arXiv subjects

Tiancheng Li

Publications and source records attributed to Tiancheng Li.

33 records · Page 2Linked to original sources

arXiv2022

Multi-sensor Suboptimal Fusion Student's $t$ Filter

A multi-sensor fusion Student's $t$ filter is proposed for time-series recursive estimation in the presence of heavy-tailed process and measurement noises. Driven from an information-theoretic optimization, the approach extends the single sensor Student's $t$ Kalman filter based on the suboptimal arithmetic average (AA) fusion approach. To ensure computationally efficient, closed-form $t$ density recursion, reasonable approximation has been used in both local-sensor filtering and inter-sensor fusion calculation. The overall framework accommodates any Gaussian-oriented fusion approach such as the covariance intersection (CI). Simulation demonstrates the effectiveness of the proposed multi-sensor AA fusion-based $t$ filter in dealing with outliers as compared with the classic Gaussian estimator, and the advantage of the AA fusion in comparison with the CI approach and the augmented measurement fusion.

eess.SY↗

arXiv2019

Second Order Statistics Analysis and Comparison between Arithmetic and Geometric Average Fusion

Two fundamental approaches to information averaging are based on linear and logarithmic combination, yielding the arithmetic average (AA) and geometric average (GA) of the fusing initials, respectively. In the context of target tracking, the two most common formats of data to be fused are random variables and probability density functions, namely $v$-fusion and $f$-fusion, respectively. In this work, we analyze and compare the second order statistics (including variance and mean square error) of AA and GA in terms of both $v$-fusion and $f$-fusion. The case of weighted Gaussian mixtures representing multitarget densities in the presence of false alarms and misdetection (whose weight sums are not necessarily unit) is also considered, the result of which appears significantly different from that for a single target. In addition to exact derivation, exemplifying analysis and illustrations are provided.

eess.SY↗

arXiv2018

A Distributed Particle-PHD Filter with Arithmetic-Average PHD Fusion

We propose a particle-based distributed PHD filter for tracking an unknown, time-varying number of targets. To reduce communication, the local PHD filters at neighboring sensors communicate Gaussian mixture (GM) parameters. In contrast to most existing distributed PHD filters, our filter employs an `arithmetic average' fusion. For particles--GM conversion, we use a method that avoids particle clustering and enables a significance-based pruning of the GM components. For GM--particles conversion, we develop an importance sampling based method that enables a parallelization of filtering and dissemination/fusion operations. The proposed distributed particle-PHD filter is able to integrate GM-based local PHD filters. Simulations demonstrate the excellent performance and small communication and computation requirements of our filter.

eess.SY↗

arXiv2017

Partial Consensus and Conservative Fusion of Gaussian Mixtures for Distributed PHD Fusion

We propose a novel consensus notion, called "partial consensus", for distributed GM-PHD (Gaussian mixture probability hypothesis density) fusion based on a peer-to-peer (P2P) sensor network, in which only highly-weighted posterior Gaussian components (GCs) are disseminated in the P2P communication for fusion while the insignificant GCs are not involved. The partial consensus does not only enjoy high efficiency in both network communication and local fusion computation, but also significantly reduces the affect of potential false data (clutter) to the filter, leading to increased signal-to-noise ratio at local sensors. Two "conservative" mixture reduction schemes are advocated for fusing the shared GCs in a fully distributed manner. One is given by pairwise averaging GCs between sensors based on Hungarian assignment and the other is merging close GCs based a new GM merging scheme. The proposed approaches have a close connection to the conservative fusion approaches known as covariance union and arithmetic mean density. In parallel, average consensus is sought on the cardinality distribution (namely the GM weight sum) among sensors. Simulations for tracking either a single target or multiple targets that simultaneously appear are presented based on a sensor network where each sensor operates a GM-PHD filter, in order to compare our approaches with the benchmark generalized covariance intersection approach. The results demonstrate that the partial, arithmetic average, consensus outperforms the complete, geometric average, consensus.

eess.SY↗

arXiv2017

Joint Smoothing, Tracking, and Forecasting Based on Continuous-Time Target Trajectory Fitting

We present a continuous time state estimation framework that unifies traditionally individual tasks of smoothing, tracking, and forecasting (STF), for a class of targets subject to smooth motion processes, e.g., the target moves with nearly constant acceleration or affected by insignificant noises. Fundamentally different from the conventional Markov transition formulation, the state process is modeled by a continuous trajectory function of time (FoT) and the STF problem is formulated as an online data fitting problem with the goal of finding the trajectory FoT that best fits the observations in a sliding time-window. Then, the state of the target, whether the past (namely, smoothing), the current (filtering) or the near-future (forecasting), can be inferred from the FoT. Our framework releases stringent statistical modeling of the target motion in real time, and is applicable to a broad range of real world targets of significance such as passenger aircraft and ships which move on scheduled, (segmented) smooth paths but little statistical knowledge is given about their real time movement and even about the sensors. In addition, the proposed STF framework inherits the advantages of data fitting for accommodating arbitrary sensor revisit time, target maneuvering and missed detection. The proposed method is compared with state of the art estimators in scenarios of either maneuvering or non-maneuvering target.

stat.AP↗

arXiv2015

Do we always need a filter?

