CN105046016A - Particle filtering weight optimization adaptive resampling method - Google Patents

Abstract

The present invention discloses a particle filtering weight optimization adaptive resampling method and relates to the field of communication and signal processing. The method comprises: carrying out sampling on a density function; carrying out weight calculation on acquired particles and carrying out normalization processing; partitioning normalized weights into three groups according to thresholds wh and wl, wherein the group of the weights greater than or equal to wh is used as an A group, the group of the weights greater than wl and smaller than wh is used as a B group and the group of the weights smaller than or equal to wl is used as a C group; judging whether the number of the particles in the C group is greater than Np, and if yes, carrying out resampling processing; carrying out resampling processing on particles in the A group and the C group, carrying out regrouping on new particles, fusing a newly obtained B group with the original B group into one group to obtain A, B and C groups of particles again so as to form new particle sets together; and abandoning the C group of particles and completing resampling, wherein the A group of particles and the B group of particles are particle sets which accord with the requirements. According to a particle filtering weight optimization adaptive resampling algorithm, sorting of a great volume of data is avoided, computation complexity is reduced, the particle sets are enriched to a certain degree and the particle degeneracy is reduced.

Description

The preferred self-adaptive re-sampling method of a kind of particle filter weights

Technical field

The present invention relates to area of pattern recognition, radio network technique field and chemical field, be used in particular for communication and signal transacting field.

Background technology

Resampling methods is the most crucial step of particle filter, it solves particle degeneration problem, improves the performance of example.The thought of resampling methods is exactly the probability density function resampling by representing particle and corresponding power, increase the population that weights are larger, abandon the less particle departing from true distribution of weights, but such practice causes the scarcity of particle and the cost of long period, make the real-time of particle filter very poor, calculated amount is very large.Seldom can use in the utilization of reality.The algorithm of the preferred adaptive resampling of particle filter weights solves so problem.

Existing method determines whether to carry out the method for resampling for first calculating to particle:

$N_{eff}\≈\frac{1}{\underset{i=1}{\overset{N}{\Σ}}{\left(w_k^i\right)}^2}$

Work as N _effwhen being less than certain value when thresholding, just carry out resampling.But if hardware calculates, needing a large amount of squares of cumulative sum division arithmetics, this not only makes the more difficult but also consumption of natural resource of computing.

Summary of the invention

In order to overcome the defect of prior art, large for traditional resampling calculated amount, the problem that real-time is low, the present invention proposes the method for the preferred adaptive resampling of a kind of particle filter weights.

Technical scheme of the present invention is the method for the preferred adaptive resampling of a kind of particle filter weights, and the method comprises:

Step 1: pair-density function is sampled, obtains N+N _pindividual particle, wherein N represents the population of actual needs, N _pfor the extra particles number according to circumstances artificially determined;

Step 2: to the N+N obtained _pindividual particle carries out weight computing, and is normalized;

Step 3: by the weights after normalization according to thresholding w _hand w _lbe divided into 3 groups, be more than or equal to w _hbe A group, be greater than w _lbe less than w _hbe B group, be less than or equal to w _lbe C group, wherein w _hand w _laccording to the metric-threshold of actual conditions setting, and 0<w _l<w _h;

Step 4: particle number in statistics C group, judges whether this number is greater than N _pif be greater than, carry out resampling process, otherwise do not carry out resampling process;

Step 5: the particle of A and C group is carried out resampling process, obtain new particle, divide into groups to new particle at the rule of classification according to step 3, permeate the B group newly obtained and former B group group, forms new particle collection together from newly obtaining A, B, C group particle;

Step 6: abandoned by C group particle, A group and B group particle are the particle collection of composite demand, complete resampling.

Profit carries out resampling in this way only to be needed by particle size classification, and calculated amount is little, is easy to realize.And two thresholding weight w can be changed according to actual conditions _hand w _lvalue, realize closing to reality more.By particle classifying process, the particle number needed for estimation is N, and choosing sampling population is N+N _p, then calculate N+N _pthe weights of individual particle, select weights by thresholding and are greater than w _lparticle participant status estimate.The particle of C class is lost when namely rear checking Probability State distribution being estimated.And resampling also only carries out resampling category-A together with C class.Minimizing particle degeneration problem so is to a great extent on the impact of Posterior distrbutionp.

Accompanying drawing explanation

Fig. 1 is that adaptive weight preferably heavily adopts particle filter sample analogous diagram;

Fig. 2 is the preferred self-adaptation root-mean-square error figure of weights.

Embodiment

1. parameter initialization: sampling time T, sampling population N _s=N+N _p, and metric-threshold w _hand w _l.And each particle is used represent, wherein represent i-th particle of kth instance sample.

2. status predication, passes through predictive equation obtain the particle state in kth moment, wherein represent weights.

3. particle weight computing, calculates weights then calculate weights to be normalized to wherein z _krepresent the measuring value in k moment, represent that the K moment is by state infer z _kprobability density function, represent the importance function in K moment.

4. the weights after normalization according to thresholding w _hand w _lbe divided into A, B, C tri-groups;

5. judge C group number of particles N _lwhether be greater than N _pif be greater than, carry out the 6th step resampling process otherwise jump to the 7th step carrying out posterior probability estimation.

