I.

INTRODUCTION

Target tracking is an essential requirement for

Multiple Hypothesis Tracking surveillance systems employing one or more sensors,
together with computer subsystems, to interpret
For Multiple Target Tracking the environment. Typical sensor systems, such as
radar, infrared (IR), and sonar, report measurements
from diverse sources: targets of interest, physical
background objects such as clutter, or internal error
sources such as thermal noise. The target tracking
SAMUEL S. BLACKMAN objective is to collect sensor data from a field of view
Raytheon (FOV) containing one or more potential targets of
interest and to then partition the sensor data into sets
of observations, or tracks that are produced by the
same object (or target). Note that the term target is
Multiple hypothesis tracking (MHT) is generally accepted as used in a general sense. Once tracks are formed and
the preferred method for solving the data association problem confirmed (so that background and other false targets
in modern multiple target tracking (MTT) systems. This paper are reduced), the number of targets of interest can
summarizes the motivations for MHT, the basic principles behind
be estimated and quantities, such as target velocity,
MHT and the alternative implementations in common use. It
future predicted position, and target classification
characteristics, can be computed for each track.
discusses the manner in which the multiple data association
Since most surveillance systems must track
hypotheses formed by MHT can be combined with multiple filter
multiple targets, multiple target tracking (MTT) is
models, such as used by the interacting multiple model (IMM)
the most important tracking application. Fig. 1, taken
method. An overview of the studies that show the advantages of from [1], shows the basic elements of a typical MTT
MHT over the conventional single hypothesis approach is given. system. Assume that tracks have been formed from
Important current applications and areas of future research and previous data and a new set of input observations
development for MHT are discussed. becomes available. In general observations can be
received at regular intervals of time (scans or data
frames) or they can occur irregularly in time. Here,
we will use the general term scan to refer to any
set of input measurements that were all produced
at the same time. Then, the input observations are
considered for inclusion in existing tracks and for
initiation of new tracks. First, a gate, based upon
the maximum acceptable measurement plus tracking
prediction error magnitudes, is placed around the
predicted track. Only those observations that are
within the track gate are considered for update of
the track. When closely spaced targets produce
closely spaced observations there will be conflicts
such that there may be multiple observations within
a track’s gate and an observation may be within
the gates of multiple tracks. This is handled by
the Observation-to-Track Association and Track
Maintenance functions.
Fig. 2, also taken from [1], shows a typical conflict
situation in which track gates are placed around
the predicted positions (P1, P2) of two tracks, and
three observations (O1, O2, O3) satisfy the gates
of either (or both) of the tracks. The conventional
data association method is denoted the global nearest
neighbor (GNN) approach. It finds the best (most
Manuscript received February 22, 2003; revised April 27, 2003.
likely) assignment of input observations to existing
Author’s current address: Raytheon, RE/R07/P572, PO Box 920, El tracks, which for example, would probably be O1
Segundo, CA 90245, E-mail: (ssblackman@raytheon.com). to track 1 and O2 to track 2. The term global is
used to refer to the fact that the assignment is made
0018-9251/04/$17.00 °
c 2004 IEEE considering all possible (within gates) associations

IEEE A&E SYSTEMS MAGAZINE VOL. 19, NO. 1 JANUARY 2004 PART 2: TUTORIALS–BLACKMAN 5
 Fig. 1. Basic elements of a conventional MTT system.

prediction covariances provide the uncertainty, in the

predicted state estimate, that is required for the gating
and association processes.
The GNN approach, which only considers the
single most likely hypothesis for track update and
new track initiation, only works well in the case of
widely spaced targets, accurate measurements, and
few false alarms in the track gates. For example, from
results given in [1], even if the true target return is
present, a single uniformly distributed false alarm
in a three dimensional radar measurement space
(typically range and 2 angles) reduces the probability
of correct association to about 0.85. Thus, in about
Fig. 2. Example of typical data association conflict situation. one out of 6 track update attempts a false alarm
will be chosen rather than the correct target return.
For the more usual case of multiple closely spaced
under the constraint that an observation can be
targets and where missed true target detections occur,
associated with at most one track. This distinguishes
the probability of false track update is much worse.
GNN from the archaic (but apparently still used in
Experience indicates that often a single false update
some systems) nearest neighbor (NN) approach in
will lead to track loss and two consecutive false
which a track is updated with the closest observation
updates will usually lead to track loss.
even if that observation may also be used by another
track. The fact that misassociation represents an
Only those tracks that are included in the best additional error source for a Kalman filter tracker
assignment are kept. Unassigned observations, in this was recognized in the very early stages of tracker
case O3, initiate new tracks. Track confirmation and development [3—5]. One approach that was proposed
deletion are typically determined by rules, such as 3 to improve GNN performance was to increase
detections in 4 frames of data for confirmation and the Kalman filter covariance matrix to reflect this
N consecutive misses (typically N = 4 to 7) for track additional source of uncertainty [3, 4]. A similar
deletion. approach, based upon work by R. Fitzgerald, also
Inherent in the standard GNN assignment is the reduces the gain for uncertain association conditions,
assumption that an observation was produced by a Sec. 6.12.1 of [1].
single target. Tracks that do not share any common A second approach, which has become the Joint
observations will be defined to be compatible. Thus, Probabilistic Data Association (JPDA) method,
only compatible tracks can appear in the same “hedges” for uncertain association conditions by
assignment solution. Relaxation of this constraint allowing a track to be updated by a weighted (by
to allow for the provision of unresolved targets that probability) sum of all observations in its gate [2, 5].
produce a single measurement will be discussed later. This also means that an observation may contribute
Once observations are assigned to tracks, these to the update of more than one track. Thus, for the
tracks are updated during the filtering process. example of Fig. 2, observations O1, O2, and O3
Conventional systems typically use a single Kalman would all contribute to the update of track 1 and
filter. However, as discussed below, modern systems observations O2 and O3 would contribute to the
should use the interacting multiple model (IMM) update of both tracks.
approach in which several Kalman filters, tuned to Both the augmented GNN approach and the JPDA
different types of target maneuver, are run in parallel method increase the Kalman filter track covariance
[1, 2]. Finally, all tracks are predicted to the time matrix to account for the association uncertainty.
of the next set of measurements. The Kalman filter However, as illustrated in [6], increasing the Kalman

