For tracking a target in a heavily cluttered environment, the Probabilistic Data Association Filter (PDAF) is very
efficient and can significantly reduce track losses. However, as shown in this paper, the PDAF will experience
difficulties at the initial stage of the filtering when the track is not accuracy enough, and the filter tends to diverge
under even modest clutter density. To address this problem we propose a technique of splitting the track of the
target into sub-tracks that run in parallel when the original track has low accuracy. Each sub-track occupies a
portion of the uncertainty region of the original track. As a result, the sub-tracks maintained using the PDAF
will be more selective over the incoming measurements (including detection and false alarms), and have less
loss in tracking accuracy and improved robustness. This approach is similar to the Gaussian Sum filter in the
literature. The major contribution of this paper is to propose a systematic method to effectively divide a less
accurate track in a high dimensional state space into a set of sub-tracks to effectively improve the robustness of
the PDAF. The splitting of the track will incur a significant amount of additional computation cost. To reduce
the number of sub-tracks a likelihood ratio test is also proposed for the problem considered to drop unlikely
sub-tracks. Simulation results are presented to demonstrate the performance of the proposed algorithm.
KEYWORDS: Information fusion, Detection and tracking algorithms, Motion models, Distributed computing, Contrast transfer function, Computer simulations, Data fusion, Algorithm development, Monte Carlo methods, Sensors
The problem of Track-to-Track Fusion (T2TF) is very important for distributed tracking systems. It allows the
use of the hierarchical fusion structure, where local tracks are sent to the fusion center (FC) as summaries of
local information about the states of the targets, and fused to get the global track estimates. Compared to the
centralized measurement-to-track fusion (CTF), the T2TF approach has low communication cost and is more
suitable for practical implementation. Although having been widely investigated in the literature, most T2TF
algorithms dealt with the fusion of homogenous tracks that have the same state of the target. However, in
general, local trackers may use different motion models for the same target, and have different state spaces. This
raises the problem of Heterogeneous Track-to-Track Fusion (HT2TF). In this paper, we propose the algorithm for
HT2TF based on the generalized Information Matrix Fusion (GIMF) to handle the fusion of heterogenous tracks
in the presence of possible communication delays. Compared to the fusion based on the LMMSE criterion, the
proposed algorithm does not require the crosscovariance between the tracks for the fusion, which greatly simplify
its implementation. Simulation results show that the proposed HT2TF algorithm has good consistency and
fusion accuracy.
KEYWORDS: Detection and tracking algorithms, Distributed computing, Telecommunications, Information fusion, Evolutionary algorithms, Matrices, Kinematics, Data fusion, Computer simulations, Monte Carlo methods
Most existing track-to-track fusion (T2TF) algorithms for distributed tracking systems are given assuming that
the local trackers are synchronized. However, in the real world, synchronization can hardly be achieved and
local trackers usually work in an asynchronous fashion, where local measurements are obtained and local tracks
are updated at different times with different rates. Communication delays between local trackers and the fusion
center (FC) also cause delays in the arrival of the local tracks at the FC. This paper presents the optimal
asynchronous T2TF algorithm for distributed tracking systems under the linear Gaussian (LG) assumption,
which is also the linear minimum mean square error (LMMSE) fuser without the Gaussian assumption. The
information configuration of asynchronous T2TF with partial information feedback (AT2TFpf) is used. This is
the most practical configuration for AT2TF with time delays, since communication delays make full information
feedback very complicated. To illustrate the algorithm, a basic scenario of the fusion of two asynchronous local
tracks is used, where one is available at the FC with no delay and the other is transmitted from a local tracker
with a time delay. The algorithm can be extended to scenarios with more than two local trackers. The optimal
asynchronous T2TF algorithm is compared with the approximate algorithms proposed by Novoselsky (denoted
as AT2TFpfApprA-C) and is shown to have performance benefit in consistency as well as in fusion accuracy.
The drawback of the optimal fusion algorithm is that it has high communication and computational cost.
Two new approximate algorithms, AT2TFpfApprD and AT2TFpfApprE, are also proposed which significantly
reduce the cost of the optimal algorithm with little loss in fusion performance.
KEYWORDS: Detection and tracking algorithms, Information fusion, Computer simulations, Distributed computing, Polonium, Monte Carlo methods, Signal processing, Data processing, Error analysis, Filtering (signal processing)
Compared to the optimal track-to-track fusion (T2TF) algorithm under linear Gaussian assumption and the
information matrix fusion, the major advantage of the covariance intersection (CI) method for the problem of
T2TF is that it neither needs the crosscovariances between the local tracks, nor does it use local information
increments which are required to be independent. This allows the CI method to be used in scenarios where the
optimal T2TF and the information matrix fusion algorithms are difficult or impractical to implement. However,
a significant drawback of the original CI algorithm is that it is too conservative and will yield unnecessary loss
in its calculated fusion accuracy. Even worse, as shown in this paper, this loss increases with the number of
local tracks for fusion. This greatly degrades the usefulness of the CI algorithm. In this paper, a new "sampling
CI" algorithm is proposed, which is simple to implement and does not have the above problematic feature of the
original CI. Simulation results from various scenarios demonstrate the effectiveness of the proposed algorithm.
