Sample Impoverishment Research Articles

Optimising CH4 simulations from the LPJ-GUESS model v4.1 using an adaptive Markov chain Monte Carlo algorithm

Abstract. The processes responsible for methane (CH4) emissions from boreal wetlands are complex; hence, their model representation is complicated by a large number of parameters and parameter uncertainties. The arctic-enabled dynamic global vegetation model LPJ-GUESS (Lund–Potsdam–Jena General Ecosystem Simulator) is one such model that allows quantification and understanding of the natural wetland CH4 fluxes at various scales, ranging from local to regional and global, but with several uncertainties. The model contains detailed descriptions of the CH4 production, oxidation, and transport controlled by several process parameters. Complexities in the underlying environmental processes, warming-driven alternative paths of meteorological phenomena, and changes in hydrological and vegetation conditions highlight the need for a calibrated and optimised version of LPJ-GUESS. In this study, we formulated the parameter calibration as a Bayesian problem, using knowledge of reasonable parameters values as priors. We then used an adaptive Metropolis–Hastings (MH)-based Markov chain Monte Carlo (MCMC) algorithm to improve predictions of CH4 emission by LPJ-GUESS and to quantify uncertainties. Application of this method on uncertain parameters allows for a greater search of their posterior distribution, leading to a more complete characterisation of the posterior distribution with a reduced risk of the sample impoverishment that can occur when using other optimisation methods. For assimilation, the analysis used flux measurement data gathered during the period from 2005 to 2014 from the Siikaneva wetlands in Southern Finland with an estimation of measurement uncertainties. The data are used to constrain the processes behind the CH4 dynamics, and the posterior covariance structures are used to explain how the parameters and the processes are related. To further support the conclusions, the CH4 flux and the other component fluxes associated with the flux are examined. The results demonstrate the robustness of MCMC methods to quantitatively assess the interrelationship between objective function choices, parameter identifiability, and data support. The experiment using real observations from Siikaneva resulted in a reduction in the root-mean-square error (RMSE), from 0.044 to 0.023 gC m−2 d−1, and a 93.89 % reduction in the cost function value. As a part of this work, knowledge about how CH4 data can constrain the parameters and processes is derived. Although the optimisation is performed based on a single site's flux data from Siikaneva, the algorithm is useful for larger-scale multi-site studies for a more robust calibration of LPJ-GUESS and similar models, and the results can highlight where model improvements are needed.

Optimal State Estimation via Adaptive Fuzzy Particle Filter

Particle Filters (PF) accomplish nonlinear system estimation and have received high interest from numerous engineering domains over the past decade. The main problem of PF is to degenerate over time due to the loss of particle diversity. One of the essential causes of losing particle diversity is sample impoverishment (most of particle’s weights are insignificant) which affects the result from the particle depletion in the resampling stage and unsuitable prior information of process and measurement noise. To address this problem, a new Adaptive Fuzzy Particle Filter (AFPF) is used to improve the precision and efficiency of the state estimation results. The error in AFPF state is avoided from diverging by using Fuzzy logic. This method is called tuning weighting factor (α) as output membership function of fuzzy logic and input memberships function is the mean and the covariance of residual error. When the motion model is noisier than measurement, the performance of the proposed method (AFPF) is compared with the standard method (PF) at various particles number. The performance of the proposed method can be compared by keeping the noise level acceptable and convergence of the particle will be measured by the standard deviation. The simulation experiment findings are discussed and evaluated.

