Convergence properties of Gram-Schmidt and SMI adaptive algorithms

The open-loop Gram-Schmidt (GS) canceler is shown to be numerically identical to the sampled matrix inversion (SMI) algorithm in the transient state if infinite numerical accuracy is assumed. Two forms of the GS canceler are discussed and analyzed: concurrent and nonconcurrent processing. Results for concurrent and nonconcurrent SMI cancelers have been obtained in the past by I.S. Reed, J.D. Mallet, and E. Brennan (see ibid., AES-10, p.853-63, 1974) under the assumption that the inputs are Gaussian. Many of those results are reproduced here using the GS structures as an analysis tool. In addition, new results are obtained when the input noises are not Gaussian. The deleterious effect of overmatching the degrees of freedom is discussed     

Adaptive array transient sidelobe levels and remedies

The transient sidelobe level of a sidelobe canceler (SLC) is a function of the external noise environment, the number of adaptive auxiliary antennas, the adaptive algorithm used, auxiliary antenna gain margins, and the number of samples used to calculate the adaptive weights. An analytical result for the adaptive sidelobe level is formulated for the case when the adaptive algorithm is the open-loop, sampled matrix inversion (SMI) algorithm. The result is independent of whether concurrent or nonconcurrent data processing is used in the SMI algorithm's implementation. It is shown that the transient sidelobe level is eigenvalue dependent and increases proportionally to the gain margin of the auxiliary antenna elements with respect to the quiescent main antenna sidelobe level. Techniques that reduce this transient sidelobe level are discussed, and it is theoretically shown that injection independent noise into the auxiliary channels significantly reduces the transient sidelobe level. It is demonstrated that using this same technique reduces the SMI noise power residue settling time     

Convergence bounds of an SMI/Gram-Schmidt canceler in colored noise

The performance of the sampled matrix inversion (SMI) adaptive algorithm in colored noise is investigated using the Gram-Schmidt (GS) canceler as an analysis tool. Lower and upper bounds of average convergence are derived, indicating that average convergence slows as the input time samples become correlated. When the input samples are uncorrelated, the fastest SMI algorithm convergence occurs. When the input samples are correlated then the convergence bounds depend on the number of channels N, the number of samples per channels K , and the eigenvalues associated with K×K correlation matrix of the samples in a given channel. This matrix is assumed identical for all channels     

Reiterative median cascaded canceler for robust adaptive array processing

A new robust adaptive processor based on reiterative application of the median cascaded canceler (MCC) is presented and called the reiterative median cascaded canceler (RMCC). It is shown that the RMCC processor is a robust replacement for the sample matrix inversion (SMI) adaptive processor and for its equivalent implementations. The MCC, though a robust adaptive processor, has a convergence rate that is dependent on the rank of the input interference-plus-noise covariance matrix for a given number of adaptive degrees of freedom (DOF), N. In contrast, the RMCC, using identical training data as the MCC, exhibits the highly desirable combination of: 1) convergence-robustness to outliers/targets in adaptive weight training data, like the MCC, and 2) fast convergence performance that is independent of the input interference-plus-noise covariance matrix, unlike the MCC. For a number of representative examples, the RMCC is shown to converge using ~ 2.8N samples for any interference rank value as compared with ~ 2N samples for the SMI algorithm. However, the SMI algorithm requires considerably more samples to converge in the presence of outliers/targets, whereas the RMCC does not. Both simulated data as well as measured airborne radar data from the multichannel airborne radar measurements (MCARM) space-time adaptive processing (STAP) database are used to illustrate performance improvements over SMI methods.     

