Graphical Interpretation of Chirp Echoes from Complex Targets

Echoes from complex targets due to chirp waveforms show different time responses for different chirp rates, because of the ambiguity of range and radial velocity information. A graphical method is described which enables the derivation of the time response for an arbitrary chirp rate when the scattering cross-section distribution in the range and radial velocity plane is known for complex targets. The graphical method can also be used to generate an approximately realistic scattering cross-section distribution when the time responses for two different chirp rates are given. An example is shown which applies to the computer simulation of the radar echo from a waking reentry space vehicle.     

Natural Resonances of Radar Targets Via Prony's Method and Target Discrimination

The dominant complex natural resonances of radar targets are obtained via Prony's method applied to calculated and measured back-scattered ramp response waveforms. Subject targets are spheres, simple wire models of straight and swept wing aircraft, and realistic models of modern fighter aircraft. It is demonstrated that when the backscattered ramp response waveforms are obtained via Fourier synthesis of limited spectral range harmonic scattering data, some resonance locations at variance with those obtained from reaction integral equation search procedures are obtained. It is also shown, however, that the Prony deduced resonances can be used successfully in predictor-correlator target discrimination.     

Precision large scale air traffic surveillance using IMM/assignmentestimators

We present the development and implementation of a multisensor-multitarget tracking algorithm for large scale air traffic surveillance based on interacting multiple model (IMM) state estimation combined with a 2-dimensional assignment for data association. The algorithm can be used to track a large number of targets from measurements obtained with a large number of radars. The use of the algorithm is illustrated on measurements obtained from 5 FAA radars, which are asynchronous, heterogeneous, and geographically distributed over a large area. Both secondary radar data (beacon returns from cooperative targets) as well as primary radar data (skin returns from noncooperative targets) are used. The target IDs from the beacon returns are not used in the data association. The surveillance region includes about 800 targets that exhibit different types of motion. The performance of an IMM estimator with linear motion models is compared with that of the Kalman filter (KF). A number of performance measures that can be used on real data without knowledge of the ground truth are presented for this purpose. It is shown that the IMM estimator performs better than the KF. The advantage of fusing multisensor data is quantified. It is also shown that the computational requirements in the multisensor case are lower than in single sensor case, Finally, an IMM estimator with a nonlinear motion model (coordinated turn) is shown to further improve the performance during the maneuvering periods over the IMM with linear models     

Multipath Tracking Errors in Elevation-Scanning and Monopulse Radars

The tracking performance of elevation- scanning and monopulse radars in the presence of multipath propagation are compared. The key difference between these two generic types of radars is the way they respond to moving targets. There are no significant differences between their responses to pure specular multipath, nor to diffuse multipath for targets on radial courses. However, they are found to respond quite differently to the diffuse com ponent for low-altitude crossing targets. For these conditions the tracking errors for elevation-scanning radars may be several times those for monopulse radars.     

Direct Intercept Guidance using Differential Geometry Concepts

This paper examines the application of differential geometry to the engagement of both nonmanoeuvring and manoeuvring targets. The kinematics of the engagement for both manoeuvring and nonmanoeuvring target are developed and expressed in differential geometric terms. Two-dimensional geometry is then used to determine the intercept conditions for a straight line target and a constant manoeuvre target. The intercept conditions for both targets are developed for the case when the interceptor missile guides onto a straight line interception. These two cases are shown to have a common set of core conditions such that it enables a unified guidance law to be developed. The guidance law is shown to be globally stable using Lyapunov theory, so that guidance capture is assured for any initial condition. The analysis and guidance law design does not rely on local linearisation and can be shown to produce guidance trajectories that mirror proportional navigation for the straight line interception of a nonmanoeuvring target for which proportional navigation was originally developed. The paper finishes with simulation in two dimensions, illustrating the convergence and solution properties of the approach.     