6 IEEE A&E SYSTEMS MAGAZINE VOL. 19, NO. 1 JANUARY 2004 PART 2: TUTORIALS
filter covariance matrix to account for uncertain
association can exacerbate the problem whereby
an increased covariance matrix leads to even more
false observations in the track gate, etc. Also, the
JPDA method suffers from a coalescence problem
whereby tracks on closely spaced targets will tend to
come together [7]. For example, from Fig. 2, since
observations O2 and O3 will contribute to the updates
of tracks 1 and 2, these tracks will be drawn together.
The problems that result from relatively simple
Fig. 3. MHT logic overview.
upgrades to the GNN method and the recent dramatic
increases in computational capabilities have led to a
near universal acceptance of the multiple hypothesis complete algorithmic approach. Reid’s algorithm
tracking (MHT) approach as the preferred data defines a systematic way in which multiple data
association method for modern systems. MHT (observation-to-track) association hypotheses can be
is a deferred decision logic in which alternative formed and evaluated for the problem of multiple
data association hypotheses are formed whenever targets in a false alarm (and/or clutter) background.
observation-to-track conflict situations, such as shown Again using the example of Fig. 2, Reid’s algorithm
in Fig. 2, occur. Then, rather than choosing the best is illustrated by defining H1 to be the hypothesis
hypothesis or, in effect, combining the hypotheses as containing T1 and T2 before the receipt of the three
in the JPDA method, the hypotheses are propagated observations. Next, define a newly formed track
into the future in anticipation that subsequent data will T3 (T1, O1) = track 3 formed from the
resolve the uncertainty. association of T1 with O1
Sections II and III will discuss the basic principles
and commonly used implementations of MHT. Section with similar definitions for T4 (T2, O2) and T5
IV discusses how modern filtering techniques (in (T2, O3). Also define NT1, NT2, and NT3 to be the
particular IMM) can be combined with MHT. Section new tracks initiated from O1, O2, and O3. Then, 3 of
V outlines some important current applications of the feasible 10 hypotheses that can be formed are
MHT and Section VI gives areas of development and H1 : T1, T2, NT1, NT2, NT3
extension.
H2 : T3, T4, NT3
(1)
H3 : T3, T5, NT2
II. MHT BASICS
..
The manner in which MHT forms multiple .
hypotheses and manages these hypotheses is Tracks are defined to be compatible if they have
illustrated by again referring to the example given in no observations in common. As illustrated by the
Fig. 2 and by referring to the overall structure shown example above, assuming T1 and T2 share no
in Fig. 3. As an example, assume that tracks T1 and observations, MHT hypotheses are composed of
T2 with predicted positions P1 and P2, represent sets of compatible tracks. Again note, as discussed
a hypothesis (H1 ) prior to the receipt of the three in more detail later, the formulation can ideally
observations (O1, O2, O3) on the current scan. Then, be expanded in order to address the problem of
there are 10 feasible hypotheses that can be generated closely-spaced unresolved targets that may produce
from the initial single hypothesis. For example, the a single measurement that should be assigned to the
two most likely hypotheses would both update T1 multiple tracks that may have been formed on these
with O1 but would update T2 with either O2 or O3. unresolved targets. Using Reid’s algorithm approach,
Another, unlikely but feasible, hypothesis would be hypotheses are carried over from the previous scan.
that all observations represent new sources (false Then, on the receipt of new data, each hypothesis is
alarms or other previously undetected targets) so expanded into a set of new hypotheses by considering
that neither T1 nor T2 would be updated and all all observation-to-track assignments for the tracks
observations would start new tracks. within the hypothesis. Again, as new hypotheses are
formed, the compatibility constraint for tracks within a
Reid’s Algorithm hypothesis is maintained.

Although Singer, Sea, and Housewright Track and Hypothesis Evaluation

[8] introduced the basic idea of propagating
multiple hypotheses for a single target in a false The evaluation of alternative track formation
alarm background, Reid [9] first developed a hypotheses requires a probabilistic expression that

IEEE A&E SYSTEMS MAGAZINE VOL. 19, NO. 1 JANUARY 2004 PART 2: TUTORIALS–BLACKMAN 7
includes all aspects of the data association problem. Thus, the LLR (track score) is all that needs to be
These aspects include the prior probability of target computed (and maintained) in order to assess the
presence, the false alarm density, the detection validity of a track. Finally, as discussed further
sequences and the dynamic (kinematic) consistency below, the track score can be used directly for
of the observations contained in the tracks. Reid track confirmation as an application of the classical
[9] presents such a probabilistic expression. A sequential probability ratio test (SPRT).
mathematically equivalent, but computationally The track score, L(k), at scan k, can be placed in a
preferable, approach is the log-likelihood ratio, LLR convenient recursive form [1, 11]
(or track score) first proposed in the pioneering paper
by Sittler [10], later detailed in [11] and summarized L(k) = L(k ¡ 1) + ¢L(k)
below. ½ (5)
ln(1 ¡ P̂D ); no update on scan k
A likelihood ratio (LR) for the formation of ¢L(k) =
¢Lu (k); track update on scan k
a given combination of data (including a priori
probability data) into a track can be defined using The loss in track score when a detection opportunity
a recursive relationship that follows directly from is missed is a function of the expected probability
Bayes’ rule of detection (P̂D ). As discussed in more detail in
p(D j H1 )P0 (H1 ) ¢ PT [1, 11], the gain, ¢Lu , in track score upon update
LR = = (2) is a function of the residual error (the difference
p(D j H0 )P0 (H0 ) PF
between the measurement and the prediction) and
Hypotheses H1 and H0 are the true target and false its covariance matrix, the expected density of false
alarm hypotheses with probabilities PT and PF , returns, as well as P̂D . In addition, if signal intensity
respectively, and D is the data, so that (such as signal-to-noise ratio, SNR) is measured, it
p(D j Hi ) = probability density function may also be used in the track score.
evaluated with the received Given the individual track scores, the hypothesis
data under the assumption that score is the sum of scores of all tracks contained
Hi is correct in that hypothesis. Then, given hypothesis scores,
the hypothesis probabilities can be computed
P0 (Hi ) = a priori probability of Hi [1, 11]. Finally, a track may be contained in multiple
(such as expected density of hypotheses so that its probability is the sum of
true targets in a given area for H1 ) probabilities of all hypotheses which contain it. For
the example of (1), the probability of T3 would be the
Note that the inclusion of a priori probabilities in
sum of probabilities for hypotheses H2, H3 and all
(2) means that LR might formally be defined to be
other hypotheses that contain it.
a probability ratio. However, following the original
To summarize, relatively simple computations
formulation of [10], we will refer to it as a likelihood
can be performed to determine hypothesis and track
ratio.
probabilities. A theoretical objection that may be
A true target is most generally defined to be an
raised is that in order to compute these probabilities,
object that will persist in the tracking volume for
such as through the track score as defined above, it is
at least several scans. Thus, this definition includes
typical to assume very approximate Gaussian models
objects, such as persistent clutter, that may not be
for target dynamics and measurement error statistics,
of interest to the tracking system but that should be
uniform distributions for false alarms (clutter and
tracked in order to minimize their interference with
noise) and new targets and a nominal P̂D . However, all
tracks on targets of interest. False alarms (or false
developers of practical MHT systems make essentially
targets) refer to erroneous detection events (such as
the same assumptions and, as discussed further
those caused by random noise or clutter) that do not
below, results show that MHT with these assumptions
persist over several scans.
performs substantially better than any other developed
It is convenient to use the log likelihood ratio
(LLR) or track score [10, 11] such that approach.

