Signal Processors and Accuracy of Three-Beam Monopulse Tracking Radar

The problem of implementing a monopulse tracking radar is considered when three beams are used rather than the customary four. Signal processors are developed for both amplitude and phase comparison radar cases and the functional form is given for the general case (a combination or hybrid case). Accuracy is investigated by applying the Cramer-Rao inequality. General results are given for the maximum theoretical accuracy of estimating target amplitude, phase, and position angles when the radar is of the amplitude comparison type. Equations sufficient for obtaining accuracies in the phase comparison and combination cases are included.     

基于高度分集的两波束米波雷达测高方法及其应用

米波雷达的波束较宽、由于地面反射引起波瓣分裂,通常只能估高而不能用来测高.针对这一难题本文提出一种基于高度分集的两波束米波雷达测高方法.该方法采用高度不同的两个天线,利用波瓣分裂情况及相互相位关系来测量目标高度.文章分析了此方法测高的精度及影响精度的一些因素.本测高方法已应用于某型雷达信号处理机中,并取得良好效果.     

Radar Partial Coherence Theory: An Introduction

The nature of physical phenomena is such that scattering from portions of an object, a number of objects, or clutter, is not completely unrelated; the underlying environment causes some degree of order in the phenomenon. Radar partial coherence theory describes a structure for the general target, or clutter, and its relationship to radar cross section, waveform coding, and the radar output signal. The clutter ambiguity function is introduced for extended bodies and embraces the (Woodward) ambiguity function for a point target. Due to nonlinear effects caused by partial coherence within the general target, radar signals and targets are formulated in terms of mutual coherence functions. The basic quantities describing the radar output are 1) the radar mutual coherence function (formulated in terms of the radar waveform) and 2) the target mutual coherence function which depends upon target properties, physical environment, and viewing aspect. Random noise (independent point scatterers) and partially coherent portions of reflecting bodies are made accountable in the theory. Partial coherence effects are treated as patches of reflected energy: self-coherent energy patches plus mutually coherent energy among the patches.     

Target Track Pulse Scheduling

The problem of scheduling radar tracking pulses in a dense target environment where the position estimation error must be constrained to avoid false return with track correlations is considered. The problem is to schedule n fixed energy pulses such that the rangerate error is minimized at some final time subject to the constraint that the position error will be smaller than some value for the whole time interval. For a fixed time interval, the problem of finding the minimum number of radar measurements required to satisfy the position estimation error constraint is solved. A closed-form solution for the optimum schedule is given in the case where the number of pulses is equal to the minimum number of pulses. For cases where one extra pulse is available, a solution method is described and an algorithm is derived.     

Radar Detection of Correlated Targets in Clutter

This paper provides general models of radar echoes from a target. The rationale of the approach is to consider the echoes as the output of a linear dynamic system driven by white Gaussian noise (WGN). Two models can be conceived to generate N target returns: samples generated as a batch, or sequentially generated one by one. The models allow the accommodation of any correlation between pulses and nonstationary behavior of the target. The problem of deriving the optimum receiver structure is next considered. The theory of "estimator-correlator" receiver is applied to the case of a Gaussian-distributed time-correlated target embedded in clutter and thermal noise. Two equivalent detection schemes are obtained (i. e., the batch detector and the recursive detector) which are related to the above mentioned procedures of generating radar echoes. A combined analytic-numeric method has been conceived to obtain a set of original detection curves related to operational cases of interest. Finally, an adaptive implementation of the proposed processor is suggested, especially with reference to the problem of on-line estimation of the clutter covariance matrix and of the CFAR threshold. In both cases detection loss due to adaptation has been evaluated by means of a Monte Carlo simulation approach. In summary, the original contributions of the paper lie in the mathematical formulation of a powerful model for radar echoes and in the derivation of a large set of detection curves.     

Adaptive polarimetric target detection with coherent radar. I.Detection against Gaussian background

The derivation of a completely adaptive polarimetric coherent scheme to detect a radar target against a Gaussian background is presented. A previously proposed Generalized Likelihood Ratio Test (GLRT) polarimetric detector is extended to the case of a general number of channels; this exploits the polarimetric characteristics of the received radar echoes to improve the detection performance. Together with the fully adaptive scheme, a model-based detector is derived that has a lower estimation loss. A complete theoretical expression is derived for the detection performance of both proposed polarimetric detectors. They are shown to have Constant False Alarm Rate (CFAR) when operating against Gaussian clutter, but to be sensitive to deviations from the Gaussian statistic. The application to recorded radar data demonstrates the performance improvement achievable in practice     

Update with out-of-sequence measurements in tracking: exact solution

In target tracking systems measurements are typically collected in "scans" or "frames" and then they are transmitted to a processing center. In multisensor tracking systems that operate in a centralized manner, there are usually different time delays in transmitting the scans or frames from the various sensors to the center. This can lead to situations where measurements from the same target arrive out of sequence. Such "out-of-sequence" measurement (OOSM) arrivals can occur even in the absence of scan/frame communication time delays. The resulting "negative-time measurement update" problem, which is quite common in real multisensor systems, was solved previously only approximately in the literature. The exact state update equation for such a problem is presented. The optimal and two suboptimal algorithms are compared on a number of realistic examples, including a GMTI (ground moving target indicator) radar case.     

