SearcharxivSearch

arXiv · 1603.04096

Multi-Target Tracking Using A Randomized Hypothesis Generation Technique

Abstract

In this paper, we present a randomized version of the finite set statistics (FISST) Bayesian recursions for multi-object tracking problems. We propose a hypothesis level derivation of the FISST equations that shows that the multi-object tracking problem may be considered as a finite state space Bayesian filtering problem, albeit with a growing state space. We further show that the FISST and Multi-Hypothesis Tracking (MHT) methods for multi-target tracking are essentially the same. We propose a randomized scheme, termed randomized FISST (R-FISST), where we sample the highly likely hypotheses using Markov Chain Monte Carlo (MCMC) methods which allows us to keep the problem computationally tractable. We apply the R-FISST technique to a fifty-object birth and death Space Situational Awareness (SSA) tracking and detection problem. We also compare the R-FISST technique to the Hypothesis Oriented Multiple Hypothesis Tracking (HOMHT) method using an SSA example.

Explore related subjects

Keep this discovery

BibTeXRIS

W. Faber, S. Chakravorty, Islam I. Hussein. 2016-03-13. Multi-Target Tracking Using A Randomized Hypothesis Generation Technique. https://arxiv.org/abs/1603.04096

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

A Scale Invariance Property of PCA

The PCA algorithm is sensitive to changes in measurement scale. Measuring one variable of a system in inches rather than centimeters, say, alters both its principal axes and principal eigenvalues. Although this scale dependence is generally complicated, we show here that it nevertheless obeys a strict invariance property: under a continuous scale adjustment, the initial state's $k$-th largest principal component (ordered by eigenvalue) continuously evolves into the final state's $k$-th largest principal component, for each $k$. In this sense, we can say that the modes of PCA are "order-stable" with respect to changes in measurement scale. A special case occurs when scaling along directions that are orthogonal to some modes. Here, apparent eigenvalue crossings can occur. However, we show that we can interpret these apparent crossings as cases where the modes instantaneously swap their orientation, in this way maintaining the required order stability.

math.ST

Small noise asymptotics for linear parabolic SPDEs in two space dimensions with unknown damping factors

We study parametric estimation for second order linear parabolic stochastic partial differential equations in two space dimensions with a small volatility parameter driven by a $Q$-Wiener process with an unknown damping parameter using high frequency spatio-temporal data. We first provide an estimator for the damping parameter of the $Q$-Wiener process utilizing realized quadratic variations based on spatial and temporal increments. We next propose minimum contrast estimators of the diffusive and advective parameters in the SPDE using a contrast function with the proposed estimator of the damping parameter. We then construct a quasi-maximum likelihood estimator of the reaction parameter in the SPDE using the approximate coordinate process derived from the estimators of the diffusive and advective parameters. We also provide simulation results of the proposed estimators.

math.ST

Spike Estimation from Heteroscedastic Noise via Random Splitting

In this paper, we consider a spiked Wigner type matrix with a heteroscedastic and unknown variance profile. It is well known that in the supercritical regime of the BBP transition, strong spikes can create outliers in the spectrum. Unfortunately, in the heteroscedastic case, in general it is not possible to estimate the spike strength from these observed outlier consistently, as the latter is a solution to a Dyson equation with unknown parameters from the variance profile. In this paper, inspired by the work on sparse matrix completion \citep{BordenaveCosteNadakuditi2023}, we introduce an asymmetrized model by randomly splitting the spiked matrix into two parts, which transforms the noisy Wigner type matrix into a non Hermitian random matrix, while preserving the Hermitian spikes at the cost of a dilution. We establish a BBP type transition for the asymmetrized model, from which we can estimate the strength of the spikes precisely, even without knowing the variance profile of the noise part. We then further apply our approach to study the correlation between two correlated spiked models, where the spike/signal parts of the two models are correlated, and the noise parts are independent but may both be heteroscedastic. By applying our asymmetrization approach to the two models separately and also jointly, we are able to obtain a precise estimate of the correlation between the signal parts of the two models.

math.ST