Input and State Estimation for Discrete-Time Linear Systems with Application to Target Tracking and Fault Detection

This dissertation first presents a deterministic treatment of discrete-time input reconstruction and state estimation without assuming the existence of a full-rank Markov parameter. Algorithms based on the generalized inverse of a block-Toeplitz matrix are given for 1) input reconstruction in the case where the initial state is known; 2) state estimation in the case where the initial state is unknown, the system has no invariant zeros, and the input is unknown; and 3) input reconstruction and state estimation in the case where the initial state is unknown and the system has no invariant zeros. In all cases, the unknown input is an arbitrary deterministic or stochastic signal. In addition, the reconstruction/estimation algorithm is deadbeat, which means that, in the absence of sensor noise, exact input reconstruction and state estimation are achieved in a finite number of steps. Next, asymptotic input and state estimation for systems with invariant zeros is considered. Although this problem has been widely studied, existing techniques are confined to the case where the system is minimum phase. This dissertation presents retrospective cost input estimation (RCIE), which is based on retrospective cost optimization. It is shown that RCIE automatically develops an internal model of the unknown input. This internal model provides an asymptotic estimate of the unknown input regardless of the location of the zeros of the plant, including the case of nonminimum-phase dynamics. The input and state estimation method developed in this dissertation provides a novel approach to a longstanding problem in target tracking, namely, estimation of the inertial acceleration of a body using only position measurements. It turns out that, for this problem, the discretized kinematics have invariant zeros on the unit circle, and thus the dynamics is nonminimum-phase. Using optical position data for a UAV, RCIE estimates the inertial acceleration, which is modeled as an unknown input. The acceleration estimates are compared to IMU data from onboard sensors. Finally, based on exact kinematic models for input and state estimation, this dissertation presents a method for detecting sensor faults. A numerical investigation using the NASA Generic Transport Model shows that the method can detect stuck, bias, drift, and deadzone sensor faults. Furthermore, a laboratory experiment shows that RCIE can estimate the inertial acceleration (3-axis accelerometer measurements) and angular velocity (3-axis rate-gyro measurements) of a quadrotor using vision data; comparing these estimates to the actual accelerometer and rate-gyro measurements provide the means for assessing the health of the accelerometer and rate gyro.PHDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/145813/1/ansahmad_1.pd

Real-Time Numerical Differentiation of Sampled Data Using Adaptive Input and State Estimation

Real-time numerical differentiation plays a crucial role in many digital control algorithms, such as PID control, which requires numerical differentiation to implement derivative action. This paper addresses the problem of numerical differentiation for real-time implementation with minimal prior information about the signal and noise using adaptive input and state estimation. Adaptive input estimation with adaptive state estimation (AIE/ASE) is based on retrospective cost input estimation, while adaptive state estimation is based on an adaptive Kalman filter in which the input-estimation error covariance and the measurement-noise covariance are updated online. The accuracy of AIE/ASE is compared numerically to several conventional numerical differentiation methods. Finally, AIE/ASE is applied to simulated vehicle position data generated from CarSim.Comment: This paper is under review at the International Journal of Contro

Dorsal and pectoral fin control of a biorobotic autonomous underwater vehicle

This thesis involves an in-depth research on the maneuvering of bio-robotic autonomous undersea vehicles (BAUVs) using bio-mimetic swimming mechanisms. Motivation was derived from the amazing flexibility and agility the fish inherit with the help of their pectoral and dorsal fins; In the first part of the thesis, control of BAUVs using dorsal fins is considered. The force produced by the cambering of the dorsal fins is used for control. An indirect adaptive controller is designed for depth tracking along constant trajectories even when the system parameters are not known. Next, for following time-varying trajectories, an adaptive control system for yaw plane control of BAUVs is developed. It is capable of working efficiently even when large uncertainties in the system parameters are present and system nonlinearities are dominant; In the second part of the thesis, pectoral fin control of BAUVs is considered. The flapping of these oscillating fins provides the necessary force and moment for control. A discrete-time optimal controller for set point (constant path) control and inverse controller for tracking time varying trajectories in the yaw plane are derived. Further, an indirect adaptive control system that can accomplish depth trajectory tracking even when the model paramters are completely unknown is developed; The performance evaluation of the controllers is done by simulation using matlab/simulink

The Fragility of Noise Estimation in Kalman Filter: Optimization Can Handle Model-Misspecification

The Kalman Filter (KF) parameters are traditionally determined by noise estimation, since under the KF assumptions, the state prediction errors are minimized when the parameters correspond to the noise covariance. However, noise estimation remains the gold-standard regardless of the assumptions - even when it is not equivalent to errors minimization. We demonstrate that even seemingly simple problems may include multiple assumptions violations - which are sometimes hard to even notice. We show theoretically and empirically that even a minor violation may largely shift the optimal parameters. We propose a gradient-based method along with the Cholesky parameterization to explicitly optimize the state prediction errors. We show consistent improvement over noise estimation in tens of experiments in 3 different domains. Finally, we demonstrate that optimization makes the KF competitive with an LSTM model - even in non linear problems

Nonlinear suboptimal and adaptive pectoral fin control of autonomous underwater vehicle

