KEYWORDS: Missiles, Protactinium, Monte Carlo methods, Navigation systems, Mathematical modeling, Motion estimation, Motion models, Statistical analysis, Optimization (mathematics), Signal to noise ratio
This work deals with the following question: using passive (line-of-sight angle) observations of a multistage
surface to air missile from an aircraft, how can one infer that the missile is or is not aimed at the aircraft. The
observations are assumed to be made only on the initial portion of the missile's trajectory. The approach is to
model the trajectory of the missile with a number of kinematic and guidance parameters, estimate them and
use statistical tools to infer whether the missile is guided toward the aircraft or not. A mathematical model is
presented for a missile under pure proportional navigation with a changing velocity (direction change as well
as speed change), to intercept a nonmaneuvering aircraft. A maximum likelihood estimator (MLE) is used for
estimating the missile's motion parameters and a goodness-of-fit test is formulated to test if the aircraft is the
aim or not. Using measurement data from several realistic missiles - single stage as well as multistage - aimed
at an aircraft, it is shown that the proposed method can solve this problem successfully. The key to the solution,
in addition to the missile model parametrization, is the use of a reliable global optimization algorithm with a
hierarchical search technique for the MLE. The estimation/decision algorithm presented here can be used for an
aircraft to decide, in a timely manner, whether appropriate countermeasures are necessary.
KEYWORDS: Missiles, Protactinium, Motion estimation, Mathematical modeling, Motion models, Statistical analysis, Solids, Monte Carlo methods, 3D modeling, Signal to noise ratio
This work deals with the following question: using passive (line-of-sight angle) observations of a missile from an aircraft, how can one infer that the missile is or is not aimed at the aircraft. The observations are assumed to be made only on the initial portion (about 1/4) of the missile's trajectory. The approach is to model the trajectory of the missile with a number of kinematic and guidance parameters, estimate them and use statistical tools to infer whether the missile is guided toward the aircraft. A mathematical model is constructed for a missile under pure proportional navigation with a changing velocity (direction change and speed change), to intercept a nonmaneuvering aircraft. A maximum likelihood estimator is presented for estimating the missile's motion parameters and a goodness-of-fit test is formulated to test if the aircraft is the aim or not. Using measurement data from a realistic missile aimed at an aircraft shows that the proposed method can solve this problem successfully. The estimation/decision algorithm presented here can also be used for an aircraft to decide whether appropriate countermeasures are necessary.
Multiple target tracking requires data association that operates in conjunction with filtering. When multiple targets are closely spaced, the conventional approach (MHT/assignment) may not give satisfactory results. This is mainly because of the difficulty in deciding what the number of targets is. Recently, the probability hypothesis density (PHD) filter, which propagates the PHD or the first moment instead of the full multitarget posterior density, was proposed. In this approach, the integral of the PHD over a region in the state space is the expected number of targets within this region and the peaks in the PHD can be regarded as the estimated locations of the targets at a given time step. In this approach the data association problem is not considered, i.e., the PHD is obtained only for a frame at a time. In our paper, a data association method combined with the PHD approach is proposed for multitarget tracking, i.e., we keep a separate tracker for each target, use the PHD filter to get the estimated number and locations of the targets at each time step, and then perform the "peak-to-track" association, whose results can provide information for PHD peak extraction at the next time step. Besides, by keeping a separate tracker for each target, our approach provides more information than the standard PHD filter. Using our approach, the multitarget tracking can be performed with automatic track initiation, maintenance, spawning, merging and termination. Simulation results demonstrate that our approach is computationally feasible and effective.
In this paper we present an algorithm for identifying the parameters of a proportional navigation guidance missile (pursuer) pursuing an airborne target (evader) using angle-only measurements from the latter. This is done for the purpose of classifying the missile so that appropriate countermeasures can be taken. In the literature, there have been numerous studies on how a pursuer tracks an evader and what the optimal guidance law should be. However, not much has been done on identifying/classifying the pursuer from the evader's point of view using angle-only measurements. This provides the motivation for our current work. Mathematical models are constructed for a pursuer with a changing velocity, i.e., a direction change and a speed change. Assuming the pursuer is launched from the ground with an acceleration, its motion can be described by a four-dimensional parameter vector consisting of its proportional navigation constant and three parameters related to thrusting (initial net specific thrust, the relative mass ejection rate and its maximum speed). Consequently, the problem can be solved as a parameter estimation problem, rather than state estimation. In this paper, we provide an estimator based on Maximum Likelihood (ML) to solve this identification problem. The parameter estimates obtained can be mapped into the time-to-go until intercept, thus the time-to-go estimate can also be obtained from the above estimator. Estimation results are presented for different scenarios together with the Cramer-Rao Lower Bound, which quantifies the best achievable estimation accuracy. The accuracy of the time-to-go estimate is also obtained. Simulation results demonstrate that the proposed estimator is efficient by meeting the CRLB.
KEYWORDS: Sensors, Radar, 3D metrology, Motion estimation, Monte Carlo methods, Detection and tracking algorithms, 3D acquisition, Personal digital assistants, Surveillance, Error analysis
In this paper we present an algorithm for initiating 3-D tracks using range and azimuth (bearing) measurements from a 2-D radar on a moving platform. The work is motivated by the need to track possibly low-flying targets, e.g., cruise missiles, using reports from an aircraft-based surveillance radar. Previous work on this problem considered simple linear motion in a flat earth coordinate frame. Our research extends this to a more realistic scenario where the earth’s curvature is also considered. The target is assumed to be moving along a great circle at a constant altitude. After the necessary coordinate transformations, the measurements are nonlinear functions of the target state and the observability of target altitude is severely limited. The observability, quantified by the Cramer-Rao Lower Bound (CRLB), is very sensitive to the sensor-to-target geometry. The paper presents a Maximum Likelihood (ML) estimator for estimating the target motion parameters in the Earth Centered Earth Fixed coordinate frame from 2-D range and angle measurements. In order to handle the possibility of false measurements and missed detections, which was not considered in, we use the Probabilistic Data Association (PDA) algorithm to weight the detections in a frame. The PDA-based modified global likelihood is optimized using a numerical search. The accuracies obtained by the resulting ML-PDA estimator are quantified using the CRLB for different sensor-target configurations. It is shown that the proposed estimator is efficient, that is, it meets the CRLB. Of particular interest is the achievable accuracy for estimating the target altitude, which is not observed directly by the 2-D radar, but can be only inferred from the range and bearing observations.
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