The effect of the clutter-to-noise ratio on Doppler filterperformance

The effect of the clutter-to-noise ratio on the performance of a Doppler filter is considered. Clutter is assumed to have a power level which is unknown and varies in range. The assessment of the performance of a Doppler filter is based on the gain of the filter, which is the normalized output signal-to-interference ratio improvement at a given Doppler. The gain is generally a complex function of the statistics of the clutter. New upper and lower bounds on the gain differential between the expected design point clutter-to-noise ratio and the actual clutter-to-noise ratio are found. These bounds are independent of the clutter covariance matrix and are only a function of the unknown clutter-to-noise ratio. The bounds are valid for both Gaussian and non-Gaussian noise and for arbitrary linear filters. The upper and lower bounds differ by the theoretical coherent integration gain, 10 logN dB, where N is the number of pulses. A tighter lower bound is found for the case when the filters are matched filters. A simple exact expression is found for matched filters assuming a Gaussian Markov clutter model as the clutter spectral width approaches zero. An easily implementable adaptive procedure is given which improves performance due to the unknown clutter-to-noise ratio. This work extends a previous result, valid for the Emerson filter, that shows the effect of clutter-to-noise ratio on performance in terms of an average quantity, the improvement factor     

弹道中段目标进动周期估计的改进自相关法

自相关法可用于估计弹道中段雷达目标的进动周期,它需要预先给出进动周期的上下限。进动周期下限可能远小于真实进动周期,此时自相关法的估计性能将严重下降。定义了自相关函数(ACF)的凸包,在此基础上提出了一种改进的自相关法。首先求出ACF和其凸包的差函数,然后搜索差函数的最大值,从而得到进动周期的估计值。理论分析和仿真结果表明:当进动周期下限和真实进动周期相差不大时,该方法的估计性能接近自相关法;当进动周期下限远小于真实进动周期时,该方法仍然具有良好的估计性能;由于进动周期的上下限之比通常大于2,因此该方法的计算量比自相关法增大的倍数小于1.4;同时它对先验信息的要求非常宽松。因此该方法具有广泛的适用性。     

具有指定闭环极点的最优控制系统鲁棒稳定摄动界

对线性二次最优控制系统,给出了选择适当加权矩阵从而保证系统具有希望闭环极点的方法。加权矩阵可以通过与期望极点有关的变换阵来调节,使得系统具有希望的动态品质。针对这种闭环系统存在不确定扰动时,得出了保证系统稳定的不确定摄动界     

二维扩压器和进气道内正交贴体曲线坐标的快速生成法

贴体曲线坐标系的形成是用有限差分法或有限元素法在诸如扩压器和进气道这类任意形状的域内数值求解各类场时,所必需要做的第一步工作。 通常,对这种贴体曲线坐标系有若干要求。首先,所形成的曲线坐标系必须是“贴体”的,以便于精确地施加边界条件。其次,曲线坐标系最好是正交的,以使得计算平面内的控制方程变得较为简单（不出现交叉导数项）,同时也使得便于应用双层零方程紊流模型。第三,所生成的网格系统的网格距要能随意控制,以便在域内计算变量变化     

Comments on "Bounds on Probability of Error in Decision Feedback Equalizers"

In the above paper1 a technique was proposed to derive an upper bound on the error probability of a decision feedback equalizer. It involves decomposition of the probability density function of residual intersymbol interference and derivation of Chebyshev-type bounds on the error functionals over the decomposed functions. In this correspondence, we demonstrate that the technique is not applicable in general. The result is not a bound in many cases.     

Comments on "Angular Spectra in Radar Applications"

In [1], we proposed using "data adaptive" spectrum estimation techniques (e.g., maximum likelihood and maximum entropy) for radar problems such as separating low angle returns from ground reflections. W. White suggests [2] that these techniques will be of little value due to the correlation between the various received signals. In this rebuttal, we present additional conceptual arguments, simulation results and field data which support the utility of the techniques set forth in [1].     

