Extended Object Tracking and Classification based on Linear Splines

TL;DR

A framework based on linear splines for 2-dimensional extended object tracking and classification based on a kinematic state, providing object position and orientation, along with a shape vector, characterizing object contour and surface is introduced.

Abstract

This paper introduces a framework based on linear splines for 2-dimensional extended object tracking and classification. Unlike state of the art models, linear splines allow to represent extended objects whose contour is an arbitrarily complex curve. An exact likelihood is derived for the case in which noisy measurements can be scattered from any point on the contour of the extended object, while an approximate Monte Carlo likelihood is provided for the case wherein scattering points can be anywhere, i.e. inside or on the contour, on the object surface. Exploiting such likelihood to measure how well the observed data fit a given shape, a suitable estimator is developed. The proposed estimator models the extended object in terms of a kinematic state, providing object position and orientation, along with a shape vector, characterizing object contour and surface. The kinematic state is estimated via a nonlinear Kalman filter, while the shape vector is estimated via a Bayesian classifier so that classification is implicitly solved during shape estimation. Numerical experiments are provided to assess, compared to state of the art extended object estimators, the effectiveness of the proposed one.

Figures (6)

• Figure 1: Illustration of the extended object model and architecture of the proposed estimator, referred to as Fitting Lambda:Omicron Recursive estimator for Extended Objects (FL:OREO). The object is represented by a sequence of vertices (red dots) collected in a vector $S$. The shape vector $S$ is recursively estimated from a dataset $Y$ composed by a random set of measurements scattered around the object (yellow dots). The vector $S$ is estimated in two steps: (1) a tracker estimates the position $g$ and the heading $h$; (2) a shaper generates the estimate $\hat{S}$. This estimation scheme is referred to as Track To Shape (T2S).
• Figure 2: Visualization of the single measurement likelihood (\ref{['eq:exactlik']}) $\mathcal{L}:y\in[-\mathrm{FoV},\mathrm{FoV}]^2\mapsto \mathbb{R}_{\geq 0},\,\,\mathrm{FoV}\triangleq 50\,\,[\mathrm{m}]$, for two different scattering domains (top row: contour of a stealth bomber with outer radius $\rho_{\max}\approx 27\,[\mathrm{m}]$; bottom row: contour of an airliner with outer radius $\rho_{\max}\approx 42\,[\mathrm{m}]$) and three different values for the noise covariance $R\triangleq \sigma^2I$ (left column: $\sigma\triangleq 5\,\,[\mathrm{m}]$; center column: $\sigma\triangleq 10\,\,[\mathrm{m}]$; right column: $\sigma\triangleq 50\,\,[\mathrm{m}]$). For $\sigma\triangleq 50\,[\mathrm{m}]$, both domains are unresolvable, i.e. cannot be distinguished in terms of the dataset likelihood (\ref{['eq:exactlik']}).
• Figure 3: visualization of $2\cdot10^3$ points uniformly distributed over the object surface.
• Figure 4: Sample scan of the classification test. Contour (surface) measurements are shown as large (small) dots.
• Figure 5: ground truth of the tracking test. Driving inputs are expressed in $\mathrm{g}\approx 9.81\,[\mathrm{m}/\mathrm{s}^{2}]$ and $\mathrm{Ma}\approx 343\,[\mathrm{m}/\mathrm{s}]$ units.

Theorems & Definitions (7)

• Remark 1
• Remark 2
• Remark 3
• Remark 4
• Remark 5
• Remark 6
• Remark 7