Accurate solution of proportional navigation for maneuveringtargets

An accurate solution is presented of the nonlinear differential equations describing motion under proportional navigation when the target is laterally maneuvering. A quasilinearization (QL) approach is used, followed by a perturbation technique to obtain closed-form solutions for trajectory parameters. An explicit expression for the pursuer lateral acceleration is derived and shown to contain contributions due to initial heading error and target maneuver, with a coupling between the two effects. The solution is shown to be a substantial and consistent generalization or an earlier accurate solution for nonmaneuvering targets and also of classical linear solutions for maneuvering targets. The generalized QL solution presented provides very accurate estimates of pursuer lateral acceleration over a much broader range of engagement geometries and target maneuvers than presently available closed-form solutions     

Average Monopulse Angle Tracking Response to Two Unresolved Sources

Theoretical equations for the average monopulse ratio response of a monopulse seeker, when tracking in angle two unresolved sources, have been applied to the case where the two sources may be either both passive, both active, or one passive and the other active. The theoretical results for four particular cases of two-source targets are derived to illustrate the effect on the average angular response of the shape of the sum pattern and of the statistical properties and magnitude and separation of the two sources. The theoretical results are verified with the results of digital computer simulation.     

Improved multi-target tracking in clutter by PDA smoothing

An algorithm is presented for the recursive tracking of multiple targets in cluttered environment by making use of the joint probabilistic data association fixed-lag smoothing (JPDAS) techniques. It is shown that a significant improvement in the accuracy of track estimation of both nonmaneuvering and maneuvering targets may be achieved by introducing a time lag of one or two sampling periods between the instants of estimation and latest measurement. Results of simulation experiments for a radar tracking problem that demonstrate the effects of fixed-lag smoothing are also presented     

Evaluation of the state and development of aerial targets for testing contemporary and promising arms systems

The results of evaluating the state and development of aerial targets designed for testing aircraft weapon, systems of air defense and combat crew training are presented. The basic types of aerial targets are examined using as an example existing ones and problems are posed to consider the necessity of creating new types of aerial targets for extending a range of FV types being simulated. The basic characteristics of aerial targets are separated and their classification is proposed.     

Accuracy of using point targets for SAR calibration

The peak and integral methods for radiometric calibration of a synthetic aperture radar (SAR) using reference point targets are analyzed. Both calibration methods are shown to be unbiased, but the peak method requires knowledge of the equivalent rectangle system resolution which is sensitive to system focus. Exact expressions for the RMS errors of both methods are derived. It is shown that the RMS error resulting from the peak method is always smaller than or equal to that from the integral method for a well-focused system. However, for robust radiometric calibration of SAR, or when nonlinear phase errors are present, the integral method is recommended, because it does not require detailed knowledge of the impulse response and the resulting RMS error is not dependent on system focus     

Detection of Target Multiplicity Using Monopulse Quadrature Angle

The feasibility of using the indicated quadrature angle of arrival of a monopulse radar to discriminate a single target from multiple targets, separated in angle within a radar resolution cell, is investigated. The analysis is performed for steady (fixed) and Rayleigh fluctuating targets which cover a broad range of target characteristics. In both cases, the interfering signals due to noise and clutter in the sum and difference monopulse channels are assumed to be independent, zero-mean Gaussian processes. Detection and false alarm probabilities are evaluated analytically and the receiver operating characteristics are obtained for both fixed and fluctuating target cases. It is shown that multiple targets can be discriminated from a single target condition by integrating the indicated monopulse quadrature angle of arrival from several independent pulses. It is also shown that the probability of detecting multiple targets increases as the fluctuation in the target radar cross section decreases, approaching the fixed amplitude case in the limit.     

Monopulse Radar Air-ti-Ground Ranging

The use of a two-lobe monopulse radar for measuring slant range to the surface of the earth in the absence of discrete targets is analyzed. It is shown that tracking dispersion can be considered as the resultant of two components. One component is independent of range and results from the finite pulse length and gate length and the random nature of the return signals. The other component is due to receiver noise and increases as the signal-to-noise ratio decreases. The dispersion component independent of range is shown to be proportional to the pulse length and tracking gate length. The variable dispersion is shown to be proportional to the five halves power of the range and the three halves power of the cotangent of the depression angle of the antenna boresight axis. Performance calculations for a specific radar are carried out and compared with experimental data.     

Improved Three Subaperture Method for Elevation Angle Estimation

The three subaperture method is a technique for estimating the arrival angles of two targets located in the main beam of a radar. The problem of estimating the arrival angle of a target in the presence of multipath is considered, and it is shown how the accuracy of the three subaperture method can be improved by making use of the information that the amplitude of the direct ray is larger than that of the reflected ray.     