LLR = ln[PT j PF ] (3) Practical Issues

Then, LLR can be directly converted to the probability As illustrated by the simple example given above,
of a true target through there is clearly a potential combination explosion in
PT the number of hypotheses (and tracks within those
PT =PF = = eLLR hypotheses) that an MHT system can generate. Thus,
1 ¡ PT (4)
a number of techniques have been developed to keep
LLR LLR
PT = e =[1 + e ] this potential growth in check. These techniques,

8 IEEE A&E SYSTEMS MAGAZINE VOL. 19, NO. 1 JANUARY 2004 PART 2: TUTORIALS
 Fig. 4. Family (node) structure with N-scan pruning.

outlined next, include clustering, hypothesis and track Based upon current data (including scan k),
pruning (deletion), and track merging. irrevocable decisions are made in the past (for the
The operation of clustering is performed to reduce example this is scan k ¡ 2). Specifically, one approach
the number of hypotheses that must be generated and finds the tracks from families F1 and F2 that are in
evaluated. Clusters are collections of tracks that are the best current (scan k) hypothesis and goes back
linked by common observations. A cluster can include N scans (in this case N = 2) to establish a new root
tracks that do not share observations directly. Thus, if node. For example, if track 2 of F1 is in the best
track 1 shares an observation with track 2 and track 2 hypothesis, the new root node is track 2 at scan k ¡ 2.
shares an observation with track 3, all three tracks are Subject to other tests, beyond the scope of this paper,
in the same cluster. if F2 does not have a track in the best hypothesis, the
Clustering, in effect, decomposes a large problem entire family would be deleted.
into a set of smaller problems. Once clustering has Note that the entire branch of F1 leading to tracks
been performed, the processing within each cluster 1, 4, and 8 has been deleted. However, track 9 has
can be done independently from other clusters. Thus, been maintained even though track 2 was in the best
processing efficiencies can be achieved using a hypothesis. This method is denoted N-scan pruning
parallel processing structure whereby the processing (or can be defined as an N-scan sliding window) and
for each cluster can be assigned to a separate we have, for convenience of presentation, chosen
processor. Then, within each cluster, hypotheses are N = 2 for the example. In practice, our experience
evaluated and low probability hypotheses and tracks is that N should generally be chosen to be at least
are deleted. 5. Also, rather than scans in the past, the decision is
The key principle of the MHT method is that probably best made using N observations in the past
difficult data association decisions are deferred but the basic principle is the same. Firm decisions are
until more data are received. Thus, an important made in the past based upon later data.
implementation feature used by all MHT developers Fig. 5, adapted from [12], shows the relationship
is the family (or node) structure illustrated in Fig. 4. between the families (track hypotheses for a given
This structure provides a convenient mechanism target) and the global (multiple track) hypotheses
for implementing a deferred decision logic and for that are formed as collections of compatible tracks.
presenting a coherent output from the MHT tracker to A global hypothesis is formed by choosing at most a
the user. single track from each family.
Fig. 4 shows how MHT track branches are formed The family representation of Fig. 4 also provides
and illustrates how a convenient structure for track a convenient way to present MHT data to a user
pruning can be defined. Using this structure, a family who typically wants one track per target, not a set
is defined as a set of tracks with a common root node. of alternative tracks with probabilities. The tracks
Alternatively, what we define to be a family (of tracks in the output trackfile are linked to the families
all emanating from a single ancestor, or root node) and, at any given time, the most likely track in the
can also be considered to be a target tree. Each branch family is presented to the user. This can lead to some
represents a different data association hypothesis for apparent inconsistencies in the output as MHT branch
the target and nodes are defined to be points where probabilities change with the receipt of more data.
one track forms two or more branches. Because each For example, it may be that track 1 of F1 was the
branch track within the family (target tree) has at least most likely track at scan k ¡ 1 but track 2 is the most
one common node (the root node), these tracks are likely track at scan k. Thus, a possible alternative
all incompatible with each other and can represent at is to provide an average state estimate, computed
most one target. using the branch track probabilities, along with a

IEEE A&E SYSTEMS MAGAZINE VOL. 19, NO. 1 JANUARY 2004 PART 2: TUTORIALS–BLACKMAN 9
 Fig. 5. Formation of hypotheses from tracks in families.

covariance that reflects the spread in the branch track of which will later be discarded based upon low
state estimates. This approach is particularly useful probability) as the tracks contained within the
for an agile beam radar system, discussed below, for hypothesis are updated in different ways. This
which data association uncertainty should be used in potential explosion of new hypotheses that may
the resource allocation logic. result from an indiscriminate expansion of the
old hypotheses has been a barrier to the practical
implementation of Reid’s algorithm. Thus, a method
III. ALTERNATIVE MHT IMPLEMENTATIONS
to only generate “good” hypotheses is required and
Although the same basic principles and has been provided by the work of Cox et al. [14].
mathematical models apply to all, there are several As discussed in [14], an efficient implementation
different approaches to MHT implementation. of Reid’s algorithm can be achieved using Murty’s
The first (hypothesis-oriented) approach follows method for finding the m-best solutions to the
the original work of Reid, outlined above. The assignment problem. Using this approach, given
computational feasibility of this approach has been mp (k ¡ 1) hypotheses from the previous scan, the
greatly enhanced by the use of Murty’s algorithm number of hypotheses formed on the current scan
[13] to more efficiently generate hypotheses [14]. can be limited to m(k) when m is an input parameter
An alternative, track-oriented approach [1, 12] does that could be set a priori or, presumably, could be
not maintain hypotheses from scan to scan. As tracks chosen adaptively. The important principle is that the
are updated on each scan they are reformed into generation of many unconsequential, low probability
hypotheses. An innovative implementation of the hypotheses, that resulted from earlier implementations
track-oriented approach is the multidimensional (or of Reid’s algorithm, is avoided.
multiple frame) assignment method [15, 16]. Finally,
a Bayesian MHT approach has been proposed by Track-Oriented MHT
van Keuk and Koch and associates [6, 17, 18]. The
methods are briefly summarized below. The track-oriented approach recomputes the
hypotheses using the newly updated tracks after each
m-Best Implementation of Reid’s Algorithm scan of data are received. Rather than maintaining,
and expanding, hypotheses from scan to scan, the
As illustrated above, Reid’s algorithm forms track-oriented approach discards the hypotheses
a large number of hypotheses that are collections formed on scan k ¡ 1. The tracks that survive pruning
of compatible tracks. These hypotheses are carried are predicted to the next scan k where new tracks are
from one scan to the next where newly received formed, using the new observations, and reformed
observations are used to update the tracks in different into hypotheses. Except for the necessity to delete
ways. Thus, each hypothesis carried from the previous some tracks based upon low probability or N-scan
scan may give rise to many new hypotheses (most pruning described above, no information is lost

