CN106526542A - Augmentation Kalman filtering method based on deterministic sampling - Google Patents

Augmentation Kalman filtering method based on deterministic sampling Download PDF

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CN106526542A
CN106526542A CN201610901537.4A CN201610901537A CN106526542A CN 106526542 A CN106526542 A CN 106526542A CN 201610901537 A CN201610901537 A CN 201610901537A CN 106526542 A CN106526542 A CN 106526542A
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augmentation
state
kalman filter
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王世元
冯亚丽
尹超
钱国兵
段书凯
王丽丹
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Southwest University
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    • 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
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    • G01S7/285—Receivers
    • G01S7/292—Extracting wanted echo-signals
    • 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

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Abstract

The invention discloses an augmentation Kalman filtering method based on deterministic sampling. The augmentation Kalman filtering method based on deterministic sampling includes the steps: utilizing a state reconstruction method to fuse the state, the process noise and the observation noise in the prediction step to expand a new state to xa of N=n+n+m dimension from the original x of n dimension; and in the error correction step, reserving deterministic sampling points which are obtained during the first sampling process. Compared with a traditional augmentation form, for the augmentation Kalman filtering method based on deterministic sampling, the state of the augmentation Kalman filter is augmented to n+n+m dimension from the original n dimension after the state of the augmentation Kalman filter fuses the process noise and the observation noise, so that the filtering accuracy in a high dimension target tracking system is substantially improved. Besides, the simulation experiment shows that in a complicated environment, the augmentation Kalman filtering algorithm shows relatively high robustness in the mutation interference and noise of the system, and can satisfy the requirement for a filter in a practical system on the premise of sacrificing certain amount of computation complexity, so that the augmentation Kalman filtering algorithm is a relatively good target tracking algorithm.

