CN110334322A - A kind of population adaptive approach of particle filter - Google Patents
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Abstract
The invention belongs to field of signal processing, are related to the particle filter problem of field of signal processing, the population adaptive approach of specially a kind of particle filter, for adjusting the size of sample set in real time in estimation procedure, to improve the tracking performance of particle filter.The key idea of the method for the present invention is the approximate error introduced based on sampled representation constrained by particle filter, and by the particle Posterior distrbutionp of time-varying come adaptive container size, if the Posterior distrbutionp of particle concentrates in the sub-fraction of state space, the method of the present invention can select small container, it is appropriate to increase sample size to improve tracking accuracy, if particle state uncertainty is very high, the method for the present invention can select big container, to weaken the surge of population.Distributed and centralized target following, which is used, as the experiment of test case shows that the method for the present invention produces significant improvement than the particle filter of fixed sample collection size.
Description
Technical field
The invention belongs to field of signal processing, specifically the particle filter problem of field of signal processing, especially relate to
In particle filter the problem of adaptive population.
Background technique
Since particle filter algorithm is got rid of, dynamical system is linear, limitation of Gauss, compared with traditional filtering method, grain
Son filtering is simple easily to be realized, therefore has obtained good application in multiple fields in recent years.For example, in Science of Economics, its quilt
It applies and is predicted in economic data；In traffic control field, it is used in vehicle or people's video monitoring；In military field, its quilt
Applied to radar tracking airflight object, air to air, air-to-ground Passive Track.
Particle filter realizes that Bayesian filter, main thought are using one group with corresponding using Monte-Carlo Simulation
The particle of weight replaces integral calculation with sample average come posterior probability density needed for indicating dynamic system states space,
Thus to obtain the estimated value of state.When population is enough, can more accurately approximate Posterior distrbutionp, however the number of particle
Amount determines the complexity of particle filter to a certain extent again, and number of particles, and the complexity that will lead to is bigger, therefore such as
It is the worth the problem of explored that, which more effectively uses existing particle collection,.For example, document " W.R.Gilks and
C.Berzuini.Following a moving target-Monte Carlo inference for dynamic
Bayesian models.Journal of the Royal Statistical Society,Series B,61(1),
A kind of method of combination Markov Chain Monte Carlo step is given in 2001. " to improve the posteriority approximation based on sampling
Energy.In addition, document " M.K.Pitt and N.Shephard.Filtering via simulation:auxiliary
particle filters.Journal of the American Statistical Association,94(446),
1999. " give a kind of method of Auxiliary Particle Filter, will be between importance function and target distribution by one-step prediction method
Mismatch minimizes, the risk minimization for further changing weight, to improve the working efficiency of particle filter.
However, up to the present, most of existing particle filter methods are in entire state estimation procedure all using solid
The particle of fixed number amount, this may be very inefficient, because over time, the state of particle distribution may sharply become
Change.That is an important means for improving particle filter efficiency is seldom studied, i.e., adjusts grain over time
The quantity of son.Document " D.Fox, W.Burgard, F.Dellaert, and S.Thrun.Monte Carlo
Localization:Efficient position estimation for mobile robots.In Proc.of the
National Conference on Artificial Intelligence proposes a kind of method based on likelihood in 1999. "
Carry out adaptive population, and this method is applied to robot localization, specifically, this method ceaselessly generates sample, directly
The sum of particle weights to nonstandardized technique are more than preassigned threshold value, and the essence of the method is: if sample set and sensor
Measured value it is consistent, then the weights of importance of each particle is very big, and sample set still very little；However, if sample set
There is very big difference with the measured value of sensor, single particle weight will become smaller, and sample set will become larger；The performance of this method
The method than fixed population is promoted to a certain extent, however, this method does not give full play of adjustment sample but
Collect the potentiality of size.Recently, Fox is in article " D.Fox, Adapting the sample size in particle
filters through KLD-sampling,The Int.Journal of Robotics Research 22(12)
(2003) 985-1003. " one kind is proposed in based on Kullback-Leibler Distance (KLD) sampling method to adjust online
The size (hereinafter referred to as the method is Fox KLD) of whole sample set, realizes the compromise of the performance and complexity of particle filter, and
It is widely used in every field；However, using the container of fixed size in the method for Fox, this may be led
Cause the surge of filtering initial stage population.
Summary of the invention
It is an object of the invention to propose a kind of adaptive particle counting method of particle filter, in estimation procedure
The size of adjustment sample set in real time, to improve the performance of particle filter.
