An assurance region at level <i>p</i>, A<sub>P=p</sub>, is
an area in motion space that contains the target with assigned
probability <i>p</i>. It is on the basis of A<sub>P=p</sub> that an action is
taken or a decision made. Common model-based trackers generate a
synthetic distribution function for the kinematic state of the target.
Unfortunately, this distribution is very coarse, and the resulting
A<sub>P=p</sub> lack credibility. It is shown that a map-enhanced, multiple
model algorithm reduces the tracking error and leads to a compact
Detecting and localizing a threat ballistic missile as quickly and accurately as possible are key ingredients required to
engage the missile during boost phase over the territory of the aggressor, and rapid and accurate launch point
determination is crucial to attack hostile facilities. Earlier research has focused on track initiation, boost phase tracking
and rapid launch point determination using augmented IMM and Kalman-based techniques. This work extends that
earlier research by comparing these IMM and Kalman-based trackers and backfitters with the newer particle filters to
see what advantages particle filters might offer in this application. Simulations used in this research assume the ballistic
missile target is in boost phase, transitioning to coast phase using a gravity turn and constant gravity. The rocket is
assumed to be single stage. The IMM tracker performs well in tracking through booster cutoff. A smoothed estimate of
the initial target state vector is used to backfit for launch point determination. Errors in this process are rather large and
there appear to be biases in the estimates. These results are compared with a particle filter implementation. Here the
correct nonlinear model of the missile dynamics was used, but the algorithm had to estimate engine thrust and the drag
coefficient as well as position and velocity states. This algorithm proved to be a large disappointment because the
number of particles required to generate reasonable results was large and the algorithm run time became unrealistically
A multiple-model tracker; e.g., the Gaussian Wavelet Estimator (GWE), employs a family of linear, local models
to represent the motion of a maneuvering target over a range of operating modes. The state estimate generated
by the GWE is a distribution with diffuse support. A road map provides contemporaneous, albeit circumscribed,
information that can be integrated into the GWE to improve location estimation. However, fusing the inelastic
restrictions of a road grid with the broad state estimates generated from conventional kinematic measurement
requires considerable care. This paper presents a modified version of the GWE which integrates a map grid
into the state estimate. The result is a state estimate consisting of a set of singular Gaussian sub-estimates. It
is shown by example that map-enhancement improves the accuracy of the location estimates and sharpens the
calculated uncertainty region.
This paper presents the results of a study of tracking algorithms for maneuvering targets. The design focuses on alternative algorithms to track two-dimensional targets during maneuvers. The algorithms explored include a standard Kalman algorithm, an extended Kalman algorithm in which the target turn rate is an additional state variable, an interactive multiple model (IMM) algorithm consisting of two models with varying plant noise, a three-model IMM specifying three distinct target turn rates, and a constant gain alpha-beta filter. The IMM trackers tended to work the best in this study, with the three-model IMM performing best overall.
Since the early 1990s, significant research has been done on a relatively new algorithm called the Probabilistic Multi-Hypothesis Tracker (PMHT). The majority of this research has concluded that there are a few weaknesses with this approach to tracking targets in the presence of clutter. First, the number of targets that are being tracked needs to be known a priori. Second, in order for the algorithm to operate properly, a very good initiation must be performed. Without a very close initiation, the PMHT usually fails to lock on to the target correctly. To address both of these issues, a hybrid approach is proposed. This hybrid approach will use a Multi-Hypothesis Tracking (MHT) algorithm to initiate new tracks and to continue tracking them until a track is stable. Then it will hand these tracks off to the PMHT to maintain. The MHT is very good at initiating new tracks, and the PMHT is best at maintaining multiple tracks because the algorithm's complexity with tracking additional targets grows linearly as opposed to exponentially.
Since the SCUD launches in the Gulf War, theater ballistic missile (TBM) systems have become a growing concern for the US military. Detection, fast track initiation, backfitting for launch point determination, and tracking and engagement during boost phase or shortly after booster cutoff are goals that grow in importance with the proliferation of weapons of mass destruction. This paper focuses on track initiation and backfitting techniques, as well as extending some earlier results on tracking a TBM during boost phase cutoff. Results indicate that Kalman techniques are superior to third order polynomial extrapolations in estimating the launch point, and that some knowledge of missile parameters, especially thrust, is extremely helpful in track initiation.
Since the SCUD launches in the Gulf War, theater ballistic missile (TBM) systems have become a growing concern for the US military. Detection, tracking and engagement during boost phase or shortly after booster cutoff are goals that grow in importance with the proliferation of weapons of mass destruction. This paper addresses the performance of tracking algorithms for TBMs during boost phase and across the transition to ballistic flight. Three families of tracking algorithms are examined: alpha-beta-gamma trackers, Kalman-based trackers, and the interactive multiple model (IMM) tracker. In addition, a variation on the IMM to include prior knowledge of a booster cutoff parameter is examined. Simulated data is used to compare algorithms. Also, the IMM tracker is run on an actual ballistic missile trajectory. Results indicate that IMM trackers show significant advantage in tracking through the model transition represented by booster cutoff.
Tracking multiple targets in a cluttered environment is extremely difficult. Traditional approaches use simple techniques to determine what are the true measurements by a combination of gating and some form of a nearest neighbor association. As clutter densities increase, these traditional algorithms fail to perform well. To counter this problem, the multi-hypothesis tracking (MHT) algorithm was developed. This approach enumerates almost every conceivable possible combination of measurements to determine the most likely. This process quickly becomes very complex and requires vast amounts of memory in order to store all of the possible tracks. To avoid this complexity, more sophisticated single hypothesis data association techniques have been developed, such as the probabilistic data association filter (PDAF). These algorithms have enjoyed some success but do not take advantage of any future data to help clarify ambiguous situations. On the other hand, the probabilistic multi-hypothesis tracking (PMHT) algorithm, proposed by Streit and Luginbuhl in 1995, attempts to use the best aspects of the MHT and the PDAF. In the PMHT algorithm, data is processed in batches, thereby using information from before and after each measurement to determine the likelihood of each measurement-to-track association. Furthermore, like the PDAF, it does not attempt to make hard assignments or enumerate all possible combinations. but instead associates each measurement with each track based upon its probability of association. Actual performance and initialization of the PMHT algorithm in the presence of significant clutter has not been adequately researched. This study focuses on the performance of the PMHT algorithm in dense clutter and the initialization thereof. In addition, the effectiveness of measurement attribute data is analyzed, especially as it relates to algorithm initialization. Further, it compares the performance of this algorithm to the nearest neighbor, MHT, and PDAF.
The design of effective pointing-and-tracking systems is particularly difficult when the target is capable of evasive maneuvers. Traditional approaches employed to detect a change in maneuver acceleration rely on observing changes in the residual error process, which introduces a time lag between the onset of a maneuver and its detection. This problem is exacerbated when only passive bearing measurements are available because measurement localization errors are infinite in one dimension. Earlier studies using active (range and bearing) measurement models have suggested the use of an augmenting imaging sensor to determine target orientation, from which the likely direction of a maneuver acceleration can be inferred. This paper extends these earlier results to the case of passive (bearing only) measurements, again using an augmenting imaging sensor to estimate target orientation. This sequence of orientation measurements is used to infer the onset and direction of a maneuver acceleration. As in these earlier studies, orientation measurements provide significant value in localizing and tracking the target during a maneuver.