CN106296727A - A kind of resampling particle filter algorithm based on Gauss disturbance - Google Patents
A kind of resampling particle filter algorithm based on Gauss disturbance Download PDFInfo
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Abstract
The invention belongs to intelligent information processing technology field, relate to a kind of resampling particle filter algorithm based on Gauss disturbance.It is specially the high weight particle increase Gauss disturbance diffusion to repeated sampling during resampling, it is used for estimating system state in non-Gaussian filtering non-linear, in undistinguishable small target tracking positions, the Loss of diversity problem of particle after resampling in solution iterative process, particle multiformity is increased on the premise of ensureing particle effectiveness, add particle and approach the probability of target, under conditions of not increasing amount of calculation and amount of storage, reduce tracking error, improve small target tracking precision；From the point of view of amount of calculation angle, although adding diffusion process based on Gauss disturbance, but owing to the convergence rate of particle is accelerated, execution time and the system resampling methods of innovatory algorithm are close.
Description
Technical field
The invention belongs to intelligent information processing technology field, relate to a kind of resampling particle filter based on Gauss disturbance and calculate
Method.
Background technology
Target Tracking Problem is actually the filtering problem of dbjective state, and the target that i.e. oneself obtains according to sensor measures number
Estimate accurately according to dbjective state of interest.To the detection of small maneuvering target in low signal-to-noise ratio photoelectric image sequence with
For tracking problem, owing to signal to noise ratio is low, target imaging area is little so that small target tracking and detection exist many difficulties, passes
The means of system are difficult to.In the many root-first search methods in recent years proposed, recursion Bayesian filter method passes through shape
States model and measurement model, really introduce the thought of tracking.Wherein, Kalman filter has proved to be linear Gauss problem
Optimum Bayes realize.But, actual tracking problem is complicated by multiple noise jamming and target travel, belongs to non-linear non-
Gauss problem, often results in linear and Gauss tracking being assumed to be basis and follows the tracks of unsuccessfully.Estimate based on Monte Carlo approximation
The particle filter method of meter achieves the Bayesian filter thought of nonlinear system in engineering, is current small target tracking problem
The emphasis of middle research.
Although weights degradation phenomena is alleviated in the resampling in particle filter method to a certain extent, but have also been introduced simultaneously
The particle filial generation that new problem, i.e. weights are the biggest is the most, and the less particle of weights is progressively weakened or rejects, the most extreme feelings
The particle collection reality that condition is new is all the filial generation of the particle of a maximum weight, causes the avalanche of sample space, namely " sample
Exhausted " phenomenon, sampled result contains many and repeats a little, thus have lost the multiformity of particle, cause particle filter state
The reduction of estimated accuracy, for small target tracking problem, can cause the failure followed the tracks of, and state to be improved in extreme circumstances
Estimated accuracy and the tracking accuracy of guarantee Small object, need to ensure the multiformity of particle in particle filter iterative process.
Summary of the invention
In order to solve the problems referred to above, the present invention proposes a kind of resampling particle filter algorithm based on Gauss disturbance, its
Being characterised by, the step of described method is
Step 1, initialization, when initial time k=0, from the priori probability density distribution function p (S of system mode0)～
In U (Λ), sampling obtains particle assemblyWherein, U represents that uniformly distributed function, Λ represent system mode
Be uniformly distributed interval, N for sampling number of particles,Represent the i-th particle obtained at k=0 instance sample,For i-th
The weights of particle, the most all particle importance weight are identical, areEnter particle filter iterative process after initialization, make k
=1；
Step 2, sampling from importance probability density function:To particle according to system
System state model is predicted；In formulaRepresent i-th particle, the p (S obtained at k instance samplek|Sk-1) it is importance probability
Density fonction；
The likelihood function that step 3, basis are determined by observation modelCalculate each particle weightsAnd to weights normalization, after normalization, the weights of particle areIn formula, ZkFor observation
Value,Weights for k moment i-th particle；Now system mode posterior probability density fonction is approximatelyS in formulakFor the system mode in k moment to be estimated, δ is unit impulse function；
Step 4, calculate the number of effective particle
Step 5, as number of effective particles mesh NeffMore than or equal to when setting threshold value, export system state estimation valueOtherwise when number of effective particles mesh is less than when setting threshold value, enter step 6；
Step 6, startup resampling process carry out resampling, to particle collectionCarry out resampling and obtain new grain
SubsetThe process of resampling is
601, [0,1] upper equally distributed random number { u is producedi}I=1 ... N；
602, produce weights cumulative function wc, meet
603, find and meet wc (m-1)≤uiThe integer m of≤wc (m) generates resampling particle subscript m, m-th particle warp
I-th position will be replicated in, i.e. after resampling For i-th particle after k moment resampling,For the k moment
M-th particle before resampling；
604, the number of times that statistics m-th particle is sampled
If 605 Cm＞ 1, then calculate size α of sampling neighborhood2,α2The effective particle mesh number concentrated with particle and system shape
Variance ε of state2It is relevant,Enter 606；
606, to byThe repeatedly particle after resamplingAdding Gauss disturbance is After resampling, the importance weight of particle concentration particle is equal, isResampling obtains new particle collection
607, output k moment system state estimation expected value is calculated
Step 7, comparing whether k arrives finish time T, if k is ＜ T, then k=k+1 skips to step 2；If k >=T, terminate.
