Kalman Filtering with Nonlinear State Constraints

An analytic method was developed by D. Simon and T. L. Chia to incorporate linear state equality constraints into the Kalman filter. When the state constraint was nonlinear, linearization was employed to obtain an approximately linear constraint around the current state estimate. This linearized constrained Kalman filter is subject to approximation errors and may suffer from a lack of convergence. We present a method that allows exact use of second-order nonlinear state constraints. It is based on a computational algorithm that iteratively finds the Lagrangian multiplier for the nonlinear constraints. Computer simulation results are presented to illustrate the algorithm.     

False alarm analysis of the envelope detection GO-CFAR processor

The greatest of constant false alarm rate processor (GO CFAR) is a useful architecture for adaptively setting a radar detection threshold in the presence of clutter edges. The GO CFAR input is often the envelope detected in-phase (I) and quadrature (Q) channels of the baseband signal (x_e=√(I²+Q²)). This envelope detection can also be approximated using x=a max{|I|,|Q|}+b min{|I|,|Q|} which requires less complex hardware (a and b are simple multiplying coefficients). The envelope GO CFAR processor and several envelope approximation GO CFAR processors are compared in terms of the probability of false alarm (PFA) performance. Closed-form expressions which describe the PFA performance are given and their accuracy evaluated. It is shown that for all cases, the PFA is proportional to the number of reference cells n for small threshold multiplier T and inversely proportional to n for large T. A region of intersection occurs where the PFA is the same for two different values of n. For example, at T'=1.68 in the |I|+|Q| GO CFAR (a=1, b=1) the PFA for n=1 is equal to the optimal n=∞ fixed-threshold PFA (PFA=0.112)     

亚/超声速楔状流层流边界层速度与温度相似解及拟合解

利用相似变换获得了楔状流层流边界层无量纲流函数的3阶非线性常微分方程,用Runge-Kutta法求解微分方程获得了不同楔形角楔状流层流边界层无量纲速度随相似变量的变化曲线;推导了亚声速和超声速楔状流层流边界层无量纲温度关于相似变量的2阶线性齐次和非齐次微分方程,获得了温度分布的通解,恒壁温条件下亚声速楔状流和绝热壁面条件下超声速楔状流层流边界层无量纲温度解析解及指数函数形式的拟合解.以楔形角为0为例利用相似变换研究了超声速条件下气体压缩性及黏度随温度变化等因素对层流边界层速度与温度的影响,得出不可压缩常物性与可压缩变物性条件下无量纲速度相对误差绝对值小于9.8%的结论.研究表明:Pr越大贴近壁面处无量纲温度变化越剧烈;超声速条件下壁温低于绝热壁温时黏性耗散作用可以使层流边界层气体温度从壁面到主流间出现先升高后降低的变化.      

SAR极坐标格式成像算法对运动目标响应特性

运动目标的合成孔径雷达（SAR）成像特征是SAR地面运动目标指示（SAR/GMTI）系统进行运动目标检测、成像和重定位的基础。为此,从信号二维解耦合校正距离徙动角度推导和分析了极坐标格式算法（PFA）对运动目标的响应特性,揭示了极坐标格式转换过程中的距离插值和方位插值对运动目标距离徙动的校正原理。理论分析表明：PFA在完成对静止目标成像的同时,还能够自动校正所有运动目标的线性距离徒动,且校正过程无需目标运动信息,因此对于径向运动目标,在忽略波前弯曲条件下PFA也能够对其进行完全聚焦。最后,通过仿真数据处理对理论分析结果进行了验证,表明PFA作为一种运动目标成像预处理方法具有很大的应用前景。     

Polar format algorithm for bistatic SAR

Matched filtering (MF) of phase history data is a mathematically ideal but computationally expensive approach to bistatic synthetic aperture radar (SAR) image formation. Fast backprojection algorithms (BPAs) for image formation have recently been shown to give improved O(N/sup 2/ log/sub 2/N) performance. An O(N/sup 2/ log/sub 2/N) bistatic polar format algorithm (PFA) based on a bistatic far-field assumption is derived. This algorithm is a generalization of the popular PFA for monostatic SAR image formation and is highly amenable to implementation with existing monostatic image formation processors. Limits on the size of an imaged scene, analogous to those in monostatic systems, are derived for the bistatic PFA.     

Solid rocket motor propellant grain burnback simulation based on fast minimum distance function calculation and improved marching tetrahedron method

To efficiently compute arbitrary propellant grain evolution of the burning surface with uniform and non-uniform burning rate for solid rocket motor, a unified framework of burning surface regression simulation has been developed based on minimum distance function. In order to speed up the computation of the mini-mum distance between grid nodes of grain and the triangular mesh of burning surface, a fast distance querying method based on the equal size cube voxel structure was employed. An improved marching tetrahedron method based on piecewise linear approximation was carried out on second-order tetrahedral elements, achieved high-efficiency and adequate accuracy of burning surface extraction simultaneously. The cases of star grain, finocyl grain, and non-uniform tube grain were studied to verify the proposed method. The observed result indicates that the grain burnback computation method could realize the accurate simulation on unstructured tetrahedral mesh with a desirable performance on computational time.     

