Multi-Object Tracking Using Labeled
Multi-Bernoulli Random Finite Sets
Stephan Reuter
∗
, Ba-Tuong Vo
†
, Ba-Ngu Vo
†
, Klaus Dietmayer
∗
∗
Institute of Measurement, Control and Microtechnology
Ulm University, Ulm, Germany,
{stephan.reuter, klaus.dietmayer}@uni-ulm.de.
†
Department of Electrical and Computer Engineering
Curtin University, Bentley, Australia
{ba-tuong.vo, ba-ngu.vo}@curtin.edu.au
Abstract—In this paper, we propose the labeled multi-
Bernoulli filter which explicitly estimates target tracks and
provides a more accurate approximation of the multi-object
Bayes update than the multi-Bernoulli filter. In particular, the
labeled multi-Bernoulli filter is not prone to the biased cardinality
estimate of the multi-Bernoulli filter. The utilization of the class of
labeled random finite sets naturally incorporates the estimation of
a targets identity or label. Compared to the δ-generalized labeled
multi-Bernoulli filter, the labeled multi-Bernoulli filter is an
efficient approximation which obtains almost the same accuracy
at significantly lower computational cost. The performance of the
labeled multi-Bernoulli filter is compared to the multi-Bernoulli
filter using simulated data. Further, the real-time capability
of the filter is illustrated using real-world sensor data of our
experimental vehicle.
Keywords—Random finite set, labeled multi-Bernoulli, Bayesian
estimation, target tracking.
I. INTRODUCTION
The aim of multi-object tracking is to jointly estimate
the number of objects and their states using a sequence of
measurements. Multi-object tracking is much more challenging
than single-object tracking due to object births and deaths
[1], [2], [3]. Further, the measurement process is prone to
missed detections and false alarms which typically leads to
ambiguities in the track to measurement association. During
the last decades, Multiple Hypotheses Tracking (MHT) [1]
and Joint Probabilistic Data Association (JPDA) [2] have been
extensively used in a variety of multi-object tracking applica-
tions. Within the random finite set approach to multi-object
tracking [3], the multi-object state is represented as a random
finite set (RFS) which naturally captures the uncertainty in the
number of objects as well as in the individual object states.
Finite set statistics facilitate the derivation of the multi-object
Bayes filter [3] which recursively propagates the multi-object
posterior density in time.
The computational complexity of the multi-object Bayes
filter induced the development of several approximations.
The Probability Hypothesis Density (PHD) [4] filter and the
Cardinalized PHD (CPHD) [5] filter approximate the recursion
by propagating the first moment and the cardinality distribution
of the multi-object posterior density over time. In contrast,
the multi-Bernoulli filters proposed in [6], [7] propagate the
parameters of a multi-Bernoulli distribution over time. Imple-
mentations of the filters using Gaussian mixture (GM) and
sequential Monte Carlo (SMC) methods are presented in [6],
[8], [9], [10], [11], [12].
The multi-Bernoulli approximations of the multi-object
Bayes filter are suitable for tracking applications which require
object individual existence probabilities or particle implemen-
tations. While the particle implementations of the PHD and
CPHD filters require error-prone track extraction algorithms,
the multi-Bernoulli representation facilitates a straightforward
extraction of the objects’ states. Several extensions of the
multi-Bernoulli filter are proposed in [13], [14], [15], [16].
Applications of the multi-Bernoulli filter include visual track-
ing and cell tracking [17], [18], tracking in sensor networks
[19], [20], as well as multi-sensor tracking using video and
audio data [21]. Further, a hybrid multi-Bernoulli and Poisson
multi-object tracking filter is proposed in [22].
This paper proposes a novel multi-object tracking algo-
rithm, the labeled multi-Bernoulli (LMB) filter. While the
approximations within the derivation of the multi-Bernoulli
filter require a high detection probability and a low false alarm
rate, the LMB filter does not depend on these restrictions.
However, the LMB filter also provides the advantages of the
multi-Bernoulli filter including particle implementations and
straightforward state estimation. Additionally, the proposed
LMB filter estimates target tracks by utilizing the class of
labeled RFSs [23], [24]. Compared to the δ-generalized la-
beled multi-Bernoulli filter [24], the LMB filter represents an
efficient approximation which significantly reduces the com-
putational complexity due to a dynamic grouping procedure.
Compared to the multi-Bernoulli filter, the LMB filter achieves
superior performance at the cost of an increased computational
complexity. The proposed filter is compared to the multi-
Bernoulli filter using simulated data. Additionally, the real-
time capability is illustrated using real-world sensor data for
typical scenarios in vehicle environment perception.
This paper is organized as follows: First, the class of
labeled random finite sets is reviewed. In Section III, the
labeled multi-Bernoulli filter is proposed. Afterwards, the
implementation of the filter using grouping and gating is
explained in detail. Finally, tracking results using simulated
as well as real world sensor data are presented in Section V.
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