Video synthetic-aperture radar (ViSAR) can obtain high-resolution images of a region of interest at a high frame rate. This feature of ViSAR is helpful for real-time detection and tracking of moving targets. Moving-target tracking using ViSAR images is a typical dim-target-tracking problem. In the context of this article, dim targets correspond to the shadows of the moving vehicles cast onto the stationary background scene, which appear at lower gray levels compared with the background clutter. To detect and track multiple slowly maneuvering targets in the ViSAR imagery, we propose a novel algorithm, the expanding and shrinking strategy-based particle filter/dynamic programming-based track-before-detect (ES-TBD) algorithm. To the best of our knowledge, our work represents the first algorithm to deal with the ViSAR-detection and tracking problem using the TBD method. Furthermore, to detect and track a time-varying number of targets, we also propose a novel region-partitioning-based ES-TBD (RP-TBD) algorithm. By exploiting the common information shared between the batches of measurement data and the modeling merit-function-integrated particle filters (PFs), the RP-TBD partitions the observation region into a predicted subregion and an innovative subregion. The RP-TBD algorithm detects newborn targets in the innovative subregion, while maintains tracks of known targets in the predicted subregion. Experimental results using real ViSAR images show that the proposed algorithms outperform the state-of-the-art algorithms on detecting and tracking multiple dim targets in terms of location accuracy and false-alarm suppression.

The trajectory estimation of a highly maneuvering target is a challenging problem and has practical applications. The interacting multiple model (IMM) filter is a well-established filtering algorithm for the trajectory estimation of maneuvering targets. In this study, we present an overview of IMM filtering algorithms for tracking a highly-maneuverable fighter aircraft using an air moving target indicator (AMTI) radar on another aircraft. This problem is a nonlinear filtering problem due to nonlinearities in the dynamic and measurement models. We first describe single-model nonlinear filtering algorithms: the extended Kalman filter (EKF), unscented Kalman filter (UKF), and cubature Kalman filter (CKF). Then, we summarize the IMM-based EKF (IMM-EKF), IMM-based UKF (IMM-UKF), and IMM-based CKF (CKF). In order to compare the state estimation accuracies of the IMM-based filters, we present a derivation of the posterior Cramér-Rao lower bound (PCRLB). We consider fighter aircraft traveling with accelerations 3g, 4g, 5g, and 6g and present numerical results for state estimation accuracy and computational cost under various operating conditions. Our results show that under normal operating conditions, the three IMM-based filters have nearly the same accuracy. This is due to the accuracy of the measurements of the AMTI radar and the high data rate.

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 $XY$-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 $XY$-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.

This paper addresses the filtering problem of a reentry vehicle (RV) using a passive sensor onboard an aircraft. The passive sensor measures the azimuth and elevation angles of the RV. We use the continuous-discrete filtering (CDF) paradigm that combines the continuous-time dynamic model with the discrete-time measurement model. Our approach benefits from a highly accurate RV dynamic model formulated as an Itô stochastic differential equation, which takes into account spherical-Earth gravity, atmospheric drag, and stochastic process noise. The RV's state is defined by its 3D Cartesian position, velocity, and a random drag parameter. For the prediction step, we present two distinct variants of the continuous extended Kalman filter, namely the CEKF and CEKF2, while for the measurement update step, we employ a cubature Kalman filter (CKF). These combined CDF algorithms are named the CEKF-CKF and CEKF2-CKF. These two filters are compared with an existing approximate discrete filter called the EKF-CKF. To assess their performance, we conduct Monte Carlo simulations to compute the root mean square errors for position, velocity, and the drag parameter. Additionally, we assess the filter's consistency by calculating the average normalized estimation error squared and the average normalized innovation squared. The simulation results show that the CEKF-CKF outperforms the CEKF2-CKF in the two scenarios examined. At higher process noise levels, the CEKF-CKF has a higher covariance consistency than the EKF-CKF.