Enhancing state and parameter estimations of a dynamic crop model by a recombination particle filter

Crop simulation models are essential tools in supporting sustainable agricultural management. However, due to uncertainty in model parameters, the model predictions may not be sufficiently accurate. Data assimilation (DA) is a common approach to improve dynamic crop modeling by combining it with observation data. Among DA approaches, particle filter (PF) is a popular choice. Since conventional PF (CPF) may suffer from sample impoverishment problems, various filter modifications have been proposed in the literature, including the application of genetic operators (arithmetic cross-over and mutations). In this study, a novel PF approach inspired by the gene’s recombination process has been developed. In this new filter, named “recombination” PF (RPF), particle diversity is increased via information exchange between surviving particles and intermediate particles which are located close to existing particles. In turn, increased particle diversity reduces the chances of sample impoverishment and thus improves filter performance. The proposed method was tested on two synthetic study cases using the open-source AquaCrop model (v5.0a) and assuming weekly observations of canopy cover and soil water content. When CPF was implemented, the overall average normalized root mean square error (NRMSE), combining state and parameter estimations, and yield forecasts, all performed throughout the season, ranged from 4.0 to 5.1 % for ensemble sizes ranging from 150 to 500 particles. When RPF was implemented with a similar number of particles, the overall average NRMSE decreased to 3.6–3.7 %, corresponding to a 7–26 % improvement. Furthermore, higher stability of the results was observed, and the final parameter estimations improved in all the ensemble sizes investigated by approximately 40 %, which would be very beneficial for predicting crop growth in the next season.

Optimal fusion‐based localization method for tracking of smartphone user in tall complex buildings

AbstractIn the event of a fire breaking out or in other complicated situations, a mobile computing solution combining the Internet of Things and wearable devices can actually assist tracking solutions for rescuing and evacuating people in multistory structures. Thus, it is crucial to increase the positioning technology's accuracy. The sequential Monte Carlo (SMC) approach is used in various applications such as target tracking and intelligent surveillance, which rely on smartphone‐based inertial data sequences. However, the SMC method has intrinsic flaws, such as sample impoverishment and particle degeneracy. A novel SMC approach is presented, which is built on the weighted differential evolution (WDE) algorithm. Sequential Monte Carlo approaches start with random particle placements and arrives at the desired distribution with a slower variance reduction, like in a high‐dimensional space, such as a multistory structure. Weighted differential evolution is included before the resampling procedure to guarantee the appropriate variety of the particle set, prevent the usage of an inadequate number of valid samples, and preserve smartphone user position accuracy. The values of the smartphone‐based sensors and BLE‐beacons are set as input to the SMC, which aids in fast approximating the posterior distributions, to speed up the particle congregation process in the proposed SMC‐based WDE approach. Lastly, the robustness and efficacy of the suggested technique more accurately reflect the actual situation of smartphone users. According to simulation findings, the suggested approach provides improved location estimation with reduced localization error and quick convergence. The results confirm that the proposed optimal fusion‐based SMC‐WDE scheme performs 9.92% better in terms of MAPE, 15.24% for the case of MAE, and 0.031% when evaluating based on the R2 Score.

A point mass proposal method for Bayesian state-space model fitting

State-space models (SSMs) are commonly used to model time series data where the observations depend on an unobserved latent process. However, inference on the model parameters of an SSM can be challenging, especially when the likelihood of the data given the parameters is not available in closed-form. One approach is to jointly sample the latent states and model parameters via Markov chain Monte Carlo (MCMC) and/or sequential Monte Carlo approximation. These methods can be inefficient, mixing poorly when there are many highly correlated latent states or parameters, or when there is a high rate of sample impoverishment in the sequential Monte Carlo approximations. We propose a novel block proposal distribution for Metropolis-within-Gibbs sampling on the joint latent state and parameter space. The proposal distribution is informed by a deterministic hidden Markov model (HMM), defined such that the usual theoretical guarantees of MCMC algorithms apply. We discuss how the HMMs are constructed, the generality of the approach arising from the tuning parameters, and how these tuning parameters can be chosen efficiently in practice. We demonstrate that the proposed algorithm using HMM approximations provides an efficient alternative method for fitting state-space models, even for those that exhibit near-chaotic behavior.

