CN105117537A - Weight comparison based resampling method for particle filter system - Google Patents

Abstract

The present invention discloses a weight comparison based resampling method for a particle filter system, and relates to the fields of communications and signal processing. The method comprises: generating N random numbers in the range of [0, 1]; recording the number of random numbers that fall in a weight threshold as a number X of copies of a subsequent particle; comparing the particle with the threshold; if the particle is bigger than the threshold, copying the particle for X times; if the particle is smaller than the threshold, comparing the size of the particle with that of a previous particle, and copying the bigger particle for X times; and finally discarding particles with the number of copying times being 0 and copying particles with the number of copying times being greater than or equal to 1 to a new particle. Therefore, according to the method provided by the present invention, particles close to a true distribution can be kept and copied accurately and particles far from the true distribution are discarded, so that an obtained estimation is more accurate.

Description

A kind of particle filter system method for resampling compared based on weights

Technical field

The present invention relates to field of audio processing, through melting field and robot controlling field, being used in particular for communication and signal transacting field.

Background technology

At present, the development comparative maturity of particle filter technology, present most of target following location, the technology such as recognition of face all adopt particle filter technology.Resampling methods is the most crucial step of particle filter, it solves the problem of particle degeneracy.The thought of resampling methods is exactly the probability density function resampling by representing particle and corresponding power, increases the population that weights are larger, abandons the less particle departing from true distribution of weights.Resampling process is exactly will be updated to system resampling is that interval [0,1] is divided into N layer, and sample is identical in the position of each level.The similarity of every one deck is the highest, and need not produce separate random number.But its algorithm has intrinsic defect, namely less particle can not be abandoned completely.Such as (0,1] be divided into N number of interval:

U＝{(0,1/N],(1/N,2/N],...,(k/N,k+1/N],...,(N-1/N,1]}

And particle weights are by cumulative, if stride across an interval just retain this particle, just need to copy m-1 time if stride across m interval.Run counter to the object of resampling methods like this, should manage to avoid.

Summary of the invention

The present invention is directed to particle in resampling and accept or reject problem, in order to overcome the defect of system resampling, the present invention proposes a kind of particle filter system method for resampling compared based on weights, avoiding to a great extent and abandon larger particle and remain small-particle; If there is continuously multiple comparatively small-particle, the particle that it is larger can be retained.

Summary of the invention of the present invention is a kind of particle filter system method for resampling compared based on weights, and the method comprises:

Step 1: produce N number of random number according to following formula:

$u_i=\frac{(i-1)+r}{N},i=1,2,...,N$

Wherein r is an equally distributed random number r ~ U [0,1] in [0,1] interval;

Step 2: pair-density function carries out first time sampling, and to its weights of each calculating particles that first time sampling obtains represent the weights of m particle;

Step 3: judge obtain qualified u _inumber, then this number is the initial replication number of times of m particle;

Step 4: judge whether set up, wherein w _thfor the weight threshold set according to actual conditions; If be false and then m-1 particle number of copy times is added 1; Otherwise m particle number of copy times adds 1, obtain the number of copy times of each particle;

Step 5: the particle being 0 number of copy times is abandoned, is then copied to new particle the particle that number of copy times is greater than 1 and completes resampling.

The invention has the beneficial effects as follows, can retain more accurately and copy the particle close to true distribution, abandon and depart from true distribution particle far away, make the estimation that obtains more accurate.

Accompanying drawing explanation

Fig. 1 is the particle filter system resampling methods figure compared based on weights;

Fig. 2 is three kinds of resampling simulation status results and real curve comparison diagram.

Embodiment

(1) N number of random number is produced according to following formula:

$u_i=\frac{(i-1)+r}{N},i=1,2,...,N$

Wherein r is an equally distributed random number r ~ U [0,1] in [0,1] interval;

(2) if then judge if be false, and establishment is then replicated number of times m-1 particle and adds 1.Otherwise m particle is replicated number of times and adds 1, initial replication number of times is all 0, can obtain m particle x like this _mthe frequency n um be replicated _m;

(3) particle being 0 number of copy times is abandoned, and then the particle that number of copy times is greater than 1 is copied to new particle.

In simulations in order to embody contrast, all importance sampling density functions all should be consistent, embodies in general emulation and all adopt standard particle filtering.In experiment simulation, the resampling methods adopted in resampling process is the innovatory algorithm (PF-systematicR_new) of polynomial expression resampling (PF-multinomialR), these two kinds of basic resampling methods of system resampling (PF-systematicR) and system resampling proposed above respectively.Adopt identical experiment parameter as follows in experiment: measurement noise adopts normal distribution u _k~ N (0,0.001), process noise v _kthen adopt and be distributed as Gamma distribution, its parameter is 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.And adopt following system equation 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 emulation of various resampling methods carries out simulation result once as shown in Figure 2.By 100 emulation, then obtaining root-mean-square error is:

Table 1 is four kinds of basic resampling methods and to the average of the root-mean-square error that the particle filter system resampling methods post-simulation compared based on weights obtains and mean value, and the averaging time of simulation run.

1. particle filter system resampling weights comparison algorithm fundamentally solves particle in resampling and accepts or rejects problem.Can retain more accurately and copy the particle close to true distribution, abandoning and depart from true distribution particle far away, making the estimation that obtains more accurate.

2., from the simulation result of Fig. 2 and can show that from the contrast of table 1 mean value of root-mean-square error of the particle filter system resampling methods (PF-systematicR_new) compared based on weights is lower by 15.8% than the root-mean-square error value of legacy system resampling methods (PF-systematicR), variance reduces 3.7%; Lower than the mean value of polynomial expression resampling (PF-multinomialR) root-mean-square error by 650%, variance is low 840%, and reduces the 130%. particle filter system resampling methods therefore compared based on weights working time and had than other traditional algorithm estimated performance and improve greatly.

Table 1 is each resampling methods square error and operation time

Claims (1)

1., based on the particle filter system method for resampling that weights compare, the method comprises:

Step 1: produce N number of random number according to following formula:

$u_i=\frac{(i-1)+r}{N},i=1,2,...,N$

Wherein r is an equally distributed random number r ~ U [0,1] in [0,1] interval;

Step 2: pair-density function carries out first time sampling, and to its weights of each calculating particles that first time sampling obtains represent the weights of m particle;

Step 3: judge obtain qualified u _inumber, then this number is the initial replication number of times of m particle;

Step 4: judge whether set up, wherein w _thfor the weight threshold set according to actual conditions; If be false and then m-1 particle number of copy times is added 1; Otherwise m particle number of copy times adds 1, obtain the number of copy times of each particle;

Step 5: the particle being 0 number of copy times is abandoned, is then copied to new particle the particle that number of copy times is greater than 1 and completes sampling.