Reconstruction of Target Reflecting Surface Using Differential Geometry

A procedure based on the envelope concept of differential geometry is described that permits the reconstruction of the contour of a smooth, moving, conducting target, satisfying the geometrical optics approximation. The target reflections are assumed to be specular in nature with either one reflection point or multiple resolvable reflection points. The time variation of the range to the reflection point of the target (assumed derivable from a high-resolution radar) and the general motion of the target (assumed derivable from tracking or trajectory information) are employed to reconstruct the contour of that portion of the assumed target surface that is illuminated by the radar. The reconstruction is accomplished by the simultaneous solution of two nonlinear differential equations which are derived using the envelope concept of differential geometry. Several reconstruction examples based on computer analysis are presented which indicate the results obtainable using this method.     

Generalized linear solution of proportional navigation

Proportional navigation (PN) equations are not solvable in closed form. Linearized solutions have been widely used for PN system analysis and design, but these are based on overly restrictive assumptions regarding the initial geometry, and are valid only for near-tail-chase pursuits. A generalization of the linearized approach is presented which yields more-accurate estimates of pursuer lateral acceleration than the classical linear solutions as verified by comparison with `exact' numerical solutions. Further, the solution is applicable over a much wider range of engagement geometries. The treatment is based on a closed-form quasilinearized solution of the PN equations followed by the small-angle approximation only to line-of-sight (LOS) angle rate     

A Baker's Dozen Magnitude Approximations and Their Detection Statistics

Thirteen linear approximations to the square root of the sum of the squares operation are examined and compared as to their peak error, average error, mean-squared error, and, most importantly, for digital radar signal processing the increase in SNR (over an exact linear detector) needed to maintain a specified PD and PFA.     

模态密集柔性空间结构二阶内平衡降阶

 给出一种针对二阶线性系统方程直接进行降阶的二阶系统内平衡降阶方法。大型柔性空间结构动力学方程采用二阶线性微分方程描述,采用传统的一阶内平衡降阶方法降阶后的状态方程是一阶形式,破坏了原系统的二阶结构和物理意义。采用新方法降阶后的系统可以保持原系统二阶结构,同时可以进一步保持原系统的对称和正定特性。柔性空间结构系统级降阶的柔性模态方程通常为对角形式,针对这种特殊形式,系统可控和可观Gramian矩阵存在闭合解析解,给出了闭合解的具体表达形式。数值仿真结果表明,二阶内平衡降阶方法可以达到一阶内平衡方法一样的降阶精度,Gramian矩阵的闭合解析解可以大幅度提高Lyapunov方程求解速度。     

乙烯燃烧化学动力学机理的简化与分析

为了获得高精度、小尺寸的乙烯简化机理,采用基于误差传播的直接关系图(DRGEP)法和反应路径分析(PFA)法对USC(University of Southern California)-Ⅱ机理在宽范围工况下进行简化,通过取交集方式得到了包含38个组分和243个反应的框架机理,采用灵敏性分析得到了包含30个组分和167个反应的框架机理,其最大点火延时误差为7.10%。在较宽的工况范围内对30个组分的框架机理进行了验证与机理分析,结果表明:此框架机理在点火延时,火焰传播速度,温度曲线,组分摩尔分数曲线,反应的灵敏性系数,反应路径和不确定性等燃烧特性参数与详细机理吻合较好。通过准稳态假设(QSSA)方法简化得到了更适用于工程应用的24个组分和20个总包反应的全局简化机理,并验证了其点火延时。      

基于两维空变滤波的PFA波前弯曲误差补偿

极坐标格式算法(PFA)因受波前弯曲误差的影响,其有效成像场景范围受到一定的限制。采用图像域的空变滤波(SVPF)处理可以有效补偿波前弯曲误差,但为了简化分析,已有SVPF方法在补偿过程中都采取了一定的近似,在对大场景进行高分辨率成像时仍然不能满足聚焦精度要求。对PFA的极坐标格式转换给出了一种新的解析解释,利用该解释推导得到了精确的波前弯曲误差表达式;基于该波前弯曲误差模型,提出了一种基于两维SVPF处理的波前弯曲误差补偿方法。最后通过仿真数据处理验证了该算法的有效性。     

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。     

Sequential nonlinear tracking using UKF and raw range-rate measurements

The three-dimensional (3D) converted measurements filtering (CMF) with both converted position and raw range-rate measurement is proposed to solve the Doppler radar target tracking, where the error between radar-target range and range rate are correlated. Firstly, not using pseudomeasurement constructed by product of range and range rate to reduce the high nonlinearity, the raw range-rate measurements are utilized by unscented Kalman filter (UKF), where the converted errors of the position and the range rate are decorrelated, then linear part (position measurements) and nonlinear part (range-rate measurement) are sequentially processed by Kalman filter (KF) and UKF. Secondly, based on the assumption of small measurement error, the mean and covariance of converted measurement errors are derived by second-order Taylor series expansion. Finally, the influence of the correlated coefficient rho between the range and range rate, and the range-rate noise deviation sigma_r are taken into account and extreme values of rho and sigma_r are used in Monte Carlo simulations. The results show that the proposed method is, in a sense, effective and practical     