Particle Filter Based on Harris Hawks Optimization Algorithm for Underwater Visual Tracking

Due to the complexity of the underwater environment, tracking underwater targets via traditional particle filters is a challenging task. To resolve the problem that the tracking accuracy of a traditional particle filter is low due to the sample impoverishment caused by resampling, in this paper, a new tracking algorithm using Harris-hawks-optimized particle filters (HHOPF) is proposed. At the same time, the problem of particle filter underwater target feature construction and underwater target scale transformation is addressed, the corrected background-weighted histogram method is introduced into underwater target feature recognition, and the scale filter is combined to realize target scaling transformation during tracking. In addition, to enhance the computational speed of underwater target tracking, this paper constructs a nonlinear escape energy using the Harris hawks algorithm in order to balance the exploration and exploitation processes. Based on the proposed HHOPF tracker, we performed detection and evaluation using the Underwater Object Tracking (UOT100) vision database. The proposed method is compared with evolution-based tracking algorithms and particle filters, as well as with recent tracker-based correlation filters and some other state-of-the-art tracking methods. By comparing the results of tracking using the test data sets, it is determined that the presented algorithm improves the overlap accuracy and tracking accuracy by 11% compared with other algorithms. The experiments demonstrate that the presented HHOPF visual tracking provides better tracking results.

Maximum Correntropy-Based Extended Particle Filter for Nonlinear System

To solve the particle degradation and sample impoverishment, a maximum correntropy-based extended particle filter method is proposed by optimizing the important density function. In the proposed method, the importance sampling is guided by the measurement information, the entropy criterion and high-order moments information of the signal are fully utilized, and the non-Gaussian heavy-tailed distribution noise and the noise with outliers are effectively suppressed. The simulation results demonstrate the effectiveness and feasibility of the filtering method.

A localization scheme based on Improving Dynamic Population Monte Carlo Localization method for large‐scale mobile wireless aquaculture sensor networks

AbstractLocalization is one of the essential problems in wireless sensor applications (WSNs). Most range‐free localization schemes for mobile WSNs are based on the Sequential Monte Carlo (SMC) algorithm. Multiple iterations, sample impoverishment and less sample diversity, leading to low localizing efficiency, are the most usual problems demanding to be solved in these SMC‐based methods. An improved localization scheme for mobile aquaculture WSNs based on the Improving Dynamic Population Monte Carlo Localization (I‐DPMCL) method is proposed. A population of probability density functions is proposed to approximate the unknown location distribution based on a set of observations through an iterative mixture importance sampling procedure, accompanied by node dynamic behaviours being analysed quantitatively or definitely. Threefold constrain rules are put forward in the I‐DPMCL scheme to decrease the iteration number and trade off iteration number and enough valid samples to obtain the optimum iteration number. Then, these localization behaviours, especial delay, are predicted based on the statistical point of view. Moreover, performance comparisons of I‐DPMCL with other SMC‐based schemes are also proposed. Simulation results show that delay of I‐DPMCL has some superiority to those of other schemes, and accuracy and energy consumption are improved in some cases of lower mobile velocity.

Covariance-Based Selection of Parameters for Particle Filter Data Assimilation in Soil Hydrology

Real-time in situ measurements are increasingly being used to improve the estimations of simulation models via data assimilation techniques such as particle filter. However, models that describe complex processes such as water flow contain a large number of parameters while the data available are typically very limited. In such situations, applying particle filter to a large, fixed set of parameters chosen a priori can lead to unstable behavior, i.e., inconsistent adjustment of some of the parameters that have only limited impact on the states that are being measured. To prevent this, in this study correlation-based variable selection is embedded in the particle filter, so that at each step only a subset of the most influential parameters is adjusted. The particle filter used in this study includes genetic algorithm operators and Monte Carlo Markov Chain for alleviating filter degeneracy and sample impoverishment. The proposed method was applied to a water flow model (Hydrus-1D) in which soil water content at various depths and soil hydraulic parameters were updated. Two case studies are presented. Overall, the proposed method yielded parameters and states estimates that were more accurate and more consistent than those obtained when adjusting all the parameters. Furthermore, the results show that the higher the influence of a parameter on the model output under the current conditions, the better the estimation of this parameter is.

