CN113225044A - Intelligent particle filtering method - Google Patents

Intelligent particle filtering method Download PDF

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CN113225044A
CN113225044A CN202110195743.9A CN202110195743A CN113225044A CN 113225044 A CN113225044 A CN 113225044A CN 202110195743 A CN202110195743 A CN 202110195743A CN 113225044 A CN113225044 A CN 113225044A
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CN113225044B (en
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刘海涛
彭博
范佳量
姜彦吉
郑四发
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Suzhou Automotive Research Institute of Tsinghua University
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Abstract

The invention discloses an intelligent particle filtering method, which divides data particles into high-weight particles, low-weight particles and bottom particles, so that the high-weight particles, the low-weight particles and the bottom particles are subjected to variation according to a self-adaptive variation strategy and output variation results, the data particles are obtained by sequentially carrying out separation processing and cross processing on initial particles, and the separation processing comprises the following steps: dividing the initial particles into initial high-weight particles and initial low-weight particles according to a preset weight threshold value; the interleaving process comprises: inputting a cross coefficient to linearly generate cross low-weight particles from the initial high-weight particles and the initial low-weight particles. The intelligent particle filtering method adds self-adaptive processing in the crossover and mutation operators, further improves the utilization rate of particles and reduces the degradation influence of the particles.

Description

Intelligent particle filtering method
Technical Field
The invention relates to the field of signal processing and target tracking, in particular to an intelligent particle filtering method.
Background
The system state estimation is a method for deducing a hidden state inside a system from system noise measurement, and a typical representation of the method is Bayesian filtering. Kalman filtering and Particle Filtering (PF) are state estimation techniques developed on the basis of bayesian filtering. For a linear and Gaussian system, Kalman filtering has good estimation performance; for a non-Gaussian and non-linear system, Kalman filtering is easy to disperse, and particle filtering estimation performance is more advantageous.
The particle filter algorithm is widely applied to the fields of robots, communication and signal processing, target tracking, target positioning and the like. The basic idea is to approximate the posterior probability distribution of a system with a set of samples (or particles) and then use this approximate representation to estimate the state of the nonlinear system. Since the particles are continuously updated, the degradation phenomenon inevitably occurs. After many iterations, most of the particles have extremely small weights, and due to degradation, the iteration continues to consume a large amount of computing resources and affect the final estimation result. Therefore, by introducing the effective sampling quantity and the resampling method, the particles with smaller weight are abandoned, and the particles with larger weight are propagated to derive more particles with equal weight. The improved resampling method mainly comprises partition resampling, parallel resampling, system resampling, residual resampling, regular resampling and the like, but the resampling method cannot effectively solve the particle degradation phenomenon.
Although particle filtering improved on the basis of traditional particle filtering can improve the particle filtering performance in a specific scene, the particle degradation phenomenon still cannot be effectively solved. And the genetic resampling algorithm provides an effective research idea for solving the problem of particle shortage. In recent years, a learner provides an Intelligent Particle Filter algorithm (IPF), the algorithm combines a genetic algorithm in a resampling process, particles are divided into a large group and a small group according to weights, the groups with the smaller weights are crossed and varied to be evolved into the particles with the larger weights, the influence of Particle degradation is effectively solved, and the estimation effect in various models is obviously higher than that of PF. The IPF effectively improves the condition of non-uniform posterior probability distribution of the particles and provides a new direction for the intelligent research of particle filtering. However, in the smart particle filter algorithm, the genetic resample particles are randomly mutated based on the mutation probability. In low weight particles, the distribution of particle weights is not uniform, the lower the particle weight, the easier it is for the particle to be culled, so that particle diversity suffers after multiple iterations.
Disclosure of Invention
In order to overcome the defects in the prior art, the invention provides an intelligent particle filtering method, which adds self-adaptive processing in crossover and mutation operators, further improves the utilization rate of particles and reduces the degradation influence of the particles. The specific technical scheme is as follows:
the invention provides an intelligent particle filtering method, which is characterized in that data particles are divided into high-weight particles, low-weight particles and bottom particles, so that the high-weight particles, the low-weight particles and the bottom particles are subjected to variation according to a self-adaptive variation strategy and output variation results, wherein the self-adaptive variation parameter of the bottom particles is larger than a preset variation probability, the self-adaptive variation parameter of the low-weight particles is smaller than the preset variation probability and the variation coefficient of the low-weight particles is smaller than the preset variation probability, and the self-adaptive variation parameter of the high-weight particles is smaller than the preset variation probability and the variation coefficient of the high-weight particles is larger than the preset variation probability.