Since the groundbreaking work of the Kalman filter in the 1960s, considerable effort has been devoted to various discrete time filters for dynamic state estimation, especially including dozens of different types of suboptimal implementations of the Bayes filters. This has been accompanied by the rapid development of simulation/approximation theories and technologies. While admitting the success of filters in many cases, this study investigates the failure cases when they are in fact ineffective for state estimation. Several classic models have shown that the straightforward observation-only (O2) inference that does not need system modeling can perform better (in terms of both accuracy and computing speed) for estimation than filters. Special attention has been paid to quantitatively analyze when and why a filter will not outperform the O2 inference from the information fusion perspective. Thanks to the rapid development of advanced sensors, the O2 inference is not only engineering friendly and computationally fast but can also be very accurate and reliable by fusing the information received from multiple sensors. The statistical attributes of the multi-sensor O2 inference are analyzed and demonstrated through simulations. In the situation with limited sensors, the O2 approach can work jointly with existing clutter filtering and data association algorithms for multi-target tracking in clutter environments. Given an adequate number of sensors, the O2 approach can employ the multi-sensor data fusion to deal with clutter and can handle the very general multi-target tracking scenario with no background information.

stat.AP↗

arXiv2014

Return on citation: a consistent metric to evaluate papers, journals and researchers

Evaluating and comparing the academic performance of a journal, a researcher or a single paper has long remained a critical, necessary but also controversial issue. Most of existing metrics invalidate comparison across different fields of science or even between different types of papers in the same field. This paper proposes a new metric, called return on citation (ROC), which is simply a citation ratio but applies to evaluating the paper, the journal and the researcher in a consistent way, allowing comparison across different fields of science and between different types of papers and discouraging unnecessary and coercive/self-citation.

cs.DL↗

arXiv2014

The Optimal Arbitrary-Proportional Finite-Set-Partitioning

This paper considers the arbitrary-proportional finite-set-partitioning problem which involves partitioning a finite set into multiple subsets with respect to arbitrary nonnegative proportions. This is the core art of many fundamental problems such as determining quotas for different individuals of different weights or sampling from a discrete-valued weighted sample set to get a new identically distributed but non-weighted sample set (e.g. the resampling needed in the particle filter). The challenge raises as the size of each subset must be an integer while its unbiased expectation is often not. To solve this problem, a metric (cost function) is defined on their discrepancies and correspondingly a solution is proposed to determine the sizes of each subsets, gaining the minimal bias. Theoretical proof and simulation demonstrations are provided to demonstrate the optimality of the scheme in the sense of the proposed metric.

math.NA↗

arXiv2014

Numerical Fitting-based Likelihood Calculation to Speed up the Particle Filter

The likelihood calculation of a vast number of particles is the computational bottleneck for the particle filter in applications where the observation information is rich. For fast computing the likelihood of particles, a numerical fitting approach is proposed to construct the Likelihood Probability Density Function (Li-PDF) by using a comparably small number of so-called fulcrums. The likelihood of particles is thereby analytically inferred, explicitly or implicitly, based on the Li-PDF instead of directly computed by utilizing the observation, which can significantly reduce the computation and enables real time filtering. The proposed approach guarantees the estimation quality when an appropriate fitting function and properly distributed fulcrums are used. The details for construction of the fitting function and fulcrums are addressed respectively in detail. In particular, to deal with multivariate fitting, the nonparametric kernel density estimator is presented which is flexible and convenient for implicit Li-PDF implementation. Simulation comparison with a variety of existing approaches on a benchmark 1-dimensional model and multi-dimensional robot localization and visual tracking demonstrate the validity of our approach.

cs.IT↗

arXiv2014

Fighting Sample Degeneracy and Impoverishment in Particle Filters: A Review of Intelligent Approaches

During the last two decades there has been a growing interest in Particle Filtering (PF). However, PF suffers from two long-standing problems that are referred to as sample degeneracy and impoverishment. We are investigating methods that are particularly efficient at Particle Distribution Optimization (PDO) to fight sample degeneracy and impoverishment, with an emphasis on intelligence choices. These methods benefit from such methods as Markov Chain Monte Carlo methods, Mean-shift algorithms, artificial intelligence algorithms (e.g., Particle Swarm Optimization, Genetic Algorithm and Ant Colony Optimization), machine learning approaches (e.g., clustering, splitting and merging) and their hybrids, forming a coherent standpoint to enhance the particle filter. The working mechanism, interrelationship, pros and cons of these approaches are provided. In addition, Approaches that are effective for dealing with high-dimensionality are reviewed. While improving the filter performance in terms of accuracy, robustness and convergence, it is noted that advanced techniques employed in PF often causes additional computational requirement that will in turn sacrifice improvement obtained in real life filtering. This fact, hidden in pure simulations, deserves the attention of the users and designers of new filters.