A Tempered Particle Filter to Enhance the Assimilation of SAR-Derived Flood Extent Maps Into Flood Forecasting Models.

Data assimilation (DA) is a powerful tool to optimally combine uncertain model simulations and observations. Among DA techniques, the particle filter (PF) has gained attention for its capacity to deal with nonlinear systems and for its relaxation of the Gaussian assumption. However, the PF may suffer from degeneracy and sample impoverishment. In this study, we propose an innovative approach, based on a tempered particle filter (TPF), aiming at mitigating PFs issues, thus extending over time the assimilation benefits. Probabilistic flood maps derived from synthetic aperture radar data are assimilated into a flood forecasting model through an iterative process including a particle mutation in order to keep diversity within the ensemble. Results show an improvement of the model forecasts accuracy, with respect to the Open Loop: on average the root mean square error (RMSE) of water levels decrease by 80% at the assimilation time and by 60% 2 days after the assimilation. A comparison with the Sequential Importance Sampling (SIS) is carried out showing that although SIS performances are generally comparable to the TPF ones at the assimilation time, they tend to decrease more quickly. For instance, on average TPF‐based RMSE are 20% lower compared to the SIS‐based ones 2 days after the assimilation. The application of the TPF determines higher critical success index values compared to the SIS. On average the increase in performances lasts for almost 3 days after the assimilation. Our study provides evidence that the application of the variant of the TPF enables more persistent benefits compared to the SIS.

Implementation of ensemble Kalman filter algorithm for underwater target tracking

ABSTRACT Surveillance of underwater for maritime warfare is traditionally being carried out by bearings-only tracking from many decades. The measurements used for state estimation here are nonlinear. Also the noise in the measurements and the process cannot be always Gaussian. The traditional nonlinear filtering algorithms like extended Kalman filter and modified gain extended Kalman filter use the linearisation of the system. The unscented Kalman filter (UKF) uses the sigma point approach based on Gaussian distribution to deal with nonlinearity. The particle filter (PF) uses the randomly generated particles based on the pdf of the state. PF is highly complex to implement and it also suffers from sample impoverishment. Hence, ensemble Kalman filter (EnKF) which is a simplified form of PF will be tried out for bearings-only tracking in this research work. The performance of EnKF is compared with PF and UKF and the results obtained using these filters in Matlab are presented.

Design of robust cubature fission particle filter algorithm in multi-source cooperative navigation

As a part of the multi-source cooperative navigation scheme, data fusion has a significant impact on the quality of state estimation. Particle filtering has gradually become the focus of many fusion methods due to its unique theoretical advantages in nonlinear non-Gaussian systems. However, the particle degradation and the resulting sample impoverishment restrict its application in complex engineering scenarios. In this paper, a robust cubature fission particle filter (RCFPF) is proposed to deal with these problems. First, in the framework of cubature rule, Huber function is used to combine the L2 norm and L1 norm to improve the importance density function(IDF), suppress the observation noise. Meanwhile, the proposed distribution(PD) is further optimized by combining the Gaussian distribution with Laplace distribution to alleviate particle degradation. Second, the particle swarm is fissioned before resampling, and the particle weight is reconstructed by fission of high weight particles and covering low weight particles to inhibit sample impoverishment. The vehicle experiments of multi-source cooperative navigation show that the proposed algorithm achieves better test results in accuracy and robustness than extended Kalman filter (EKF), strong tracking particle filter (STPF), and cubature particle filter (CPF).

An enhanced particle filter technology for battery system state estimation and RUL prediction

The particle filter (PF) technique can model nonlinear degradation features of battery’s system, and conduct battery state estimation based on noisy measurements. However, PF has some limitations in system state estimation related to sample degeneracy and impoverishment. In addition, its posterior probability density function cannot be updated during the prognostic period due to the absence of new battery measurements. In this work, an enhanced PF technology is proposed to deal with these problems so as to improve PF modeling accuracy for battery state-of-health monitoring and remaining useful life (RUL) prediction. Specifically, an enhanced particles method is proposed to reduce the impact of sample degeneracy and impoverishment in state estimation. An evolving fuzzy predictor is adopted and fused into the enhanced PF structure to deal with the lack of new battery measurements during the prognostic period. The effectiveness of the proposed enhanced PF technology is validated through simulation tests.

