive Kalman filtering-based estimation method for bias attack |
| CN115529606A (en) * | 2021-06-25 | 2022-12-27 | 中国移动通信集团吉林有限公司 | Parameter updating method and system and electronic equipment |
| CN115902667A (en) * | 2023-02-15 | 2023-04-04 | 广东电网有限责任公司东莞供电局 | Lithium battery SOC estimation method based on weight and volume point self-adaption |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN109031276A (en) | Adaptive iteration volume kalman filter method in target following with forgetting factor | |
| CN105021092B (en) | A kind of guidance information extracting method of strapdown homing target seeker | |
| Zhang et al. | Hybrid algorithm based on MDF-CKF and RF for GPS/INS system during GPS outages (April 2018) | |
| Mu et al. | Iterated cubature Kalman filter and its application | |
| Zhao et al. | A filtering approach based on MMAE for a SINS/CNS integrated navigation system | |
| Yu et al. | State dependent multiple model-based particle filtering for ballistic missile tracking in a low-observable environment | |
| Chan et al. | Real-time approaches to the estimation of local wind velocity for a fixed-wing unmanned air vehicle | |
| Kaba et al. | Generalized bias compensated pseudolinear Kalman filter for colored noisy bearings-only measurements | |
| CN114608568A (en) | Multi-sensor-based information instant fusion positioning method | |
| CN114462293A (en) | Method for predicting medium and long-term trajectory of hypersonic target | |
| Park et al. | Grid support adaptation for point mass filter based terrain referenced navigation using mutual information | |
| Bruno et al. | Improved particle filters for ballistic target tracking | |
| Garapati Vaishnavi et al. | Underwater bearings-only tracking using particle filter | |
| Zhao et al. | Multiple model adaptive estimation algorithm for SINS/CNS integrated navigation system | |
| Yang et al. | Particle swarm optimization algorithm for passive multi-target tracking | |
| Zhang | An adaptive unscented kalman filter for dead reckoning systems | |
| Duong et al. | Non-linear, non-Gaussian estimation for INS/GPS integration | |
| CN112595319A (en) | Model adaptive compensation return trajectory estimation algorithm | |
| Flåten et al. | Rao-blackwellized particle filter for turn rate estimation | |
| Nie et al. | Adaptive tracking algorithm based on 3D variable turn model | |
| Nie et al. | Comparison of nonlinear filtering approach in tightly-coupled GPS/INS navigation system | |
| Sönmez et al. | Analysis of performance criteria for optimization based bearing only target tracking algorithms | |
| Rutkowski et al. | Path planning for cooperative navigation with inter-agent range measurements | |
| Gao et al. | Improved regularized particle filter algorithm for SINS/SAR integrated navigation | |
| CN111796271B (en) | Target tracking method and device under constraint of proportional guidance destination |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| WD01 | Invention patent application deemed withdrawn after publication | ||
| WD01 | Invention patent application deemed withdrawn after publication |
Application publication date: 20181218 |