10 IEEE A&E SYSTEMS MAGAZINE VOL. 19, NO. 1 JANUARY 2004 PART 2: TUTORIALS
because the track scores, that are maintained, contain into hypotheses can be formulated as an optimization
all the relevant statistical data. The basic, currently problem with the goal of maximizing the hypothesis
unresolved, issue is whether it is more efficient to score (sum of all track scores in hypothesis) with
expand the old hypotheses using Murty’s method or the constraints that no tracks in the hypothesis share
to reform the hypotheses using the updated tracks and observations.
their compatibilities with other tracks. The basic principle of the Langrangian relaxation
A strong argument for the track-oriented approach approach is to replace constraints (in this case that
to MHT can be made by noting that the combinatories an observation can be used by at most a single track)
of hypothesis formation are such that there are by Lagrange multipliers in the objective function
typically many more hypotheses formed than tracks. (in this case the sum of track scores) used in the
Typically, for difficult scenarios, there may be several maximization. The “art” of this method involves
thousand comparable hypotheses formed from several the proper choice of Lagrange multipliers so that
hundred tracks in a cluster. Then, the process of the solution formed from maximizing the objective
maintaining a thousand (or more) hypotheses and function approaches the best feasible solution, in
expanding these hypotheses using Murty’s method which each observation is used by at most a single
to find the best thousand new hypotheses may be track.
prohibitive. On the other hand, our experience with This optimization is very complex and requires
track-oriented MHT has shown that several hundred sophisticated mathematics but we will (at least attempt
tracks can easily be maintained and expanded into to) summarize the basic principles. Two solutions to
new hypotheses for difficult scenarios. Typical the hypothesis formation problem are obtained with
computational results for a difficult scenario with 100 cost defined to be the negative of score. The first
closely spaced targets and a high radar update rate solution, defined to be the relaxed or dual solution,
indicate the feasibility of real-time operation for a may not satisfy the constraints (that an observation
track-oriented MHT [19]. This study was performed should be used once and only once). However,
using a single 866 Mhz Pentium III computer. Newer Lagrange multipliers are introduced into this solution
computers and/or parallel processing with several and are chosen so that constraint violations are,
computers would allow real-time tracking for even effectively, given high costs. Thus, the number of
more difficult scenarios. constraint violations should be reduced over time with
Our implementation uses a relatively simple set of successive iterations of the method.
heuristic search methods, based upon a breadth-first A second solution, denoted the recovered or
method described in [1] and the A* search method primal solution, is obtained from the dual solution by
described in [20]. The multiframe assignment (MFA) enforcing the constraints. For example, one method
method, outlined next, represents a potentially more for obtaining this solution starts with the assignment
accurate and efficient implementation of track-oriented of the first two scans of data that was obtained by the
MHT. dual solution. Then, it adds observations from the later
scans by solving an assignment matrix, that enforces
Multi Dimensional (Multiframe) Assignment the constraints, on each later scan. Thus, a feasible,
but likely suboptimal, solution is obtained.
Deb [15] and Poore [16] and their associates The costs of the dual solution, q(u), where u
independently recognized that the MTT data represents the Lagrangian multipliers, and the primal
association problem can be placed in a form where solution, v(z̄), represent bounds on the cost, v(z), of
a multi dimensional assignment approach that uses the the true, but unknown, solution
Lagrangian relaxation method is directly applicable.
q(u) · v(z) · v(z̄)
Like track-oriented MHT, this approach forms and
maintains tracks from scan (frame) to scan and where z and z̄ are the set of binary variables that
reforms tracks into hypotheses after each new scan define which tracks are included in the true and the
of data are received. It also uses a sliding window primal solutions, respectively [1, 15, 16].
approach which is similar to the N-scan pruning Successive iterations are performed by using
method used in conventional MHT and illustrated updated Lagrange multipliers in an attempt to increase
in Fig. 4. The unique feature of this method is the q(u) and decrease v(z̄) and a stopping rule is defined
manner in which a Lagrangian relaxation method is so that the feasible primary solution is accepted when
used to find the most likely hypothesis or a set of the q(u) and v(z̄) are “close enough,” or when time runs
m-best hypotheses [21]. out and a solution is required.
The input is a set of tracks with their scores and The multiscan assignment method outlined
their compatibilities with other tracks. Again, two above can be used to implement the N-scan pruning
tracks are defined to be incompatible, and thus cannot method used for track-oriented MHT, as illustrated
be in the same hypothesis, if they share one or more in Fig. 4. Performing N-scan pruning requires a
observations. The process of arranging these tracks solution to the N + 2 scan assignment problem.

IEEE A&E SYSTEMS MAGAZINE VOL. 19, NO. 1 JANUARY 2004 PART 2: TUTORIALS–BLACKMAN 11
 Fig. 6. Implementation of N = 3 scan pruning using 5D assignment. (a) First five scans of observations. (b) Tracks formed from first
two scans and four scans of observations. (Adapted from notes by A. B. Poore.)

Fig. 6 illustrates the process for N = 3 (five-scan with a single maneuver model, multiple models,
assignment). Referring to Fig. 6(a), initially five scans representing different potential target maneuver
of data are collected with the observations on scan 1 states, are run in parallel and continuously evaluated
effectively being the initial root nodes. The output of using filter residual histories. Bayes’ rule and the
the 5D assignment problem will be a set of tracks in residuals are used to determine the probabilities of
the most likely (solution) hypothesis. These tracks are validity of the models. The output is then typically
traced back N = 3 scans to their root nodes (tracks) on a probability-weighted composite of the individual
scan 2. Then, all tracks that were in existence on scan filters.
2 and that do not have one of these root node tracks There are two basic approaches that can be used
as their ancestor on scan 2 are deleted. to combine MHT with multiple model filtering. The
As illustrated in Fig. 6(b), the root nodes are taken first, outlined in [12], is to add a set of maneuver
to be the tracks on scan 2 that were the ancestors hypotheses to the MHT data association hypotheses.
of the tracks in the most likely hypothesis. The next Thus, an additional set of hypotheses which differ
scan of data is used to update the tracks that survived in target dynamics history will be formed. Use of
pruning on the previous scan. The process continues interacting multiple model (IMM) filtering appears
with, in general, new observations received on scan to be difficult for this approach.
k + 1, a sliding window of observations received on IMM filtering has become generally accepted
scans k, k ¡ 1, : : : , k ¡ N + 1 and the root node tracks as the best method for using multiple filter models
on scan k ¡ N. This process is illustrated in Fig. 6(b) [2]. The unique feature of the IMM approach is
for k = 5 and N = 3. See [22, 23] for more details on
the manner in which the state estimates and the
efficient implementation.
covariance matrices are combined via the process
defined to be mixing. The basic principle is that
Bayesian MHT
the currently more accurate (as determined by the
The technique denoted Bayesian MHT [6, 17, 18] computed model probabilities) models transfer their
is designed to more closely represent the probability state estimates to the less accurate models. For
density functions (PDF) of alternative data association example, in the case of a maneuvering target, the
hypotheses. The PDF is represented as a Gaussian state estimates from the maneuver models, that should
mixture that represents the joint distribution of the follow the target motion fairly well, are transferred to
targets under track. Thus, the method effectively the nonmaneuver filter that otherwise would develop a
requires knowledge, or assumption, of the number of large lag.
targets in track. Reference [18] addresses the problem In order to conveniently do IMM filtering within
of estimating this number. an MHT framework, we believe that it is most
convenient to define tracks according to their data
association history. A similar approach is presented
IV. MHT AND MULTIPLE MODEL FILTERING
in [24]. Then, the track score (or probability) is
It is widely accepted that accurate tracking of computed using all component IMM filter models.
dynamic targets requires the use of multiple Kalman Thus, hypothesis formation and pruning are done on
filter models. The basic idea of all multiple model the composite tracks, containing contributions from
approaches, as applied to tracking maneuvering all IMM filter models, rather than on the IMM model
targets, is that maneuvers are typically abrupt tracks independently. Using this approach the mixing
deviations from basically straight-line target motion. process is conveniently done for each track, rather
Because this process is very difficult to represent than requiring mixing across tracks.