PDR/Geomagnetic Fusion Localization Method Based on AOFA-Improved Particle Filter

Particle filter is commonly used in various indoor positioning schemes, but sample impoverishment and weight degradation generally exist in particle filter. To solve this problem, this article uses the firefly algorithm to optimize particle filter. Using the global optimal value in the particle swarm to guide the remaining particles to update their positions, the particles tend to move to the high likelihood area, which can more accurately describe the true state of the target observation. At the same time, to avoid particles falling into local optimum and oscillating repeatedly at the extreme point, the mathematical model of the firefly algorithm is reconstructed in this article, which is named as adaptive optimization firefly algorithm (AOFA). The experimental results show that the positioning scheme can provide the positioning accuracy with an average error of less than 0.5 m. Compared with the traditional particle filter, the positioning accuracy is improved by 120%.

Joint Tracking of Source and Environment Using Improved Particle Filtering in Shallow Water

Shallow water is a complex sound propagation medium, which is affected by the varying spatial–temporal ocean environment. Taking this complexity into account, the classical processing techniques of source localization and environmental inversion may be improved. In this work, a joint tracking approach for the moving source and environmental parameters of the range-dependent and time-evolving environment in shallow water is presented. The tracking scheme treats both the source parameters (e.g., source depth, range, and speed) and the environmental parameters (e.g., water column sound speed profile (SSP) and sediment parameters) at the source location as unknown variables that evolve as the source moves. To counter sample impoverishment and robustly characterize the evolution of the parameters, an improved particle filter (PF), which is an extension of the standard PF, is proposed. Two examples with simulated data in a slowly changing environment and experimental data collected during the ASIAEX experiment are utilized to demonstrate the effectiveness of the joint approach. The results show that we were able to track the source and environmental parameters simultaneously, and the uncertainties were evaluated in the form of time-evolving posterior probability densities (PPDs). The performance comparison confirms that the improved PF is superior to the standard PF, as it can reduce the parameter uncertainties. The tracking capabilities of the improved PF were verified with high accuracy in real-time source localization and well-estimated rapidly varying parameters. Moreover, the influence of different particle numbers on the improved PF tracking performance is also illustrated.

Intelligent Trigonometric Particle Filter for visual tracking

Visual tracking is one of the pre-eminent tasks in several computer vision applications. Particle filter (PF) is extensively used in visual tracking for intelligent surveillance system applications, hugely significant. But the re-sampling procedure of PF will result in sample impoverishment, which will affect the precision of tracking simultaneously. In this paper, a new tracking technique, called Trigonometric Particle Filter (TPF), based on PF optimized by Sine Cosine Algorithm (SCA), which contains trigonometric sine and cosine functions, is proposed. An enhanced method for improving the number of target particles used in a Sine Cosine Algorithm for trigonometric particle filter includes SCA ahead of the re-sampling step. This step ensures a more extensive particle set Achievement of the proposed TPF tracker is inspected and assessed on Visual Tracker Benchmark (VOT) databases. The proposed TPF tracker is compared with evolutionary-based methods like the Spider monkey optimization assisted PF (SMO-PF), Firefly algorithm-based PF (FAPF) method, Particle swarm optimization-based PF (PSO-PF) and Particle filter, recent four correlation filter-based trackers, and also with other ten state-of-the-art tracking methods. We demonstrate that visual tracking using TPF delivers additional consistent and proficient tracking outcomes than compared trackers.

