Direction set based Algorithms for adaptive least squares problems improvements and innovations.

The main objective of this research is to provide a mathematically tractable solutions to the adaptive filtering problem by formulating the problem as an adaptive least squares problem. This approach follows the work of Chen (1998) in his study of direction-set based CDS) adaptive filtering algorithm. Through the said formulation, we relate the DS algorithm to a class of projection method. Objektif utama penyelidikan ini ialah untuk menyediakan penyelesaian matematik yang mudah runut kepada masalah penurasan adaptif dengan memfonnulasikan masalah tersebut sebagai masalah kuasa dua terkecil adaptif. Pendekatan ini rnengikut hasil kerja oleh Chen (1998) dalam kajian beliau tentang algoritma penurasan adaptif berasaskan 'direction-set' (DS). Melalui fornulasi tersebut, kami menghubungkaitkan algoritma DS kepada satu kelas kaedah unjuran. Secara khususnya, versi rnudah aigoritma itu, iaitu algoritma 'Euclidean direction search' (EDS) ditunjukkan mempunyai hubungkait dengan satu kelas kaedah berlelaran yang dipanggil kaedah 'relaxation'. Penernuan ini rnembolehkan kami menambahbaik algoritma EDS kepada 'accelerated EDS' eli mana satu parameter pemecutan diperkenalkan untuk rnengoptirnumkan saiz langkah sernasa setiap pencarian garis

Regularized adaptive long autoregressive spectral analysis

This paper is devoted to adaptive long autoregressive spectral analysis when (i) very few data are available, (ii) information does exist beforehand concerning the spectral smoothness and time continuity of the analyzed signals. The contribution is founded on two papers by Kitagawa and Gersch. The first one deals with spectral smoothness, in the regularization framework, while the second one is devoted to time continuity, in the Kalman formalism. The present paper proposes an original synthesis of the two contributions: a new regularized criterion is introduced that takes both information into account. The criterion is efficiently optimized by a Kalman smoother. One of the major features of the method is that it is entirely unsupervised: the problem of automatically adjusting the hyperparameters that balance data-based versus prior-based information is solved by maximum likelihood. The improvement is quantified in the field of meteorological radar

Efficient multiscale regularization with applications to the computation of optical flow

Includes bibliographical references (p. 28-31).Supported by the Air Force Office of Scientific Research. AFOSR-92-J-0002 Supported by the Draper Laboratory IR&D Program. DL-H-418524 Supported by the Office of Naval Research. N00014-91-J-1004 Supported by the Army Research Office. DAAL03-92-G-0115Mark R. Luettgen, W. Clem Karl, Alan S. Willsky

Convex optimization of launch vehicle ascent trajectories

This thesis investigates the use of convex optimization techniques for the ascent trajectory design and guidance of a launch vehicle. An optimized mission design and the implementation of a minimum-propellant guidance scheme are key to increasing the rocket carrying capacity and cutting the costs of access to space. However, the complexity of the launch vehicle optimal control problem (OCP), due to the high sensitivity to the optimization parameters and the numerous nonlinear constraints, make the application of traditional optimization methods somewhat unappealing, as either significant computational costs or accurate initialization points are required. Instead, recent convex optimization algorithms theoretically guarantee convergence in polynomial time regardless of the initial point. The main challenge consists in converting the nonconvex ascent problem into an equivalent convex OCP. To this end, lossless and successive convexification methods are employed on the launch vehicle problem to set up a sequential convex optimization algorithm that converges to the solution of the original problem in a short time. Motivated by the computational efficiency and reliability of the devised optimization strategy, the thesis also investigates the suitability of the convex optimization approach for the computational guidance of a launch vehicle upper stage in a model predictive control (MPC) framework. Being MPC based on recursively solving onboard an OCP to determine the optimal control actions, the resulting guidance scheme is not only performance-oriented but intrinsically robust to model uncertainties and random disturbances thanks to the closed-loop architecture. The characteristics of real-world launch vehicles are taken into account by considering rocket configurations inspired to SpaceX's Falcon 9 and ESA's VEGA as case studies. Extensive numerical results prove the convergence properties and the efficiency of the approach, posing convex optimization as a promising tool for launch vehicle ascent trajectory design and guidance algorithms

Adaptive Graph Signal Processing: Algorithms and Optimal Sampling Strategies

The goal of this paper is to propose novel strategies for adaptive learning of signals defined over graphs, which are observed over a (randomly time-varying) subset of vertices. We recast two classical adaptive algorithms in the graph signal processing framework, namely, the least mean squares (LMS) and the recursive least squares (RLS) adaptive estimation strategies. For both methods, a detailed mean-square analysis illustrates the effect of random sampling on the adaptive reconstruction capability and the steady-state performance. Then, several probabilistic sampling strategies are proposed to design the sampling probability at each node in the graph, with the aim of optimizing the tradeoff between steady-state performance, graph sampling rate, and convergence rate of the adaptive algorithms. Finally, a distributed RLS strategy is derived and is shown to be convergent to its centralized counterpart. Numerical simulations carried out over both synthetic and real data illustrate the good performance of the proposed sampling and reconstruction strategies for (possibly distributed) adaptive learning of signals defined over graphs.Comment: Submitted to IEEE Transactions on Signal Processing, September 201