Corrected Differential Evolution Particle Filter for Nonlinear Filtering

2014 ◽  
Vol 981 ◽  
pp. 422-425
Author(s):  
Chao Zhu Zhang ◽  
Lin Li
Keyword(s):  
Differential Evolution ◽  
Particle Filter ◽  
Nonlinear Filtering ◽  
Nonlinear Filter ◽  
Initial Population ◽  
Critical Problem ◽  
Fitness Functions ◽  
Estimation Precision ◽  
Particle Impoverishment

Particle filter is the most successful nonlinear filter for nonlinear filtering. However its resampling process has the critical problem existing is the particle impoverishment problem. In this letter, we propose a new corrected differential evolution particle filter for solving this problem. In this algorithm, the particles sampling from the importance distribution are regarded as the initial population of the Corrected Differential Evolution (CDE) algorithm, and the corresponding weights as the fitness functions. The optimal particles are obtained by the process of the CDE algorithm. Experiment results indicate that the proposed method relieves the particle degeneracy and impoverishment and improves the estimation precision.

An Implicit Algorithm of Solving Nonlinear Filtering Problems

2014 ◽  
Vol 16 (2) ◽  
pp. 382-402
Author(s):  
Feng Bao ◽  
Yanzhao Cao ◽  
Xiaoying Han
Keyword(s):  
Kalman Filter ◽  
Particle Filter ◽  
Nonlinear Filtering ◽  
State Equation ◽  
Nonlinear Filter ◽  
Filter Method ◽  
Simulation Methods ◽  
Current State ◽  
Numerical Simulation Methods ◽  
Kalman Filter Method

AbstractNonlinear filter problems arise in many applications such as communications and signal processing. Commonly used numerical simulation methods include Kalman filter method, particle filter method, etc. In this paper a novel numerical algorithm is constructed based on samples of the current state obtained by solving the state equation implicitly. Numerical experiments demonstrate that our algorithm is more accurate than the Kalman filter and more stable than the particle filter.

scholarly journals A New Linear Regression Kalman Filter with Symmetric Samples

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2139
Author(s):  
Xiuqiong Chen ◽  
Jiayi Kang ◽  
Mina Teicher ◽  
Stephen S.-T. Yau
Keyword(s):  
Kalman Filter ◽  
Linear Regression ◽  
Particle Filter ◽  
Normal Distribution ◽  
Extended Kalman Filter ◽  
Nonlinear Filtering ◽  
Unscented Kalman Filter ◽  
Standard Normal Distribution ◽  
Leibler Divergence ◽  
Standard Normal

Nonlinear filtering is of great significance in industries. In this work, we develop a new linear regression Kalman filter for discrete nonlinear filtering problems. Under the framework of linear regression Kalman filter, the key step is minimizing the Kullback–Leibler divergence between standard normal distribution and its Dirac mixture approximation formed by symmetric samples so that we can obtain a set of samples which can capture the information of reference density. The samples representing the conditional densities evolve in a deterministic way, and therefore we need less samples compared with particle filter, as there is less variance in our method. The numerical results show that the new algorithm is more efficient compared with the widely used extended Kalman filter, unscented Kalman filter and particle filter.

A SLAM based on auxiliary marginalised particle filter and differential evolution

2013 ◽  
Vol 45 (9) ◽  
pp. 1913-1926 ◽  
Author(s):  
R. Havangi ◽  
M.A. Nekoui ◽  
M. Teshnehlab ◽  
H.D. Taghirad
Keyword(s):  
Differential Evolution ◽  
Particle Filter

scholarly journals An Improved Grey Wolf Optimizer Based on Differential Evolution and OTSU Algorithm

2020 ◽  
Vol 10 (18) ◽  
pp. 6343
Author(s):  
Yuanyuan Liu ◽  
Jiahui Sun ◽  
Haiye Yu ◽  
Yueyong Wang ◽  
Xiaokang Zhou
Keyword(s):  
Differential Evolution ◽  
Image Recognition ◽  
Optimal Solution ◽  
Tsallis Entropy ◽  
Grey Wolf Optimizer ◽  
Initial Population ◽  
Grey Wolf ◽  
Particle Swarm Optimizer ◽  
De Algorithm ◽  
Local Optimal Solution