To achieve the above object, the technical solution adopted by the present invention is as follows
A kind of population adaptive approach of particle filter, which comprises the following steps:
Step 1: at the k moment, calculate the range of particle diffusion:
When target moves (one-dimensional) in x-axis:
Sk=max { (2 × 3 α11),(2×3α22)=6max { α11,α22}
When target moves (two dimension) in x-y plane:
Sk=max { (2 × 3 α11)×(2×3α33),(2×3α22)×(2×3α44)}
=36max { α11α33,α22α44}
When target is in x-y-z plane motion (three-dimensional):
Sk=max { (2 × 3 α11)×(2×3α33)×(2×3α55),(2×3α22)×(2×3α44)×(2×3α66)}
=216max { α11α33α55,α22α44α66}
Wherein,For the leading diagonal member for predicting particle covariance matrix in k moment particle filter method
Element；
Step 2: in the adaptive adjustment container size delta of moment kk:
Wherein, εk> 0 indicates that the upper limit of preset KLD, parameter lambda meet condition:It is the preset population upper limit and population lower limit respectively；
Step 3: in moment k, initialization expectation populationCurrent particle number Mk=0, the appearance of particle diffusion
Device number
Step 4: the population that moment k needs is calculated according to current particle number and desired population
It is sampled out according to prediction distributionParticle updates the number of vessels of particle diffusion further according to the particle collection newly obtained
Current particle number is updated simultaneously
Step 5: update expectation population:
Wherein,Indicate the upper 1- δ of Gaussian ProfilekQuantile；
Step 6: judge whether current particle number meets condition:AndIf satisfied, returning to step
5, otherwise, export current particle number
The beneficial effects of the present invention are:
A kind of adaptive particle counting method of particle filter proposed by the present invention has the following advantages that
1. method proposed by the present invention is measured using Kullback-Leibler Distance (KLD) by particle filter
Sampled representation introduce approximate error, further by constrain the error, come in real time adjust required for population, it can be achieved that
The compromise of particle filter tracking performance and algorithm complexity；
2. method proposed by the present invention is not only suitable for centralized particle filter algorithm, it is also applied for distributed particle filter calculation
Method has a wide range of application；
3, method proposed by the present invention can more quickly determine required population, favorably compared with the method for Fox
It is adjusted online, in real time in realization population；
4, method proposed by the present invention by the upper limit and lower limit value that limit population come adaptive adjustment container size,
Compared with the method for Fox, the problem of population that filtering initial stage is likely to occur is increased sharply can be weakened, and promote the steady of particle filter
State tracking performance；
5, method proposed by the present invention includes several adjustable parameters, and different parameter values can be selected according to practical application, is had
Stronger flexibility；Such as: the population upper limitAnd lower limitAnd the error upper limit ε of preset KLDk, lead to
It crosses and adjusts these parameters, can be further improved the optimization performance of filter, to meet the various demands in practical problem；
Even if method proposed by the present invention can also be reasonable by being arranged 6, in the case where practical priori knowledge is deficient
Parameter is adaptively adjusted the number of required particle.
Detailed description of the invention
Fig. 1 is to realize structure chart using the particle filter algorithm of the method for the present invention in embodiment.
Fig. 2 is " 3 σ " principle explanatory diagram of normal distribution in embodiment.
Fig. 3 is network topology structure in embodiment (for having 15 nodes in network).
Fig. 4~Fig. 9 is simulation result diagram in embodiment.
Specific embodiment
The present invention will be further explained below with reference to the attached drawings:
A kind of population adaptive approach of particle filter is provided in the present embodiment, process is as shown in Figure 1, due to grain
The expression based on sampling of subfilter can introduce approximate error, and the present invention measures this with KLD to constrain the approximate error
Approximate error defines the KLD between true distribution and the maximal possibility estimation based on sampling are as follows:
Wherein, p (x) indicates that true Posterior distrbutionp, q (x) indicate the maximal possibility estimation based on sampling；It is noted that by
True Posterior distrbutionp is unknown in particle filter algorithm, and the present invention is true with being replaced based on the prediction distribution of particle sampler
Real Posterior distrbutionp.