Description

It is a kind of based on a determination that property sampling extended kalman filter method
Technical field
It is the invention belongs to target following technical field, more particularly to a kind of based on a determination that the extended kalman filter of property sampling Method.
Background technology
Target following mainly passes through radar or wireless senser receiving data, carries out state by Kalman filter and estimates Meter, so that obtain positional information and the velocity information of moving target.The application of target following is extended from the military field of early stage Arrive in daily life, be one of more important Applied research fields of Kalman filtering algorithm.In order to efficiently solve target In tracing process in the high non-linearity and environment of modeling unknown disturbances impact, realize preferable tracking effect, it is all kinds of Non-linear Kalman filtering algorithm is suggested in succession.That what is be most widely used is extended Kalman filter (extended Kalman filter, EKF).The filtering accuracy of EKF is caused directly to receive mission nonlinear the first-order linear of nonlinear function The impact of degree, when nonlinear degree is higher, it may appear that filtering accuracy declines situations such as even dissipating.Additionally, EKF algorithms are needed The Jacobian matrix of computing system is wanted, this is difficult to for some nonlinear systems.Therefore, various integration sides Method is suggested, and to the Gauss weighted integral in effectively approximate nonlinear filtering, thus generates a class based on a determination that property is adopted The non-linear Kalman filtering device of sample.Wherein, based on Unscented transform (unscented transformation, UT) without mark card Thalmann filter (unscented Kalman filter, UKF) is by a series of weighting Sigma containing state distributed intelligence Point can obtain the single order and second-order statisticses of gaussian variable.But, in UKF, the selection of optimized parameter is still under study for action.People Mostly by test or empirically carry out arrange parameter, this have impact on the precision of filtering to a certain extent.By contrast, Volume Kalman filter (cubature Kalman filter, CKF) and sphere simplex-radial direction volume Kalman filtering Device (simplex spherical-radial cubature Kalman filter, SSRCKF), because of its higher numerical stability Property and need not consider that Parametric optimization problem becomes study hotspot in recent years.Compared with EKF, nonlinear degree it is higher be In system, UKF, CKF and SSRCKF can obtain higher precision and stability while using less amount of calculation.And high-order (referring mainly to five ranks) is although the proposition of volume criterion generates preferable filter effect, high-order weight negative value to a certain extent Appearance directly affects filter stability, thus the importance of low order (three ranks) has still obtained more accreditations.Based on true The non-linear Kalman filtering algorithm of qualitative sampling is both needed to independent sampling site once in prediction and two stages of error correction, and in some feelings Under condition, point repeatedly generates the loss that can cause higher-order statistics, so as to reducing filtering accuracy.Occur that earliest augmentation without Mark Kalman filter (augmented unscented Kalman filter, AUKF), its advantageous are in non additivity Under noise circumstance, after state and process noise and observation noise fusion, Jing once samples the statistical information of transmission state so that The filtering performance of AUKF is substantially better than UKF；But, it is under the hypothesis of additivity in process noise and observation noise, UKF can be The filter effect similar to AUKF is obtained while reducing amount of calculation.
In sum, the traditional lower order nonlinear Kalman filtering algorithm of solution is when high dimensional nonlinear tracking problem is processed The problems such as filtering accuracy decline of appearance, poor robustness, is necessary.
The content of the invention
It is an object of the invention to provide a kind of based on a determination that the extended kalman filter method of property sampling, it is intended to solve to pass The filtering accuracy that the lower order nonlinear Kalman filtering algorithm of system occurs when high dimensional nonlinear tracking problem is processed declines, robust Property difference problem.
The present invention is achieved in that a kind of based on a determination that the extended kalman filter method of property sampling, described based on true The extended kalman filter method adoption status reconstructing method of qualitative sampling, in forecast period by state vector x and process noise q And observation noise r three fusion is got up so that new state expands to N=n+n+m dimensions by the x that original n is tieed up By taking augmentation UKF as an example, a Sigma point is produced in the quantity of state of forecast period augmentation, and in error correction stages, remain first The Sigma points that secondary sampling is obtained.
Further, it is described based on a determination that property sampling extended kalman filter method include：
I) system initialization:In the initial value given state estimationAnd covarianceAfterwards, the first of augmented state is set Initial value isCovariance matrix is：
Ii) predict:Obtain sampled point
The N-dimensional sampled point for obtainingIn, the 1st arrives n behavior state sampled points(n+1)th arrives 2n behaviors Journey noise samples point2n+1 to 2N measuring behaviors noise samples point
Sampled pointWithSubstitute into state procedure EQUATION xk=f (xk-1)+qk-1In, obtain a series of through conversion Sampled point：
Calculate the predictive value and corresponding error co-variance matrix of augmented state：
Iii) error correction:Calculate the point after observational equation conversion：
The predictive value of difference calculating observation vector, the covariance of new breath, and the mutual association side between state and observation vector Difference matrix：