Beneficial effect
The present invention is used for estimating system state non-linear in non-Gaussian filtering, is applied to undistinguishable small target tracking
In location.The method that method increases Gauss disturbance diffusion to high weight particle during resampling, is ensureing particle effectiveness
On the premise of increase particle multiformity, the problem solving particle sample space avalanche, therefore, use based on Gauss distribution disturbance
Resampling methods particle filter algorithm during the tracking of Small object, add particle and approach the probability of target, do not increasing
Under conditions of adding amount of calculation and amount of storage, reduce tracking error, improve small target tracking precision.On the other hand, from calculating
From the point of view of measuring angle, although adding diffusion process based on Gauss disturbance, but owing to the convergence rate of particle is accelerated, improve and calculate
Execution time and the system resampling methods of method are close.
Accompanying drawing explanation
Fig. 1 is the flow chart of the inventive method；
Fig. 2 classics resampling and improvement resampling methods target following result；
Fig. 3 is classical and the present invention 100 Monte-Carlo Simulation RMSE of two kinds of resampling methods；
Fig. 4 a classics resampling methods particle scattergram；
Fig. 4 b is resampling methods particle scattergram in the present invention；
Fig. 5 is that the RMSE and average CPU of classical resampling and 100 Monte-Carlo Simulation of resampling methods of the present invention run
Time.
Detailed description of the invention
The present invention proposes a kind of resampling particle filter algorithm based on Gauss disturbance, its process flow diagram flow chart such as Fig. 1 institute
Show, concretely comprise the following steps
Step 1, initialization, when initial time k=0, from the priori probability density distribution function p (S of system mode0)～
In U (Λ), sampling obtains particle assemblyWherein, U represents that uniformly distributed function, Λ represent system mode
Be uniformly distributed interval, N for sampling number of particles,Represent the i-th particle obtained at k=0 instance sample,For i-th
The weights of particle, the most all particle importance weight are identical, areEnter particle filter iterative process after initialization, make k
=1；
Step 2, sampling from importance probability density function:To particle according to system
System state model is predicted；In formulaRepresent i-th particle, the p (S obtained at k instance samplek|Sk-1) it is importance probability
Density fonction；
The likelihood function that step 3, basis are determined by observation modelCalculate each particle weightsAnd to weights normalization, after normalization, the weights of particle areIn formula, ZkFor observation
Value,Weights for k moment i-th particle；Now system mode posterior probability density fonction is approximatelyS in formulakFor the system mode in k moment to be estimated, δ is unit impulse function；
Step 4, calculate the number of effective particle
Step 5, as number of effective particles mesh NeffMore than or equal to when setting threshold value, export system state estimation valueOtherwise when number of effective particles mesh is less than when setting threshold value, enter step 6；
Step 6, startup resampling process carry out resampling, to particle collectionCarry out resampling and obtain new grain
SubsetThe process of resampling is
601, [0,1] upper equally distributed random number { u is producedj}I=1 ... N；
602, produce weights cumulative function wc, meet
603, find and meet wc (m-1)≤uiThe integer m of≤wc (m) generates resampling particle subscript m, m-th particle warp
I-th position will be replicated in, i.e. after resampling For i-th particle after k moment resampling,For the k moment
M-th particle before resampling；
604, the number of times that statistics m-th particle is sampled
If 605 Cm＞ 1, then calculate size α of sampling neighborhood2,α2The effective particle mesh number concentrated with particle and system shape
Variance ε of state2It is relevant,Enter 606；
606, to byThe repeatedly particle after resamplingAdding Gauss disturbance is After resampling, the importance weight of particle concentration particle is equal, isResampling obtains new particle collection
607, output k moment system state estimation expected value is calculated
Step 7, comparing whether k arrives finish time T, if k is ＜ T, then k=k+1 skips to step 2；If k >=T, terminate.