存在观测站位置误差的转发式时差无源定位

无源定位中,由于观测站安放在运动平台等原因造成的观测站位置误差会影响无源定位精度性能。另外到达时间差(简称时差)(TDOA)的转发式测量需要将不同观测站截获到的辐射源信号都转发到同一位置,如主观测站。针对这两个问题,提出了基于约束总体最小二乘(CTLS)的无源定位算法。首先将转发式时差的非线性定位方程转化为不需要中间变量的直接线性方程,再基于CTLS算法依次转化为约束优化问题和无约束优化问题,最后推导给出定位近似闭式解。仿真实验表明在观测站误差较大时,该算法与其他算法相比定位精度性能较好。     

地形跟踪/地形回避飞行器航迹优化

提出了一种新的地形跟踪／地形回避（ＴＦ／ＴＡ）飞行器透迹优化方法,该方法将地形、威胁和障碍综合在一起用特定的地形模型来描述,并通过将地形模型与飞行器运动方程有机结合,使有约束最优控制问题转化为无约束最优控制问题,最后利用极大值原理给出了航迹优化算法,算法生成的航透既能以给定的高度跟踪地形又能自动回避危险和障碍物。     

Comments on `Existence and uniqueness of GPS solutions' by J.S.Abel and J.W. Chaffee

The commenter points out that a direct Global Positioning System (GPS) algorithm together with discussions on the existence and uniqueness of the solution appeared in his paper (J. Guidance, Control, and Dynamics, vol.9, p.715-17, Nov./Dec. 1986). Since the GPS solution is reduced to solving a quadratic equation, the existence and uniqueness can be easily tested. J.S. Abel and J.W. Chaffee, in the above-titled paper (ibid., vol.26, no.6, p.748-53, Sept. 1990), show that the GPS solution problem is similar to the hyperbolic-fix problem. The commenter notes that it can be inferred from his later work (ibid., vol.26. no.5, p.748-53, Sept. 1990) that the two solutions exist if and only if the four GPS satellites are coplanar, in which case the two solutions are mirror-symmetric with respect to the GPS plane     

Convergence properties of Gram-Schmidt and SMI adaptive algorithms.II

For pt.I see ibid., vol.26, no.1, p.44-56, Jan. 1990. Theorems and relationships associated with the convergence rate of the Gram-Schmidt (GS) and sampled matrix inversion (SMI) algorithms are presented. Two forms of the GS canceler are discussed: concurrent block processing and sliding window processing. It is shown (as has been stated by other researchers) that the concurrent block processed GS canceler converges rapidly to its optimal signal-to-noise ratio. However, it is also shown that the result is deceptive in that the output residue samples may be highly correlated, which would significantly degrade postdetection processing. It is demonstrated that a specific form of a sliding window GS canceler has the same convergence properties as the concurrent block processed GS canceler     

Outlier resistant adaptive matched filtering

Robust adaptive matched filtering (AMF) whereby outlier data vectors are censored from the covariance matrix estimate is considered in a maximum likelihood estimation (MLE) setting. It is known that outlier data vectors whose steering vector is highly correlated with the desired steering vector, can significantly degrade the performance of AMF algorithms such as sample matrix inversion (SMI) or fast maximum likelihood (FML). Four new algorithms that censor outliers are presented which are derived via approximation to the MLE solution. Two algorithms each are related to using the SMI or the FML to estimate the unknown underlying covariance matrix. Results are presented using computer simulations which demonstrate the relative effectiveness of the four algorithms versus each other and also versus the SMI and FML algorithms in the presence of outliers and no outliers. It is shown that one of the censoring algorithms, called the reiterative censored fast maximum likelihood (CFML) technique is significantly superior to the other three censoring methods in stressful outlier scenarios.     

Adaptive variable structure tracking control for constrained robots

The problem of controller design for constrained robots with the consideration of computational efficiency is addressed. An efficient adaptive variable structure control algorithm based on a reduced dynamics formulation, is presented for trajectory tracking of an end-effector on a constrained surface with specified constraint forces. It is shown that the objective can be achieved without exact knowledge of robot dynamics and on-line calculation of nonlinear dynamic functions. The control algorithm is constructed with at most three control parameters to be adjusted adaptively, and that number is determined independently of the number of degrees of freedom of the robotic manipulators. A numerical example is presented to illustrate the developed method     

