scholarly journals The Particle Filter Sample Impoverishment Problem in the Orbit Determination Application

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Paula Cristiane Pinto Mesquita Pardal ◽  
Helio Koiti Kuga ◽  
Rodolpho Vilhena de Moraes
Keyword(s):  
Particle Filter ◽  
Particle Filters ◽  
Orbital Motion ◽  
Artificial Satellite ◽  
Real Data ◽  
Orbital State ◽  
Computational Implementation ◽  
The Difference ◽  
Bootstrap Algorithm ◽  
Number Of Particles

The paper aims at discussing techniques for administering one implementation issue that often arises in the application of particle filters: sample impoverishment. Dealing with such problem can significantly improve the performance of particle filters and can make the difference between success and failure. Sample impoverishment occurs because of the reduction in the number of truly distinct sample values. A simple solution can be to increase the number of particles, which can quickly lead to unreasonable computational demands, which only delays the inevitable sample impoverishment. There are more intelligent ways of dealing with this problem, such as roughening and prior editing, procedures to be discussed herein. The nonlinear particle filter is based on the bootstrap filter for implementing recursive Bayesian filters. The application consists of determining the orbit of an artificial satellite using real data from the GPS receivers. The standard differential equations describing the orbital motion and the GPS measurements equations are adapted for the nonlinear particle filter, so that the bootstrap algorithm is also used for estimating the orbital state. The evaluation will be done through convergence speed and computational implementation complexity, comparing the bootstrap algorithm results obtained for each technique that deals with sample impoverishment.

A New Adaptive UPF Algorithm through Improved Relative Entropy

2013 ◽  
Vol 658 ◽  
pp. 569-573
Author(s):  
Wen Tao Yu ◽  
Jun Peng ◽  
Xiao Yong Zhang
Keyword(s):  
Particle Filter ◽  
Relative Entropy ◽  
Particle Number ◽  
Time Step ◽  
Unscented Particle Filter ◽  
Posterior Probability Density ◽  
The Difference ◽  
Particle Filter Algorithm ◽  
Non Gaussian ◽  
Number Of Particles

Unscented particle filter (UPF) has high accuracy of state estimation for nonlinear system with non-Gaussian noise. While the computation of traditional unscented particle filter is huge and this depends on the particle number. In this paper we propose a new adaptive unscented particle filter algorithm AUPF through improved relative entropy which can adaptively adjust the particle number during filtering. Firstly the relative entropy is used to measure the distance between the posterior probability density and the importance proposal and the least number of particles for the next time step is decided according to the relative entropy. Then the least number is adjusted to offset the difference between the importance proposal and the true distribution. This algorithm can effectively reduce unnecessary particles meanwhile reduce the computation. The simulation results show the effectiveness of AUPF.

Applied Technology in Adapting the Number of Particles while Maintaining the Diversity in the Particle Filter

2014 ◽  
Vol 951 ◽  
pp. 202-207 ◽  
Author(s):  
Rui Rui Zhi ◽  
Tian Cheng Li ◽  
Ming Fei Siyau ◽  
Shu Dong Sun
Keyword(s):  
Particle Filter ◽  
Particle Filters ◽  
Trade Off ◽  
Approximation Quality ◽  
Leibler Divergence ◽  
Applied Technology ◽  
System Requirement ◽  
Simulation Results ◽  
Computing Speed ◽  
Number Of Particles

Determining the required number of particles is a challenging task toward the application of particle filters (PF). As smaller number of particles means faster computing speed while larger number of particles means better approximation ability, it is vital to balance the trade-off between computing speed and approximation quality. Moreover, to match the system requirement that often varies in time, the number of particles should be adapted in time. To achieve these, an Adaptive Deterministic Resampling (ADR) is proposed in this paper. The new resampling employs techniques combine Deterministic resampling and Kullback–Leibler Divergence (KLD)-resampling (both with slight changes made) and gain their respective advantages, which not only allow online adaptation of the number of particles according to the system requirement but also guarantee the diversity of particles. Simulation results demonstrate and confirm the validity of our approach.

