Abstract
We consider the state estimation of a maneuvering target in 3D using bearing and elevation measurements from a passive infrared search and track (IRST) sensor. Since the range is not observable, the sensor must perform a maneuver to observe the state of the target. The target moves with a nearly constant turn (NCT) in the -plane and nearly constant velocity (NCV) along the Z-axis. The natural choice for the NCT motion is to allow perturbations in speed and angular rate in the stochastic differential equation, as has been pointed out previously for a 2D scenario using range and bearing measurements. The NCT motion in the -plane cannot be discretized exactly, whereas the NCV motion along the Z-axis is discretized exactly. We discretize the continuous-time NCT model using the first and second-order Taylor approximations to obtain discrete-time NCT models, and we consider the polar velocity and Cartesian velocity-based states for the NCT model. The dynamic and measurement models are nonlinear in the target state. We use the cubature Kalman filter to estimate the target state. Accuracies of the first and second-order Taylor approximations are compared using the polar velocity-based and Cartesian velocity-based models using Monte Carlo simulations. Numerical results for realistic scenarios considered show that the second-order Taylor approximation provides the best accuracy using the polar velocity or Cartesian velocity-based models.
Highlights
Academic Editor: Andrzej StatecznyAngle-only filtering in 2D and 3D finds many important applications in passive tracking [1,2,3,4,5,6,7,8,9,10,11,12,13]
In [8], we performed a comprehensive study of the angle-only filtering (AOF) problem for a non-maneuvering target in 3D using the extended Kalman filter (EKF), unscented Kalman filter (UKF), and particle filter (PF) with Cartesian state vector and modified spherical coordinates (MSC)
To compare the accuracies of the filters used in the AOF problem with the best achievable accuracy, we computed the posterior Cramér-Rao lower bound (PCRLB) [40] for a non-maneuvering target using the nearly constant velocity (NCV) model in [41]
Summary
Angle-only filtering in 2D and 3D finds many important applications in passive tracking [1,2,3,4,5,6,7,8,9,10,11,12,13]. In [8], we performed a comprehensive study of the AOF problem for a non-maneuvering target in 3D using the EKF, UKF, and PF with Cartesian state vector and MSC. To compare the accuracies of the filters used in the AOF problem with the best achievable accuracy, we computed the posterior Cramér-Rao lower bound (PCRLB) [40] for a non-maneuvering target using the NCV model in [41]. A PF is not considered for this problem due to its lack of state estimation accuracy and high computational cost It has been observed in [33,34,35] that when the measurement accuracy and data rate are high (which is true for the current problem), the UKF and CKF have nearly the same accuracy, and the accuracy of the EKF is somewhat lower.
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