基于脉冲暂态混沌神经网络的可靠度分析方法

工程中计算结构可靠度系数β可以看做一个优化问题。考虑极限状态函数的非线性程度很高且存在非凸失效域时,传统的求解非线性优化方法,如序列二次规划（SQP）法、罚函数法和梯度投影法等都有其使用范围和局限性,无法解决局部极小解问题。如何避免局部极小解问题并且兼顾计算精度和效率目前仍很难处理。提出一种新的可靠度计算方法：将求解转化为带有约束条件的非线性规划问题,利用罚函数法转化成无约束条件的非线性规划问题,引入脉冲暂态混沌神经网络（PTCNN）模型快速有效地进行全局寻优,从而解决具有局部极小解的约束非线性规划问题。最后采用不同类型的非线性极限状态函数算例进行算法验证,验证该方法在处理高维、高非线性、不可微、非凸失效域问题时具有可行性、高效性。     

Reduced-rank STAP for high PRF radar

Due to the range ambiguity of high pulse-repetition frequency (HPRF) radars, echoes from far-range fold over near-range returns. This effect may cause low Doppler targets to compete with near-range strong clutter. Another consequence of the range ambiguity is that the sample support for estimating the array covariance matrix is reduced, leading to degraded performance. It is shown that space-time adaptive processing (STAP) techniques are required to reject the clutter in HPRF radar. Four STAP methods are studied in the context of the HPRF radar problem: low rank approximation sample matrix inversion (SMI), diagonally loaded SMI, eigencanceler, and element-space post-Doppler. These three methods are evaluated in typical HPRF radar scenarios and for various training conditions, including when the target is present in the training data     

发动机故障方程的最少故障整体优化解

 发动机故障诊断是根据有限的发动机性能参数的测量值在众多的可能发生但不一定发生的故障之中确定出故障的类别和程度。测量参数与故障参数之间的关系通常表示为亚定的线性方程组△y=A△x,式中△y为测量参数向量而△x为故障参数向量。引入最少故障原理可以对亚定的故障方程组求解。求解方法可分为整体优化解法和组合优化解法两大类。本文给出两种基于最少故障原理的约束整体优化解法。最少故障原理和约束条件的引入可以有效地保证最优解的确定性和合理性。文中还给出了利用整体优化解法进行发动机故障诊断的实例。     

基于混合规划策略的自由漂浮冗余机械臂减振运动规划(英文)

对自由漂浮柔性冗余机械臂系统的减振运动规划问题进行研究。首先,采用拉格朗日方法建立系统的动力学模型,并给出了减振运动规划的模型。其次,提出一种基于高斯伪谱法与直接打靶法的混合规划策略,用于求解运动规划问题。先利用高斯伪谱法将运动规划问题转化为一个非线性参数优化问题,并用遗传算法确定近似解,随后利用直接打靶法建立优化模型,将得到的近似解作为优化变量的初值,并采用序列二次规划算法求得精确解。最后,对算例进行分析,验证了基于混合规划策略得到的关节运动轨迹能够明显减小柔性臂杆的全局振动以及残余振动。数值计算的结果表明该方法对减振运动规划问题的求解是有效且稳定的。     

Multiple-constraint cooperative guidance based on two-stage sequential convex programming

An improved approach is presented in this paper to implement highly constrained cooperative guidance to attack a stationary target. The problem with time-varying Proportional Navigation (PN) gain is first formulated as a nonlinear optimal control problem, which is difficult to solve due to the existence of nonlinear kinematics and nonconvex constraints. After convexification treatments and discretization, the solution to the original problem can be approximately obtained by solving a sequence of Second-Order Cone Programming (SOCP) problems, which can be readily solved by state-of-the-art Interior-Point Methods (IPMs). To mitigate the sensibility of the algorithm on the user-provided initial profile, a Two-Stage Sequential Convex Programming (TSSCP) method is presented in detail. Furthermore, numerical simulations under different mission scenarios are conducted to show the superiority of the proposed method in solving the cooperative guidance problem. The research indicated that the TSSCP method is more tractable and reliable than the traditional methods and has great potential for real-time processing and on-board implementation.     

