Optimum Realizable Continuous Range Estimation

The ability to detect the presence or absence of a target is no longer the fundamental design criterion when the vehicle to be tracked is cooperative. In spacecraft tracking or navigation systems, for example, emphasis is placed on post-acquisition performance. Therefore, classical radar theory and design techniques are not specifically applicable. On the other hand, there are optimization techniques for extracting the tracking data from noise that are more to the point. In particular, optimum demodulation theory is directed specifically to the problem of continuously extracting data from a nonlinear modulation process. In this paper, the tracking properties of a multitone PM ranging signal are reviewed and are shown to be nearly optimum for cooperative vehicles. An optimum, but nonrealizable, maximum a posteriori (MAP) continuous estimator of range is derived for this signal. The linearized model of this receiver is the optimum nonrealizable Wiener filter for the data. Interpretation of this optimum nonrealizable estimator leads to a receiver design that is both practical and intuitively satisfying. With the aid of post-detection processing in the Wiener-Hopf sense, almost optimum performance is obtained from the resulting receiver, above threshold.     

柔性转子的优化平衡

本文提出一种柔性转子优化平衡准则—有约束的最小应变能准则,它能满足航空燃气涡轮发动机结构强度和性能一体化设计的要求。应用该准则时,平衡校正量(大小和方位)是优化参数,转子—支承系统的总应变能为目标函数;转子若干截面的振动幅值作为约束条件。选用了鲍威尔法和网格随机射线法,进行优化计算。编制了优化全过程的FORTRAN程序,并经算例和实验考核、验证。      

Optimum Signals for High-Resolution Radio Transmission Systems

This paper reports on progress in signal design that has led to improvedresolution capability in radar and communication systems without theuse of complicated signal-processing techniques.Two approaches to the problem of improving resolution capabilityare made. The first approach emphasizes the need to produce sharplypeaked autocorrelation functions. The optimum signal amplitude infrequency is specified to accomplish this, and the spectral density ofthe deterministic signal is shown to satisfy a homogeneous Wiener-Hopfequation. The second approach emphasizes the need to producelow and flattened cross-correlation functions, in order to distinguishthem (since they correspond to error outputs) from the sharply peakedautocorrelation functions. With the use of stationary phase integration,a detailed method for producing any desired cross-correlationamplitude is presented. In particular, the techniques necessary to producesinusoidally modulated cross-correlation functions are discussed.These tools are applied to a realistic N-signal processing system,and the resulting optimum signals are shown to be amplitude-modulatedchirped sinusoids. Detailed examples for physically justifiablesystem parameters are included.     

Doppler ambiguity resolution using multiple PRF

An algorithm for velocity ambiguity resolution in coherent pulsed Doppler radar using multiple pulse repetition frequencies (PRF) is presented. It relies on the choice of particular values for the PRFs. The folded frequency of the target signal is obtained by averaging the folded frequency estimates for each PRF, and a quasi maximum likelihood criterion is maximized for ambiguity order estimation. The fast implementation of this nonambiguous estimation procedure is based on the fast Fourier transform (FFT), The proposed waveform allows full exploitation of any (even) number of PRFs, which appears to be important for estimation improvement. The effects of the waveform parameters and the folded frequency estimation variance on the performance of the ambiguity order estimation procedure are evaluated theoretically and through computer simulations. Mean square error (MSE) curves are given to assess the Doppler frequency estimation accuracy. Finally, the new method is compared with a classical technique and the implementation of the algorithm in a clutter environment is addressed.     

Simplified Optimum Modulation Indices

The design of a narrowband, phase-modulated, multisubcarrier, phase-coherent, space-communication system requires that the subcarrier modulation indices be kept within close tolerance limits. This need arises since the modulation indices directly affect the division of power among the carrier and subcarriers. If the system is not designed in an optimum manner to handle large tolerance variation, the system performance may degrade sharply in an adverse environment. A universal graphical technique?modulation loss contours?is developed as a design tool for the ?optimum? selection of modulation indices. The technique is novel in that it yields solutions directly from the universal curves and does not require the drawing of additional curves. Two criteria of optimization are considered, simultaneous thresholding and minimal sensitivity. The minimally sensitive case is considered as weighted simultaneous thresholding and is solved by the aid of a graphical algorithm. The technique is applicable to k subcarriers (sinusoidal and/or square wave), considering three subcarriers at a time-two subcarriers as direct variables and the third as a parameter?all other subcarriers remaining constant. Previous techniques required trial and error methods, drawing of curves, or computerized search techniques to arrive at the proper modulation indices and maximum tolerance bands. This method allows a quick solution to the tolerance problem and optimum selection of modulation indices, facilitating the design and/or analysis of narrowband PM systems.     

