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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.
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