On cross-ambiguity properties of Welch-Costas arrays

We discuss cross-ambiguity properties of a specific family of Costas arrays called Welch-Costas (W-C) arrays. These properties are of interest in multiuser radar and sonar system, especially since Costas arrays are known to possess ideal auto-ambiguity functions. The theory of W-C arrays is reviewed. It is then proved that only pairs of W-C arrays can have at most two hits in their cross-ambiguity function (best possible case). The maximum number of hits in the cross-ambiguity functions of a family of W-C arrays is shown to be a function of the number of W-C arrays in the family. The upper bound on the number of hits in the cross ambiguity functions for a family of W-C arrays is also derived. Specific examples of how reducing the number of W-C arrays improves the cross-ambiguity properties are given for various types of prime numbers     

Time-frequency hop codes based upon extended quadratic congruences

Time-frequency hop codes are developed that can be used for coherent multiuser echolocation and asynchronous spread spectrum communication systems. They represent a compromise between Costas codes, which have nearly ideal autoambiguity but not so good cross-ambiguity properties, and linear congruential codes, which have nearly ideal cross-ambiguity but unattractive autoambiguity properties. Extended quadratic congruential code words are shown to have reasonably good autoambiguity and cross-ambiguity properties across the whole class of code sets considered. A uniform upper bound is placed on the entire cross-ambiguity function surface, and bounds are placed on the position and amplitude of spurious peaks in the autoambiguity function. These bounds depend on the time/bandwidth product and code length exclusively and lead naturally to a discussion of the design tradeoffs for these two parameters. Examples of typical autoambiguity and cross-ambiguity functions are given to illustrate the performance of the new codes     

Detection of polyphase pulse compression waveforms using the radon-ambiguity transform

The recently developed Radon-ambiguity transform (RAT) detects unknown linear frequency modulated (LFM) signals by computing line integrals through the origin of the signal's ambiguity function (AF) magnitude. It is shown that this method also detects the step LFM and frequency-derived polyphase pulse compression waveforms with varying performance degradation. Simulations are provided to estimate the detection loss relative to the LFM.     

Efficient dynamic programming in presence of nuisance parameters

The dynamic programming approach for maximum a posteriori (MAP) estimation of Markov sequences is frequently proposed for problems in control theory, communications, and signal processing. It is usually assumed that the observation sequence is a perfectly known function of the Markov sequence of interest, except for some additive noise with known statistics. However, often the observation is not only a function of the Markov sequence but also of a vector of unknown nuisance parameters. It is shown how the dynamic programming methodology can be extended to estimate both the nuisance parameters and the Markov sequence, using a combined maximum-likelihood and MAP framework. The technique is efficient relative to other possible solutions. The problem of detecting and tracking moving targets observed by imaging sensors is used to demonstrate the efficiency of the procedure     

Ambiguity properties of quadratic congruential coding

The ambiguity characteristics of multiple access frequency hop codes based on standard quadratic congruences are investigated in the light of results obtained for codes based on Costas arrays and extended quadratic congruences. While the autoambiguity properties are found to be very similar to those of Costa codes, i.e. nearly ideal, the cross-ambiguity properties of quadratic congruential codes are much better. These results are valid across the whole class of code sets considered, but they are obtained at some expense in the pulse compression characteristics of the codes. A uniform upper bound is placed on the entire cross-ambiguity function surface, and bounds are placed on the amplitude of spurious peaks in the autoambiguity function. These bounds depend on the time-bandwidth product and code length exclusively and lead naturally to a discussion of the design tradeoffs for these two parameters. Examples of typical autoambiguity and cross-ambiguity functions are given to illustrate the performance of quadratic congruential coding with respect to Costas coding     

FrFT-CSWSF:Estimating cross-range velocities of ground moving targets using multistatic synthetic aperture radar

Estimating cross-range velocity is a challenging task for space-borne synthetic aperture radar（SAR）, which is important for ground moving target indication（GMTI）. Because the velocity of a target is very small compared with that of the satellite, it is difficult to correctly estimate it using a conventional monostatic platform algorithm. To overcome this problem, a novel method employing multistatic SAR is presented in this letter. The proposed hybrid method, which is based on an extended space-time model（ESTIM） of the azimuth signal, has two steps： first, a set of finite impulse response（FIR） filter banks based on a fractional Fourier transform（FrFT） is used to separate multiple targets within a range gate; second, a cross-correlation spectrum weighted subspace fitting（CSWSF） algorithm is applied to each of the separated signals in order to estimate their respective parameters. As verified through computer simulation with the constellations of Cartwheel, Pendulum and Helix, this proposed time-frequency-subspace method effectively improves the estimation precision of the cross-range velocities of multiple targets.     