Track-to-track fusion (T2TF) is very important in distributed tracking systems. When tracks of a target at
different sensors are fused for increased accuracy, an important issue is to account for the crosscorrelations
among the tracks. In this paper, an exact solution for the general problem of T2TF is proposed. It can be used
with various information structures, e.g., memoryless T2TF or sequential T2TF with information feedback at
arbitrary times. Simulation results for a 1-D tracking scenario evaluate the benefit of the various configurations for
T2TF. It is also observed that T2TF, although done optimally, can be suboptimal w.r.t. centralized measurement
fusion. This is because the locally optimal filter gains are, in general, globally suboptimal. Furthermore, it is
shown that feedback can lead to degradation of the accuracy of the (optimally) fused tracks. Based on the exact
T2TF algorithms, an approximate implementation which requires less communications between the fusion center
and the local trackers is also proposed. This allows the algorithms to be implemented in distributed tracking
systems with low communication capacity. Examples of tracking in two dimensions with two radars, show that
the proposed T2TF algorithms are consistent and can provide significant improvement in accuracy over unfused
tracks. For the sensors-target geometry considered, the T2TF algorithm can even meet the performance bound
of the centralized measurement fusion at the fusion times.
In this paper a real-time cooperative path decision algorithm for UAV surveillance is proposed. The surveillance
mission includes multiple objectives: i) Navigate the UAVs safely in a hostile environment; ii) Search for new
targets in the surveillance region; iii) Classify the detected targets; iv) Maintain tracks on the detected targets.
To handle these competing objectives, a layered decision framework is proposed, in which different objectives are
relevant at different decision layers according to their priorities. Compared to previous work, in which multiple
objectives are integrated into a single global objective function, this layered decision framework allows detailed
specification of the desired performance for each objective and guarantees that an objective with high priority will
be first satisfied by eliminating possible compromises from other less important ones. In addition, path decision
strategies that are suited to individual objectives can be used at different decision layers. The layered decision
framework, along with a multi-step look-ahead path decision strategy based on a Roll-out policy is shown to be
able to guide the UAV group effectively for the multi-objective surveillance in a hostile environment.
The measurement conversion from a radar's r-u-v coordinate system to a Cartesian coordinate system is discussed
in this paper. Although the nonlinearity of this coordinate transformation appears insignificant based on the
evaluation of the bias of the converted measurements, it is shown that this nonlinearity can cause significant
covariance inconsistency in the conventional (first order) converted measurements (CM1). Since data association
depends critically on filter consistency, this issue is very important. Following this, it is shown that a suitable
corrected version (with second order terms) of the conversion equations (CM2) eliminates the inconsistency.
The decision between using the standard conversion and the second order version is based on a condition ratio,
namely, for an r-u-v measurement whose condition ratio is lower than a certain threshold, CM2 should be used.
Results on various tracking filter using these conversions are presented in part I [1].
KEYWORDS: Filtering (signal processing), Radar, Electronic filtering, Error analysis, Monte Carlo methods, Detection and tracking algorithms, Digital filtering, Phased arrays, Signal processing, Data processing
The problem of tracking with very long range radars is studied in this paper. An important feature of the
measurement conversion from a radar's r-u-v coordinate system to the Cartesian coordinate system is that,
beyond a certain limit, measurement conversion based on the second order Taylor expansion (CM2) is necessary
(and sufficient) to guarantee the consistency of the converted measurements (see part II [1] for the details).
Initialized with the converted measurements (using CM2), four Cartesian filters are evaluated. It is shown that,
among these filters, the Converted Measurement Kalman Filter with second order Taylor expansion (CM2KF)
is the only one that is consistent for very long range tracking scenarios. Another two approaches, the
Range-Direction-Cosine Extended Kalman Filter (ruvEKF) and the Unscented Kalman Filter (UKF) are also evaluated
and shown to suffer from consistency problems. However, the CM2KF has the disadvantage of reduced accuracy
in the range direction. To fix this problem, a consistency-based modification for the standard Extended Kalman
Filter (E1KF) is proposed. This leads to a new filtering approach, designated as Measurement Covariance
Adaptive Extended Kalman Filter (MCAEKF). For very long range tracking scenarios, the MCAEKF is shown
to produce consistent filtering results and be able to avoid the loss of accuracy in the range direction. It is also
shown that the MCAEKF meets the Posterior Carmer-Rao Lower Bound for the scenarios considered.
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