Specific step is as follows:
Step 1: at the k moment, target is set in x-y plane and moves (two dimension),Wherein, xk,yk
Respectively indicate the x of target, the position in the direction y,Respectively indicate the x of target, the speed in the direction y；For each in the present invention
Tie up dbjective state vector, container size deltakIt is identical, and four-dimensional state vector is divided into two class of position and speed；
The range S of k moment particle diffusion is calculated belowk: the present invention extracts the covariance matrix of particleMaster it is diagonal
Line elementNotice that the particle in Gaussian particle filtering is all satisfied normal distribution, then in moment k, according to just
" 3 σ " principle (as shown in Figure 2) of state distribution, the Range Representation of particle diffusion are as follows:
Sk=max { (2 × 3 α11)×(2×3α33),(2×3α22)×(2×3α44)}
=36max { α11α33,α22α44}
If target then calculates the range S of particle diffusion in x-y-z plane motion (three-dimensional)k:
Sk=max { (2 × 3 α11)×(2×3α33)×(2×3α55),(2×3α22)×(2×3α44)×(2×3α66)}
=216max { α11α33α55,α22α44α66}
If target moves (one-dimensional) in x-axis, then the range S of particle diffusion is calculatedk；
Sk=max { (2 × 3 α11),(2×3α22)=6max { α11,α22}
Step 2: the quantity by limiting particle, according to the variation in particle state space, in the adaptive adjustment container of moment k
Size deltak, that is, track initial stage, container ΔkIt can be larger, because particle dispersion range is larger at this time, select biggish ΔkIt can
Effectively to weaken population；And as tracking progressivelyes reach metastable state, ΔkCan be smaller, because of particle at this time
Relatively centralized can increase population using smaller container to a certain extent, further promote tracking performance；
Container size deltakIt calculates according to the following formula
Wherein, εkIndicate the upper limit (ε of preset KLDk> 0), parameter lambda meets condition It is the upper limit of previously given population and the lower limit of population respectively；
Step 3: in moment k, initialization expectation populationCurrent particle number Mk=0, the appearance of particle diffusion
Device number
Step 4: the population that moment k needs is calculated according to current particle number and desired population
It is sampled out according to prediction distributionParticle updates the number of vessels of particle diffusion further according to the particle collection newly obtainedTogether
Shi Gengxin current particle number
Step 5: expectation population is updated, in order to guarantee that true prediction distribution and the maximum likelihood based on sampling are distributed it
Between KLD with 1- δkProbability be no more than upper limit εk, it is expected that population is calculate by the following formula:
Wherein,Indicate the upper 1- δ of Gaussian ProfilekQuantile；
Step 6: judge whether current particle number meets condition:AndIf satisfied, returning to step
5, otherwise, export current particle number
It should be understood that
According to the more new formula for it is expected population in step 6:
It is found that expectation population and KLD upper limit εkIt is inversely proportional, the number of vessels with distributionIn first-order linear relationship, therefore, above formula can
It is approximately:That is:And due toAnd then it obtains holding in step 3 of the present invention
Device size deltak:
In addition illustrate: " 3 σ " principle of normal distribution are as follows:
Probability of the numeric distribution in (μ-σ, μ+σ) is 0.6827
Probability of the numeric distribution in (+2 σ of μ -2 σ, μ) is 0.9545
Probability of the numeric distribution in (+3 σ of μ -3 σ, μ) is 0.9973
σ represents standard deviation in normal distribution, and μ represents mean value；It is believed that the value almost all of Y concentrates on (μ -3
+ 3 σ of σ, μ) in section, super a possibility that going beyond the scope, only accounts for less than 0.3%.
It is respectively embedded into centralized particle filter below by by the method for the present invention (abbreviation KLD) and Fox KLD method and divides
The exemplary embodiments of cloth particle filter, to illustrate feasibility of the invention, superiority.
Emulation 1: using the distributed network comprising 15 nodes, and network topology structure is as shown in Figure 3, it is assumed that target is in x-
Y plane is mobile, and specific simulated conditions are as follows: the method for the present invention (KLD) is embedded in a kind of centralization based on time delay and Doppler
The direct tracking problem of adaptive particle filter (A.Y.Sidi, A.J.Weiss, Delay and Doppler induced
direct tracking by particle filter,IEEE Trans.Aerosp.Electron.Syst.50(1)
(2014) 559-572.) in (hereinafter referred to as it is CPF KLD), the insertion of Fox KLD method is above-mentioned based on time delay and Doppler
The direct tracking problem of centralized adaptive particle filter in (hereinafter referred to as CPF Fox KLD), with individual CPF method pair
0dB is all set as than, nodes signal-to-noise ratio, initiating particle number 50, Monte Carlo experiment 100 times, εk=0.2, in order into
One step is coincide our design object, and λ is set as λ=1+0.99k；The location error simulation result of three compare as shown in figure 4,
The simulation result of three's velocity error is as shown in figure 5, the population of three is as shown in Figure 6 with the number of iterations result of variations.