Identical model and parameter is used to emulate for resampling methods after system resampling methods and improvement.Display
The tracking result of two kinds of resampling methods, is shown that two kinds of algorithms for small target tracking estimating on x, y-coordinate in Fig. 3
Evaluation and actual value.From figure 3, it can be seen that due to the multiformity enhancing particle, compared with system method for resampling, this
The method of bright proposition has followed the tracks of target faster.
For verifying effectiveness of the invention further, two kinds of methods are carried out 100 Monte-Carlo Simulation, according toCalculate actual value during each frame is followed the tracks of imitative with 100 times of estimated value
Genuine root-mean-square error RMSE.It can be seen that with the addition of resampling methods based on Gauss distribution disturbance reduce with
Track error, improves tracking accuracy.
It is noted that resampling is only for particle s during classical resamplingiSimple m time replicate, because of
This is during resampling, although reduces the impact of sample degeneracy, but have also been introduced particle tcam-exhaustion simultaneously, reduces
The multiformity of particle, i.e. after successive ignition and resampling, all particles occupy the same point of state space, all particle values
Identical.And the position in this space representated by particle value very likely offsets real system mode, it is right to be the most just difficult to
The tracking of Small object.In particle filter algorithm, due to system mode posterior probability density function p (S in actual tracking problemk|
Z1:k) be difficult to obtain, generally with importance function p (Sk|Sk-1) instead of real system mode posterior probability density function, should
Up-to-date systematic perspective measured value is not taken into account by importance function, and therefore the calculating of particle weights exists error all the time.In pole
In the case of end, work as single particleWeighted value is 1 and time other particle weights are zero, after resampling, weight is the particle of 1
Being replicated N-1 time, the most whole sample space avalanche is a particleDuring the prediction in follow-up kth moment, this grain
Son will be predicted by target movement model, but, for the target of the motion of automobile, it is difficult to set up motion mould accurately
Type describes this motor process, more owing to there is process noise and model error, with this model pairThe particle fortune of prediction
Move and can offset real system mode, the namely state of target.Particle when predictionWhen offseting real system mode,
The weight calculated according to measurement modelIt is zero or approaches zero, the posteriority state probability density p (S of estimationk|Z1:k) also will force
Nearly zero, ultimately result in the loss of all samples, follow the tracks of procedure failure.And in the present invention, in order to ensure the multiformity of particle, at weight
Sampling process with the addition of sampling disturbance based on Gauss distribution.It not simple for particle that weight is high during resampling
Replicate, but from high weight particleNeighborhood sampling based on Gauss distribution, It is in sampling
During need the particle that is replaced,It is the particle of high weight, α2Determine the size of sampling neighborhood.α2With particle concentration
Number of effective particles is relevant with the variance of system mode:α2It is inversely proportional to number of effective particles, as number of effective particles Neff
During minimizing, sampling neighborhood needs expansion to ensure the multiformity of particle.α2With variance ε2It is directly proportional, ε2It it is the estimation of system mode
Precision, works as ε2During increase, representing the state needing more different particle to represent system, therefore sampling neighborhood is expanded the most therewith,
Vice versa.Fig. 4 a-b is the scattergram of particle in a small target tracking emulation experiment, and what wherein red circle represented is little
The actual position of target.In Fig. 4 a, when using direct clone method to carry out resampling, particle does not the most approach the shape of target
State.And 4b shows, after the multiformity that with the addition of disturbance enhancing particle, particle distribution covers real target location.