12 IEEE A&E SYSTEMS MAGAZINE VOL. 19, NO. 1 JANUARY 2004 PART 2: TUTORIALS
 Fig. 7. Score function approach as an application of SPRT.

Given that hypothesis formation and pruning compare their results, and to share ideas. Another
are performed using all the IMM filter models for problem is that very little comparative study of
each track, the next issue is how to perform gating MHT performance, versus that of alternative tracking
and how to update the combined track score. One methods, has been reported in the tracking literature.
approach is to form a composite track state estimate However, the brief summary of reported comparative
and covariance matrix before gating and to perform studies, such as [25], given in [1] and the growing
gating using the composite quantities. acceptance of MHT among those in the tracking
The composite state estimate and covariance community clearly indicate that MHT is the currently
matrix are formed from weighted (by the filter preferred method for difficult tracking problems. We
model probabilities) sums of the state estimates next summarize some important applications with
and covariance matrices of the individual filters. which the author is familiar.
Alternatively, using a second approach, each
filter model can be used separately for gating. In Track Confirmation and Maintenance for Dim Targets in
this case, there will be separate state estimates Clutter
(and corresponding covariance matrices) that
will be individually compared with the candidate As illustrated by Fig. 7, and discussed further
observations. The observation-to-track gating test in [1, 18, 26], a confirmation test that uses the
will then be satisfied if the gating test is satisfied track score (LLR) is essentially an application
for any filter model. Similarly, the track score can of the classical sequential probability ratio test
be computed from the composite track residual (and (SPRT). Then, as detailed in [1], the choice of
residual statistics) or a combined track score can be confirmation and deletion thresholds (T1 and
computed using the individual residual data from the T2, respectively, shown in Fig. 7) can be related
different IMM filter models. to tracking requirements (such as the number
It has been our experience that the second of false tracks allowed per hour) through the
approach is preferred. During times of nonmaneuver, parameters ® = false track confirmation, and ¯ =
the composite state and covariance matrix (and true track deletion probability. This approach also
resulting gate) may become so heavily weighted provides a convenient analysis tool for preliminary
towards the nonmaneuver models that an abrupt target system design [1, 26].
maneuver can lead to track loss. Finally, the extension The application of SPRT theory to MHT
to the track score required when multiple filter models track confirmation assumes that false alarms are
are used is straight forward [1]. uncorrelated in time. In practice, such as for tracking
targets against a background of ground clutter, clutter
V. MHT APPLICATIONS returns tend to be correlated in time. In this case, it
is best to maintain tracks on the stationary sources
The actual practical implementation of MHT of ground clutter that produce the returns. Thus,
has been impeded by the, currently incorrect [19], special logic using motion or signal characteristics
perception that its complexity precludes real-time is developed to inhibit the output of these tracks to the
application. Also, the security restrictions that user [27].
surround technologies, such as tracking, being A number of studies, discussed further in [1],
developed for current military applications and have indicated that an MHT tracker will provide
company proprietary policies have greatly restricted performance that is comparable to the conventional,
the ability of MHT tracker developers to publish and single hypothesis (GNN) method at 10 to 100 times

IEEE A&E SYSTEMS MAGAZINE VOL. 19, NO. 1 JANUARY 2004 PART 2: TUTORIALS–BLACKMAN 13
the false alarm density of the GNN method. This
allows a system using MHT to operate at a lower
detection threshold, in order to detect and track dim
targets [28]. However, the comparative study given in
[29] showed that a well-designed track-before-detect
(TBD) approach that, in effect, combines the detection
and tracking functions, will confirm tracks on
nonmaneuvering dim targets at much lower SNR
(about 4—5 dB lower for the cases considered in [29]).

Agile Beam Radar Fig. 8. Triangulation with angle tracks leads to false intersections
that can be resolved with MHT and later data.
Efficient allocation of radar resources is one
of the major issues in the design of an agile beam
(or electronically scanned) radar tracking system. First, objects (RVs and various types of decoys) are
Moreover, following [1, 30—32] use of an MHT deployed from the PBV with basically the same
tracker can greatly enhance the effectiveness of velocity as the PBV. Thus, a “warm start” track
an allocation scheme. Specifically, the combined initiation (or spawning) procedure is used in order to
quickly obtain the required tracking accuracy.
use of MHT data association and IMM filtering
Referring to Fig. 2, observations O2 and O3
and prediction methods provides the most accurate
would be candidates for “warm start” new track
estimates of tracking error that are required for
initiation (in addition to the hypotheses that they
efficient sensor allocation. The IMM filter model
update T2 or possibly T1 also). Thus, the new tracks
probabilities and covariance matrices provide
would be given a position estimate based upon the
estimates of the error due to target maneuver and the
measurement and a velocity estimate based upon
potential error due to data association is computed
the velocity of the parent tracks (either T1 or T2
from alternative MHT hypotheses. Further discussions
or an average of the two) for which they satisfied a
of the radar benchmark study that demonstrated the
gating relationship. For the SBIR system, in which
effectiveness of an IMM/MHT solution to the agile
only angle measurements are available, the range
beam radar resource allocation problem are given in
from the sensor platform, as well as the platform
[30] and the Introduction of [33].
position, will be used along with the measured
angles to form the initial position estimate. The
Missile Defense Systems initial “warm start” track filter covariance matrices
are defined using the measurement error variances
Post boost tracking scenarios for missile defense and the parent track range (for SBIR) and velocity
systems are characterized by a large number error covariance matrices. Also, terms to account
(potentially hundreds or even thousands) of closely for the potential differences in velocity of the newly
spaced objects. These objects are deployed over detected (resolved) object and the parent track object
time by the post boost vehicle (PBV or bus) and are added. Finally, once spawning occurs, MHT
very accurate tracks are required for impact point processing will take over to determine, using later
prediction. In addition, track purity (defined to be data, which observations (in our example O2 or O3)
the proportion of observations in a track that were should start new tracks and which should update
produced by the same source) must be high so existing tracks (or possibly be discarded).
that discrimination can be successfully performed. An additional source of data association
Discrimination methods employ Bayesian or uncertainty occurs for the angle-only measurements of
Dempster-Shafer reasoning to determine the target an SBIR system. Tracks on targets that are separated
type using the characteristics (such as intensity from existing tracks (so that spawning cannot be
profile) of the measurements in the track as examined accurately used) must be initiated by the triangulation
over time. For example, it is very important to process, illustrated in Fig. 8 and discussed further in
discriminate between the lethal reentry vehicle (RV) [1]. Using this procedure, the intersections (or near
and decoys that are employed to “trick” the tracking intersections) of mono (angle-only) tracks from two
and discrimination algorithms. platforms (S1, S2) are used to initiate stereo (3D
Both radar and space-based infrared (SBIR) position and velocity) tracks. The problem, shown in
tracking systems are being developed. Given the Fig. 8, is that, for closely spaced targets, there may
stringent tracking requirements, it is generally be false intersections that form ghost tracks, as well
accepted that MHT should be used for both types of as the correct intersection where the targets actually
sensors and there are several special features, outlined exist. Thus, an MHT approach is required so that all
next, that must be addressed for these applications. feasible tracks are maintained until either the evolving

