Optimum Windows for Image Registration

Two-dimensional cross-correlation techniques are applied to the problem of image registration under the assumption of small geometric distortion. Optimum window functions are derived for two performance measures of interest: peak-to-sidelobe ratio and mean-square registration error. The latter is examined in terms of the contribution caused by noise and the contribution caused by geometric distortion. A generalized Lagrange multiplier approach is used to derive approximate solutions assuming random images. The case of Gaussian autocorrelation functions is examined in detail. Results of applying the theoretically derived window functions to real data are presented, showing significant improvement in correlator performance.     

Optimum Filters for Image Registration

Two-dimensional cross-correlation techniques are applied to the problem of image registration under the assumption of small geometric distortion. Optimum filter functions for use with arbitrary window functions are derived for two performance measures of interest: peak-to-sidelobe ratio, and mean- square registration error; the latter is examined in terms of the contribution due to distortion and the contribution due to noise. A generalized Lagrange multiplier approach is used to derive at least approximate ate solutions to the case where the images are modeled as random processes and to the case where the images are assumed to be deterministic.     

On Transient and Periodic Signal Detection in Time-Varying Noise Power

Detectability of periodic and synchronously recurrent transient signals in a noisy environment in which the noise power is time varying is investigated. For at least one noise model, it is shown that the basic nonlinearity of the optimum detector is a limiter. Performance of this optimum detector is compared with analog cross-correlation and clipper cross-correlation (CCC) detectors. It is shown that the CCC performs nearly optimally, especially at low signal-to-noise ratios, and that its performance is significantly better than that of the analog cross correlator.     

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.     

Bayesian Quickest Signal Detection in a Discrete-Time Observation

This paper deals with the problem of quickest detection of a signal in discrete-time observations where the noise is not necessarily additive. By introducing a new cost function, penalizing the decision delay, in addition to penalizing wrong decisions as in the classical case, a global risk function is derived for use in a Bayesian framework. The minimization of the average risk leads to the optimum Bayesian decision regions, giving the structure of the optimum receiver. Some simplifications for elementary costs and some applications are investigated. The optimum receiver is shown to be a parallel bank of classical optimum filters, each one matched to a particular delay of the signal to be detected. Our approach is shown to apply to the detection of certain changes in a stochastic process.     

Transmit Beamforming for MIMO Radar Systems using Signal Cross-Correlation

Proposed next-generation radar systems will have multiple transmit apertures with complete flexibility in the choice of the signals transmitted at each aperture. Here we propose the use of multiple signals with arbitrary cross-correlation matrix R, and show that R can be chosen to achieve or approximate a desired spatial transmit beampattern. Two specific problems are addressed. The first is the constrained optimization problem of finding the value of R which causes the true transmit beampattern to be close in some sense to a desired beampattern. This is approached using convex optimization techniques. The second is the problem of designing multiple constant-modulus waveforms with given cross-correlation R. The use of coded binary phase shift keyed (BPSK) waveforms is considered. A method for finding the code sequences based on random signaling with a structured correlation matrix is proposed. It is also shown that by restricting the class of admissible waveforms one reduces the set of possible signal correlation matrices.     

Optimum Signals for Radar

The research reported herein deals with the general problem of the selection of radar waveforms. The investigation is specifically concerned with the synthesis of radar signals which are optimum in the sense that they are characterized by ambiguity surfaces minimized over certain predetermined regions of the ambiguity plane. The weighted ambiguity surface is utilized as the weighted error criterion. This error criterion is mathematically tractable and pertinent to radar system performance but is not unduly restrictive as some orientation parameters are left unspecified for subsequent cost or penalty function analysis. The signal optimization is approached by variational techniques augmented by equality and inequality constraints, for example, limiting the amount of bandwidth or frequency modulation to be less than some system requirement. Several examples are presented demonstrating the optimization techniques and providing a minimum error for the stated problem. It is shown that for any given type of amplitude modulation of the radar signal, the variance or dispersion of the ambiguity surface is not decreased for any type of phase modulation added. The optimum signal for an elliptical weighting function is derived for several cases. The minimum error is shown to depend upon the constraints and the unspecified orientation parameters and, for one case, on the second moment of the signal.     