Data assimilation of SMAP soil moisture into the PCR-GLOBWB hydrological model to improve discharge estimates via A Novel Local Particle Filter

2021 ◽  
Author(s):  
Zhenwu Wang ◽  
Rolf Hut ◽  
Natthachet Tangdamrongsub ◽  
Nick van de Giesen
Keyword(s):  
Soil Moisture ◽  
Data Assimilation ◽  
Particle Filter ◽  
Particle Filters ◽  
Hydrological Model ◽  
Surface Soil ◽  
Test Theory ◽  
Surface Soil Moisture ◽  
The Impact ◽  
Number Of Particles

<p>Assimilating surface soil moisture data or GRACE data, retrieved from satellite, into hydrological models has been proven to improve the accuracy of hydrological model estimations and predictions. For data assimilation applications in hydrology, the ensemble Kalm filter(EnKF) is the most commonly used data assimilation(DA) method. Particle filters are a type of non-Gaussian filter that doesn’t need the normality assumption that the EnKF needs. Adding localization defeats the curse of dimensionality that is a problem in normal particle filters. In the present study, we investigated our adaption of the local particle filter based on the Gamma test theory(LPF-GT) to improve discharge estimates by assimilating SMAP satellite soil moisture into the PCR-GLOBWB hydrological model. The study area is the Rhine river basin, driven by forcing data from April 2015 to December 2016. The improved discharge estimates are obtained by using DA to adjust the surface soil moisture in the model. The influence of DA to discharge is not direct but works through the dynamics of the hydrological model.  To explore the potential of LPF-GT, serval sensitivity experiments were conducted to figure out the impact of localization scales and the number of particles on DA's performance. The DA estimates were validated against in situ discharge measurements from gauge stations. To demonstrate the benefit of LPF-GT, EnKF was used as a benchmark in this research. Increases in Nash-Sutcliffe (0.05%– 38%) and decreases in normalized RMSE (0.02%–3.4%) validated the capability of LPF-GT. Results showed that localization scales' impact was substantial. The optimal value of the localization scale was obtained by tuning. LPF-GT achieved a satisfactory performance when only using a few particles, even with as little as five particles. The sample errors posed an adverse impact on the open-loop results. Further improvement could be achieved by considering reduce sample errors due to a small number of particles.</p>

Particle Filters

2015 ◽  
Author(s):  
Edward P. Herbst ◽  
Frank Schorfheide
Keyword(s):  
Particle Filter ◽  
Bayesian Estimation ◽  
Particle Filtering ◽  
Particle Filters ◽  
Likelihood Function ◽  
Nonlinear Models ◽  
Dsge Models ◽  
Filtering Algorithm ◽  
Bootstrap Filter ◽  
Number Of Particles

This chapter explains how the key difficulty that arises when the Bayesian estimation of DSGE models is extended from linear to nonlinear models is the evaluation of the likelihood function, and focuses on the use of particle filters to accomplish this task. The basic bootstrap particle filtering algorithm is remarkably straightforward, but may perform quite poorly in practice. Thus, much of the literature about particle filters focuses on refinements of the bootstrap filter that increases the efficiency of the algorithm. The accuracy of the particle filter can be improved by choosing other proposal distributions. While the tailoring (or adaption) of the proposal distributions tends to require additional computations, the number of particles can often be reduced drastically, which leads to an improvement in efficiency.

Effect of leakage and blockage on the acoustic behavior of particle filters

2019 ◽  
Vol 67 (6) ◽  
pp. 483-492
Author(s):  
Seonghyeon Baek ◽  
Iljae Lee
Keyword(s):  
Transfer Matrix ◽  
Particle Filters ◽  
Acoustic Analysis ◽  
Transmission Loss ◽  
One Dimensional ◽  
Filter System ◽  
The Difference ◽  
The One ◽  
Analytical Approaches ◽  
Good Agreement