The same formula of renewal of state estimation and state estimation error co-variance matrixWith
Another object of the present invention is to provide it is a kind of by it is described based on a determination that property sampling extended kalman filter method The augmentation volume Kalman filter of preparation.
Another object of the present invention is to provide it is a kind of by it is described based on a determination that property sampling extended kalman filter method The augmentation sphere simplex of preparation-radial direction volume Kalman filter.
The present invention provide based on a determination that property sampling extended kalman filter method, compared with traditional augmentation form, this In invention extended kalman filter device after state fusion process noise and observation noise, augmentation is tieed up to n+n+m by original n Dimension, the filtering accuracy in higher-dimension Target Tracking System are significantly increased；Additionally, emulation experiment shows, in complex environment, For mutation disturbance and the noise of system itself, extended kalman filter algorithm proposed by the present invention shows stronger robust Property, can reach the requirement to performance of filter in real system on the premise of a certain amount of computation complexity is sacrificed, be one The preferable target tracking algorism of class.
Description of the drawings
Fig. 1 is the geometry schema schematic diagram of the movement of falling object provided in an embodiment of the present invention.
Fig. 2 is the mean square error curve synoptic diagram of target drop-off positions provided in an embodiment of the present invention.
Fig. 3 is track following schematic diagram provided in an embodiment of the present invention.
Fig. 4 is track following position mean square error curve synoptic diagram provided in an embodiment of the present invention.
Specific embodiment
In order that the objects, technical solutions and advantages of the present invention become more apparent, with reference to embodiments, to the present invention It is further elaborated.It should be appreciated that specific embodiment described herein is not used to only to explain the present invention Limit the present invention.
The present invention proposes a class based on a determination that the augmentation non-linear Kalman filtering algorithm of property sampling；Such algorithm is by shape State is merged with process noise and observation noise, only need to build a numerical integration point in whole filtering.This can not only More prior informations are obtained, the loss of the order of information that repeated sampling is caused is it also avoid.By target freely falling body and association Adjust two High-Dimensional Models of turning motion to demonstrate carried augmentation track algorithm can effectively reduce in real-time modeling method Mutation disturbance and effect of noise, improve tracking effect.
Below in conjunction with the accompanying drawings the application principle of the present invention is explained in detail.
1 based on a determination that the non-linear Kalman filtering algorithm of property sampling
1.1 Gaussian approximation filter frames
General Discrete Nonlinear dynamic system can be described as：
xk=f (xk-1)+qk-1 (1)
yk=h (xk)+rk (2)
Wherein state variable xk∈Rn, observation vector yk∈Rm；F () and h () are given nonlinear functions；qk-1With rkIt is the white Gaussian noise of zero-mean respectively, corresponding covariance matrix is Q respectivelykAnd Rk；
On the premise of Gauss assumes, with reference to bayesian theory, Bayesian filter can be regarded as and to a series of shapes be The solution of the multidimensional Gauss integration of nonlinear function × Gaussian probability density；It is theoretical using numerical integration, work as Gaussian probability density Function is that standard type is distributed N (x；0；When I), integration can be approximated to be：
Here, g (x) represents arbitrary nonlinear function, and L represents the total number of point, wiAnd ξiWeight and corresponding is represented respectively Point.
By linear transformationWith regard toIntegration can be similar to：
Wherein,The On Square-Rooting Matrices of P are represented, i.e., It is Multi-dimensional Gaussian distribution respectively with PAverage and covariance matrix.OrderThe Gauss of the system for then being described based on formula (1) and (2) is near May be summarized as follows like filter frame：
I) forecast period：
Wherein,Represent point, Sk-1It is Pk-1On Square-Rooting Matrices.
Ii) error correction stages：
Wherein：
Here,It is Pk|k-1On Square-Rooting Matrices.
1.2 based on the different sampled points for integrating criterions and weight
Numerical approximation integral expression shown in formula (4), the use of different integration criterions can obtain difference Numerical integration point and corresponding weight, wherein, modal point and weight have following several.
1.2.1 Sigma points
Weight size is accordingly：
Wherein,The i order components of the On Square-Rooting Matrices of representing matrix (n+ λ) P；0.001≤α≤1 is one Constant parameter, determines diffusion of the sampled point near average；β is the parameter of a consideration state prior information, in height Under this is assumed, general value is 2；λ=α2(n+k)-n is a scalar parameter, and parameter k is usually arranged as 0 in state estimation； WeightWithIt is respectively used to calculate average and covariance.
1.2.2 volume point
Based on L=2n volume point of three rank spheres-radial direction volume criterion and its being calculated as follows for weight：
Here eiA unit vector is represented, i-th element value is 1.
1.2.3 simple form point
L=2n+2 simple form point and corresponding weight coefficient based on three rank sphere simplexs-radial direction volume criterion is such as Under：
It is different from sphere-radial direction volume criterion, vectorial a hereiTo be made up of n+1 summit of n simplexs, i.e. ai =[ai,1,ai,2,…,ai,n]T, i=1,2 ..., n+1 is calculated as follows：
