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Adaptive Real-Time Numerical Differentiation: Theory and Application to Autonomous Systems
Adaptive Real-Time Numerical Differentiation: Theory and Application to Autonomous Systems
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20260202103649
- ISBN
- 9798314875599
- DDC
- 620
- 저자명
- Verma, Shashank.
- 서명/저자
- Adaptive Real-Time Numerical Differentiation: Theory and Application to Autonomous Systems
- 발행사항
- [Sl] : University of Michigan, 2025
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2025
- 형태사항
- 211 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 86-11, Section: B.
- 주기사항
- Advisor: Bernstein, Dennis S.
- 학위논문주기
- Thesis (Ph.D.)--University of Michigan, 2025.
- 초록/해제
- 요약Numerical differentiation is an essential component of control, signal processing, and state estimation, yet it remains notoriously sensitive to noise when derived from sampled sensor data. The unbounded nature of the differentiation operator introduces high sensitivity to measurement noise and necessitates careful design of real-time algorithms. Four fundamental challenges hinder real-time numerical differentiation: (1) it must operate causally, relying exclusively on present and recent past data, (2) it must work with discrete-time signals rather than continuous-time signals, (3) all available data are noisy with noise that is unknown and has potentially changing spectral characteristics due to sensor degradation or environmental factors, and (4) no ground truth is available to assess real-time derivative accuracy.This dissertation addresses these challenges by introducing adaptive input state estimation (AISE), a novel real-time numerical differentiation method that computes derivative estimates under unknown and time-varying noise and signal conditions. AISE employs a dynamically updated estimator whose coefficients are recursively refined at each sample time. Specific innovations include: (1) a variable-rate forgetting (VRF) mechanism to enhance resilience against varying signal and noise characteristics, (2) an exponential resetting (ER) strategy to mitigate covariance windup when persistency of excitation in the signal is low, and (3) an adaptive Kalman filter for real-time noise-covariance adaptation. AISE operates entirely in discrete time, using only current and past data to generate an estimate of the nth-order derivative with minimal latency.The performance and versatility of AISE are demonstrated through applications including proportional-integral-derivative (PID) control, sensor-fault detection, extremum seeking, and trajectory tracking and prediction. Notably, integrating AISE into a PID loop significantly improves control performance, while the kinematics-based sensor fault detection (KSFD) framework leverages AISE for fault detection in autonomous vehicles. By providing a self-adjusting, noise-resilient, real-time differentiation capability, AISE offers a flexible and practical solution for generating reliable derivative estimates, supporting signal processing and control in modern autonomous systems and other real-time applications.
- 일반주제명
- Engineering
- 일반주제명
- Aerospace engineering
- 일반주제명
- Applied mathematics
- 일반주제명
- Computer engineering
- 키워드
- Adaptive systems
- 키워드
- Target tracking
- 기타저자
- University of Michigan Aerospace Engineering
- 기본자료저록
- Dissertations Abstracts International. 86-11B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■00520260202103649
■006m o d
■007cr#unu||||||||
■020 ▼a9798314875599
■035 ▼a(MiAaPQ)AAI32092671
■035 ▼a(MiAaPQ)umichrackham006146
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a620
■1001 ▼aVerma, Shashank.
■24510▼aAdaptive Real-Time Numerical Differentiation: Theory and Application to Autonomous Systems
■260 ▼a[Sl]▼bUniversity of Michigan▼c2025
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2025
■300 ▼a211 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 86-11, Section: B.
■500 ▼aAdvisor: Bernstein, Dennis S.
■5021 ▼aThesis (Ph.D.)--University of Michigan, 2025.
■520 ▼aNumerical differentiation is an essential component of control, signal processing, and state estimation, yet it remains notoriously sensitive to noise when derived from sampled sensor data. The unbounded nature of the differentiation operator introduces high sensitivity to measurement noise and necessitates careful design of real-time algorithms. Four fundamental challenges hinder real-time numerical differentiation: (1) it must operate causally, relying exclusively on present and recent past data, (2) it must work with discrete-time signals rather than continuous-time signals, (3) all available data are noisy with noise that is unknown and has potentially changing spectral characteristics due to sensor degradation or environmental factors, and (4) no ground truth is available to assess real-time derivative accuracy.This dissertation addresses these challenges by introducing adaptive input state estimation (AISE), a novel real-time numerical differentiation method that computes derivative estimates under unknown and time-varying noise and signal conditions. AISE employs a dynamically updated estimator whose coefficients are recursively refined at each sample time. Specific innovations include: (1) a variable-rate forgetting (VRF) mechanism to enhance resilience against varying signal and noise characteristics, (2) an exponential resetting (ER) strategy to mitigate covariance windup when persistency of excitation in the signal is low, and (3) an adaptive Kalman filter for real-time noise-covariance adaptation. AISE operates entirely in discrete time, using only current and past data to generate an estimate of the nth-order derivative with minimal latency.The performance and versatility of AISE are demonstrated through applications including proportional-integral-derivative (PID) control, sensor-fault detection, extremum seeking, and trajectory tracking and prediction. Notably, integrating AISE into a PID loop significantly improves control performance, while the kinematics-based sensor fault detection (KSFD) framework leverages AISE for fault detection in autonomous vehicles. By providing a self-adjusting, noise-resilient, real-time differentiation capability, AISE offers a flexible and practical solution for generating reliable derivative estimates, supporting signal processing and control in modern autonomous systems and other real-time applications.
■590 ▼aSchool code: 0127.
■650 4▼aEngineering
■650 4▼aAerospace engineering
■650 4▼aApplied mathematics
■650 4▼aComputer engineering
■653 ▼aReal-time numerical differentiation
■653 ▼aAutonomous systems
■653 ▼aSensor-fault detection
■653 ▼aAdaptive systems
■653 ▼aTarget tracking
■690 ▼a0538
■690 ▼a0537
■690 ▼a0364
■690 ▼a0464
■71020▼aUniversity of Michigan▼bAerospace Engineering.
■7730 ▼tDissertations Abstracts International▼g86-11B.
■790 ▼a0127
■791 ▼aPh.D.
■792 ▼a2025
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17358139▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