Moving Targets Processing in SAR Spatial Domain

This paper presents a novel technique to estimate the initial coordinates and velocity vector of moving targets, including those with velocities above the Nyquist limit, using a single synthetic aperture radar (SAR) sensor without increasing the pulse repetition frequency (PRF). The basic reasoning is that, although the returned echoes may be undersampled in the azimuth direction, their phase and amplitude are informative with respect to the moving target trajectory parameters. Therefore, the so-called blind angle ambiguity, inherent to systems using a single SAR sensor, is overcome. The proposed method samples the data in the spatial domain, along the signature curve which depends on the moving target trajectory parameters. The resulting algorithm is a highly efficient (from the computational point of view) ID matched filter. The effectiveness of the proposed scheme is illustrated using simulated SAR data and real data from the MSTAR public release data set, corresponding to a static SAR scene and a static BTR-60 with simulated motion.     

机动目标“当前”统计模型与自适应跟踪算法

本文提出机动目标“当前”统计模型的概念并建议用修正的瑞利-马尔科夫过程描述目标随机加速机动的统计特性。文中指出了在机动目标运动模型中状态（机动加速度）估值与状态噪声之间的内在联系。在此基础上提出了具有机动加速度均值及方差自适应的卡尔曼滤波算法。对一维和三维的情形进行了计算机模拟。计算结果表明,在仅对目标位置进行观测的情况下,这类自适应估值算法无论对高度机动或无机动的目标均可绘出较好的位置、速度及加速度估值。     

Directed Subspace Search ML-PDA with Application to Active Sonar Tracking

The maximum likelihood probabilistic data association (ML-PDA) tracking algorithm is effective in tracking Very Low Observable targets (i.e., very low signal-to-noise ratio (SNR) targets in a high false alarm environment). However, the computational complexity associated with obtaining the track estimate in many cases has precluded its use in real-time scenarios. Previous ML-PDA implementations used a multi-pass grid (MPG) search to find the track estimate. Two alternate methods for finding the track estimate are presented-a genetic search and a newly developed directed subspace (DSS) search algorithm. Each algorithm is tested using active sonar scenarios in which an autonomous underwater vehicle searches for and tracks a target. Within each scenario, the problem parameters are varied to illustrate the relative performance of each search technique. Both the DSS search and the genetic algorithm are shown to be an order of magnitude more computationally efficient than the MPG search, making possible real-time implementation. In addition, the DSS search is shown to be the most effective technique at tracking a target at the lowest SNR levels-reliable tracking down to 5 dB (postprocessing SNR in a resolution cell) using a 5-frame sliding window is demonstrated, this being 6 dB better than the MPG search.     

一种基于新三维随机Hough变换的航迹起始算法

针对雷达跟踪多目标时,目标点迹受杂波、噪声等因素影响,航迹起始难度大的问题,利用三维空间直线表示方法提出了一种4参数三维Hough变换算法.该算法是对传统二维Hough变换的拓展,它结合了传统的二维随机Hough变换理论,是一种新的三维随机Hough变换算法.通过该算法对理论数据和实测数据进行验证,结果表明,对于航迹区别较大的目标,该算法的航迹起始成功概率为98.5％;对于空间航迹相近的目标,该算法可成功将目标航迹从杂波中提取出来,虽然可能会出现航迹混淆,但利用目标先验信息可解决该问题,实现航迹起始.     