Choosing a Vision Model for Optimizing DPCM Video

The efficient transmission of video signals can be effected by the reduction of statistical redundancy, based on linear prediction. It is clear that economic transmission of video signals must be based on the characteristics of human vision where man is the end user. There are several characteristics of sight which can be used for this purpose. Contrast sensitivity is the important characteristic of vision for the predictive system. We consider the case of the Laplacian curve as an approximation for the contrast sensitivity of vision. It is shown that the differences between a Gaussian and a Laplacian approximation to the contrast sensitivity characteristic are insignificant.     

Event-triggered control for containment maneuvering of second-order MIMO multi-agent systems with unmatched uncertainties and disturbances

This paper is concerned with distributed containment maneuvering of second-order Multi-Input Multi-Output (MIMO) multi-agent systems with non-periodic communication and actuation. The agent is subject to unmatched nonlinear dynamics and external disturbances. Event-triggered containment maneuvering control methods is developed based on a modular design. Specifically, an estimator module is constructed based on neural networks and the non-periodic obtained follower information through event-triggered communication. Next, a controller module is designed by using the identified information from the estimator module and a third-order linear tracking differentiator. An event-triggered mechanism is introduced for updating the actuator. Then, a path update law is designed based on the non-periodic leader information through event-triggered communication. The closed-loop system cascaded by the estimation subsystem and control subsystem is proved to be input-to-state stable, and Zeno behavior is excluded in the control process. The proposed method is capable of reducing the consumption of communication and actuation. A simulation example is provided to substantiate the effectiveness of the proposed event-triggered control method for distributed containment maneuvering of second-order MIMO multi-agent systems.     

Simultaneous ISAR imaging of group targets flying in formation

This paper proposes a novel inverse synthetic aperture radar(ISAR) imaging method based on second-order keystone transform(KT) and Sandglass transform for group targets flying in a formation with constant accelerated rectilinear motion in the same radar beam. First, range curvature and range walk of each sub-target among group targets are corrected by the second-order KT combined with the quadratic phase term compensation. After range alignment, the signals in each range frequency cell can be modelled as multiple chirp signals and then the Sandglass transform is utilized to cross-range imaging, which transforms the time–frequency distribution of the signals in each range frequency cell into beelines parallel to the slow time axis simultaneously. Finally, cross-range profiles of group targets in each range frequency cell are obtained via a projection of the perk of every scatterer in the two-dimensional accumulation plane onto the frequency axis. The advantage of the proposed method is that it can align range profiles of each sub-target simultaneously and image cross-range profiles directly without separating the returned signals, which simplifies the operation procedure. Simulation results are used to demonstrate the effectiveness of the proposed method.     

A Comparison of Numerical Methods for Solving Optimal Control Problems

Linear systems with quadratic performance criteria typically lead to two-point boundary value problems. The numerical solution of such problems is often difficult because of roundoff and truncation errors. In this paper numerical methods for digital computer solutions are considered for a system described by a given second-order linear differential equation and the results are compared. The results show that where accurate analytic solutions cannot be obtained, the invariant imbedding technique yields more accurate results, for a given integration grid interval, than the other methods considered.     

基于Navier-Stokes方程跨声速翼型和机翼气动优化设计

将响应面方法引入到气动优化设计上来,进行了基于N-S方程跨声速翼型、机翼气动优化设计。通过去掉完全二阶多项式响应面模型中的二阶交叉项,大大减少了构造高维响应面模型所需要的计算量。合理地选择优化设计空间,保证了构造的响应面模型具有较高精度。跨声速翼型、机翼减阻优化算例结果表明该方法能有效地适用于气动优化设计问题,设计质量高,方法实用可靠,有较高的工程应用前景。     

Adaptive Radar Detection with Asymptotically Regulated False-Alarm Rate

An adaptive detection procedure is described by which the detection threshold is so adjusted as to provide an asymptotic false-alarm probability PFA that is approximately invariant with changes in radar clutter return amplitude probability density functions (pdf's) in a broad class. The class includes Rayleigh, chi, Weibull, and lognormal pdf's. The receiver noise is also taken into account. The clutter-plus-noise pdf is approximated by a truncated generalized Laguerre series, the coefficients of which are estimated from the radar returns using "cell averaging" techniques. This estimation is assumed to be perfect. The results obtained indicate that the "bias" error, defined as the normalized difference between the design PFA and the asymptotic PFA corresponding to the computed threshold, lies within a fraction of an order of magnitude for 10-3?PFA ? 10-6. For PFA ?10-6 the bias error is more than an order of magnitude. These results are for the case when a single independent radar return is processed at a time. The bias error decreases as the number of postdetection integrations of independent returns increases.