高效亚音轴流压气机级几何参数最佳选择

将亚音速轴流压气机级的设计问题表述为气动力学损失和重量为极小化、压气机喘振边界极大化的多目标非线性数学规划问题。求优中考虑了多种气动与机械约束条件。介绍了压气机级性能估算的模型, 给出了最大效率、最小重量、最大喘振边界以及效率、重量、喘振边界三者权衡最优条件下的算例。此方法可拓广用于多级轴流压气机中。      

Linear Minimum Variance Estimation with Complex Phase Errors

The linear minimum variance estimator of a random signal, received multiplied by a complex Gaussian phase error and added to random noise, is investigated. The results apply to the propagation of images through the turbulent atmosphere, fading channels, and synthetic-aperture radar. Among others, a result is that the multiplicative error can be replaced by an additive error, usually white. The best signal modulation is found in two important special cases.     

Ambiguity Resolution in Interferometry

A comprehensive theory of interferometry from a system viewpoint with particular emphasis on the ambiguity resolution problem is developed. The derived error equations include contributions from all system uncertainties, i.e., phase measurement, frequency, and element phase center position errors in three dimensions. The direction-of-arrival errors are inversely proportional to the interferometer baseline and it is customary to make the baseline large enough to meet the accuracy requirements. A system with a baseline greater than a half-wavelength results in the well known direction-of-arrival ambiguity problem with the addition of a third element to each baseline being a common method for resolving the ambiguity. It is shown that contrary to previous thinking there are many equally optimal positions for adding the third element to resolve the ambiguity. In addition, it is shown how the measurement made to resolve the ambiguity can also be applied to increase the accuracy of the angle-of-arrival measurement. A central result is the derivation of expressions specifying the probability of correct resolution of ambiguities as a function of system parameters and system errors. Moreover the concept of an acceptance criterion designed to reduce processing of erroneous measurements is developed. Narrowing the criterion reduces the percentage of data accepted for processing, but increases the probability of correct ambiguity resolution. This is analogous to the relationship between the probability of detection and the probability of false alarm in radar theory.     

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.     

Weight effects on the periodic ambiguity function

CW radar signals and processors are discussed. The use of the periodic ambiguity function (PAF) to analyze the delay-Doppler performance of CW signals and their corresponding correlation receivers, is extended to include weight function effects. This work provides tools which can predict the delay-Doppler response of almost any phase-coded CW radar. Examples demonstrate that a combination of CW signals having perfect periodic autocorrelation, a matched reference signal with a large number of modulation periods and a smooth weight function, can create a delay-Doppler response with extremely low sidelobes, strongly resembling the response of a coherent pulse train     

A Logarithmic Frequency Allocation Algorithm for Wideband Discrete Frequency Pulse Trains

It is shown that signal waveforms utilizing discrete frequency modulation (DFM) which are generated using a narrowband or frequency shift algorithm have ambiguity sidelobe distortion which is caused by the approximation of time compression by frequency shift. A logarithmic frequency allocation algorithm is presented which couches the signal design problem in terms of band and step ratios, rather than in terms of bandwidth and frequency steps, and is consistent with the wideband formulation of the ambiguity function. The algorithm makes use of the same basic code generating sequence used for narrowband frequency allocation, but the resulting signal will have invariant ambiguity sidelobe positions for any receiver realization in the delay-time compression plane.     

Optimum Signal and Filter Design in Underwater Acoustic Echo Ranging Systems

Optimization of the filter, the signal, and the signal and filter jointly are studied in the sonar environment under noise and reverberation limited conditions. The maximization of the receiver output signal-to-interference ratio is used as a performance criterion with unit energy constraint on both signal and filter. In the filter design problem, the optimum filter function is the solution of a linear integral equation. The kernel of the integral equation is a function of the target and medium scattering functions and the reverberation distribution. In the signal design problem, a similar type of integral equation is obtained as in the filter optimization problem. In the joint signal and filter design problem, it is shown that the optimum signal and filter functions are the solutions to a pair of linear integral equations with the largest (SIR)O. Several examples are investigated for different mediums and reverberation distributions with the finite matrix approximation method. An interative technique is used to compute the joint optimization of signal and filter.     

Clutter Suppression by Complex Weighting of Coherent Pulse Trains

Uniform coherent pulse trains offer a practical solution to the problem of designing a radar signal possessing both high range and range-rate resolution. The Doppler sensitivity provides some rejection of off-Doppler (clutter) returns in the matched filter receiver. This paper considers the use of a processor in which members of the received pulse train are selectively weighted in amplitude and phase to improve clutter suppression. The techniques described are particularly suitable for rejecting interference entering the processor through ambiguous responses (range sidelobes) of the signal. The complex weights which are derived are optimum in the sense that they produce the maximum clutter suppression for a given detection efficiency. In determining these weights, it is assumed that the distribution of clutter in range and range rate relative to targets of interest is known. Thus, clutter suppression is achieved by reducing the sidelobe levels in specified regions of the receiver response. These techniques are directly applicable to array antennas; the analogous antenna problem would be to reduce sidelobe levels in a particular sector while preserving gain. Complex weighting is most successful when the clutter is limited in both range and velocity.     

