An alternative approach to data association is analyzed. The technique, based on an automatic target recognition
scheme, uses an image correlation scheme that relies on the phase-only filter. The phase-only filter can compare tracklevel
data (or tagged data) over multiple scans simultaneously. The approach can also combine kinematic and attribute
data to be scored simultaneously. The technique requires that the track information be mapped into an image
representation, referred to as a tile. The generation of the tile can be based on an amplitude representation of the targettrack
variations. Alternatively, phase variations, rather than amplitude could be used to generate the tile. These tiles can
represent multiple track attributes over multiple reports. The capabilities of the phase-only filter correlation technique
are compared to the chi-squared metric standard.
An important component of tracking fusion systems is the ability to fuse various sensors into a coherent picture of the
scene. When multiple sensor systems are being used in an operational setting, the types of data vary. A significant but
often overlooked concern of multiple sensors is the incorporation of measurements that are unobservable. An
unobservable measurement is one that may provide information about the state, but cannot recreate a full target state. A
line of bearing measurement, for example, cannot provide complete position information. Often, such measurements
come from passive sensors such as a passive sonar array or an electronic surveillance measure (ESM) system.
Unobservable measurements will, over time, result in the measurement uncertainty to grow without bound. While some
tracking implementations have triggers to protect against the detrimental effects, many maneuver tracking algorithms
avoid discussing this implementation issue.
One maneuver tracking technique is the neural extended Kalman filter (NEKF). The NEKF is an adaptive estimation
algorithm that estimates the target track as it trains a neural network on line to reduce the error between the a priori target
motion model and the actual target dynamics. The weights of neural network are trained in a similar method to the state
estimation/parameter estimation Kalman filter techniques. The NEKF has been shown to improve target tracking
accuracy through maneuvers and has been use to predict target behavior using the new model that consists of the a priori
model and the neural network.
The key to the on-line adaptation of the NEKF is the fact that the neural network is trained using the same residuals as
the Kalman filter for the tracker. The neural network weights are treated as augmented states to the target track.
Through the state-coupling function, the weights are coupled to the target states. Thus, if the measurements cause the
states of the target track to be unobservable, then the weights of the neural network have unobservable modes as well. In
recent analysis, the NEKF was shown to have a significantly larger growth in the eigenvalues of the error covariance
matrix than the standard EKF tracker when the measurements were purely bearings-only. This caused detrimental
effects to the ability of the NEKF to model the target dynamics. In this work, the analysis is expanded to determine the
detrimental effects of bearings-only measurements of various uncertainties on the performance of the NEKF when these
unobservable measurements are interlaced with completely observable measurements. This analysis provides the ability
to put implementation limitations on the NEKF when bearings-only sensors are present.
In many fusion problems, such as Level 2 (situational assessment) or Level 3 (impact assessment), observations
frequently provide indirect, rather than direct, evidence. In such cases, the measurements affect the evidence level of
interest through a functional relationship, such as speed being measured through the functional relationship between it
and position observations over time. A general evidence accrual system that incorporates indirect observations into the
evidence generation is developed. The technique, based on the concepts of first-order and reduced-order observer
theory, can incorporate both observation quality and level of doctrine understanding in the uncertainty measure of the
evidence. The technique does use a network structure with links and propagation of evidence, but, unlike a Bayesian
taxonomy, it does not rely upon the strict probabilistic underpinnings. In this work, to demonstrate its proof of
capability, the technique is applied to a force-on-force Level 2 fusion problem. The technique, based upon a Level 1
fusion target classification evidence accrual algorithm, uses a fuzzy Kalman filter to inject new evidence into the nodes
of interest to modify the level of evidence. The fuzzy Kalman allows for the level of evidence to incorporate an
uncertainty or quality measure into the report.
The neural extended Kalman filter is an adaptive estimation technique that has been shown to learn on-line the
maneuver model of the trajectory of a target. This improved motion model can be used to better predict the location of
a target at given point in time, especially when the target, such as a mortar shell, has limited maneuvering capabilities.