Further, the adaptive mutation strategy is
Figure RE-GDA0003128040370000021
Wherein the content of the first and second substances,
Figure RE-GDA0003128040370000022
in order to obtain the particles by variation,
Figure RE-GDA0003128040370000023
in the case of the initial high-weight particles,
Figure RE-GDA0003128040370000024
for crossing low-weight particles, pMThe probability of the mutation is a preset probability of the mutation,
Figure RE-GDA0003128040370000025
to adapt the variation parameter, rl∈[0,1]Is a randomly selected coefficient of variation.
Further, the data particles are obtained by sequentially performing separation processing and cross processing on the initial particles, wherein the separation processing comprises: dividing the initial particles into initial high-weight particles and initial low-weight particles according to a preset weight threshold value; the interleaving process comprises: inputting a cross coefficient to linearly generate cross low-weight particles from the initial high-weight particles and the initial low-weight particles.
Further, the adaptive variation parameter is
Figure RE-GDA0003128040370000026
Wherein the content of the first and second substances,
Figure RE-GDA0003128040370000031
for adapting the variation parameter, pMIs a predetermined mutation probability, nlThe number of initial low-weight particles,
Figure RE-GDA0003128040370000032
wherein the content of the first and second substances,
Figure RE-GDA0003128040370000033
is the weight of the corresponding particle.
Further, the cross low-weight particles are generated as follows:
Figure RE-GDA0003128040370000034
wherein a is ∈ [0, 1 ]]For the randomly selected cross-over coefficient of the particles,
Figure RE-GDA0003128040370000035
in the case of the initial high-weight particles,
Figure RE-GDA0003128040370000036
are the initial low-weight particles.
Further, the crossing coefficient is greater than or equal to 0, and the crossing coefficient is less than or equal to 1.
And further, updating the weight of the varied bottom-layer particles, judging whether the updated weight falls into a preset range, if so, outputting a variation result, and otherwise, performing one or more operations of separation processing, cross processing and variation according to the self-adaptive variation parameters on the bottom-layer particles.
Further, before the initial particles are subjected to separation processing, the weight values of the initial particles are calculated.
Further, no crossover processing is performed in the variance of the high-weight particles.
Further, the variation probability is 0.8-0.9.
The technical scheme of the invention has the beneficial effects that:
a. the problem of particle degradation is solved, and the influence of particle degradation is reduced;
b. the diversity of the particles is improved;
c. the utilization rate of the particles is improved.
Drawings
In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings needed to be used in the description of the embodiments will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.
FIG. 1 is a schematic diagram of a comparison between a prior art smart particle filtering method and a smart particle filtering method provided by an embodiment of the present invention;
FIG. 2 is a schematic diagram of an adaptive mutation strategy in the IIPF in an embodiment of the present invention;
FIG. 3 is a schematic diagram of a smart particle filter algorithm provided in an embodiment of the present invention;
FIG. 4 is an estimation diagram of PF and EKF status in an embodiment of the present invention;
FIG. 5 is a diagram of the estimation of IPF and IIPF states in an embodiment of the present invention;
fig. 6 is a schematic view of particle distribution when k is 11 and N is 500 in the embodiment of the present invention;
FIG. 7 is a first schematic of a multi-dimensional simulation model height error in an embodiment of the present invention;
FIG. 8 is a second schematic of a multi-dimensional simulation model velocity error in an embodiment of the present invention;
FIG. 9 is a graph of EKF estimation under non-Gaussian random noise and multiplicative noise in an embodiment of the invention.