Aimed at solving the problems of poor stability and easily falling into the local optimal solution in the grey wolf optimizer (GWO) algorithm, an improved GWO algorithm based on the differential evolution (DE) algorithm and the OTSU algorithm is proposed (DE-OTSU-GWO). The multithreshold OTSU, Tsallis entropy, and DE algorithm are combined with the GWO algorithm. The multithreshold OTSU algorithm is used to calculate the fitness of the initial population. The population is updated using the GWO algorithm and the DE algorithm through the Tsallis entropy algorithm for crossover steps. Multithreshold OTSU calculates the fitness in the initial population and makes the initial stage basically stable. Tsallis entropy calculates the fitness quickly. The DE algorithm can solve the local optimal solution of GWO. The performance of the DE-OTSU-GWO algorithm was tested using a CEC2005 benchmark function (23 test functions). Compared with existing particle swarm optimizer (PSO) and GWO algorithms, the experimental results showed that the DE-OTSU-GWO algorithm is more stable and accurate in solving functions. In addition, compared with other algorithms, a convergence behavior analysis proved the high quality of the DE-OTSU-GWO algorithm. In the results of classical agricultural image recognition problems, compared with GWO, PSO, DE-GWO, and 2D-OTSU-FA, the DE-OTSU-GWO algorithm had accuracy in straw image recognition and is applicable to practical problems. The OTSU algorithm improves the accuracy of the overall algorithm while increasing the running time. After adding the DE algorithm, the time complexity will increase, but the solution time can be shortened. Compared with GWO, DE-GWO, PSO, and 2D-OTSU-FA, the DE-OTSU-GWO algorithm has better results in segmentation assessment.

scholarly journals A Particle Filter Track-Before-Detect Algorithm Based on Hybrid Differential Evolution

Algorithms ◽  
2015 ◽  
Vol 8 (4) ◽  
pp. 965-981 ◽  
Author(s):  
Chaozhu Zhang ◽  
Lin Li ◽  
Yu Wang
Keyword(s):  
Differential Evolution ◽  
Particle Filter ◽  
Track Before Detect

COMPUTING TWO LINCHPINS OF TOPOLOGICAL DEGREE BY A NOVEL DIFFERENTIAL EVOLUTION ALGORITHM

2005 ◽  
Vol 05 (03) ◽  
pp. 335-350 ◽  
Author(s):  
FEI GAO ◽  
HENG-QING TONG
Keyword(s):  
Differential Evolution ◽  
Topological Degree ◽  
Large Scale ◽  
Uniform Design ◽  
Lipschitz Constant ◽  
Differential Evolution Algorithm ◽  
Initial Point ◽  
Benchmark Problems ◽  
Initial Population ◽  
Evolution Algorithm

How to detect the topological degree (TD) of a function is of vital importance in investigating the existence and the number of zero values in the function, which is a topic of major significance in the theory of nonlinear scientific fields. Usually a sufficient refinement of the boundary of the polyhedron decided by Boult and Sikorski algorithm (BS) is needed as prerequisite when the well known method of Stenger and Kearfott is chosen for computing TD. However two linchpins are indispensable to BS, the parameter δ on the boundary of the polyhedron and an estimation of the Lipschitz constant K of the function, whose computations are analytically difficult. In this paper, through an appropriate scheme that transforms the problems of computing δ and K into searching optimums of two non-differentiable functions, a novel differential evolution algorithm (DE) combined with established techniques is proposed as an alternative method to computing δ and K. Firstly it uses uniform design method to generate the initial population in feasible field so as to have the property of large scale convergence, without better approximation of the unknown parameter as iterative initial point. Secondly, it restrains the normal DE's local convergence limitation virtually through deflection and stretching of objective function. The main advantages of the put algorithm are its simplicity and its ability to work by using function values solely. Finally, details of applying the proposed method into computing δ and K are given, and experimental results on two benchmark problems in contrast to the results reported have demonstrated the promising performance of the proposed algorithm in different scenarios.

A New Approximate Solution of the Optimal Nonlinear Filter for Data Assimilation in Meteorology and Oceanography

2008 ◽  
Vol 136 (1) ◽  
pp. 317-334 ◽  
Author(s):  
I. Hoteit ◽  
D-T. Pham ◽  
G. Triantafyllou ◽  
G. Korres
Keyword(s):  
Approximate Solution ◽  
Data Assimilation ◽  
Particle Filter ◽  
Weighted Average ◽  
Ocean Model ◽  
Nonlinear Filter ◽  
Low Rank ◽  
Low Rank Approximation ◽  
Type Particle ◽  
Rank Approximation

Abstract This paper introduces a new approximate solution of the optimal nonlinear filter suitable for nonlinear oceanic and atmospheric data assimilation problems. The method is based on a local linearization in a low-rank kernel representation of the state’s probability density function. In the resulting low-rank kernel particle Kalman (LRKPK) filter, the standard (weight type) particle filter correction is complemented by a Kalman-type correction for each particle using the covariance matrix of the kernel mixture. The LRKPK filter’s solution is then obtained as the weighted average of several low-rank square root Kalman filters operating in parallel. The Kalman-type correction reduces the risk of ensemble degeneracy, which enables the filter to efficiently operate with fewer particles than the particle filter. Combined with the low-rank approximation, it allows the implementation of the LRKPK filter with high-dimensional oceanic and atmospheric systems. The new filter is described and its relevance demonstrated through applications with the simple Lorenz model and a realistic configuration of the Princeton Ocean Model (POM) in the Mediterranean Sea.

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