三维空间中目标机动加速度的估值问题

建立了描述目标在三维空间中进行切向与法向机动的非线性状态模型。目标切向与法向机动加速度的幅值表示为修正的瑞利-马尔可夫随机过程;法向加速度的方向角则假定在2π区间内具有均匀的概率密度。在仅有含噪声位置观察数据的情况下,发展了一种推广的卡尔曼滤波和自适应算法,并由此获得一种机动目标切向与法向加速度估值的直接方法。提供了某些计算结果以证实方法的有效性。     

Novel Approach for ISAR Image Cross-Range Scaling

Inverse synthetic aperture radar (ISAR) imaging systems produce electromagnetic images of targets in the range-Doppler domain. In order to rescale the image in a homogeneous range-cross range domain (meters by meters), the modulus of the target effective rotation vector must be known. Although in some cases it can be retrieved by means of ancillary data, in most cases the modulus of the target effective rotation vector must be estimated. A blind technique is proposed for estimating the modulus of the target effective rotation vector that exploits information carried by the chirp rate of scattering centres. A technique based on image segmentation, local polynomial Fourier transform (LPFT), and image contrast (IC) maximisation is used in order to extract the scattering centres and estimate their chirp rate. Simulated and real data analyses are provided to confirm the effectiveness of the proposed algorithm.     

Multifrequency Imaging of Radar Turntable Data

In recent years synthetic-aperture radars (SAR) have proven to be very useful two-dimensional imaging tools in various fields. Based on the synthetic-aperture concepts, different imaging modes are possibe with various operating characteristics. We describe a special case where circular-projection radar data are coherently processed to yield both azimuth and range resoultion. Experiments are performed using data obtained from the radar target scatter site (RAT SCAT) radar cross-section facility. Fairly good results are obtained which illustrate the versatility of coherent syntheticaperture processing of pulse-to-pulse high-range-resolution radar returns. A discrete multifrequency stepped and pulsed waveform is the basic transmitted signal from which range-Doppler images are generated. The RAT SCAT turntable facility allows interesting model targets to be illuminated from which radar images can then be computed. One such application of the processing is described.     

Multiple-Model Probability Hypothesis Density Filter for Tracking Maneuvering Targets

Tracking multiple targets with uncertain target dynamics is a difficult problem, especially with nonlinear state and/or measurement equations. With multiple targets, representing the full posterior distribution over target states is not practical. The problem becomes even more complicated when the number of targets varies, in which case the dimensionality of the state space itself becomes a discrete random variable. The probability hypothesis density (PHD) filter, which propagates only the first-order statistical moment (the PHD) of the full target posterior, has been shown to be a computationally efficient solution to multitarget tracking problems with a varying number of targets. The integral of PHD in any region of the state space gives the expected number of targets in that region. With maneuvering targets, detecting and tracking the changes in the target motion model also become important. The target dynamic model uncertainty can be resolved by assuming multiple models for possible motion modes and then combining the mode-dependent estimates in a manner similar to the one used in the interacting multiple model (IMM) estimator. This paper propose a multiple-model implementation of the PHD filter, which approximates the PHD by a set of weighted random samples propagated over time using sequential Monte Carlo (SMC) methods. The resulting filter can handle nonlinear, non-Gaussian dynamics with uncertain model parameters in multisensor-multitarget tracking scenarios. Simulation results are presented to show the effectiveness of the proposed filter over single-model PHD filters.     

一种基于径向加速度的Singer-EKF机动目标跟踪算法

针对雷达均不能提供目标加速度信息,在目标机动时会出现跟踪精度差甚至跟踪发散的问题,提出一种基于径向加速度的Singer-EKF算法。该算法在信号处理阶段利用Radon-Ambiguity变换（RAT）估计出目标的径向加速度,并通过坐标转换将其引入量测向量中,然后采用基于Singer模型的扩展卡尔曼滤波（EKF）算法实现机动目标的跟踪。仿真验证了该方法的有效性,并与传统的不带径向加速度的扩展卡尔曼滤波（EKF）方法进行了比较,结果表明该方法在径向距离、位置、加速度和速度估计精度方面都有所提高。     