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.     

面向声源定位的改进广义互相关时延估计方法

面向以数字微机电系统(MEMS)麦克风作为声传感器的声源定位阵列,完成了前端麦克风阵列的电路设计和以现场可编程逻辑门阵列(FPGA)为核心的数据采集系统的开发,并对麦克风输出的脉冲密度调制信号进行了降采样处理.针对传统的广义互相关算法在低信噪比下时延估计误差较大的问题,提出了一种改进PHAT加权函数的方法.在同等条件下对基于不同加权函数的广义互相关算法进行了MATLAB仿真验证,实验结果表明,在低信噪比条件下该方法相较于传统的广义互相关算法,时延估计误差更小且抗噪性能更强.     

航天器DOR信号本地相关处理的建模与仿真

详述了DOR（差分单向测距）信号的本地相关处理方法。首先根据轨道预报确定先验时延模型值,利用高精度频率估算方法估计航天器DOR信号的星上发射频率,然后通过时延模型值与频率估计值构造DOR本地模型信号,再将此模型信号分别与测站接收的DOR实测信号进行互相关运算,提取相关相位,解算高精度时延观测量。推导了DOR信号本地相关处理的数学模型,通过信号仿真验证了该方法的有效性,在仅考虑系统噪声影响与轨道预报误差的条件下,仿真时延测量精度达到0.1 ns,为深空航天器精密轨道测量提供了一种可借鉴的技术方法。     

Signal Sequence Detection Given Noisy, Common Background Image Sets

The optimum processing (likelihood functional) is found for a set of M images {Zm = Sm + Y + Nm}, each the sum of a member Sm of a signal sequence {Sm}, due to an object to be detected and its parameters estimated, a sample function Nm of a noise field {Nm}, and a sample function Y of a common background field {Y}. The noise fields {{Nm}} are independent, zero mean, white Gaussian fields, all independent of the background field {Y}; the latter is assumed to be either 1} completely unknown or of known mean and covariance functions with 2) a certain fluctuation property or 3) Gaussian. Three equivalent forms of the optimum processing are found: 1) a summation of generalized matched filterings of the images, 2) a summation of matched filtering of certain generalized differences of the images, 3) a summation of ?estimator-correlator? type filterings. The detection performance and optimum signal/image selection under the Neyman-Pearson criterion is given and the singularity of the ({{Nm = O}} and M > 1) case noted. It is shown that optimum processor and signal design can completely eliminate any effect of the background on detectability (M > 1). The Cramer-Rao lower bound for the signal parameter estimates meansquare error is given along with an example; optimum signal/image selection in the single parameter case is discussed.     

Comparison of Bit Synchronization Schemes Using AM and Summed Clocks

This paper considers bit synchronization through the use of a separate clock signal which is either amplitude modulated onto or summed with the data signal. For continuous data transmission, such schemes are known to be inferior, in the sense of efficient use of power, to schemes which derive synchronization directly from the data signal. However, these techniques have application in burst systems such as spacecraft command systems, and in systems where receiver simplicity is more important than power conservation. For systems in which the composite data-clock signal subsequently modulates an RF carrier, it is shown that the summed clock signal performs slightly better than the AM clock signal, and that for both signal types, the optimum allocation of power between data and clock is approximately 9:1.     