The effects of leakage and blockage on the acoustic performance of particle filters have been examined by using one-dimensional acoustic analysis and experimental methods. First, the transfer matrix of a filter system connected to inlet and outlet pipes with conical sections is measured using a two-load method. Then, the transfer matrix of a particle filter only is extracted from the experiments by applying inverse matrices of the conical sections. In the analytical approaches, the one-dimensional acoustic model for the leakage between the filter and the housing is developed. The predicted transmission loss shows a good agreement with the experimental results. Compared to the baseline, the leakage between the filter and housing increases transmission loss at a certain frequency and its harmonics. In addition, the transmission loss for the system with a partially blocked filter is measured. The blockage of the filter also increases the transmission loss at higher frequencies. For the simplicity of experiments to identify the leakage and blockage, the reflection coefficients at the inlet of the filter system have been measured using two different downstream conditions: open pipe and highly absorptive terminations. The experiments show that with highly absorptive terminations, it is easier to see the difference between the baseline and the defects.

scholarly journals Dynamic Indoor Localization Using Maximum Likelihood Particle Filtering

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1090
Author(s):  
Wenxu Wang ◽  
Damián Marelli ◽  
Minyue Fu
Keyword(s):  
Maximum Likelihood ◽  
Particle Filtering ◽  
Indoor Localization ◽  
Real Data ◽  
High Accuracy ◽  
Classical Particle ◽  
Popular Approach ◽  
Filtering Method ◽  
Essential Idea ◽  
Number Of Particles

A popular approach for solving the indoor dynamic localization problem based on WiFi measurements consists of using particle filtering. However, a drawback of this approach is that a very large number of particles are needed to achieve accurate results in real environments. The reason for this drawback is that, in this particular application, classical particle filtering wastes many unnecessary particles. To remedy this, we propose a novel particle filtering method which we call maximum likelihood particle filter (MLPF). The essential idea consists of combining the particle prediction and update steps into a single one in which all particles are efficiently used. This drastically reduces the number of particles, leading to numerically feasible algorithms with high accuracy. We provide experimental results, using real data, confirming our claim.

scholarly journals Estimating Differential Latent Variable Graphical Models with Applications to Brain Connectivity

Biometrika ◽  
2020 ◽  
Author(s):  
S Na ◽  
M Kolar ◽  
O Koyejo
Keyword(s):  
Graphical Models ◽  
Latent Variable ◽  
Graphical Model ◽  
Brain Connectivity ◽  
Statistical Error ◽  
Real Data ◽  
Low Rank ◽  
Conditional Dependence ◽  
Gradient Descent Algorithm ◽  
The Difference

Abstract Differential graphical models are designed to represent the difference between the conditional dependence structures of two groups, thus are of particular interest for scientific investigation. Motivated by modern applications, this manuscript considers an extended setting where each group is generated by a latent variable Gaussian graphical model. Due to the existence of latent factors, the differential network is decomposed into sparse and low-rank components, both of which are symmetric indefinite matrices. We estimate these two components simultaneously using a two-stage procedure: (i) an initialization stage, which computes a simple, consistent estimator, and (ii) a convergence stage, implemented using a projected alternating gradient descent algorithm applied to a nonconvex objective, initialized using the output of the first stage. We prove that given the initialization, the estimator converges linearly with a nontrivial, minimax optimal statistical error. Experiments on synthetic and real data illustrate that the proposed nonconvex procedure outperforms existing methods.

scholarly journals A Robust Rerank Approach for Feature Selection and Its Application to Pooling-Based GWA Studies

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Jia-Rou Liu ◽  
Po-Hsiu Kuo ◽  
Hung Hung
Keyword(s):  
Characteristic Curve ◽  
Real Data ◽  
Tuning Parameter ◽  
Practical Implementation ◽  
Tuning Parameters ◽  
Genome Wide ◽  
Feature Based ◽  
The Difference ◽  
Gwa Studies ◽  
Selection Of