Detailed Description
In order to make the technical solutions of the present invention better understood and more clearly understood by those skilled in the art, the technical solutions of the embodiments of the present invention will be described in detail and completely with reference to the accompanying drawings. It is to be understood that the described embodiments are merely exemplary of a portion of the invention and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention. In addition, the terms "comprises" and "comprising," and any variations thereof, in the description and claims of this invention, are intended to cover a non-exclusive inclusion, such that a process, method, apparatus, article, or apparatus that comprises a list of steps or elements is not necessarily limited to those steps or elements expressly listed, but may include other steps or elements not expressly listed or inherent to such process, method, article, or apparatus.
In the prior art, the basic algorithm of the smart particle filter algorithm is as follows:
a. separation of
Figure RE-GDA0003128040370000041
Figure RE-GDA0003128040370000042
b. Crossing
Figure RE-GDA0003128040370000051
c. Variation of
Figure RE-GDA0003128040370000052
In one embodiment of the present invention, a method for positioning multiple sound sources based on array reconstruction is provided, which includes the following steps:
step (1): the separation and the crossing are carried out,
a. separation of
Figure RE-GDA0003128040370000053
Wherein WTIs a preset weight threshold;
b. crossing
Figure RE-GDA0003128040370000054
c. Variation of
Step (2): the separation and crossover operators in the improved intelligent particle filter algorithm are the same as those in the intelligent particle filter algorithm, and the separated and crossed particles are obtained by the formulas (1) and (3)
Figure RE-GDA0003128040370000055
And
Figure RE-GDA0003128040370000056
the mutation operator for improving the intelligent particle filter is different from the intelligent particle filter, is based on the adaptive mutation parameter, and is obtained byObtaining final new particles through a self-adaptive mutation strategy;
the adaptive variation parameters are:
Figure RE-GDA0003128040370000057
Figure RE-GDA0003128040370000058
wherein the content of the first and second substances,
Figure RE-GDA0003128040370000059
in order to improve the adaptive variation parameters,
Figure RE-GDA00031280403700000510
is the reciprocal of the normalized particle weight, nlIs CLThe number of particles. As shown in formulas (5) and (6), when the weight of the particles is smaller,
Figure RE-GDA0003128040370000061
the larger, at the same time
Figure RE-GDA0003128040370000062
The larger;
and (3): the particles in the improved intelligent particle filter are automatically divided into high-weight particles, low-weight particles and bottom-layer particles (also called bottom-layer low-weight particles) according to the weight of the particles, and the high-weight particles keep the state information of the high-weight particles; the low weight particles will be randomly mutated according to the mutation probability; the bottom-layer low-weight particles are used as special groups in the low-weight particles and have the qualification of preferential variation; the mutation strategy of the bottom layer low-weight particles is not to mutate according to the mutation probability, but to mutate directly. The adaptive variation strategy for improving the intelligent particle filtering is shown as a formula (7);
Figure RE-GDA0003128040370000063
wherein the content of the first and second substances,
Figure RE-GDA0003128040370000064
particles obtained for improved mutation processes. When it is satisfied with
Figure RE-GDA0003128040370000065
Under the condition (2), the particle is judged to be a bottom particle and is directly mutated. If not satisfied with
Figure RE-GDA0003128040370000066
If so, judging that the particle is a non-bottom particle, and carrying out variation on the particle according to the variation probability; when the condition r is satisfiedl≤pMThe particle undergoes mutation, otherwise, the particle remains. In the improved mutation process, the lower weight value is, the higher the particle mutation probability is. When in use
Figure RE-GDA0003128040370000067
Above 1, the particle must be mutated. A flow chart of an adaptive mutation strategy for improving smart particle filtering is shown in fig. 2.
The improved variation process can greatly increase the variation probability of particles (bottom particles) with very low weight, effectively improve the utilization rate of the bottom particles, reduce the influence of particle depletion and improve the particle filtering performance. The improved smart particle filter algorithm is shown in fig. 3.
Fig. 1 visually compares the smart particle filtering method of the prior art with the smart particle filtering method of the present embodiment, wherein the left graph corresponds to the prior art, and the right graph corresponds to the method of the present embodiment, and it can be seen that the method of the present embodiment retains more low-weight particles than the prior art.
