Stephen C. Stubberud

Data Association for Multiple Sensor Types Using Fuzzy Logic

The concept of target tracking, a part of level 1 data fusion, is to combine measures from various sensors to form a coherent picture of the scene. A key component of the fusion problem is data association, the assignment of various measurements to existing target tracks. For the typical case in target association where both the target tracks and the measurements are described with Gaussian random variables, the standard association uses the chi2 metric, a weighted inner product of the residual formed by an estimated measurement and the true measurement. There are cases where the measurements are not well described as Gaussian random variables, including those from sensors that have uncertainties that are better approximated as uniform distributions or where the Gaussian distribution is corrupted by sensor blockage or target constraints. Based upon the proven concept of the chi2 metric, a straightforward fuzzy-logic-based association method is developed that can emulate this metric for Gaussian measurements but can be modified to address problems where the Gaussian assumption on the track and/or measurement is not appropriate

On-Line Sensor Modeling Using a Neural Kalman Filter

Sensor measurement systems rely upon knowledge of the functional dynamics between system states and the measured outputs. Errors in sensor measurements come from a variety of source. While there are well known techniques to compensate for those that result from such issues as noise and sensor accuracy limitations, other types of errors, such as those that are more deterministic, can result in biases that are not easily compensated for in standard systems. A modification of an adaptive tracking technique based upon the neural extended Kalman filter is proposed as a technique to provide for on-line calibration for the sensor models. Previously, the technique has been applied to tracking problems and successfully improved the motion model of a target when a maneuver occurs. Here, the sensor dynamics are learned rather than the target dynamics

Feature Object Extraction: Evidence Accrual for the Level 1 Fusion Classification Problem

Classification of a target is a key element of the Level 1 Fusion problem. Estimation of the classification of a potential target could be used to determine whether it should be prosecuted. This increasingly important problem requires the development of a quality estimate based on fusing reports across time and from a variety of sensors. The most common automated techniques for the classification problem provide a probability measure of the possible classes. Another concept in classification is the use of evidence accrual. As opposed to the creation of scoring techniques that use a random variable representation of the classification, the evidence accrual technique builds scores based on the information that can be compared to other scores or thresholds of the decision process. Since evidence affects the various potential classes differently, the technique developed is based on decoupled fuzzy-logic-based Kalman filters, similar to the concept of first-order observers. The proposed technique addresses three key issues in the classification problem. First, it is designed to incorporate both numeric and nonnumeric sensor reports. Second, it incorporates measurement uncertainty. Finally, it provides a level of uncertainty for each class. The technique is implemented in two forms: one that emulates the Bayesian taxonomy and one that allows for evidence to be independently applied to each potential class.

Analysis and implementation of a neural extended Kalman filter for target tracking.

Having a better motion model in the state estimator is one way to improve target tracking performance. Since the motion model of the target is not known a priori, either robust modeling techniques or adaptive modeling techniques are required. The neural extended Kalman filter is a technique that learns unmodeled dynamics while performing state estimation in the feedback loop of a control system. This coupled system performs the standard estimation of the states of the plant while estimating a function to approximate the difference between the given state-coupling function model and the behavior of the true plant dynamics. At each sample step, this new model is added to the existing model to improve the state estimate. The neural extended Kalman filter has also been investigated as a target tracking estimation routine. Implementation issues for this adaptive modeling technique, including neural network training parameters, were investigated and an analysis was made of the quality of performance that the technique can have for tracking maneuvering targets.

Predictive guidance intercept using the neural extended Kalman filter tracker

The target intercept problem has two main components. The first is the development of a control loop for the interceptor. The second is the target-tracking system that provides the location of the target to the control law. The tracking system is a significant element, particularly when predictive control is used and the target motion is unknown a priori. A neural Kalman filter approach to target tracking is presented as a technique to improve the motion model of the target while it is being tracked in flight. A linearized version of that model is then used to provide an improved estimate of the predicted location of the target. The technique uses an augmented Kalman filter that couples the tracking capabilities and a neural network training algorithm. The motion model then becomes a composite of the a priori motion model and neural network. The model is then linearized at the state for which it was computed; and this linearized model is used to propagate the state estimate forward to a given intercept time. The improved model generally gives a better result than the standard straight-line motion tracking performance, even with target maneuvering included in the process noise.

Image Correlation Based Video Tracking

Image correlation can be used for quality testing, pattern recognition, image searching, and image tracking. Image tracking of a video image was the focus of a frequency domain based approach using two-dimensional Fourier transforms for image correlation. When tracking a moving object that varies in size over time, a technique to identify the position of a template image within the larger picture was used. This approach requires the dynamic resizing of the template image in the video as it grows and shrinks in size. This approach allows for accurate image placement and the subsequent path of the image through a video screen can be followed. The solution can be implemented to provide real time results to provide the path of the image tracked.

Track-to-track association using a phase-only filter

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.

Target Data Association Using a Fuzzy-Logic Based Approach

Level 1 data fusion is defined as object assessment (Hall & Linus, 2001). This process of estimation and prediction of an entity can be decomposed into a functional series of subprocesses as defined by the well known Bowman model (Steinberg, et al, 1999) that is depicted in Figure 1. While data fusion can apply to a host of applications, this chapter looks at the problem from a target tracking point of view.

Incorporation of Partially Observable Evidence Into an Evidence Accrual Data Fusion Technique

In many sensor fusion problems, such as level 1 (object refinement), 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 or level of interest through a functional relationship. Often, these observations can be considered partially observable, such as the relationship between a bearings-only measurement and target position. A general evidence accrual system that incorporates these partially- observable 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 into the uncertainty measure of the evidence. Unlike a Bayesian taxonomy, the proposed method does not rely upon the strict probabilistic underpinnings, but instead uses a network structure with links and propagation of evidence. In this work, proof of capability is demonstrated by applying the technique to a Level 1 classification fusion problem where the observations are target attributes. The technique, based upon an existing 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 filter allows for the level of evidence to incorporate an uncertainty or quality measure into the report.

KINEMATIC PREDICTION FOR INTERCEPT USING A NEURAL KALMAN FILTER

Abstract The neural extended Kalman filter is a technique that learns unmodelled dynamics while performing state estimation. This coupled system performs the state estimation of the plant while estimating a function approximation of the difference between the system model and the dynamics of the true plant. At each sample step, this approximation is added to the existing model improving the state estimate. This neural estimator is applied to a two-dimensional intercept problem as a target tracker providing the control reference signal. Comparisons between different prediction times used in the control are provided for both the neural tracker and a baseline tracker.