Large-p-small-ndatasets are commonly encountered in modern biomedical studies. To detect the difference between two groups, conventional methods would fail to apply due to the instability in estimating variances int-test and a high proportion of tied values in AUC (area under the receiver operating characteristic curve) estimates. The significance analysis of microarrays (SAM) may also not be satisfactory, since its performance is sensitive to the tuning parameter, and its selection is not straightforward. In this work, we propose a robust rerank approach to overcome the above-mentioned diffculties. In particular, we obtain a rank-based statistic for each feature based on the concept of “rank-over-variable.” Techniques of “random subset” and “rerank” are then iteratively applied to rank features, and the leading features will be selected for further studies. The proposed re-rank approach is especially applicable for large-p-small-ndatasets. Moreover, it is insensitive to the selection of tuning parameters, which is an appealing property for practical implementation. Simulation studies and real data analysis of pooling-based genome wide association (GWA) studies demonstrate the usefulness of our method.

scholarly journals VLT/SPHERE astrometric confirmation and orbital analysis of the brown dwarf companion HR 2562 B

2018 ◽  
Vol 615 ◽  
pp. A177 ◽  
Author(s):  
A.-L. Maire ◽  
L. Rodet ◽  
C. Lazzoni ◽  
A. Boccaletti ◽  
W. Brandner ◽  
...  
Keyword(s):  
Orbital Motion ◽  
Orbital Plane ◽  
Real Data ◽  
Far Infrared ◽  
Brown Dwarf ◽  
Orbital Parameters ◽  
System A ◽  
Low Mass ◽  
Debris Disk ◽  
Orbital Periods

Context. A low-mass brown dwarf has recently been imaged around HR 2562 (HD 50571), a star hosting a debris disk resolved in the far infrared. Interestingly, the companion location is compatible with an orbit coplanar with the disk and interior to the debris belt. This feature makes the system a valuable laboratory to analyze the formation of substellar companions in a circumstellar disk and potential disk-companion dynamical interactions. Aims. We aim to further characterize the orbital motion of HR 2562 B and its interactions with the host star debris disk. Methods. We performed a monitoring of the system over ~10 months in 2016 and 2017 with the VLT/SPHERE exoplanet imager. Results. We confirm that the companion is comoving with the star and detect for the first time an orbital motion at high significance, with a current orbital motion projected in the plane of the sky of 25 mas (~0.85 au) per year. No orbital curvature is seen in the measurements. An orbital fit of the SPHERE and literature astrometry of the companion without priors on the orbital plane clearly indicates that its orbit is (quasi-)coplanar with the disk. To further constrain the other orbital parameters, we used empirical laws for a companion chaotic zone validated by N-body simulations to test the orbital solutions that are compatible with the estimated disk cavity size. Non-zero eccentricities (>0.15) are allowed for orbital periods shorter than 100 yr, while only moderate eccentricities up to ~0.3 for orbital periods longer than 200 yr are compatible with the disk observations. A comparison of synthetic Herschel images to the real data does not allow us to constrain the upper eccentricity of the companion.

scholarly journals Slash Truncation Positive Normal Distribution and Its Estimation Based on the EM Algorithm

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2164
Author(s):  
Héctor J. Gómez ◽  
Diego I. Gallardo ◽  
Karol I. Santoro
Keyword(s):  
Expectation Maximization Algorithm ◽  
Likelihood Estimation ◽  
Real Data ◽  
Simulation Studies ◽  
R Software ◽  
Data Application ◽  
The Em Algorithm ◽  
Kurtosis Parameter ◽  
Computational Implementation ◽  
Moments Method

In this paper, we present an extension of the truncated positive normal (TPN) distribution to model positive data with a high kurtosis. The new model is defined as the quotient between two random variables: the TPN distribution (numerator) and the power of a standard uniform distribution (denominator). The resulting model has greater kurtosis than the TPN distribution. We studied some properties of the distribution, such as moments, asymmetry, and kurtosis. Parameter estimation is based on the moments method, and maximum likelihood estimation uses the expectation-maximization algorithm. We performed some simulation studies to assess the recovery parameters and illustrate the model with a real data application related to body weight. The computational implementation of this work was included in the tpn package of the R software.

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