Application of Sigma Point Particle Filter Method for Passive State Estimation in Underwater

Bearings-only tracking (BOT) plays a vital role in underwater surveillance. In BOT, measurement is tangentially related to state of the system. This measurement is also corrupted with noise due to turbulent underwater environment. Hence state estimation process using BOT becomes nonlinear. This necessitates the use of nonlinear filtering algorithms in place of traditional linear filters like Kalman filter. In general, these nonlinear filters utilize the assumption of measurements being corrupted with Gaussian noise for state estimation. The measurements cannot be always corrupted with Gaussian noise because of the highly unstable sea environment. These problems indicate the necessity for development of nonlinear non-Gaussian filters like particle filter (PF) for underwater tracking. However, PF suffers from severe problems like sample degeneracy and impoverishment and also it is tedious to select an appropriate technique for resampling. To overcome these difficulties in PF implementation, the strategy of combining PF with another filter like unscented Kalman filter is proposed for target’s state estimation. The detailed analysis of the same is presented in comparison with other particle filter combinations using the simulation results obtained in Matlab.

Efficient robot localization and SLAM algorithms using Opposition based High Dimensional optimization Algorithm

Particle filter (PF) is introduced to tackle the limitations of the Kalman filter which adopts Gaussian in the state and noise of the system. PFs have the problem of sample impoverishment and one approach to solve this problem is to optimize the proposal distribution shown by particles. This paper introduces a novel evolutionary PF based on Opposition based High Dimensional optimization Algorithm (OHDA) to reposition the particles of PF in high probable regions for estimation. OHDA will preserve the diversity of particles while emphasizing the more informative ones by information sharing and angular movement operators. Opposite particles are introduced in this paper to speed up the convergence of PF. Virtual forward movement by angular movement of OHDA is employed to better guide the search process. The optimized PF can improve the performance of the estimation algorithms in problems such as localization and SLAM. In robot localization problem, particles show the location of the robot in a known environment. For SLAM (Simultaneous Localization And Mapping), particles contain the location of the robot as well as estimated map of the environment. The application of the resulting evolutionary particle filter is tested in both localization and SLAM. Comparing the results of the proposed evolutionary particle filter with other algorithms confirms the efficiency of applying OHDA to PF in terms of improving estimation accuracy in the well-known Victoria park dataset and some other generated test environments. Comparing optimization algorithms on FASTSLAM and UFASTSLAM are PSO, FA, MVO, and MGWO.

An intelligent particle filter with resampling of multi-population cooperation

The particle filter (PF) has excellent estimation performance for nonlinear non-Gaussian systems. However, this method misleads the results due to sample impoverishment and the sensitivity on the initial values of state and process noise variance. To overcome this, an intelligent PF method with a resampling of multi-population cooperation is presented in this paper. Firstly, an intelligent resampling mechanism based on a circular collaborative structure is proposed. In this mechanism, the particles are divided into multiple populations, which are generated by importance densities with different initial state values and variances individually. Secondly, a collaborative strategy based on Gaussian mutation is designed to improve particle diversity so as to raise estimation accuracy of PF. This strategy reserves the high-weight particles in each population, and replaces the low-weight ones with the particles generated by Gaussian mutation on high-weight particles in the previous population based on the circular collaborative structure. Finally, three systems are introduced to test the performance of the proposed method. The results illustrate that the proposed method can effectively improve the estimation accuracy and robustness of PF when the initial values of state and variance of process noise are unknown compared with three existing methods.

전자 유압 엑추에이터를 포함하는 비선형 능동 서스펜션의 상태추정을 위한 가우시안 분포 리샘플링 기반 입자 필터 설계

This paper proposes a GDRPF (Gaussian Distribution Resampling Particle Filter) for electro-hydraulic active suspension systems. In order to estimate the state of the nonlinear/non-Gaussian suspension system effectively, a particle filter-based state estimator was developed, and the computational burden and sample impoverishment problems were overcome through the GDR algorithm. The proposed GDRPF-based state estimator not only reduces the computational burden of the particle filters efficiently, but also has better estimate performance than other linearization-based state estimators. Simulation results for nonlinear active suspension system demonstrate the effectiveness of the proposed algorithm.