A branch-and-bound algorithm applied to optimal radar search pattern

In the article, the radar acquisition problem, e.g. the determination of a directional energy allocation sequence, is studied. The radar search pattern goal is the detection of a moving target whose initial location is approximately known. We have turned towards the general search theory where the observer allocates indivisible search efforts while the target presence probability spreads due to its dynamics. A few years ago, a Branch and Bound algorithm was proposed to determine the optimal sequence for a conditionally deterministic target. This operational research algorithm supposes a negative exponential detection function and a one over N detection logic, meaning that the target is declared detected if it has been detected once over a horizon of N looks. We have applied it to a narrow-beam tracking radar attempting to acquire a ballistic target. Non-trivial search patterns, such as expanding-contracting spirals, are obtained.     

On the Accuracy And Resolution of Radar Signals

Information matrices are derived for estimates of the range parameters of moving targets as obtained by combining a priori information (if available) with reflected radar signals observed in the presence of additive white Gaussian noise. The inverse of the information matrix provides a lower bound on the covariance matrix of any unbiased parameter estimates. This bound can be approached with a high signal-to-noise ratio and optimum data processing (matched filters). Arbitrary frequency modulation, amplitude modulation, and target motion as well as various assumptions on processing the RF phase are considered. The multiple-target case makes possible investigation of a signal's resolution ability, as well as its accuracy potentials. Results for a carrier frequency much greater than the effective signal bandwidth are obtained as a special case. A main purpose of the paper is the reduction of the original radar problem to a linear model which is equivalent in the sense of having the same information matrix. These models provide valuable insight into the relative effects of multiple targets, choice of modulation, a priori information, and assumptions regarding RF phase and bandwidth. The linear equivalent model also leads to a valuable computational algorithm for investigations using digital or hybrid computers. The various special cases of interest are obtained by simple modifications of the general case, and thus the algorithm can provide a very versatile tool for evaluating and designing radar signals.     

Classification of radar targets using synthetic neural networks

Radar target classification performance of neural networks is evaluated. Time-domain and frequency-domain target features are considered. The sensitivity of the neural network algorithm to changes in network topology and training noise level is examined. The problem of classifying radar targets at unknown aspect angles is considered. The performance of the neural network algorithms is compared with that of decision-theoretic classifiers. Neural networks can be effectively used as radar target classification algorithms with an expected performance within 10 dB (worst case) of the optimum classifier     

FM Laser Noise Effects on Optical Doppler Radar Systems

A detailed analytical study is made of the effect of FM noise on a laser carrier frequency which is used in a Doppler radar. Both long-term drift and short-term FM noise are considered. The case of high modulation index of the noise is permitted by the theory. Forward as well as slanted beams are examined. Curves have been calculated for each case to allow rapid estimates of the bandwidth requirements to accomodate the laser noise. This, in turn, will give the resolution limit of the radar caused by that noise. A summary of the results is given.     

Detection of moving targets in wideband SAR

A likelihood ratio is proposed for moving target detection in a wideband (WB) synthetic aperture radar (SAR) system. WB is defined here as any systems having a large fractional bandwidth, i.e., an ultra wide frequency band combined with a wide antenna beam. The developed method combines time-domain fast backprojection SAR processing methods with moving target detection using space-time processing. The proposed method reduces computational load when sets of relative speeds can be tested using the same clutter-suppressed subaperture beams. The proposed method is tested on narrowband radar data.     

Linear FM signal parameter estimation from discrete-timeobservations

The authors consider the problem of estimating the parameters of a complex linear FM signal from a finite number of noisy discrete-time observations. An estimation algorithm is proposed, and its asymptotic (large sample) performance is analyzed. The algorithm is computationally simple, consisting of two fast Fourier transforms (FFTs) accompanied by one-dimensional searches for maxima. The variance of the estimates is shown to be close to the Cramer-Rao lower bound when the signal-to-noise ratio is 0 dB and above. The authors applied the algorithm to the problem of estimating the kinematic parameters of an accelerating target by pulse-Doppler radar. A representative test case was used to exhibit the usefulness of the algorithm for this problem, and to verify the analytical results by Monte Carlo simulations     

Difference beam aided target detection in monopulse radar

The classical detection step in a monopulse radar system is based on the sum beam only,the performance of which is not optimal when target is not at the beam center. Target detection aided by the difference beam can improve the performance at this case. However, the existing difference beam aided target detectors have the problem of performance deterioration at the beam center, which has limited their application in real systems. To solve this problem, two detectors are proposed in this paper. Assuming the monopulse ratio is known, a generalized likelihood ratio test(GLRT) detector is derived, which can be used when targeting information on target direction is available. A practical dual-stage detector is proposed for the case that the monopulse ratio is unknown. Simulation results show that performances of the proposed detectors are superior to that of the classical detector.     