By Fig. 4,5 it is found that in centralized scene, Fox KLD method (the CPF Fox KLD i.e. in figure) is compared to individual
CPF method improves the convergence rate of the NRMSE curve of position, but steady-state performance improvement effect is not significant, and the two speed
Tracking performance also very close to；And method proposed by the present invention is also compared to CPF Fox KLD and individual CPF, either position
It is that the steady-state performance of the NRMSE curve of speed has and significantly promoted；Meanwhile individual CPF method is compared, it is proposed by the present invention
Method also improves the convergence rate of position NRMSE curve.
As seen from Figure 6, in centralized scene, at the initial stage of filtering, population has significantly to swash Fox KLD method
Increase, and method proposed by the present invention can effectively weaken the surge of filtering initial stage population, and after the filtering the phase pass through it is suitable
When reducing container size, the further tracking performance for promoting particle filter.
Emulation 2: using the distributed network comprising 15 nodes, and network topology structure is as shown in Figure 3, it is assumed that target is in x-
Y plane is mobile, and specific simulated conditions are as follows: the method for the present invention (KLD) is embedded in a kind of distribution based on time delay and Doppler
The direct method for tracking and positioning of adaptive particle filter (Xia Wei, Wang Yanyan, Zhu Julei application number: 2017105840733. applyings date
Phase: 2017.7.18. application publication number: CN107367710A) in (hereinafter referred to as D-GPF KLD), Fox KLD method is embedding
Enter (hereinafter referred to as D- in the above-mentioned direct method for tracking and positioning of the distributed self-adaption particle filter based on time delay and Doppler
GPF Fox KLD), it is compared with individual D-GPF method.Under the conditions of distributed particle filter, nodes signal-to-noise ratio is all
It is set as 0dB, initiating particle number 50；Monte Carlo experiment 100 times, εk=0.2, for our the design mesh of further coincideing
Mark, λ are set as λ=1+0.99k；The location error simulation result of three compares the emulation knot as shown in fig. 7, three's velocity error
Fruit is as shown in figure 8, the population of three is as shown in Figure 9 with the number of iterations result of variations.
By Fig. 7,8 as it can be seen that in distributed scene, Fox KLD method (the CPF Fox KLD i.e. in figure) is compared to individual
D-GPF method does not show the improvement effect of its steady-state performance although improving the convergence rate of the NRMSE curve of position
Write, and the two speed tracing performance also very close to.And method proposed by the present invention is compared to D-GPF Fox KLD and individually
The steady-state performance of the NRMSE curve of D-GPF, either position or speed, which has, significantly to be promoted.Meanwhile comparing individual D-
GPF method, method proposed by the present invention also improve the convergence rate of position NRMSE curve.
As seen from Figure 9, in distributed scene, Fox KLD method has significantly in the initial stage of filtering, population
It increases sharply, and method proposed by the present invention can effectively weaken the surge of filtering initial stage population, and the phase passes through after the filtering
It is appropriate to reduce container size, further improve the tracking performance of particle filter.
The above description is merely a specific embodiment, any feature disclosed in this specification, except non-specifically
Narration, can be replaced by other alternative features that are equivalent or have similar purpose；Disclosed all features or all sides
Method or in the process the step of, other than mutually exclusive feature and/or step, can be combined in any way.
Claims (1)
1. a kind of population adaptive approach of particle filter, which comprises the following steps:
Step 1: at the k moment, calculate the range of particle diffusion:
When target moves (one-dimensional) in x-axis:
Sk=6max { α11,α22}
When target moves (two dimension) in x-y plane:
Sk=36max { α11α33,α22α44}
When target is in x-y-z plane motion (three-dimensional):
Sk=216max { α11α33α55,α22α44α66}
Wherein,Indicate the elements in a main diagonal that particle covariance matrix is predicted in k moment particle filter method；
Step 2: in the adaptive adjustment container size delta of moment kk:
Wherein, εk> 0 indicates that the upper limit of preset KLD, parameter lambda meet condition: Point
It is not the preset population upper limit and population lower limit；
Step 3: in moment k, initialization expectation populationCurrent particle number Mk=0, the container number of particle diffusion
Mesh
Step 4: the population that moment k needs is calculated according to current particle number and desired populationAccording to
Prediction distribution samples outParticle updates the number of vessels of particle diffusion further according to the particle collection newly obtainedSimultaneously more
New current particle number
Step 5: update expectation population:
Wherein,Indicate the upper 1- δ of Gaussian ProfilekQuantile；
Step 6: judge whether current particle number meets condition:AndIf satisfied, step 5 is returned to, it is no
Then, current particle number is exported
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| CN113534222A (en) * | 2020-04-17 | 2021-10-22 | 宝马股份公司 | Method for vehicle positioning, device for vehicle positioning and vehicle |
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