The present invention carries out small maneuvering target in the photoelectric image sequence of the signal to noise ratio snr=6.02dB of 30 frame emulation generations
Tracking test.Test result indicate that, improve particle owing to improvement resampling methods adds diffusion based on Gauss disturbance
Multiformity, the problem solving particle sample space avalanche, therefore, use resampling methods particle based on Gauss distribution disturbance
Filtering algorithm, during the tracking of Small object, under conditions of not increasing amount of calculation and amount of storage, reduces tracking error, carries
High tracking accuracy.To particle filter, improve resampling particle filter algorithm and carry out 100 Monte-Carlo Simulation experiments, with
Average root-mean-square error RMSE between estimated value and the target location actual value followed the tracks of is as the criterion of tracking accuracy, knot
Fruit shows, compares with particle filter, improves resampling particle filter algorithm tracking accuracy and improves 40%, as shown in Figure 5.Another
Aspect, from the point of view of amount of calculation angle, although adding diffusion process based on Gauss disturbance, but due to the convergence rate of particle
Accelerating, execution time and the system resampling methods of innovatory algorithm are close, merely add 0.05 second.
Claims (2)
1. a resampling particle filter algorithm based on Gauss disturbance, it is characterised in that the step of described method is
Step 1, initialization, when initial time k=0, from the priori probability density distribution function p (S of system mode0)～U (Λ)
Middle sampling obtains particle assemblyWherein, U represents that uniformly distributed function, Λ represent the equal of system mode
Even distributed area, N is sampling number of particles,Represent the i-th particle obtained at k=0 instance sample,For i-th particle
Weights, the most all particle importance weight are identical, areEnter particle filter iterative process after initialization, make k=1；
Step 2, sampling from importance probability density function:To particle according to system shape
States model is predicted；In formulaRepresent i-th particle, the p (S obtained at k instance samplek|Sk-1) it is importance probability density
Distribution function；
The likelihood function that step 3, basis are determined by observation modelCalculate each particle weightsAnd to weights normalization, after normalization, the weights of particle areIn formula, ZkFor observation
Value,Weights for k moment i-th particle；Now system mode posterior probability density fonction is approximatelyS in formulakFor the system mode in k moment to be estimated, δ is unit impulse function；
Step 4, calculate the number of effective particle
Step 5, as number of effective particles mesh NeffMore than or equal to when setting threshold value, export system state estimation value
Otherwise when number of effective particles mesh is less than when setting threshold value, enter step 6；
Step 6, startup resampling process carry out resampling, to particle collectionCarry out resampling and obtain new particle collection
Step 7, comparing whether k arrives finish time T, if k is ＜ T, then k=k+1 skips to step 2；If k >=T, terminate.
A kind of resampling particle filter algorithm based on Gauss disturbance the most according to claim 1, it is characterised in that described
The process of the resampling in step 6 is
601, [0,1] upper equally distributed random number { u is producedi}I=1 ... N；
602, produce weights cumulative function wc, meet
603, find and meet wc (m-1)≤uiThe integer m of≤wc (m) generates resampling particle subscript m, and m-th particle is through resampling
After will be replicated in i-th position, i.e. For i-th particle after k moment resampling,For k moment resampling
Front m-th particle；
604, the number of times that statistics m-th particle is sampled
If 605 Cm＞ 1, then calculate size α of sampling neighborhood2,α2The effective particle mesh number concentrated with particle and system mode
Variance ε2It is relevant,Enter 606；
606, to byThe repeatedly particle after resamplingAdding Gauss disturbance is Weight
After sampling, the importance weight of particle concentration particle is equal, isResampling obtains new particle collection
607, output k moment system state estimation expected value is calculated
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| CN110113030A (en) * | 2019-04-18 | 2019-08-09 | 东南大学 | A kind of particle filter algorithm of double sampling |
| CN110702093A (en) * | 2019-09-27 | 2020-01-17 | 五邑大学 | Particle filter-based positioning method and device, storage medium and robot |
| CN112039496A (en) * | 2020-09-10 | 2020-12-04 | 南京航空航天大学 | Rapid Gaussian particle filter data fusion method based on artificial fish shoal optimization |
| CN113032510A (en) * | 2021-04-02 | 2021-06-25 | 中国人民解放军国防科技大学 | LBGM method initial value disturbance generation method based on Gaussian weight |
| CN112039496B (en) * | 2020-09-10 | 2024-04-19 | 南京航空航天大学 | Rapid Gaussian particle filter data fusion method based on artificial fish swarm optimization |
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| CN112039496B (en) * | 2020-09-10 | 2024-04-19 | 南京航空航天大学 | Rapid Gaussian particle filter data fusion method based on artificial fish swarm optimization |
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Application publication date: 20170104 |