By above-mentioned Sigma points, volume point, simple form point and respective weight substitute into the filter shown in 1.1 sections respectively Ripple framework, can obtain a class based on a determination that the non-linear Kalman filtering device of property sampling, i.e. UKF, CKF and SSRCKF.
2 one classes are based on a determination that the augmentation non-linear Kalman filtering device of property sampling
Under known to nonlinear model, UKF is respectively necessary for independently taking Sigma points twice in forecast period and error correction stages, But in some cases, repeatedly generating for Sigma points not only increases amount of calculation and can also cause some higher-order statistics Lose, so as to have influence on filtering accuracy.In order to solve this problem, arithmetic accuracy is improved, augmentation Unscented kalman filtering is adopted More thoroughly state reconstruction method, i.e., got up state with process noise and observation noise three fusion in forecast period, So that new state is expanded to the x of N=n+n+m dimensions by the x that original n is tieed upa.In error correction stages, not resampling, but protect The Sigma points for having stayed first time sampling to obtain.By taking UKF as an example, the specific algorithm step of augmentation Unscented kalman filtering is summarized such as Under.
I) system initialization:In the initial value given state estimationAnd covarianceAfterwards, the first of augmented state is set Initial value isCovariance matrix is：
Ii) predict:Obtain sampled point
The N-dimensional sampled point for obtainingIn, the 1st arrives n behavior state sampled points(n+1)th arrives 2n behaviors Journey noise samples point2n+1 to 2N measuring behaviors noise samples pointShown in the same formula of the calculating (14) of weight size.
Sampled pointWithSubstitute in state procedure equation (1), obtain a series of sampled points through conversion：
Calculate the predictive value and corresponding error co-variance matrix of augmented state：
Iii) error correction:Calculate the point after observational equation conversion：
The predictive value of difference calculating observation vector, the covariance of new breath, and the mutual association side between state and observation vector Difference matrix：
The same formula of the renewal (7) of state estimation and state estimation error co-variance matrix, (8).
Based on above-mentioned algorithm frame, a class can be obtained based on a determination that the augmentation non-linear Kalman filtering device of property sampling, Such as augmentation volume Kalman filter (augmented cubature Kalman filter, ACKF), augmentation sphere simplex- Radial direction volume Kalman filter (augmented simplex-spherical cubature Kalman filter, ASSRCKF).From unlike class algorithm proposed by the present invention, this augmentation form is in forecast period only state and process Both noises merge, will n dimension state augmentation to n+n dimension, during so as to initializingCovariance matrix is：
In order to be distinguish between comparing, the wave filter of only fusion observation noise is expressed as AUKF1, ACKF1 in emulation And ASSRCKF1.And the class proposed in the present invention new based on a determination that the augmentation non-linear Kalman filtering device point of property sampling AUKF2, ACKF2 and ASSRCKF2 is not expressed as.
3 algorithm simulatings and analysis
In order to verify feasibility and robustness of the new extended kalman filter algorithm in tracking system, give in text Two models of the target movement of falling object and coordinate turn, and emulated using monte carlo method.Main ratio in emulation Compared with object be non-extended kalman filter algorithm such as UKF, CKF, SSRCKF and new extended kalman filter algorithm AUKF2, ACKF2, ASSRCKF2.Meanwhile, emulation part is also compared to the performance of the wave filter under two classes difference augmentation form.It is imitative In true example, the parameter in UKF is distinguished value and is:α=0.1, β=2, k=0.
3.1 models one
Using 3 D auto falling bodies trace model, the present invention verifies that a class proposed by the present invention is new based on a determination that property is adopted Effectiveness and superiority of the augmentation non-linear Kalman filtering algorithm of sample in multidimensional model.The model passes through radar detection reality When height when estimating that target falls, speed, and ballistic coefficient.Continuous state space model is described as follows：
It is expressed as at the k moment through the range finding of discretization：
Here discretization is carried out to the continuous time system shown in formula (28) using fourth order Runge-Kutta way, when discrete Spacer step a length of 1/64；The sampling interval of sensor is 1s；In order to more intuitively understand movement of falling object physical model, give Corresponding geometry schema, as shown in Figure 1；Variable x1(t), x2(t) and x3Position height when () represents that target falls respectively t, speed Degree and ballistic coefficient D1Represent target and the distance in radar detedtor horizontal direction, D2Represent the position height of radar. hereIt is known constant value coefficient, rkBe variance size be R zero mean noise；Starting stage, target drop-off positions are higher, and fast The change of degree is slower so thatTend to 0 value, system can be approximately linear；When target range radar is nearer, radar for Therefore observation noise is more and more sensitive, and mission nonlinear degree also can increase suddenly, this just the performance of wave filter is proposed compared with High requirement；State actual value during system initialization is set to x (0)=[3 × 105,2×104,1×10-3]T, initial estimation It is worth and isInitial variance size is：
The size of other specification is respectively set to:D1=D2=1 × 105, Q=0, R=1 × 104；In order to right The performance of all wave filter com-parison and analysis in addition, the mean square error (root mean square error, RMSE) of definition status For：