Tangent-impulse transfer from elliptic orbit to an excess velocity vector

The two-body orbital transfer problem from an elliptic parking orbit to an excess veloc-ity vector with the tangent impulse is studied. The direction of the impulse is constrained to be aligned with the velocity vector, then speed changes are enough to nullify the relative velocity. First, if one tangent impulse is used, the transfer orbit is obtained by solving a single-variable function about the true anomaly of the initial orbit. For the initial circular orbit, the closed-form solution is derived. For the initial elliptic orbit, the discontinuous point is solved, then the initial true anomaly is obtained by a numerical iterative approach; moreover, an alternative method is proposed to avoid the singularity. There is only one solution for one-tangent-impulse escape trajectory. Then, based on the one-tangent-impulse solution, the minimum-energy multi-tangent-impulse escape trajectory is obtained by a numerical optimization algorithm, e.g., the genetic method. Finally, several examples are provided to validate the proposed method. The numerical results show that the minimum-energy multi-tangent-impulse escape trajectory is the same as the one-tangent-impulse trajectory.     

Automatic differentiation based discrete adjoint method for aerodynamic design optimization on unstructured meshes

A systematic methodology for formulating, implementing, solving and verifying discrete adjoint of the compressible Reynolds-averaged Navier-Stokes (RANS) equations for aerodynamic design optimization on unstructured meshes is proposed. First, a general adjoint formulation is con-structed for the entire optimization problem, including parameterization, mesh deformation, flow solution and computation of the objective function, which is followed by detailed formulations of matrix-vector products arising in the adjoint model. According to this formulation, procedural components of implementing the required matrix-vector products are generated by means of auto-matic differentiation (AD) in a structured and modular manner. Furthermore, a duality-preserving iterative algorithm is employed to solve flow adjoint equations arising in the adjoint model, ensur-ing identical convergence rates for the tangent and the adjoint models. A three-step strategy is adopted to verify the adjoint computation. The proposed method has several remarkable features:the use of AD techniques avoids tedious and error-prone manual derivation and programming;duality is strictly preserved so that consistent and highly accurate discrete sensitivities can be obtained; and comparable efficiency to hand-coded implementation can be achieved. Upon the cur-rent discrete adjoint method, a gradient-based optimization framework has been developed and applied to a drag reduction problem.     

Parallel Distributed CFAR Detection Optimization Based on Genetic Algorithm with Interval Encoding

Aiming at parallel distributed constant false alarm rate (CFAR) detection employing K/N fusion rule, an optimization algorithm based on the genetic algorithm with interval encoding is proposed. N-1 local probabilities of false alarm are selected as optimization variables. And the encoding intervals for local false alarm probabilities are sequentially designed by the person-by-person optimization technique according to the constraints. By turning constrained optimization to unconstrained optimization, the problem of increasing iteration times due to the punishment technique frequently adopted in the genetic algorithm is thus overcome. Then this optimization scheme is applied to spacebased synthetic aperture radar (SAR) multi-angle collaborative detection, in which the nominal factor for each local detector is determined. The scheme is verified with simulations of cases including two, three and four independent SAR systems. Besides, detection performances with varying K and N are compared and analyzed.     

Optimization of multiple-impulse minimum-time rendezvous with impulse constraints using a hybrid genetic algorithm

The minimum-time multiple-impulse rendezvous with impulse constraints is investigated in this paper. Based on the Clohessy–Wiltshire (C–W) equations, an optimization model including several different kinds of impulse constraints such as the maximum impulse magnitude, the total velocity change magnitude and the time of imposing impulse for multiple-impulse minimum-time rendezvous is established. A generalized inverse matrix solution for linear equation is applied to avoid handling the terminal equality constraints. In order to obtain the global solution efficiently, a hybrid optimizer combining the advantages of a floating-coded genetic algorithm and simplex method is employed. A low-earth orbit multiple-impulse rendezvous problem is used as an example. The influence of the number of impulses, the optimization variables and the constraints on the solution is analyzed, and the different optimization algorithms are compared. Results indicate our proposed model and approach is effective in designing linearized minimum-time rendezvous trajectory with impulse constraints.     

Convergence Rate of the Extended SMI Algorithm for Narrowband Adaptive Arrays

An extended sample matrix inversion (SMI) algorithm can be used for minimizing the mse (mean-squared error) between the output of an N-element adaptive array and a desired reference signal. This algorithm is shown to yield mse within 3 dB of minimum (on the average) after (2N - 1) observations of the antenna element outputs.