Improved target classification using optimum polarimetric SARsignatures

We present a new method for automatic target/object classification by using the optimum polarimetric radar signatures of the targets/objects of interest. The state-of-the-art in radar target recognition is based mostly either on the use of single polarimetric pairs or on the four preset pairs of orthogonal polarimetric signatures. Due to these limitations, polarimetric radar processing has been fruitful only in the area of noise suppression and target detection. The use of target separability criteria for the optimal selection of radar signal state of polarizations is addressed here. The polarization scattering matrix is used for the derivation of target signatures at arbitrary transmit and receive polarization states (arbitrary polarization inclination angles and ellipticity angles). Then, an optimization criterion that minimizes the within-class distance and maximizes the between-class metrics is used for the derivation of optimum sets of polarimetric states. The results of the application of this approach on real synthetic aperture radar (SAR) data of military vehicles are obtained. The results show that noticeable improvements in target separability and consequently target classification can be achieved by the use of the optimum over nonoptimum signatures     

Radar Altimeter Optimization for Geodesy Over the Sea

The optimum processor and its accuracy limit for radar altimetry for geodetic use over the sea are studied with a model accounting for random surface reflectivity, sea height variation, additive noise, and pointing errors, and allowing for arbitrary antenna patterns, signal modulations, and other system parameters. The ?threshold? case solution (which can have any specified accuracy) dictates a signal modulation bandwidth just shy of resolving the sea height variation and/or illuminated sea area (as scaled into time delay and ?smeared? by pointing errors). For such a modulation a relatively complete solution is obtained. These results are used to determine practical radar altimeter designs, additionally accounting for antenna size, stability, and peak power restraints. Conditions allowing neglecting of limiting or complicating effects due to temporally varying reflectivity, sea height, and vehicle position are given and shown to be satisfied for a typical satellite.     

Monopulse Radar Angle Tracking Accuracy with Sum Channel Limiting

The variance of angle tracking error is found for an amplitude-comparison form of monopulse radar when the sum channel contains a limiter prior to the angle error detector. The error expression is valid for any shape of transmitted pulse and any duration of range tracking gate but does assume matched filters in signal processing channels. The procedures used are rigorous and an example of results is worked out for the special case of a rectangular transmitted pulse envelope. It is shown, for rectangular pulses, that achievable angle tracking error variance with sum channel limiting is not more than 2.22 dB larger than the theoretical minimum for any processor and not more than 1.29 dB larger than a similar signal processor that uses a "linear" angle error detector. Results apply for large single-pulse signal-to-noise ratio.     

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.     

复合材料翼面结构综合优化设计技术

概要介绍了复合材料翼面结构在静力、振动、位移、舵面效率、发散速度、颤振、尺寸限制等多种约束条件下的最小重量设计技术。对优化过程中遇到的复合材料的静强度准则、均衡约束、动态上限等问题提出了相应的解决方法。用基于该技术和方法而编制出的综合设计程序系统对一个三角机翼复合材料结构进行了综合优化设计研究,在满足许用应变、尺寸限、均衡、颤振速度等约束条件下,经6次迭代得到了最佳的铺层设计结果。该机翼全尺寸静强度、耐久性/损伤容限及共振试验结果表明：理论计算与试验符合;复合材料构件中的最大应变小于许用应变约束限;按许用应变设计出的复合材料翼面蒙皮构件可满足耐久性/损伤容限要求;颤振速度比同状态金属机翼提高23%;减重效率为20%.     

Radar/Sonar Signal Design for Bounded Doppler Shifts

In many detection and estimation problems, Doppler frequency shifts are bounded. For clutter or multipath that is uniformly distributed in range and symmetrically distributed in Doppler shift relative to the signal, detectability of a point target or a communication signal is improved by minimizing the weighted volume of the magnitude-squared autoambiguity function. When clutter Doppler shifts are bounded, this volume is in a strip containing the range axis on the range-Doppler plane. For scattering function estimation, e.g., for weather radar, Doppler flow meters, and distributed target classifiers, it is again relevant to minimize ambiguity volume in a strip. Strip volume is minimized by using a pulse train, but such a signal has unacceptably large range sidelobes for most applications. Other waveforms that have relatively small sidelobe level within a strip on the range-Doppler plane, as well as small ambiguity volume in the strip, are obtained. The waveforms are composed of pulse pairs that are phase modulated with Golay complementary codes.     

一种步进频率信号认知雷达波形优化设计方法

认知雷达常用于完成探测、跟踪、成像及识别等多重任务,为提高其综合性能,需兼顾多方面因素研究其波形优化设计问题。基于此,提出一种基于压缩感知（CS）RIPless准则的步进频率信号认知雷达波形优化设计方法。首先,建立了目标回波信号稀疏模型,分析了其与发射信号模糊函数之间的关系。其次,根据模型中观测矩阵的构造,基于RIPless准则,将波形设计问题转化为概率分布的互相干参数及其协方差矩阵的条件数的优化问题,从而通过自适应寻优算法,获得优化的步进频率信号脉冲重复时间间隔序列和子脉冲频率序列。相较于传统方法,所提方法在信号发射与接收之间形成了信息实时反馈和信号优化重构的闭环,在高概率准确重构目标径向一维距离像的同时,也实现了发射信号模糊函数的优化。最后,仿真计算验证了所提方法的有效性。