Wherein, M is Monte Carlo total degree, value 100 in emulation,WithK moment jth time Meng Teka is represented respectively The actual value of i-th dimension state and estimated value in the test of Lip river；
In order that the display of result is relatively sharp, the position mean square error curve in target dropping process, such as Fig. 2 is given It is shown；And the average of the mean square error of all kinds of wave filter and the time of an emulation experiment consumption is listed, as shown in table 1； Can be seen by Fig. 2, in 10s, the mean square error curve of all wave filter is almost overlapped, no obvious performance difference, this be by Linear institute is close to extremely in starting stage system；After 10s, the mean square error curve of extended kalman filter algorithm is corresponding to which Non- augmentation algorithm lower section.Additionally, table 1 more intuitively to show that although extended kalman filter algorithm consumes a certain amount of Time, but be enhanced in precision.
Average mean square error of the table 1 based on the target location of 100 Monte Carlo simulations
Comparison of the 2 liang of class augmentation wave filter of table in the average mean square error of target location
Table 2 sets forth the estimation difference of the Kalman filter of two classes difference augmentation form, as can be seen from the table, On the premise of it increased less amount of calculation, the Kalman filter of the augmentation form of process noise and observation noise has been incorporated AUKF2, ACKF2 and ASSRCKF2 respectively than only incorporating the extended kalman filter device AUKF1 of process noise, ACKF1 and The state estimation error of ASSRCKF1 is little, is more suitable for real-time modeling method.
3.2 models two
Extended kalman filter is verified with famous coordinate turn model (coordinated turn, CT) in this part The preferable robustness that algorithm is shown in state mutation；Shown in model is described as follows：
WhereinxkAnd ykRepresent direction,WithK moment x directions and y directions is represented respectively On speed；ωkAngular speed is represented, is set in simulations：
Other specification in model is arranged:Sensing station (Sx,Sy)=(0,0), qk-1And rkIt is the white Gaussian noise of zero-mean, its variance size is respectively：
Real state initial value is x0=[1000,300, 1000,-3/180×π]T, initial estimateN (the x from distribution；x0,P0) randomly select, the initial variance of state is set to P0 =diag ([100,10,100,10,1 × 104])；For the robust performance of preferably detection filter algorithm, except formula (34) Beyond the time-varying of angular speed is arranged, in the moment k=20 of each experiment, the mutation of location status is also introduced：
The time-varying of shown angular speed arrange and location status mutation, that can regard that complex environment in practice brings as makes an uproar Sound interference.Fig. 3 is tracking result of all kinds of wave filter to target location, it can be seen that all wave filter can carry out reality to position When track, compared to non-extended kalman filter device, the filtering algorithm of its corresponding augmentation form is demonstrated by higher robustness, Tracking effect is more preferable.
The mean square error for defining positional information is as follows：
Wherein, M=100 represents Monte Carlo total degree；WithK moment variable x are represented respectivelykIn jth time Meng Teka Actual value and estimated value in the emulation of Lip river；WithK moment variable y are represented respectivelykIt is true in jth time Monte Carlo simulation Value and estimated value.
The locative mean square error curves of Fig. 4, extended kalman filter algorithm can effectively gram as can be seen from Figure 4 The impact that time-varying disturbance and state mutation bring is taken, so as to reduce estimation difference.
Average mean square error of the table 3 based on the target location of 100 Monte Carlo simulations
Comparison of the 4 liang of class augmentation wave filter of table in the average mean square error of target drop-off positions
The quantitative analyses of form 3 relatively also show extended kalman filter for the tracking effect of location status is better than which Corresponding non-augmentation form, i.e. extended kalman filter algorithm can reduce the estimation mistake that system itself and environmental disturbances are produced Difference, so as to effectively improve filtering accuracy, reaches the requirement made to filter effect in practice. additionally, in form 4, two classes The Kalman filter of different augmentation forms relatively shows proposed by the present invention while incorporating process noise and observation noise The wave filter of augmentation form there is more preferable robustness.
State is merged by the present invention with process noise and observation noise, is calculated in conjunction with traditional non-linear Kalman filtering Method framework, has obtained a class new based on a determination that the augmentation non-linear Kalman filtering algorithm of property sampling.Simulation result shows In Higher Dimensional Nonlinear Systems, such filtering algorithm using the increase of a certain amount of computation complexity brought filtering accuracy compared with It is big to improve, preferable robustness is also shown simultaneously for the time-varying interference that system itself and environment bring；Additionally, emulation Experiment it is also shown that with only state compared with the extended kalman filter algorithm that process noise merge, it is of the invention in propose this Class it is new based on a determination that property sampling augmentation non-linear Kalman filtering algorithm preferably can reach realistic objective tracking in it is right The requirement of performance of filter, is particularly suited for real-time modeling method.
Presently preferred embodiments of the present invention is the foregoing is only, not to limit the present invention, all essences in the present invention Any modification, equivalent and improvement made within god and principle etc., should be included within the scope of the present invention.