An efficient algorithm for multisensor track fusion

An efficient algorithm for track-to-track fusion by incorporating cross-covariance between tracks created by dissimilar sensors is described. An analytical solution of this problem is complicated if cross-correlation between sensors tracking the same target is taken into account. An explicit solution of the cross-covariance matrix at steady state is derived in terms of an integral. It is shown that solution of this integral involves inversion of a matrix whose elements are functions of parameters of individual trackers. Structure of this matrix is analyzed. An efficient analytical solution for inversion of this matrix is obtained. For fusion of similar sensors, it is shown that this matrix is reduced to the Routh-Hurwitz matrix which arises in the study of steady state stability of linear systems. Numerical results showing the amount of reduction of fused track covariance by taking into account the effects of cross-correlation between candidate tracks for fusion is also presented     

几何规划在飞机总体设计中的应用

系统地讨论了代数多项式的算术－ 几何均值定理,并对原型几何规划理论作出了简明的推导与分析。提出了具有缩并迭代特性的几何规划求解理论和编程步骤。还用２ 个工程设计的优化求解算例来说明这种缩并迭代几何规划优化求解特点和优点。例１ 显示了几何规划的工程实用性和简易性;例２ 通过轻型飞机总体方案参数优化,说明所提出的优化方法,可随设计人员思路的变动而得到及时地相适应。     

Cross-correlation properties of algebraically constructed Costasarrays

The problem of determining the cross-correlation properties of signals based on algebraically constructed Costas arrays is addressed by examining the discrete cross-correlation of the algebraically constructed Costas arrays for a given construction and dimension. Finding two arrays that minimally correlate implies that the signals based on these arrays also minimally correlate. The properties of finite fields are reviewed, and the major algebraic constructions for Costas arrays are presented, i.e. the Welch construction and the Golomb construction. The discrete cross-correlation properties of the Costas arrays are derived for arrays of the same dimension derived from the same construction. The use of Costas arrays in the signal design problem is discussed, and examples are given to show the cross-correlation of the signals based on the algebraically constructed arrays     

Detectability of signals in Laplace noise

Closed-form expressions for the false-alarm and detection probabilities attained by the optimum and the linear detectors of a positive signal in n independent samples of noise having a bilateral exponential or Laplace distribution require lengthy computation when n is large, and those for the optimum detector suffer from round-off error because their terms alternate in sign. It is shown how the method of saddlepoint integration can be conveniently applied to compute these probabilities, and numerical comparisons of the accuracies of the methods are presented. The relative efficiency of the two detectors is calculated as a function of n and found to approach the asymptotic value of 2 very slowly     

Time-Frequency HOP Signals Part I: Coding Based upon the Theory of Linear Congruences

Time-frequency hop codes are developed based upon the theory of linear congruences. These codes can be used for multiuser radar and asynchronous spread spectrum communications systems. A uniform upper bound is placed on the cross-correlation function between any two elements of the code set. The upper bound is minimized by choice of time-bandwidth product and is shown to diminish as 2/N, where N is the number of elements in the code set. The size and position of spurious peaks in the autocorrelation functions are discussed. The results are extended to narrowband ambiguity functions.     

Track-to-track fusion with dissimilar sensors

An analysis is described of a kinematic state vector fusion algorithm when tracks are obtained from dissimilar sensors. For the sake of simplicity, it is assumed that two dissimilar sensors are equipped with nonidentical two-dimensional optimal linear Kalman filters. It is shown that the performance of such a track-to-track fusion algorithm can be improved if the cross-correlation matrix between candidate tracks is positive. This cross-correlation is introduced by noise associated with target maneuver that is common to the tracking filters in both sensors and is often neglected. An expression for the steady state cross-correlation matrix in closed form is derived and conditions for positivity of the cross-correlation matrix are obtained. The effect of positivity on performance of kinematic track-to-track fusion is also discussed     

Output Probability Density Functions for Cross Correlators Utilizing Sampling Techniques

Sampling techniques provide a practical means of obtaining cross-correlation functions. In this paper, the correlation function is described by sums of the form Z = begin{equation*}Z = Sigma^{N}_{j=1}X_{j}Y_{j}end{equation*}. A general expression is derived for the probability density function of the random variable Z under the condition that Xj and Yj are stationary, jointly Gaussian random processes with nonzero means and unit variances.