The particle filter performance of the present invention is explained in detail by the following concrete simulation examples:
1. multidimensional simulation model under Gaussian random noise
In order to better test the performance of the proposed particle filter algorithm, a multi-dimensional simulation model is additionally introduced. The model is that an object falls into the atmosphere from the high altitude. The following formulae (8) and (9):
Figure RE-GDA0003128040370000071
Figure RE-GDA0003128040370000072
wherein x is1、x2、x3Respectively representing the height, speed and constant ballistic coefficient of an object falling into the atmosphere, m1、m2、m3Is the gaussian random noise of the system and t is the observation noise. r is0The air density at sea level, c the coefficient of the relationship between altitude and air density, g the acceleration of gravity, and a the observed altitude.
TABLE 1 multidimensional model parameters
Figure RE-GDA0003128040370000073
Selection of the probability of variation pMThe value is 0.8, the cross coefficient a is 0.9, and 100 times of simulation calculation are carried out. Fig. 4 and 5 show the results of PF, EKF, IPF, and IIPF estimation when 1000 particles were selected. The IPF and IIPF velocity estimation performance in the graph is significantly better than PF and EKF. And the height estimation PF starts to "wander" at 11 s.
In order to detect the diversity of the intelligent particle filter particles, IPF and IIPF are respectively carried out on the same group of parent particles to obtain new particle state distribution, and the diversity is judged according to the particle distribution condition. In model two, the system has a high degree of nonlinearity between 11s and 13s, and the 11 th s is selected to analyze the state of the particle. Fig. 6 shows the state distribution of the new particles obtained at 11 s. From the comparison of the results in the figure, the particle distribution of the particle posterior probability distribution area of the IIPF is more uniform, which fully demonstrates that the resampling strategy proposed herein can effectively improve the performance of particle filtering.
The system tracking error is shown in table 2 below, fig. 7 and fig. 8, and since the PF error is too large, the PF is omitted in fig. 7 and fig. 8. In both fig. 7 and 8, IIPF performance is superior to IPF, EKF and PF, and IIPF height and velocity are lower than other algorithms in both root mean square error and mean error. Wherein, the height root mean square error is reduced by 11.5 percent compared with the IPF, and the speed root mean square error is reduced by 6.8 percent compared with the IPF; the average error of the height is reduced by 7.6 percent compared with the IPF, and the average error of the speed is reduced by 4.4 percent compared with the IPF.
TABLE 2 Multi-dimensional model RMS error and average error Table
Figure RE-GDA0003128040370000081
2. Multidimensional simulation model under non-Gaussian random noise and multiplicative noise
In order to further verify the IIPF performance, system random Gaussian noise in the multidimensional simulation model is respectively changed into non-Gaussian random noise and multiplicative noise, and the settings of other parameters are unchanged. Wherein multiplicative system noise is shown as equation (10).
Figure RE-GDA0003128040370000082
Wherein, mu'1、μ′2、μ′3For multiplicative noise of the system, e is a three-dimensional non-gaussian random diagonal matrix with a mean value of 1. In order to ensure that the noise amplitude is close to the additive noise of the system, a diagonal matrix is added in the formula (10) to adjust the multiplicative noise.
Experimental results show that the IIPF and the IPF under non-Gaussian random noise can both have good tracking performance. As shown in fig. 9, the EKF deviates from the actual trajectory in both scenarios. And IPF and IIPF have obvious advantages in non-Gaussian random noise systems and multiplicative noise systems, and IIPF still keeps more than 10% of performance advantage than IPF. Table 3 shows the root mean square error of IPF and IIPF in non-gaussian random noise and multiplicative noise systems, which were not counted due to excessive PF and EKF errors. The result shows that the performance of IIPF is superior to IPF in height and speed root mean square error, and the IIPF has the performance advantage of more than 10% in height root mean square error; the root mean square error is also less than the IPF in terms of speed.
The improved intelligent particle filtering performance of the embodiment is proved to be superior to that of intelligent particle filtering and other particle filtering in the prior art through the two sets of simulation experiments.