Claims (4)

1. a kind of based on a determination that property sampling extended kalman filter method, it is characterised in that it is described based on a determination that property sampling State vector x is made an uproar with process noise q and observation by extended kalman filter method adoption status reconstructing method in forecast period Sound r three fusion is got up so that new state expands to N=n+n+m dimensions by the x that original n is tieed upWith augmentation UKF it is Example, produces a Sigma point in the quantity of state of forecast period augmentation, and in error correction stages, remains first time sampling acquirement Sigma points.
2. as claimed in claim 1 based on a determination that the extended kalman filter method of property sampling, it is characterised in that described to be based on The extended kalman filter method of deterministic sampling includes：
I) system initialization:In the initial value given state estimationAnd covarianceAfterwards, the initial value of augmented state is set ForCovariance matrix is：
P 0 a = P 0 0 0 0 Q n × n 0 0 0 R m × m N × N ;
Ii) predict:Obtain sampled point
The N-dimensional sampled point for obtainingIn, the 1st arrives n behavior state sampled points(n+1)th to 2n action process is made an uproar Sound sampled point2n+1 to 2N measuring behaviors noise samples point
Sampled pointWithSubstitute into state procedure EQUATION xk=f (xk-1)+qk-1In, obtain a series of adopting through conversion Sampling point：
Calculate the predictive value and corresponding error co-variance matrix of augmented state：
x ^ k | k - 1 a = Σ i = 1 N ω i m χ i , k | | k - 1 a ;
P k | k - 1 a = Σ i = 1 N ω i c ( χ i , k | k - 1 a - x ^ k | k - 1 a ) ( χ i , k | k - 1 a - x ^ k | k - 1 a ) T ;
Iii) error correction:Calculate the point after observational equation conversion：
The predictive value of difference calculating observation vector, the covariance of new breath, and the cross covariance square between state and observation vector Battle array：
y ^ k a = Σ i = 1 N ω i m χ i , k | k - 1 * a ;
P x y a = Σ i = 1 N ω i c ( χ i , k | k - 1 * a - y ^ k a ) ( χ i , k | k - 1 * a - y ^ k a ) T ;
P y y a = Σ i = 1 N ω i c ( χ i , k | k - 1 * a - x ^ k | k - 1 a ) ( χ i , k | k - 1 * a - y ^ k a ) T ;
The same formula of renewal of state estimation and state estimation error co-variance matrixWith
3. it is a kind of by described in claim 1～2 any one based on a determination that property sampling extended kalman filter method prepare Augmentation volume Kalman filter.
4. it is a kind of by described in claim 1～2 any one based on a determination that property sampling extended kalman filter method prepare Augmentation sphere simplex-radial direction volume Kalman filter.
CN201610901537.4A 2016-10-17 2016-10-17 Augmentation Kalman filtering method based on deterministic sampling Pending CN106526542A (en)