cs.AI↗

arXiv2013

Bias of the SIR filter in estimation of the state transition noise

This Note investigates the bias of the sampling importance resampling (SIR) filter in estimation of the state transition noise in the state space model. The SIR filter may suffer from sample impoverishment that is caused by the resampling and therefore will benefit from a sampling proposal that has a heavier tail, e.g. the state transition noise simulated for particle preparation is bigger than the true noise involved with the state dynamics. This is because a comparably big transition noise used for particle propagation can spread overlapped particles to counteract impoverishment, giving better approximation of the posterior. As such, the SIR filter tends to yield a biased (bigger-than-the-truth) estimate of the transition noise if it is unknown and needs to be estimated, at least, in the forward-only filtering estimation. The bias is elaborated via the direct roughening approach by means of both qualitative logical deduction and quantitative numerical simulation.

eess.SY↗

arXiv2013

A Gap between Simulation and Practice for Recursive Filters: On the State Transition Noise

In order to evaluate and compare different recursive filters, simulation is a common tool and numerous simulation models are widely used as 'benchmark'. In the simulation, the continuous time dynamic system is converted into a discrete-time recursive system. As a result of this, the state indeed evolves by Markov transitions in the simulation rather than in continuous time. One significant issue involved with modeling of the system from practice to simulation is that the simulation parameter, particularly e.g. the state Markov transition noise, needs to match the iteration period of the filter. Otherwise, the simulation performance may be far from the truth. Unfortunately, quite commonly different-speed filters are evaluated and compared under the same simulation model with the same state transition noise for simplicity regardless of their real sampling periods. Here the note primarily aims at clarifying this problem and point out that it is very necessary to use a proper simulation noise that matches the filter's speed for evaluation and comparison under the same simulation model.

cs.DM↗

arXiv2013

Roughening Methods to Prevent Sample Impoverishment in the Particle PHD Filter

Mahler's PHD (Probability Hypothesis Density) filter and its particle implementation (as called the particle PHD filter) have gained popularity to solve general MTT (Multi-target Tracking) problems. However, the resampling procedure used in the particle PHD filter can cause sample impoverishment. To rejuvenate the diversity of particles, two easy-to-implement roughening approaches are presented to enhance the particle PHD filter. One termed as "separate-roughening" is inspired by Gordon's roughening procedure that is applied on the resampled particles. Another termed as "direct-roughening" is implemented by increasing the simulation noise of the state propagation of particles. Four proposals are presented to customize the roughening approach. Simulations are presented showing that the roughening approach can benefit the particle PHD filter, especially when the sample size is small.

cs.OH↗

arXiv2013

Adapting sample size in particle filters through KLD-resampling

This letter provides an adaptive resampling method. It determines the number of particles to resample so that the Kullback-Leibler distance (KLD) between distribution of particles before resampling and after resampling does not exceed a pre-specified error bound. The basis of the method is the same as Fox's KLD-sampling but implemented differently. The KLD-sampling assumes that samples are coming from the true posterior distribution and ignores any mismatch between the true and the proposal distribution. In contrast, we incorporate the KLD measure into the resampling in which the distribution of interest is just the posterior distribution. That is to say, for sample size adjustment, it is more theoretically rigorous and practically flexible to measure the fit of the distribution represented by weighted particles based on KLD during resampling than in sampling. Simulations of target tracking demonstrate the efficiency of our method.

stat.AP↗

arXiv2009

Slicing: A New Approach to Privacy Preserving Data Publishing

Several anonymization techniques, such as generalization and bucketization, have been designed for privacy preserving microdata publishing. Recent work has shown that generalization loses considerable amount of information, especially for high-dimensional data. Bucketization, on the other hand, does not prevent membership disclosure and does not apply for data that do not have a clear separation between quasi-identifying attributes and sensitive attributes. In this paper, we present a novel technique called slicing, which partitions the data both horizontally and vertically. We show that slicing preserves better data utility than generalization and can be used for membership disclosure protection. Another important advantage of slicing is that it can handle high-dimensional data. We show how slicing can be used for attribute disclosure protection and develop an efficient algorithm for computing the sliced data that obey the l-diversity requirement. Our workload experiments confirm that slicing preserves better utility than generalization and is more effective than bucketization in workloads involving the sensitive attribute. Our experiments also demonstrate that slicing can be used to prevent membership disclosure.

cs.DB↗