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.Comment: 9 pages, 2 figures. Interesting experiment evidence of the bias of SIR filter in estimation of the state transition nois

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

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.Comment: This is a short technical note pointing out a common unfair treatment of the transition noise in the discrete simulation modeling for recursive filter

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.Comment: 13 pages, codes available upon e-mail reques

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

Creation of Tunable Homogeneous Thermal Cloak with Constant Conductivity

Invisible cloak has long captivated the popular conjecture and attracted intensive research in various communities of wave dynamics, e.g., optics, electromagnetics, acoustics, etc. However, their inhomogeneous and extreme parameters imposed by transformation-optic method will usually require challenging realization with metamaterials, resulting in narrow bandwidth, loss, polarization-dependence, etc. On the contrary, we demonstrate that tunable thermodynamic cloak can be achieved with homogeneous and finite conductivity only employing naturally available materials. The controlled localization of thermal distribution inside the coating layer has been presented, and it shows that an incomplete cloak can function perfectly. Practical realization of such homogeneous thermal cloak has been suggested by using two naturally occurring conductive materials, which provides an unprecedentedly plausible way to flexibly realize flexible thermal cloak and manipulate thermal flow.Comment: 12 pages, 4 figure

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.Comment: short letter of 2 pages, a Finishing Touch of appling KLD measure for sample size adaption for particle filters. In Electronics Letters 201

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.Comment: 16 pages, 8 figures, 5 tables, 80 references; Codes availabl

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.Comment: 16th International Conference on Information Fusion(FUSION2013), 9-12 July 201

t-Closeness: Privacy Beyond k-Anonymity and ℓ-Diversity

The k-anonymity privacy requirement for publishing microdata requires that each equivalence class (i.e., a set of records that are indistinguishable from each other with respect to certain “identifying” attributes) contains at least k records. Recently, several authors have recognized that k-anonymity cannot prevent attribute disclosure. The notion of ℓ-diversity has been proposed to address this; ℓ-diversity requires that each equivalence class has at least ℓ well-represented values for each sensitive attribute. In this paper we show that ℓ-diversity has a number of limitations. In particular, it is neither necessary nor sufficient to prevent attribute disclosure. We propose a novel privacy notion called t-closeness, which requires that the distribution of a sensitive attribute in any equivalence class is close to the distribution of the attribute in the overall table (i.e., the distance between the two distributions should be no more than a threshold t). We choose to use the Earth Mover Distance measure for our t-closeness requirement. We discuss the rationale for t-closeness and illustrate its advantages through examples and experiments