A study in the cognition of individuals’ identity: Solving the problem of singular cognition in object and agent tracking

This article compares the ability to track individuals lacking mental states with the ability to track intentional agents. It explains why reference to individuals raises the problem of explaining how cognitive agents track unique individuals and in what sense reference is based on procedures of perceptual-motor and epistemic tracking. We suggest applying the notion of singular-files from theories in perception and semantics to the problem of tracking intentional agents. In order to elucidate the nature of agent-files, three views of the relation between object- and agent-tracking are distinguished: the Independence, Deflationary and Organism-Dependence Views. The correct view is argued to be the latter, which states that perceptual and epistemic tracking of a unique human organism requires tracking both its spatio-temporal object-properties and its agent-properties

Practical Implementation of Attitude-Control Algorithms for an Underactuated Satellite

The challenging problem of controlling the attitude of satellites subject to actuator failures has been the subject of increased attention in recent years. The problem of controlling the attitude of a satellite on all three axes with two reaction wheels is addressed in this paper. This system is controllable in a zero-momentum mode. Three-axis attitude stability is proven by imposing a singular quaternion feedback law to the angular velocity trajectories.Two approaches are proposed and compared to achieve three-axis control: The first one does not require angular velocity measurements and is based on the assumption of a perfect zero momentum, while the second approach consists of tracking the desired angular velocity trajectories. The full-state feedback is a nonlinear singular controller. In-orbit tests of the first approach provide an unprecedented practical proof of three-axis stability with two control torques. The angular velocity tracking approach is shown to be less efficient using the nonlinear singular controller. However, when inverse optimization theory is applied to enhance the nonlinear singular controller, the angular velocity tracking approach is shown to be the most efficient. The resulting switched inverse optimal controller allows for a significant enhancement of settling time, for a prescribed level of the integrated torque

Robust Subspace Learning: Robust PCA, Robust Subspace Tracking, and Robust Subspace Recovery

PCA is one of the most widely used dimension reduction techniques. A related easier problem is "subspace learning" or "subspace estimation". Given relatively clean data, both are easily solved via singular value decomposition (SVD). The problem of subspace learning or PCA in the presence of outliers is called robust subspace learning or robust PCA (RPCA). For long data sequences, if one tries to use a single lower dimensional subspace to represent the data, the required subspace dimension may end up being quite large. For such data, a better model is to assume that it lies in a low-dimensional subspace that can change over time, albeit gradually. The problem of tracking such data (and the subspaces) while being robust to outliers is called robust subspace tracking (RST). This article provides a magazine-style overview of the entire field of robust subspace learning and tracking. In particular solutions for three problems are discussed in detail: RPCA via sparse+low-rank matrix decomposition (S+LR), RST via S+LR, and "robust subspace recovery (RSR)". RSR assumes that an entire data vector is either an outlier or an inlier. The S+LR formulation instead assumes that outliers occur on only a few data vector indices and hence are well modeled as sparse corruptions.Comment: To appear, IEEE Signal Processing Magazine, July 201

Aggressive Longitudinal Aircraft Path Tracking Using Nonlinear Control

We study the problem of converting a trajectory tracking controller to a path tracking controller for a nonlinear non-minimum phase longitudinal aircraft model. The solution of the trajectory tracking problem is based on the requirement that the aircraft follows a given time parameterized trajectory in inertial frame. In this paper we introduce an alternative nonlinear control design approach called path tracking control. The path tracking approach is based on designing a nonlinear state feedback controller that maintains a desired speed along a desired path with closed loop stability. This design approach is different from the trajectory tracking approach where aircraft speed and position are regulated along the desired path. The path tracking controller regulates the position errors transverse to the desired path but it does not regulate the position error along the desired path. First, a trajectory tracking controller, consisting of feedforward and static state feedback, is designed to guarantee uniform asymptotic trajectory tracking. The feedforward is determined by solving a stable noncausal inversion problem. Constant feedback gains are determined based on LQR with singular perturbation approach. A path tracking controller is then obtained from the trajectory tracking controller by introducing a suitable state projection.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73425/1/j.1934-6093.2001.tb00068.x.pd

Subspace Tracking and Least Squares Approaches to Channel Estimation in Millimeter Wave Multiuser MIMO

The problem of MIMO channel estimation at millimeter wave frequencies, both in a single-user and in a multi-user setting, is tackled in this paper. Using a subspace approach, we develop a protocol enabling the estimation of the right (resp. left) singular vectors at the transmitter (resp. receiver) side; then, we adapt the projection approximation subspace tracking with deflation and the orthogonal Oja algorithms to our framework and obtain two channel estimation algorithms. We also present an alternative algorithm based on the least squares approach. The hybrid analog/digital nature of the beamformer is also explicitly taken into account at the algorithm design stage. In order to limit the system complexity, a fixed analog beamformer is used at both sides of the communication links. The obtained numerical results, showing the accuracy in the estimation of the channel matrix dominant singular vectors, the system achievable spectral efficiency, and the system bit-error-rate, prove that the proposed algorithms are effective, and that they compare favorably, in terms of the performance-complexity trade-off, with respect to several competing alternatives.Comment: To appear on the IEEE Transactions on Communication

Digital Acoustic Tracking Analysis Program

The purpose of this report is to investigate the processing of tracking data for acoustic targets. The programs developed for two- and three- dimensional space calculate the target\u27s position via hyperbolic-fix navigation (geometric) considerations using the Newton-Raphson algorithm. The computer programs and the tracking solution approach contained herein is based on knowledge of only the sensors\u27 locations and the relative time-difference at which a target\u27s referenced, singular, acoustic pressure wavefronts are received at the sensors. Omnidirectional sensors are found to be sufficient for the two-dimensional space tracking problem. However, it is found that the three-space problem required usage of directional frequency and ranging (DIFAR) sensors. Line printer plots are provided for the target position solutions; also; tabular track position solutions are provided