14 IEEE A&E SYSTEMS MAGAZINE VOL. 19, NO. 1 JANUARY 2004 PART 2: TUTORIALS
 TABLE I
Comparative Conventional and MHT Tracking Errors Referenced to an Idealized System

Early Time Intermediate Late

System Position Velocity Position Velocity Position Velocity

Conventional 3.3 2.9 2.8 5.0 3.0 3.3

MHT 1.7 2.1 1.4 2.0 1.5 1.2
Idealized 1.0 1.0 1.0 1.0 1.0 1.0

geometry or data from additional sensors (S3) allows detect stopped (or slow moving) targets that cannot be
the system to sort out the ghosts from the true target distinguished from the ground clutter.
tracks. The difficulty of tracking ground targets has led
In order to illustrate the advantages of MHT over to the consensus that multiple filter models, for on
conventional single hypothesis (GNN) tracking, Table and off-road tracking, and MHT data association are
I gives recent comparative results for a difficult SBIR required. For example, see [34—38] and Chapt. 6 of
application. Table I gives comparative 97 percent [33].
Monte Carlo simulation derived position and velocity An example of the interesting challenges of the
errors for three tracking systems. The 97 percent level ground target tracking problem are targets that use
values were defined such that only 3 percent of the move-stop-move motion in order to evade detection
tracking error (averaged over multiple targets and by GMTI radar. This necessitates the development of
multiple Monte Carlo runs) exceeded these values a special stopping target filter model and the inclusion
at the sampling times. A highly optimistic reference of the hypothesis that a missing detection results from
for Table I was an idealized system for which perfect a stopped target, rather than a random miss or an
observation-to-track association was performed. incorrect track prediction [36—38]. In particular, the
The observations were assigned target truth tags, lack of detection can actually be used to infer target
which were used for the association, but the effects position by forming the hypothesis that a missed
of unresolved targets and missed detections were detection results from the fact that the target has
included. stopped [37].
The MHT and conventional (GNN) tracking
system RMS position and velocity tracking errors are
normalized with respect to the idealized system errors. VI. MHT RESEARCH AND DEVELOPMENT AREAS
Results are presented at three times. The initial (early)
time is when targets are beginning to become resolved As stated by Daum several years ago [39], a major,
so that by the last (late) time nearly all targets were mostly ignored, tracking problem is the presence
resolved. Of course, the tracking errors decreased of unresolved, or partially resolved, measurements
for all systems (even though some ratios increased) produced by closely spaced targets. In closely-spaced
with time but the comparative advantage of the MHT target scenarios, such as aircraft flying in formation,
system is clearly apparent over the entire scenario. an observation will often be produced by two, or
Finally, note that the MHT errors closely approach more, targets. Thus, for these conditions, the standard
those of the idealized system towards the end of MHT assumption that an observation was produced
the scenario while the conventional tracker errors by a single target, and thus can only be assigned to
remain at about 3 times the values for the idealized a single track, must be modified. This issue becomes
system. particularly important when tracking with sensors of
different resolution capability, such as radar and IR.
Ground Target Tracking References [1, 40—42] and [33, ch. 4] present methods
that are applicable to the extension of MHT to include
Probably the most important, and challenging, hypotheses that allow a potentially merged observation
current tracking application uses data from airborne to update more than one track.
(or spaced-based) sensors to track ground targets. Another important area of research is the
Difficult target dynamics include move-stop-move combination of MHT with group tracking. An
and on and off-road target motion as well as closely example where combined group and MHT tracking
spaced targets moving in groups (convoys). Sensor will be required is the missile defense problem where
difficulties result from potentially long revisit times large numbers of objects may be deployed from
(greater than 10 sec.), obscured (by mountains or the PBV (bus) in a short time period [43, 44]. As
building) sensor line-of-sight, unresolved targets, out discussed in [44], there may be time intervals, as
of sequence measurements in multiple sensor systems, the targets are first deployed, when the proliferation
and the fact that a radar operating in the standard of closely spaced targets may cause the number of
ground moving target detection (GMTI) mode will not MHT hypotheses formed to become prohibitive. The