Autonomous underwater vehicles (AUVs) are used for numerous applications in the deep sea, such as hydrographic survey, sea bed mining and oceanographic mapping, etc. Presently, significant amount of effort, is being made in developing biorobotic AUVs (BAUVs) with biologically inspired control surfaces. However, the dynamics of AUVs and BAUVs are highly nonlinear and the hydrodynamic coefficients are not precisely known. As such the development of nonlinear and adaptive control systems is of considerable importance; We consider the suboptimal dive plane control of AUVs using the state-dependent Riccati equation (SDRE) technique. This method provides effective means of designing nonlinear control systems for minimum as well as nonminimum phase AUV models. Moreover, hard control constraints are included in the design process; We also attempt to design adaptive control systems for BAUVs using biologically-inspired pectoral-like fins. The fins are assumed to be oscillating harmonically with a combined linear (sway) and angular (yaw) motion. The bias (mean) angle of the angular motion of the fin is used as a control input. Using discrete-time state variable representation of the BAUV, adaptive sampled-data control systems for the trajectory control are derived using state feedback as well as output feedback. We develop direct as well as indirect adaptive control systems for BAUVs. The advantage of the indirect adaptive law lies in its applicability to minimum as well as nonminimum phase systems. Simulation results are presented to evaluate the performance of each control system

Space Station Human Factors Research Review. Volume 4: Inhouse Advanced Development and Research

A variety of human factors studies related to space station design are presented. Subjects include proximity operations and window design, spatial perceptual issues regarding displays, image management, workload research, spatial cognition, virtual interface, fault diagnosis in orbital refueling, and error tolerance and procedure aids

Classification-Aided Robust Multiple Target Tracking Using Neural Enhanced Message Passing

We address the challenge of tracking an unknown number of targets in strong clutter environments using measurements from a radar sensor. Leveraging the range-Doppler spectra information, we identify the measurement classes, which serve as additional information to enhance clutter rejection and data association, thus bolstering the robustness of target tracking. We first introduce a novel neural enhanced message passing approach, where the beliefs obtained by the unified message passing are fed into the neural network as additional information. The output beliefs are then utilized to refine the original beliefs. Then, we propose a classification-aided robust multiple target tracking algorithm, employing the neural enhanced message passing technique. This algorithm is comprised of three modules: a message-passing module, a neural network module, and a Dempster-Shafer module. The message-passing module is used to represent the statistical model by the factor graph and infers target kinematic states, visibility states, and data associations based on the spatial measurement information. The neural network module is employed to extract features from range-Doppler spectra and derive beliefs on whether a measurement is target-generated or clutter-generated. The Dempster-Shafer module is used to fuse the beliefs obtained from both the factor graph and the neural network. As a result, our proposed algorithm adopts a model-and-data-driven framework, effectively enhancing clutter suppression and data association, leading to significant improvements in multiple target tracking performance. We validate the effectiveness of our approach using both simulated and real data scenarios, demonstrating its capability to handle challenging tracking scenarios in practical radar applications.Comment: 15 page

Sequential Monte Carlo Samplers For Nonparametric Bayesian Mixture Models

Tez (Doktora) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 2012Thesis (PhD) -- İstanbul Technical University, Institute of Science and Technology, 2012Bu çalışmanın temel amacı, parametrik olmayan Bayesçi model seçim teknikleri içinde önemli bir yere sahip olan Dirichlet süreci karışım modelleri (DPM) için etkin ardışık Monte Carlo (SMC) örnekleyiciler tasarlamaktır. Tasarlanan algoritmalar, önerilen sınıf güncelleme metotları sayesinde, yeni gelen gözlemlerin ışığında parçacık gezingelerinde değişiklik yaparak gerçek DPM sonsal dağılımına daha iyi bir yaklaşıklık sağlamaktadır. Önerilen metot, DPM sonsal dağılımının çözümünde kullanılan diğer ardışık Monte Carlo örnekleyicileri genelleme özelliğe sahiptir. Tek ve çok boyutlu olasılık dağılımı kestirim problemlerinde yapılan değerlendirmelerde, özellikle sonsal dağılımın izole modlara sahip olduğu koşullarda, önerilen metodun klasik metotlara göre çok daha yüksek doğrulukta sonuca yakınsayabildiği görülmüştür. Ayrıca, manevralı hedeflerin takibinde ortaya atılan en yenilikçi modellerden biri olan değişken oranlı parçacık süzgeçleri (VRPF) tezde ele alınmış ve çoklu model yaklaşımları değişken oranlı modeller ile birleştirilerek, takip başarımını arttıran çoklu model değişken oranlı parçacık süzgeçleri (MM-VRPF) önerilmiştir. Çoklu model yaklaşımının manevralı hedef gezingelerini daha iyi modellediği benzetim sonuçları ile gösterilmiştir.In this thesis, we developed a novel online algorithm for posterior inference in Dirichlet Process Mixture (DPM) models that is based on the sequential Monte Carlo (SMC) samplers framework. The proposed method enables us to design new clustering update schemes, such as updating past trajectories of the particles in light of recent observations, and still ensures convergence to the true DPM posterior distribution asymptotically. Our method generalizes many sequential importance sampling based approaches and provides a computationally efficient improvement to particle filtering that is less prone to getting trapped in isolated modes. Performance has been evaluated in univariate and multivariate infinite Gaussian mixture density estimation problems. It is shown that the proposed algorithm outperforms conventional Monte Carlo approaches in terms of estimation variance and average log-marginal. Moreover, in this thesis we dealt with the maneuvering target tracking problem. We incorporated multiple model approach with the recently introduced variable rate particle filters (VRPF) in order to improve the tracking performance. The proposed variable rate model structure, referred as Multiple Model Variable Rate Particle Filter (MM-VRPF) results in a much more accurate tracking.DoktoraPh