6. resampling process, carries out resampling process A and C group particle.Obtain new N _h+ N _lindividual new particle so the particle after resampling integrates the combination of the new particle obtained as particle B group and A and C resampling: ${\left\{x_k^j,w_k^j\right\}}_{j=1}^N={\left\{x_k^{j*},{\tilde{w}}_k^{j*}\right\}}_{j=1}^{N_h+N_l}\&cup;{\left\{x_k^j,{\tilde{w}}_k^j\right\}}_{j=1}^{N_b}.$

7. the combination of A group and B group is normalized again, calculates new particle weights and carry out rear checking estimation, ${\tilde{w}}_k^{i*}={\tilde{w}}_k^i/\left(\underset{i=1}{\overset{N_h}{\&Sigma;}}{\tilde{w}}_k^i+\underset{i=1}{\overset{N_b}{\&Sigma;}}{\tilde{w}}_k^i\right).$

8. couple real posterior probability density function p (z _k| z _1:k) carry out state estimation.The iteration that the 2nd step carries out subsequent time is returned after having calculated.

Particles all in algorithm all needs the particle carrying out any moment to upgrade.This algorithm is changed on a kind of right-value optimization thought particle filter algorithm basis.Right-value optimization thought needs N number of particle exactly, and adopts N _s(N _s>N) individual particle is sampled.Then after normalization N _sindividual particle sequence, is fixed particle number N and carries out posteriority state estimation.This algorithm can improve the diversity of particle to a certain extent, but this fixing particle does Posterior estimator, causes sequence process.When number of particles is very large, its complexity is O (N _si (N _s-1)/2), direct result is exactly that calculated amount is too large.All this methods for realization and unreliable.And adopt the method for threshold classification, only need to compare classification, its complexity is O (N).So improve implementation efficiency greatly, improve the real-time of calculating.And thresholding is sorted out, and makes the time of resampling also reduce.What this algorithm should be noted that is also not enough place is exactly need the particle of A and category-B to be again normalized.For parallel processor, state estimation can with resampling methods Parallel Implementation.Further increase efficiency.

By experiment adaptive algorithm is emulated, preferred for weights adaptive resampling algorithm and weights optimization algorithm are once carried out the feasibility emulating comparatively validate algorithm.Identical experiment parameter is adopted: process noise v in experiment _kemploying is distributed as Gamma distribution, and its parameter is measurement noise adopts Gaussian distribution u _k~ N (0,0.001).Particle of sampling in computing is counted and is got N=1000.Each operation time gets T=30, i.e. iteration 30 times, is equivalent to 30 time elementary cells.The system equation adopting many documents all to adopt and observation equation:

x _k＝0.1+sin(0.04πt)-0.25sin(x _k-1)+0.5x _k-1+v _k-1

y _k＝0.2x _k ²+0.5x _k+0.2sin(x _k)-2+u _k

The innovatory algorithm of the preferred thought of various weights carries out emulating and compares a simulation result figure obtaining respectively as experiment is carried out 100 emulation by Fig. 1, and the parameter of each emulation is all identical with information.Then root-mean-square error is calculated as Fig. 2.

Patent advantage

1 traditional resampling calculated amount is large, and the problem that real-time is low, traditional resampling generally need not be beneficial to Project Realization.Particle filter weights (PF-optimal-adaption) preferably adaptive resampling algorithm overcome above shortcoming, may be used for the realization of FPGA, algorithm is had actual value

2 by analogous diagram 1, Fig. 2, table 1 is known, particle filter weights preferred adaptive resampling algorithm is only 1/2 of traditional Weights-selected Algorithm and the system resampling time, and the variance of square error is only 1/234 and 1/80 of other two kinds of algorithm variances, mean value error is higher than traditional algorithm (PF-optimal-traditional) 1/5, fewer than system resampling (PF-systematicR) 2.5 times.Therefore particle filter weights preferred adaptive resampling algorithm estimated performance has had considerable raising.

A large amount of squares of cumulative sum division arithmetics of decision threshold in traditional algorithm are changed into the computing that size is compared in classification by the preferred adaptive resampling algorithm of 3 particle filter weights, have saved the hardware resource of 70%, have greatly reduced resources costs.

Table 1 be each resampling methods square error and working time comparison sheet

Claims (1)

1. a method for the preferred adaptive resampling of particle filter weights, the method comprises:

Step 1: pair-density function is sampled, obtains N+N _pindividual particle, wherein N represents the population of actual needs, N _pfor the extra particles number according to circumstances artificially determined;

Step 2: to the N+N obtained _pindividual particle carries out weight computing, and is normalized;

Step 3: by the weights after normalization according to thresholding w _hand w _lbe divided into 3 groups, be more than or equal to w _hbe A group, be greater than w _lbe less than w _hbe B group, be less than or equal to w _lbe C group, wherein w _hand w _laccording to the metric-threshold of actual conditions setting, and 0<w _l<w _h;

Step 4: particle number in statistics C group, judges whether this number is greater than N _pif be greater than, carry out resampling process, otherwise do not carry out resampling process;

Step 5: the particle of A and C group is carried out resampling process, obtain new particle, divide into groups to new particle at the rule of classification according to step 3, permeate the B group newly obtained and former B group group, forms new particle collection together from newly obtaining A, B, C group particle;

Step 6: abandoned by C group particle, A group and B group particle are the particle collection of composite demand, complete resampling.