Improving the State Estimates of a Maneuvering Target Using a Constrained Grid-Based Filter: A Comparative Study Open Access
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Tracking maneuvering targets is an important but difficult problem. This problem occurs when tracking maneuvering boats or even people wandering around. If the target motion is linear and the measurement errors are Gaussian, then a Kalman filter provides the optimal estimates. However, since maneuvering targets do not generally exhibit linear motion, a Kalman filter will often produce poor estimates for these targets. A better approach would be to exploit the kinematic constraints of the target motion to restrict the predicted states to those where the target could have transitioned. But exploiting these constraints will produce bounded, non-Gaussian prediction distributions. A Kalman filter must assume that this prediction distribution is Gaussian. Grid-based filters (GBFs) can work with any prediction distribution so they allow the kinematic constraints to be exploited. As a result, GBFs should be very effective at producing accurate state estimates. But current implementations of GBFs typically require large memories and exponential processing. As a result, although grid-based filters should be effective, they have been avoided due to their perceived exponential computational complexity. A novel approach for implementing a GBF, called a constrained grid-based filter (CGBF), has been developed that can track targets moving in two dimensions by using a well-confined, two-dimensional grid. This paper will expose the problems with current GBFs and then explain how they are avoided in a CGBF. As a result, this grid-based approach is enormously more computationally efficient and can effectively exploit the kinematic constraints of the target. The paper will discuss how the kinematic constraints of the target are used to restrict the possible predicted states, including the formalism to show how the predicted state from the CGBF is better bounded than from a Kalman filter.In systems engineering, when two or more alternative solutions exist, it is important to conduct an analysis of alternatives (AoA) to determine the best systems approach. An AoA will be conducted to compare the tracking performance of a CGBF to a Kalman filter for maneuvering target scenarios. The target state estimates (position and velocity) will be analyzed via Monte Carlo analysis. This study will employ two comparison methods including the comparison paradigm presented by Kirubarajan and Bar-Shalom. The intent of this study is to determine how maneuverable the target must be to gain the benefit from a CGBF over a Kalman filter. Keep in mind that when all Kalman filter assumptions hold, it is the optimal filter. This paper will discuss the target motion model, the CGBF implementation, and the Kalman filter used for the study. The results will show that by restricting the prediction distribution based on the presumed (realistic) kinematic constraints of the target, a more informed filter will result. Thus, by violating the one key Kalman filter assumption, it will be shown that the CGBF consistently outperforms a Kalman filter, even for the linear motion target case. Furthermore, the improvement from the CGBF increases relative to a Kalman filter as the target becomes more maneuverable.Although the CGBF is much less computational than current GBF methods, it is still more computational than a Kalman filter. The paper will discuss the grid and sample sizing needed to obtain quality estimates from a CGBF. It will be shown that the sizes are much smaller than what may be expected and that the CGBF is quite stable even when using these small sizes.