Radar target classification using doppler signatures of human locomotion models

The problem of target classification for ground surveillance Doppler radars is addressed. Two sources of knowledge are presented and incorporated within the classification algorithms: 1) statistical knowledge on radar target echo features, and 2) physical knowledge, represented via the locomotion models for different targets. The statistical knowledge is represented by distribution models whose parameters are estimated using a collected database. The physical knowledge is represented by target locomotion and radar measurements models. Various concepts to incorporate these sources of knowledge are presented. These concepts are tested using real data of radar echo records, which include three target classes: one person, two persons and vehicle. A combined approach, which implements both statistical and physical prior knowledge provides the best classification performance, and it achieves a classification rate of 99% in the three-class problem in high signal-to-noise conditions.     

Beam resource scheduling for a VHF-MIMO radar network in low-angle tracking

The low-angle tracking in multipath interference is a challenging problem for the Very High Frequency (VHF) radar. The colocated Multi-Input Multi-Output (MIMO) technique can remedy such a defect. In this paper, a Joint Beam-Target Assignment and Power Allocation (JBTAPA) strategy is proposed for the VHF-MIMO radar network tracking low-angle targets. The core of the JBTAPA strategy is to improve the worst tracking accuracy among multiple targets by assigning appropriate beams to targets and allocating the power resource in each beam using the feedback information in the tracking cycle. Taking into account the transmit multipath and receive multipath, we derive the Cramér-Rao Lower Bound (CRLB) on angle estimate, which is then incorporated in the Predicted Conditional CRLB (PC-CRLB). A more accurate and consistent lower bound is provided as the optimization metric since the PC-CRLB is based on the most recently realized measurements. A two-stage-based technique is proposed to solve the JBTAPA problem, which is originally NP-hard. Simulation results verify the effectiveness and efficiency of the proposed method. The results also imply that the target reflectivity plays one of the important roles in resource allocation.     

Multiple model particle flter track-before-detect for range ambiguous radar

The middle pulse repetition frequency（MPRF）and high pulse repetition frequency（HPRF）modes are widely adopted in airborne pulse Doppler（PD）radar systems,which results in the problem that the range measurement of targets is ambiguous.The existing data processing based range ambiguity resolving methods work well on the condition that the signal-to-noise ratio（SNR）is high enough.In this paper,a multiple model particle flter（MMPF）based track-beforedetect（TBD）method is proposed to address the problem of target detection and tracking with range ambiguous radar in low-SNR environment.By introducing a discrete variable that denotes whether a target is present or not and the discrete pulse interval number（PIN）as components of the target state vector,and modeling the incremental variable of the PIN as a three-state Markov chain,the proposed algorithm converts the problem of range ambiguity resolving into a hybrid state fltering problem.At last,the hybrid fltering problem is implemented by a MMPF-based TBD method in the Bayesian framework.Simulation results demonstrate that the proposed Bayesian approach can estimate target state as well as the PIN simultaneously,and succeeds in detecting and tracking weak targets with the range ambiguous radar.Simulation results also show that the performance of the proposed method is superior to that of the multiple hypothesis（MH）method in low-SNR environment.     

一种基于u检验的空海目标分类方法

阐述了对于机载雷达,测高精度不高,特别是对远距离目标的测高精度更差,因而利用机载雷达提供的高度信息进行空海目标分类存在很大的不确定性。为了能有效地利用目标高度信息进行空海目标分类,把空海目标分类问题看成是一个u检验问题。首先,给出了用于空海目标分类的判别函数;然后,给出了一种决策规则,并推导出决策门限的计算公式和空中目标误判为海面目标的概率的计算公式;最后,通过仿真表明该算法的简易性和有效性。     

A Real-Time Statistical Radar Target Model

Radar glint arises from the spatial phase perturbations of the radar signal echoed from a complex target. The glint phenomenon is closely related to the target radar cross section (RCS). This relationship plays a significant part in modern missile seeker signal processing. We present a statistical glint/RCS target model for realtime simulation of target signatures. Particular emphasis is placed upon the modeling and simulation of the appropriate glint/RCS statistical dependency. The fundamental approximation of locating uniformly distributed scatterers around the instantaneous radar centroid employed in the Delano-Gubonin [1, 2, 3] model is removed. A key result which follows from this representation is that the mean glint estimator is unbiased. This enables the estimation of model parameters from the first-order glint and RCS statistics which can easily be computed from measured data. A method of estimating model parameters is presented, and the results are applied to data from a typical combat aircraft target. It is shown that the Delano-Gubonin results are a special case of the results presented here. The 14.6 percent probability of glint falling beyond the target extent as derived by Delano [1] is not true in general. It is further shown that glint and RCS are uncorrelated but are statistically dependent. A Monte-Carlo simulation is performed to verify the assumptions made and to demonstrate the feasibility of the working models.