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Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109787584A (en) * 2019-01-23 2019-05-21 桂林航天工业学院 A kind of mixing uncertain system guaranteed cost Robust Kalman Filter design method
CN111563918A (en) * 2020-03-30 2020-08-21 西北工业大学 Target tracking method for data fusion of multiple Kalman filters
CN112036630A (en) * 2020-08-25 2020-12-04 长安大学 Highway pavement rainfall distribution estimation method, storage medium and computing device

Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101852615A (en) * 2010-05-18 2010-10-06 南京航空航天大学 Improved mixed Gaussian particle filtering method used in inertial integrated navigation system
CN103278163A (en) * 2013-05-24 2013-09-04 哈尔滨工程大学 Nonlinear-model-based SINS/DVL (strapdown inertial navigation system/doppler velocity log) integrated navigation method
CN103278813A (en) * 2013-05-02 2013-09-04 哈尔滨工程大学 State estimation method based on high-order unscented Kalman filtering
CN103761450A (en) * 2014-02-24 2014-04-30 中国石油大学(华东) Dynamic process fault forecasting method based on fuzzy self-adaptive prediction
US20140149034A1 (en) * 2012-11-26 2014-05-29 Electronics And Telecommunications Research Institute Apparatus for integrating multiple rate systems and method of operating the same
CN106030430A (en) * 2013-11-27 2016-10-12 宾夕法尼亚大学理事会 Multi-sensor fusion for robust autonomous filght in indoor and outdoor environments with a rotorcraft micro-aerial vehicle (MAV)

Patent Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101852615A (en) * 2010-05-18 2010-10-06 南京航空航天大学 Improved mixed Gaussian particle filtering method used in inertial integrated navigation system
US20140149034A1 (en) * 2012-11-26 2014-05-29 Electronics And Telecommunications Research Institute Apparatus for integrating multiple rate systems and method of operating the same
CN103278813A (en) * 2013-05-02 2013-09-04 哈尔滨工程大学 State estimation method based on high-order unscented Kalman filtering
CN103278163A (en) * 2013-05-24 2013-09-04 哈尔滨工程大学 Nonlinear-model-based SINS/DVL (strapdown inertial navigation system/doppler velocity log) integrated navigation method
CN106030430A (en) * 2013-11-27 2016-10-12 宾夕法尼亚大学理事会 Multi-sensor fusion for robust autonomous filght in indoor and outdoor environments with a rotorcraft micro-aerial vehicle (MAV)
CN103761450A (en) * 2014-02-24 2014-04-30 中国石油大学(华东) Dynamic process fault forecasting method based on fuzzy self-adaptive prediction

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
潘泉 等: "一类非线性滤波器UKF综述", 《控制与决策》 *

Cited By (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109787584A (en) * 2019-01-23 2019-05-21 桂林航天工业学院 A kind of mixing uncertain system guaranteed cost Robust Kalman Filter design method
CN111563918A (en) * 2020-03-30 2020-08-21 西北工业大学 Target tracking method for data fusion of multiple Kalman filters
CN111563918B (en) * 2020-03-30 2022-03-04 西北工业大学 Target tracking method for data fusion of multiple Kalman filters
CN112036630A (en) * 2020-08-25 2020-12-04 长安大学 Highway pavement rainfall distribution estimation method, storage medium and computing device
CN112036630B (en) * 2020-08-25 2023-08-04 长安大学 Highway pavement rainfall distribution estimation method, storage medium and computing equipment

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