In this paper, the neural extended Kalman filter is used to predict, with multiple-sensor-systems provided measurement
reports, impact point and impact time of a ballistic-like projectile when the drag on the shell was not accurately modeled
in the motion model. In previous work, the neural extended Kalman filter was shown to work well with a single sensor
with a uniform sample rate. Multiple sensors can incorporate two major differences into the problem. The first
difference is that of the multiple aspect angles and uncertainty that are used in the model adaptation. The second
difference is that of a non-uniform update rate of the measurements to the tracking system. While most tracking
systems can easily handle this difference, the adaptation of the neural network training parameters can be deleteriously
affected by these variations. The first of these two differences, potential concerns to the neural extended Kalman filter's
implementation, is investigated in this effort. In this effort, performance of this adaptive and predictive scheme with
multiple sensors in a three dimensional space is shown to provide a quality impact estimate.
Part of target tracking is the use of existing information to predict behavior. Often, this part of the tracking algorithm is used for data association and the update step of the fusion process as well as, recently, to guide weapons to the target. Another application is to estimate the point of impact of enemy ballistic munitions. The determination of the actual threat posed by enemy position permits prioritization of targets for response and can limit the need to expose friendly units.
The flight trajectory of ballistic ordinance, while theoretically understood, can be affected by a number of unknown factors, such as air turbulence and drag. To accurately predict the projectile's flight path, an adaptive Kalman filter approach is proposed to track and predict the target trajectory. The Kalman filter uses a neural network as an on-line function approximator to improve the motion model of the target tracking. The neural network is trained in conjunction with the tracking algorithm. Both track states and neural network weights use the same residual information. The neural network model is added to the motion model and provides an improved track prediction of a mortar impact time and its location. Analysis of the approach's performance is compared to varying tracking systems with different levels of target motion accuracy. Two a priori motion models for the neural approach are applied: a straight-line motion model and a basic ballistic trajectory. The results show the ability of the technique to provide accurate target predictions with limited a priori information.
One technique that has been applied to the tracking of maneuvering targets is the neural extended Kalman filter. The technique adapts the motion model used by the Kalman filter tracker. This adaptation of the model is performed by a neural network that trains on-line using the same residuals as the track states. The behavior of this technique with multiple sensors providing different measurement types and different update rates has not previously been discussed; previous works have always employed a single sensor, usually providing a position measurement or a range-bearing measurement. In actual applications, multiple sensors are typically employed. These sensors often provide measurements at different rates or with the different accuracy. Such issues can have a detrimental effect on the performance of the neural network. The results of multiple-sensor data with variations in the update rates and measurement accuracy to an NEKF estimation system are analyzed. The analysis is based upon the case of two non-collocated sensors providing range-bearing measurements at varying rates applied to the tracking of an actual aircraft flight trajectory.
The best method to track through a maneuver is to know the motion model of the maneuvering target. Unfortunately, a priori knowledge of the maneuver is not usually known. If the motion model of the maneuver can be estimated quickly from the measurements then the resulting track estimate will be better than the a priori static model.
An adaptive function approximation technique to improve the motion model while tracking is analyzed for its potential to track through various maneuvers. The basic function approximation technique is that of a Gaussian sum. The Gaussian sum approximates the function which represents the error between the initial static model and the actual model of the maneuver. The parameters of the Gaussian sum are identified on-line using a Kalman filter identification scheme. This scheme, used in conjunction with a Kalman filter tracker, creates a coupled technique that can improve the motion model quickly.
This adaptive Gaussian sum approach to maneuver tracking has its performance analyzed for three maneuvers. These maneuvers include a maneuvering ballistic target, a target going through an s-curve, and real target with a multiple racetrack flight path. The results of these test cases demonstrate the capabilities of this approach to track maneuvering targets.