This paper considers the problem of estimating the trajectory of a ballistic target in the reentry phase using 2D measurements (azimuth and elevation angles) from a moving passive sensor. Previous works investigated the estimation problem of an object in the thrusting and initial ballistic phase from a single fixed passive sensor. This work shows that the 3D trajectory in the reentry phase can be obtained by estimating the target's state at the end of the observation interval. The 7-dimensional motion parameter vector (velocity azimuth angle, velocity elevation angle, drag coefficient, target speed and 3D position) is estimated by the Maximum Likelihood (ML) estimator with numerical search. Then we can predict the future position at an arbitrary time and the impact point of the target. The observability of the system for a sensor on a fast aircraft moving with constant velocity or maneuvering is verified via the invertibility of the Fisher Information Matrix. This is a major extension of the applicability of the recent observability proof for a stationary passive sensor observing a target in a gravitational field. The Cramer--Rao lower bound for the estimated parameters is evaluated and it shows that the estimates are statistically efficient. The angle estimation performance for the ML estimator is also compared with that of the polynomial fitting method. Simulation results illustrate the effectiveness of the proposed method.

This paper investigates Man-Portable Air Defense Systems (MANPAD) missile threat detection and an effective maneuvering strategy for aircraft (A/C) destruction avoidance. The 3D trajectory of a multistage missile (boost and sustain phases) under Pure Proportional Navigation is first estimated. The maximum likelihood estimator is used to estimate its motion parameters of the two-stage missile considered using only angle measurements from a low-altitude A/C. Missile threat detection is investigated based on two methods: estimation-based as a baseline method and threat plane-based. The former can provide a miss distance between the A/C and the missile, but more measurements are required. The latter is shown to give a faster threat alert, allowing the A/C to start the evasive maneuver earlier. An efficient evasion maneuver for avoiding destruction, is banking away from the missile by a turning maneuver in the horizontal plane, due to its low-altitude. The survivability probability of the A/C is evaluated with and w/o countermeasures (flares). There are two key factors that affect the evasion performance: maneuver start time and the maximum acceleration during the maneuver. Simulations show that the A/C can start maneuvering earlier using the threat plane-based method compared with the estimation-based method. It can successfully evade the missile with the help of maneuvering. It is also shown that using flares, the necessary maneuver is less drastic (lower $g$ 's). Simulation results compare the necessary $g$ 's for obtaining a certain minimal distance from the missile.

The problem of measurement extraction for two point-targets in the focal plane array (FPA) of an optical sensor has been investigated in[10, 16].However, when the separation between the two targets is too small they become unresolved — they yield a single unresolved merged measurement. This paper presents an effective way to enhance the resolution for two such closely-spaced objects. One frame has the original image of the two targets while a second frame has the FPA slightly shifted by a fraction of a pixel (called offset frame). The measurement extraction consists of two parts: estimation and detection. Firstly, the targets' positions and intensities are jointly estimated based on the two frames' measurements (the original frame and the offset frame) under the resolved and unresolved target assumption. The Cramer-Rao lower bound evaluates the estimation accuracy. Secondly, a hypothesis test is used to decide whether the two targets can be resolved or are unresolved. The generalized likelihood ratio test is used to perform the decision making. Simulations investigate the effect of offset types, target separation, and SNR on the measurement extraction and resolution. It is shown that adding offset to the image can provide more information about the closely-spaced objects, and offset enhances the resolution probability when compared to the two frames without offset.

Under the same principle, laser radar could be more sensitive to the micro-Doppler (m-D) effect due to its wave length, as the characteristic of multi-resolution, S transform could reduce the influence of the micro-Doppler component and enhance the imaging effect. This paper presents a method for micro-Doppler feature extraction in Inverse Synthetic Aperture Imaging Laser Radar (ISAIL) imaging. It is accessible and comprehensive, applying Random Sample Consensus (RANSAC) for the separation and reconstruction of micro-Doppler and rigid body signals. Experiments show that the method can effectively remove the micro-Doppler information and obtain a clear target distance-instantaneous Doppler image.