TABLE 3 root mean square error of multidimensional simulation model under non-Gaussian random noise and multiplicative noise
Figure RE-GDA0003128040370000091
The intelligent particle filter can reduce the particle degradation phenomenon by using the thought of a genetic algorithm. On the basis of intelligent particle filtering based on a genetic algorithm, a self-adaptive processing strategy for low-weight particles is provided. After the particles are separated and crossed, genetic operators are optimized, and self-adaptive processing is carried out on the low-weight particles. The low weight particles automatically judge whether the particles are bottom particles according to the weight; the bottom particles will be mutated directly, and the other low-weight particles will be mutated randomly according to the mutation probability. Simulation results show that the improved intelligent particle filtering performance is superior to intelligent particle filtering, general particle filtering algorithm and Kalman filtering expansion. In a one-dimensional simulation experiment, the improved intelligent particle filtering error is respectively reduced by 10.5% and 8.5% compared with a common particle filtering algorithm and intelligent particle filtering, and the improved intelligent particle filtering method has better convergence; in a multi-dimensional simulation experiment, the improved intelligent particle filter reduces the height root mean square error and the average error by 8.5 percent and 7.5 percent respectively compared with the intelligent particle filter, and reduces the speed root mean square error and the average error by 11.5 percent and 7.6 percent respectively; in multiplicative noise and non-gaussian random noise, the improved smart particle filter has performance advantage of more than 10%.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.

Claims (10)

1. An intelligent particle filtering method is characterized in that data particles are divided into high-weight particles, low-weight particles and bottom particles, so that the high-weight particles, the low-weight particles and the bottom particles are subjected to variation according to a self-adaptive variation strategy and a variation result is output, wherein the self-adaptive variation parameter of the bottom particles is larger than a preset variation probability, the self-adaptive variation parameter of the low-weight particles is smaller than the preset variation probability and the variation coefficient of the low-weight particles is smaller than the preset variation probability, and the self-adaptive variation parameter of the high-weight particles is smaller than the preset variation probability and the variation coefficient of the high-weight particles is larger than the preset variation probability.
2. The smart particle filtering method of claim 1, wherein the adaptive mutation strategy is
Figure FDA0002946369820000011
Wherein the content of the first and second substances,
Figure FDA0002946369820000012
in order to obtain the particles by variation,
Figure FDA0002946369820000013
in the case of the initial high-weight particles,
Figure FDA0002946369820000014
for crossing low-weight particles, pMThe probability of the mutation is a preset probability of the mutation,
Figure FDA0002946369820000015
to adapt the variation parameter, rl∈[0,1]Is a randomly selected coefficient of variation.
3. The smart particle filter method as claimed in claim 1 or 2, wherein the data particles are obtained from the initial particles by sequentially performing a separation process and a crossover process, the separation process comprising: dividing the initial particles into initial high-weight particles and initial low-weight particles according to a preset weight threshold value; the interleaving process comprises: inputting a cross coefficient to linearly generate cross low-weight particles from the initial high-weight particles and the initial low-weight particles.
4. The smart particle filtering method as claimed in claim 1 or 2, wherein said adaptive variation parameter is
Figure FDA0002946369820000016
Wherein the content of the first and second substances,
Figure FDA0002946369820000017
for adapting the variation parameter, pMIs a predetermined mutation probability, nlThe number of initial low-weight particles,
Figure FDA0002946369820000021
wherein the content of the first and second substances,
Figure FDA0002946369820000022
is the weight of the corresponding particle.
5. The smart particle filtering method of claim 3, wherein the cross low weight particles are generated by:
Figure FDA0002946369820000023
wherein a is ∈ [0, 1 ]]For the randomly selected cross-over coefficient of the particles,
Figure FDA0002946369820000024
in the case of the initial high-weight particles,
Figure FDA0002946369820000025
are the initial low-weight particles.
6. The smart particle filtering method of claim 3, wherein the crossing coefficient is greater than or equal to 0 and the crossing coefficient is less than or equal to 1.
7. The smart particle filtering method according to claim 1, wherein the weight of the varied bottom-layer particles is updated, and whether the updated weight falls within a preset range is determined, if yes, a variation result is output, otherwise, one or more operations of separation processing, cross processing, and variation according to adaptive variation parameters are performed on the bottom-layer particles.
8. The smart particle filter method as recited in claim 3, wherein the weights of the initial particles are calculated before the initial particles are subjected to the separation process.
9. The method of smart particle filtering as recited in claim 1, wherein no crossover processing is performed in the variance of the high weight particles.
10. The smart particle filtering method according to claim 1, wherein the mutation probability is 0.8 to 0.9.
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