IEEE A&E SYSTEMS MAGAZINE VOL. 19, NO. 1 JANUARY 2004 PART 2: TUTORIALS–BLACKMAN 15
proposed solution [44] uses group tracking until the receives a measurement. The AMR contains the
targets separate sufficiently to allow feasible MHT association decision, made by the platform that
tracking of individual targets. The determination produced the measurement, which is broadcast to all
of when (and how) to make the transition from a other platforms in the network who update their tracks
group track to MHT tracking of individual targets is accordingly, without any further association logic
the major issue. Other applications where combined being performed.
MHT and group tracking will be required for optimal Maintaining SIAP for an MHT system is much
performance include tracking formations of aircraft more difficult because multiple current association
[18] and convoys of ground moving targets [45]. hypotheses are maintained so that, as shown in
As shown in [28], the track-before-detect (TBD) Fig. 4, final irrevocable decisions are delayed. In the
approach may significantly outperform MHT for the meanwhile, as the result of imperfect communication
task of track confirmation of dim nonmaneuvering (missing and out-of-sequence data), the family
targets. However, the TBD approach, which essentially structures on the different platforms may diverge.
integrates signal intensity along a set of potential, Also, track initiation and confirmation decisions may
nearly straight line paths, is not applicable to highly differ as different platforms use different sequences of
maneuvering targets and has questionable applicability measurements to initiate duplicate tracks on the same
in dense target environments. Thus, the goal is to target. This is an important area of current research
combine use of the powerful TBD methods, such as with approaches discussed in [50—52] and [33, ch. 6].
the dynamic programming algorithm, DPA [1, 46] and
Bayesian tracking [28, 47], for detecting and tracking REFERENCES
widely-spaced dim targets with IMM/MHT techniques
that are most applicable to maneuvering targets in [1] Blackman, S., and R. Popoli (1999)
Design and Analysis of Modern Tracking Systems.
dense environments. Reference [46] discusses a Norwood, MA: Artech House, 1999.
combined DPA/MHT tracking system. [2] Bar-Shalom, Y., and X-R. Li (1995)
Standard track and hypothesis evaluation methods Multitarget-Multisensor Tracking: Principles and
currently only use metric (measured position, range Techniques.
rate, etc.) and possibly intensity (measured SNR, etc.) Storrs, CT: YBS Publishing, 1995.
[3] Nahi, N. (1969)
data. The increased capability of sensors to measure
Optimal recursive estimation with uncertain observation.
other feature data, such as high range resolution IEEE Transactions on Information Theory, IT-15, 4 (July
(HRR) and jet engine modulation (JEM) radar 1969), 457—462.
measurements, and the development of multiple sensor [4] Singer, R. A., and Stein, J. J. (1971)
tracking systems dictate that features, attributes and An optimal tracking filter for processing sensor data of
target classification/ID should be used to improve data imprecisely determined origin in surveillance systems.
In Proceedings of 1971 IEEE Conference on Decision and
association. This is particularly true for the problem Control, Miami Beach, FL, Dec. 1971, 171—175.
of maintaining tracks on high priority targets for the [5] Bar-Shalom, Y., and Tse, E. (1975)
ground target tracking problem [48]. Tracking in a cluttered environment with probabilistic
A basic issue is how to weight attribute/ID data data association.
versus metric measurements. For example, a radar Automatica, 11 (Sept. 1975), 451—460.
[6] Fleskes, W., and van Keuk, G. (1987)
return might contain JEM information regarding
On single target tracking in dense clutter
engine type that is consistent with other target environment-quantitative results.
type information contained in the track, but the In Proceedings of 1987 International Radar Conference,
measured range rate may differ significantly from 130—134.
the track’s predicted range rate. How should the [7] Fitzgerald, R. J. (1985)
observation-to-track score reflect these two different, Track biases and coalescence with probabilistic data
association.
and possibly inconsistent, data sources? As outlined in IEEE Transactions on Aerospace and Electronic Systems,
[1, 49] a mapping to likelihood (or LLR) is required. 21, 6 (Nov. 1985), 822—825.
However, to the author’s knowledge this approach has [8] Singer, R. A., Sea, R. G., and Housewright, K. B. (1974)
not yet been implemented for a practical system. Derivation and evaluation of improved tracking filters for
As discussed further in [33, ch. 1], the multisensor use in dense multitarget environments.
IEEE Transactions on Information Theory, 20, 4 (July
distributed tracking problem is of great practical
1974), 423—432.
importance. One basic issue/goal for a distributed [9] Reid, D. B. (1976)
platform system is to attempt to ensure that all An algorithm for tracking multiple targets.
platforms have a Single Integrated Air Picture (SIAP) IEEE Transactions on Automatic Control, 21, 1 (Feb.
so that, for example, track 1 on platform 1 represents 1976), 101—104.
the same target as track 1 on platform 2, etc. Methods [10] Sittler, R. W. (1964)
An optimal data association problem in surveillance
for maintaining SIAP for conventional (single theory.
hypothesis) tracking use an associated measurement IEEE Transactions on Military Electronics, 8 Apr. 1964,
report (AMR) that is sent from the platform that 125—139.

16 IEEE A&E SYSTEMS MAGAZINE VOL. 19, NO. 1 JANUARY 2004 PART 2: TUTORIALS
[11] Blackman, S. (1986) [25] de Feo, M., et al. (1997)
Multiple Target Tracking with Radar Applications. IMMJPDA versus MHT and Kalman filter with nn
Norwood, MA: Artech House, 1986. correlation: Performance comparison.
[12] Kurien, T. (1990) IEE Proceedings, Radar, Sonar, Navigation, 144, 2 (Apr.
Issues in the design of practical multitarget tracking 1997), 49—56.
algorithms. [26] Blackman, S., Dempster, R., and Broida, T. (1993)
In Y. Bar-Shalom (Ed.), Multitarget-Multisensor Tracking: Multiple hypothesis track confirmation for infrared
Advanced Applications, Norwood, MA: Artech House, surveillance systems.
1990, ch. 3. IEEE Transactions on Aerospace and Electronic Systems,
[13] Murty, K. G. (1968) 29, 3 (July 1993), 810—823.
An algorithm for ranking all the assignments in order of
[27] Attili, J. B., et al. (1996)
increasing cost.
False track discrimination in a 3-d signal/track processor.
Operations Research, 16 (1968), 682—687.
In O. E. Drummond (Ed.), Signal and Data Processing
[14] Cox, I. J., and Hingorani, S. L. (1996)
of Small Targets 1996, SPIE Proceedings, 2759 (1996),
An efficient implementation of Reid’s multiple
205—217.
hypotheses tracking algorithm and its evaluation for the
purposes of visual tracking. [28] Chang, K. C., Mori, S., and Chong, C. Y. (1994)
IEEE Transactions on Pattern Analysis and Machine Evaluating a multiple-hypothesis multitarget tracking
Intelligence, 18, 2 (Feb. 1996), 138—150. algorithm.
[15] Deb. S., et al. (1997) IEEE Transactions on Aerospace and Electronic Systems,
A generalized s-d assignment algorithm for 20, 2 (Apr. 1994), 578—590.
multisensor-multitarget state estimation. [29] Barlow, C. A., and Blackman, S. S. (1998)
IEEE Transactions on Aerospace and Electronic Systems, A new Bayesian track-before-detect design and
33, 2 (Apr. 1997), 523—538. comparative performance study.
[16] Poore, A. B., and Robertson, A. J. (1997) In O. E. Drummond (Ed.), Signal and Data Processing
A new Lagrangian relaxation based algorithm for a class of Small Targets 1998, SPIE Proceedings, 3377 (1998),
of multidimensional assignment problems. 181—191.
Computational Optimization and Applications, 8, 2 (Sept. [30] Blackman, S. S., et al. (1999)
1997), 129—150. IMM/MHT solution to radar benchmark tracking
[17] Koch, W. (1996) problem.
Retrodiction for Bayesian multiple hypothesis/multiple IEEE Transactions on Aerospace and Electronic Systems,
target tracking in densely cluttered environment. 35, 2 (Apr. 1999), 730—738.
In O. E. Drummond (Ed.), Signal and Data Processing of
Small Targets, SPIE Proceedings, 2759 (1996), 429—440. [31] van Keuk, G. (1995)
Multiplehypothesis tracking with electronically scanned
[18] van Keuk, G. (2002)
radar.
MHT extraction and track maintenance of a target
IEEE Transactions on Aerospace and Electronic Systems,
formation.
31, 3 (July 1995), 916—927.
IEEE Transactions on Aerospace and Electronic Systems,
38, 1 (Jan. 2002), 288—295. [32] Koch, W. (1999)
[19] Blackman, S., Dempster, R., and Reed, R. (2001) On adaptive parameter control for phased-array tracking.
Demonstration of multiple hypothesis tracking (MHT) In O. E. Drummond (Ed.), Signal and Data Processing
practical real-time implementation feasibility. of Small Targets 1999, SPIE Proceedings, 3809 (1999),
In O. E. Drummond (Ed.), Signal and Data Processing 444—455.
of Small Targets 2001, SPIE Proceedings, 4473 (2001), [33] Bar-Shalom, Y., and Blair, W. D. (Eds.)(2000)
470—475. Multitarget-Multisensor Tracking: Applications and
[20] Pearl, J. (1984) Advances, Vol. 3, Norwood, MA: Artech House, 2000.
Heuristics: Intelligent Search Strategies for Computer
[34] Kurien, T., et al. (2000)
Problem Solving.
Discoverer-II GMTI tracker.
Addison Wesley, 1984.
Prepared for Discoverer-II Joint Program Office,
[21] Popp, R. L., Pattipati, K. R., and Bar-Shalom, Y. (2001) Alphatech Technical Report TR-984, Nov. 15, 2000.
An m-best s-d assignment for multiple target tracking.
IEEE Transactions on Aerospace and Electronic Systems, [35] Kirubarajan, T., et al. (2000)
37, 1 (Jan. 2001), 22—39. Ground target tracking with variable structure IMM
[22] Poore, A. B. (1997) estimator.
Hot starts for track maintenance in multisensor- IEEE Transactions on Aerospace and Electronic Systems,
multitarget tracking. 36, 1 (Jan. 2000), 26—46.
Signal and Data Processing of Small Targets, SPIE [36] Shea, P. J., et al. (2000)
Proceedings, 3163 (July 1997), 341—450. Improved state estimation through use of roads in ground
[23] Poore, A. B., and Drummond, O. E. (1997) tracking.
Track initiation and maintenance using multidimensional In O. E. Drummond (Ed.), Signal and Data Processing
assignment problems. of Small Targets 2000, SPIE Proceedings, 4048 (2000),
In P. M. Pardalos, D. Hearn, and W. Hager (Eds.), 321—332.
Network Optimization, New York: Springer-Verlag, 1997, [37] Koch, W. (2001)
407—422. GMTI-tracking and information fusion for ground
[24] Torelli, R., Graziano, A., and Farina, A. (1999) surveillance.
IM3HT algorithm: A joint formulation of IMM and MHT In O. E. Drummond (Ed.), Signal and Data Processing
for multi-target tracking. of Small Targets 2001, SPIE Proceedings, 4473 (2001),
European Journal of Control, 5 (1999), 46—53. 381—392.