A Note on Bounds for Target Tracking with pd>1

Recently several new results for Cramer-Rao lower bounds (CRLBs) in dynamical systems have been developed. Several different approaches and approximations have been presented. For the general case of target tracking with a detection probability smaller than one and possibly in the presence of false measurements, two main approaches have been presented. The first approach is the information reduction factor (IRF) approach. The second approach is the enumeration (ENUM) approach, also referred to as the conditioning approach. It has been found that the ENUM approach leads to a strictly larger covariance matrix than the IRF approach, however, still providing a lower bound on the attainable error covariance. Thus, the ENUM approach provides a strictly tighter bound on the attainable performance. It has been conjectured that these bounds converge to one another in the limit or equivalently after an initial transition stage. We demonstrate, using some recent results from the modified Riccati equation (MRE) and by means of counter examples, that this conjecture does not hold true in general. We also demonstrate that the conjecture does hold true in the special case of deterministic target motion, or equivalently in the absence of process noise. Furthermore, we show that the detection probability has an influence on the limiting behaviors of the bounds. Moreover, we show that the MRE approximation provides a very good and computationally efficient approximation of the ENUM bound. The various results are illustrated by means of representative examples.     

Output voltage bounds of a three-phase boost rectifier

A general closed-form duty cycle control law is derived based on the linear combination of two sets of continuous duty cycle control laws. From this general solution one can generate infinitely many pulsewidth modulation (PWM) control strategies to achieve the same ideal performance. Then, from the resulting closed-form solution, a general explicit lower bound and a general explicit upper bound of the output dc voltage are derived. Besides the academic interests, these bounds are very useful practically as a convenient guideline for helping quickly design the three-phase boost rectifier. Finally, some illustrative examples are given and some experimental results provided for verifying the derived bounds     

Interval analysis of rotor dynamic response based on Chebyshev polynomials

Uncertainty is extensively involved in the rotor systems of rotating machinery, which may cause an unstable vibrational response. To take the uncertainty into consideration for the uncertain rotor-bearing system, an improved unified interval analysis method based on the Chebyshev expansion is established in this paper. Firstly, the Chebyshev Interval Method (CIM) to calculate not only the critical speeds but also the dynamic response of rotor with uncertain parameters is introduced. Then, the numerical investigation is carried out based on the developed double disk rotor model and computation procedure, and the results demonstrate the validity. But when the uncertainty is sufficiently large to influence critical speeds, the upper and lower bounds are far from the actual bounds. In order to overcome the defects, a Bound Correction Interval analysis Method (BCIM) is proposed based on the Chebyshev expansion and the modal superposition. In use of the improved method, the bounds of the interval responses, especially the upper bound, are corrected, and the comparison with other methods demonstrates that the higher accuracy and a wider application range.     

复合材料层板等强最优设计方法

 本文对复合材料无矩对称层板的最优设计,提出了一种概念直观、方法简便、收敛迅速、效果较好的等强最优设计方法。给出了几个算例的结果,并与文献[1、2]的方法作了对比,结果表明,本文的方法具有显著的优越性。     

Sensitivity Analysis of Finite-Lag Receivers

This paper presents the sensitivity analysis of a class of receivers called finite-lag receivers, introduced by the authors in [1] through [3]. Since these receivers are based on the use of fixed-lag smoothing techniques, algorithms for the calculation of large-scale and small-scale sensitivities of fixed-lag smoothing are derived using a state augmentation approach. Steady-state analysis of these algorithms shows that an explicit relation can be obtained between sensitivity coefficients of fixed-lag smoothing and filtering. The specific case of sensitivity to variations in the measurement (channel) noise is considered as an example. These results are applied to study the sensitivity performance of the finite-lag receivers for analog communication. It is shown, for example, that finite-lag receivers for AM signals, besides being superior in performance [1]-[3], [11], in terms of output SNR or error variance, are also much less sensitive to the additive noise power level, compared to zero-lag receivers.     

A General Steepest Descent Algorithm

The following paper derives a general gradient process for extremization ion by imposing an " exponential decay" condition on the controlled variable. The general process is applied to two adaptive linear filter problems; a sonar application by Widrow [3] and a radar problem of Brennan & Reed [4]. The results are discussed in sections 11 and Ill, respectively. A central feature of the Fletcher-Powell process [1] is a matrix modification algorithm due to Davidon [2]. It is shown in Appendix A that this algorithm may be derived using the same exponential condition imposed on the proper error term.     