PHD filters of higher order in target number

The multitarget recursive Bayes nonlinear filter is the theoretically optimal approach to multisensor-multitarget detection, tracking, and identification. For applications in which this filter is appropriate, it is likely to be tractable for only a small number of targets. In earlier papers we derived closed-form equations for an approximation of this filter based on propagation of a first-order multitarget moment called the probability hypothesis density (PHD). In a recent paper, Erdinc, Willett, and Bar-Shalom argued for the need for a PHD-type filter which remains first-order in the states of individual targets, but which is higher-order in target number. In this paper we show that this is indeed possible. We derive a closed-form cardinalized PHD (CPHD) filter, which propagates not only the PHD but also the entire probability distribution on target number.     

基于时间反转和降阶Keystone的SAR-GMTI快速聚焦方法

对合成孔径雷达（SAR）地面运动目标聚焦技术进行了研究。针对现有运动目标聚焦方法存在的问题,提出了一种基于时间反转和降阶Keystone的SAR地面运动目标检测（SAR-GMTI）快速聚焦方法。首先,根据目标的机动特性建立了3阶距离模型;其次,针对目标多普勒中心模糊引起的多普勒谱分裂现象,结合所提时间反转处理（TRP）和降阶Keystone变换处理估计出运动目标2阶参数。此后,构造2阶相位补偿函数补偿运动目标的2阶距离徙动和多普勒徙动,从而完成运动目标的聚焦。同时,所提方法没有任何参数搜索过程,降低了计算复杂度。最后,仿真实验验证了所提算法的正确性和有效性。     

Generalized Response of a Linear FM Pulse Compression Matched Filter

A pulse compression matched filter is analyzed so that the response may be computed when the pulse width, FM rate, and center frequency simultaneously differ from design conditions. Unilateral and bilateral time domain amplitude weighting for sidelobe reduction is included. A general cross-ambiguity function is defined to include these effects and some basic computed results are presented for the peak envelope response with various degrees of Hamming weighting. Computer evaluation of this cross-ambiguity function allows one to choose a combination of mismatches for signal design trade-off between resolution and detection performance. Since no restrictions are placed upon the mismatch parameters, this analysis may also be used to evaluate the filter discrimination against various interfering signals.     

Multiple moving target detection and trajectory estimation using a single SAR sensor

A novel methodology is presented for determining the velocity and location of multiple moving targets using a single strip-map synthetic aperture radar (SAR) sensor. The so-called azimuth position uncertainty problem is therefore solved. The method exploits the structure of the amplitude and phase modulations of the returned echo from a moving target in the Fourier domain. A crucial step in the whole processing scheme is a matched filtering, depending on the moving target parameters, that simultaneously accounts for range migration and compresses two-dimensional signatures into one-dimensional ones without losing moving target information. A generalized likelihood ratio test approach is adopted to detect moving targets and derive their trajectory parameters. The effectiveness of the method is illustrated with synthetic and real data covering a wide range of targets velocities and signal-to-clutter ratios (SCRs). Even in the case of parallel to platform moving target motion, the most unfavorable scenario, the proposed method yields good results for, roughly, SCR > 10 dB.     

直达与非直达环境中的多目标解耦直接定位方法

针对直达（LOS）与非直达（NLOS）环境中的定位问题,提出了一种波形已知条件下的单阵地多目标直接定位（DPD）算法。该算法针对发射时间已知和未知两种情况,利用多径信号到达角度与时延关于障碍物（或反射体）、观测站与目标位置参数的数学关系,建立了三维目标位置的最大似然（ML）函数,无需估计测量参数,避免了传统两步定位方法所需的非直达径识别与数据关联。为了克服多目标定位中的高维非线性优化问题,该算法利用独立波形信息将多目标定位解耦为对各个目标单独求解。通过对目标函数有效近似,算法在发射时间已知和未知两种情况下均仅需三维网格搜索,比相应的两步定位方法具有更低的计算量。此外,基于多径定位场景,推导了发射时间已知和未知两种情况下的位置估计克拉美罗界（CRB）。仿真结果表明：算法的定位性能能够逼近相应的克拉美罗界,比传统两步定位方法和子空间直接定位算法具有更高的定位精度。