IEEE A&E SYSTEMS MAGAZINE VOL. 19, NO. 1 JANUARY 2004 PART 2: TUTORIALS–BLACKMAN 17
[38] Lin, L., Kirubarajan, T., and Bar-Shalom, Y. (2002) [46] Shaw, S., and Arnold, J. F. (1995)
New assignment-based data association for tracking Design and implementation of a fully automated OTH
move-stop-move targets. radar tracking system.
Proceedings of the Fifth International Conference on IEEE Proceedings of the 1995 International Radar
Information Fusion, Annapolis, MD, July 2002. Conference, May 1995, 294—298.
[39] Daum, F. E. (1994) [47] Stone, L. D., Barlow, L. A., and Corwin, T. L. (1999)
The importance of resolution in multiple target tracking. Bayesian Multiple Target Tracking.
In O. E. Drummond (Ed.), Signal and Data Processing Norwood, MA: Artech House, 1999.
of Small Targets 1994, SPIE Proceedings, 2235 (1994), [48] Nguyen, D. H., et al. (2002)
329—338. Feature-aided tracking of moving ground vehicles.
[40] Koch W., and van Keuk, G. (1997) In E. G. Zelnio (Ed.), Algorithms for Synthetic Aperture
Multiple hypotheses track maintenance with possibly Radar Imagery IX, SPIE Proceedings, 4727 (2002),
unresolved measurements. 234—245.
IEEE Transactions on Aerospace and Electronic Systems, [49] Drummond, O. E. (2001)
33, 3 (July 1997), 883—891. Feature, attribute, and classification aided target tracking.
[41] Blair, W. D., and Brandt-Pearce, M. (1999) In O. E. Drummond (Ed.), Signal and Data Processing
NNJPDA for tracking closely-spaced Rayleigh targets of Small Targets 2001, SPIE Proceedings, 4473 (2001),
with possibly merged measurements. 542—558.
In O. E. Drummond (Ed.), Signal and Data Processing [50] Lu, S., Poore, A. B., and Suchomel, B. J. (2001)
of Small Targets 1999, SPIE Proceedings, 3809 (1999), Network MFA tracking architectures.
396—408. In O. E. Drummond (Ed.), Signal and Data Processing
[42] Sinha, A., Kirubarajan, T., and Bar-Shalom, Y. (2002) of Small Targets 2001, SPIE Proceedings, 4473 (2001),
Maximum likelihood angle extractor for two closely 447—457.
spaced targets. [51] Lu, S. (2001)
IEEE Transactioins on Aerospace and Electronic Systems, Network Multiple Frame Assignment Architectures.
38, 1 (Jan. 2002), 182—203. Ph.D. thesis, Colorado State University, 2001.
[43] Kovacich, M., et al. (1991) [52] Dunham, D., Blackman, S., and Dempster, R. (2004)
An application of MHT to group to object tracking. Multiple hypothesis tracking (MHT) for a distributed
In O. E. Drummond (Ed.), Signal and Data Processing platform system.
of Small Targets 1991, SPIE Proceedings, 1481 (1991), To appear Signal and Data Processing of Small Targets
357—370. 2004, SPIE Proceedings, Apr. 2004.
[44] Gadaleta, S., et al. (2002)
Multiple frame cluster tracking.
In O. E. Drummond (Ed.), Signal and Data Processing
of Small Targets 2002, SPIE Proceedings, 4728 (2002),
275—289.
[45] Koch, W. (2002)
On expectation maximization applied to GMTI convoy
tracking.
In O. E. Drummond (Ed.), Signal and Data Processing
of Small Targets 2002, SPIE Proceedings, 4728 (2002),
450—460.

Samuel S. Blackman received the B.A. degree in mathematics from the

University of Hawaii, Honolulu, in 1960 and the M.S. degree in physics from the
University of New Mexico, Albuquerque in 1963.
He has been employed by Hughes Aircraft Company (now Raytheon) since
1963 and has worked principally in the development of tracking systems. His
current research interests include the applications of tracking and estimation
techniques to ground targets.
Mr. Blackman is the author of Multiple Target Tracking with Radar
Applications, Artech House (1986), Design and Analysis of Modern Tracking
Systems, Artech House (1999), and numerous papers related to estimation and
tracking. He is a member of Phi Beta Kappa.

18 IEEE A&E SYSTEMS MAGAZINE VOL. 19, NO. 1 JANUARY 2004 PART 2: TUTORIALS