A non-Bayesian segmenting tracker for highly maneuvering targets

The segmenting track identifier (STI) is introduced as a new methodology for tracking highly maneuvering targets. This nonBayesian approach dynamically partitions a target track into a sequence of track segments, making hard estimates of when the target's maneuvering mode transitions occur, and then estimates the parameters of the target model for each segment. STI is compared with two variable structures interacting multiple model (VS-IMM) algorithms through simulations, where it is shown to have a three fold performance advantage in median absolute turn rate estimation errors, as well as better position estimation for very highly maneuvering targets. STI is also shown to outperform a Rauch-Tung-Striebel (RTS) fixed-interval smoother when estimates are retrospectively derived, and STI accurately characterize the temporal pattern of maneuvers.     

Beam Shape Loss and Surveillance Optimization for Pencil Beam Arrays

A radar in its surveillance mode requires the programming of the radar beam in fixed angular increments throughout the surveillance volume. Though radar coverage of the volume is complete, returns from possible targets differing only in angular position generally have unequal signal strengths. This is due to both beam shape and multiple beam coverage. The resulting nonuniformity in signal strength results in a loss factor termed beam shape loss (BSL). This correspondence contains the results of a valid computational procedure for determining this loss factor for the case of an electronically steerable array in a search mode. Results consist of curves showing BSL for a wide range of system parameters and for various target types. In addition, it is shown how optimum search beam locations can be determined from the BSL computations.     

基于高斯混合概率假设密度滤波的扫描型光学传感器像平面多目标跟踪算法

高斯混合概率假设密度(GM-PHD)滤波是一种基于随机有限集理论的次优贝叶斯多目标跟踪方法,本文研究了该算法在扫描型光学传感器像平面的多目标跟踪问题.针对典型的锥扫模式和推扫模式,根据其扫描特性建立目标的运动模型和测量模型.介绍高斯混合概率假设密度滤波的基本原理.针对原算法在强杂波环境中的低效率问题,借鉴传统多目标跟踪...     

On Computing the Cramer-Rao Bound for a Random Signal

The Cramer-Rao bound for estimating parameters of a random signal is obtained using a sampled data approach. A numerical example is presented to illustrate the result. In two limiting cases, it is shown that this bound converges to the well-known bounds for the point and Rayleigh targets.     

Airborne GMTI radar position bias estimation using static-rotatortargets of opportunity

In target tracking systems: using GMTI (ground moving target indicator) radars on airborne platforms, the locations of these platforms are available from GPS-based estimates. However, these estimated locations are subject to errors that are, typically, stationary autocorrelated random processes, i.e., slowly varying biases. In situations where there are no known-location targets to estimate these biases, the next best recourse is to use targets of opportunity at fixed but unknown locations. Such targets can be, e.g., static rotators (ground-based radars with rotating antenna), which yield detections in moving target indicator (MTI) radars. It is shown that these biases can be estimated in such a scenario, i.e., they meet the complete observability condition. Following this, the achievable accuracy for a generic scenario is evaluated. It is shown that accurate georegistration can be obtained even with a small number of measurements     

Effect of a Few Dominant Specular Reflectors Target Model Upon Target Detection

Some data indicate that aircraft targets viewed from certain aspects are well modeled as consisting of a few specular reflectors. The effect of a simplified form of this target model upon radar detection performance for two different waveforms has been analyzed. The signal-to-noise ratio (SNR) required for detection as a function of waveform bandwidth for a conventional-single-channel waveform and for a four-channel frequency diversity waveform is evaluated. It is shown that for either waveform there is an optimum bandwidth to minimize the SNR required for detection. In addition, the single-channel minimum is less than the four-channel minimum. The best performance occurs for the single-channel waveform when the waveform bandwidth just resolves the individual reflectors. For typical targets, this bandwidth is of the order of 35 to 75 MHz. It is also shown that only a 0.8-dB loss relative to this minimum is incurred when using a four-channel narrow bandwidth waveform.     

带失调叶片的盘片耦合系统振动特性

本文以带16个叶片的平面盘片结构作为试验件和计算模型,研究了叶片频率失调分布形式、失调幅度,失调阶次对盘片耦合系统的动力特性及受迫振动的影响。实验和计算表明这个力学模型能较全面地反映系统的特性。