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.     

Kullback-Leibler Approach to Gaussian Mixture Reduction

A common problem in multi-target tracking is to approximate a Gaussian mixture by one containing fewer components; similar problems can arise in integrated navigation. A common approach is successively to merge pairs of components, replacing the pair with a single Gaussian component whose moments up to second order match those of the merged pair. Salmond [1] and Williams [2, 3] have each proposed algorithms along these lines, but using different criteria for selecting the pair to be merged at each stage. The paper shows how under certain circumstances each of these pair-selection criteria can give rise to anomalous behaviour, and proposes that a key consideration should the the Kullback-Leibler (KL) discrimination of the reduced mixture with respect to the original mixture. Although computing this directly would normally be impractical, the paper shows how an easily computed upper bound can be used as a pair-selection criterion which avoids the anomalies of the earlier approaches. The behaviour of the three algorithms is compared using a high-dimensional example drawn from terrain-referenced navigation.     

Bounds on the Probability of Error in Digitial Communications

A class of upper bounds and lower bounds on the probability of error in digital communications are derived. Several degrading factors like intersymbol interference, cochannel interference, inaccurate carrier synchronization, and incoherent detection can be considered in obtaining the bounds. Several examples are given and it is shown that many situations not considered so far can be put into the conceptual framework developed here.     

Comments on: "Design of MTI Radar on the Basis of Detection Probability"

The main comment of the above paper [1] is that radar integration after MTI processing is not taken into account. For this reason, its numerical results (and curves) show processing losses much higher than practical values. The latter can be obtained in a relatively easy way by means of a computer simulation of the entire signal processor.     

Performance of a Square Law Pseudonoise Ranging Time-of-Arrival Estimator

The performance of a square law time-of-arrival (TOA) estimator that has been proposed for use in ASTRO-DABS, part of a possible satellite-based fourth generation air traffic control system is considered. The transmitted message consists of a pulse amplitude modulated (PAM) ranging sequence that, due to transmitter characteristics, is corrupted by an unknown frequency offset. The optimum TOA estimator, for the case of no frequency uncertainty, is first presented, together with a lower bound on the variance of the estimate generated. This is followed by the consideration of a suboptimum TOA estimator for which a high signal-to-noise ratio (SNR) performance analysis is carried out; here, the effects of frequency uncertainty are included. Next, the zero-crossing properties of the derivative of the (suboptimum) estimation statistic are presented and the results used to derive an upper bound to the TOA estimate variance that is valid for all SNR values. This latter result is significant because it displays the system threshold effect and complements performance lower bounds that may be derived via other methods. In addition, the method presented here may be applied to other optimum and suboptimum systems where a discrete set of parameters is to be estimated.     

空气动力迟滞引起飞机横航向极限环振荡的一种近似解法

 本文给出近似解析公式,确定空气动力迟滞引起的飞机横航向极限环振荡特性。计算表明,它与文献[1、2]中提出的数值迭代法求得的结果相当一致,并消除了该文中求出的滚转迟滞引起的滚转速率极限环振荡振幅不是最大幅值的缺陷。     

Accuracy of source localization using multipath delays

The depth and range of underwater source can be estimated from measurements of propagation delay differences along multiple propagation paths. The accuracy of depth and range estimation using the Cramer-Rao lower bound is studied. The formulas derived can be used in conjunction with a propagation medium (nonconstant velocity profile). Explicit formulas for the bounds are derived for the case of homogeneous medium (constant velocity profile). Numerical examples are presented to illustrate the behavior of these bounds     

Probability of Anomaly Expressions for Random Waveform Registration

Registration by integral-square error correlation of one-dimensional discrete-time waveforms which are treated as random processes with specified autocorrelation functions is considered. An important design parameter for this class of problems is the probability of anomaly (a false dip in the correlation function) because it gives an indication of system immunity to gross registration errors. Explicit expressions for this parameter are not possible, so bounds and appoximations must be derived. Two upper bounds and an approximation for the probability of anomaly are derived here. The use of these expressions is illustrated by an example. The relative utility of these performance indicators is shown for the example by comparison with actual values of the probability of anomaly obtained by computer simulation.