User:Ouwerbie/Signals & System Engineering

Signals & System Engineering DRAFT

For Inertial Measurement and Navigation Systems

Author: Jaap Overschie
Signal Processing: Signal (electrical engineering); Signal processing
Errors, Uncertainty & Covariance,...... Probability: Measurement uncertainty; Variance; Covariance; Covariance matrix; Expected value; Median; Location parameter; Squared deviations; Accuracy and precision; Signal-to-noise ratio; Coefficient of variation; Probability theory; Univariate distribution; Probability mass function; Probability distribution; Probability density function; Cumulative distribution function; Characteristic function (probability theory); Moment (mathematics); Central moment; Cumulant; Moment-generating function; List of probability distributions; Multivariate statistics; Joint probability distribution
Error Compounding, Additive or Multiplicative: Round-off error; Kahan_summation_algorithm; Engineering tolerance; Statistical interference; Normal distribution; Log-normal distribution; Benford's law
Error and Uncertainty Propagation, Sensitivity Analysis: Propagation of uncertainty; Sensitivity analysis; Linear differential equation; Partial derivative; Total derivative; Jacobian matrix and determinant; Hessian matrix

Sampling, Quantisation and AD conversion: Sampling (signal processing); Nyquist–Shannon sampling theorem; Sampling rate; Sample and hold; Oversampling; Undersampling; Quantization (signal processing); Analog-to-digital converter; Delta-sigma modulation; Pulse-code modulation; Linear pulse-code modulation; Pulse-density modulation; Delta modulation
Sampling Issues: Truncation error; Quantization error; Discretization error; Aliasing; Anti-aliasing filter
Signal Reconstruction: Zero-order hold; First-order hold; Whittaker–Shannon interpolation formula; Lanczos resampling; Rectangular function; Sinc filter; Sinc function; Low-pass filter
Numerical Integration, Numerical Methods and Analysis: Explicit and implicit methods; Numerical stability; Numerical integration; Truncation error (numerical integration); Rectangle method; Riemann sum; Trapezoidal rule; Simpson's rule; Numerical methods for ordinary differential equations; Euler method; Backward Euler method; Runge–Kutta methods; List of Runge–Kutta methods; Energy drift; List of numerical analysis topics; List of numerical analysis software; List of numerical libraries
Time series & Spectral Analysis: Time series; Convolution; Fourier transform; Discrete Fourier transform; Fast Fourier transform; Periodogram; Spectral density; Spectral density estimation; Window function; Spectral leakage; Bartlett's method; Welch's method; Multitaper; Cepstrum; Complex logarithm
Noise Characteristics a.k.a. Uncertainty, Freedom of Motion: Noise (electronics); List of noise topics; White noise; Colors of noise; Phase noise; Jitter; Flicker noise; Random walk; Brownian noise; Autoregressive model; Noise spectral density
Allan Variance: Allan variance; Modified Allan variance
Filters: Filter design; Finite impulse response; Infinite impulse response; Cascaded integrator-comb filter; Matched filter; Savitzky–Golay filter; Hodges–Lehmann estimator
Stochastic Systems & Wiener Process: Stationary process; Stationary ergodic process; Wiener–Khinchin theorem; Stochastic process; Gauss–Markov process; Wiener process; Regression toward the mean; Jump diffusion; Ornstein–Uhlenbeck process; Wiener filter
Estimation & Least Squares: Principal axis theorem; Spectral theorem; Estimator; Bias of an estimator; Estimation theory; Gauss–Markov theorem; Least squares; Ordinary least squares; Linear least squares (mathematics); Shrinkage estimator; Stein's example; James–Stein estimator; Decorrelation; Canonical correlation; Whitening transformation; Principal component analysis; Independent component analysis; Regularization (mathematics); Tikhonov regularization; Regularization by spectral filtering
LSE special problem Optimal Estimation of Rotation Matrices: Procrustes transformation; Affine transformation; Procrustes analysis; Orthogonal Procrustes problem; Kabsch algorithm; Wahba's problem
LSE taken further: Taxicab geometry; Mahalanobis distance; Total least squares; Recursive least squares filter; Random_sample_consensus ; RANSAC; Iterative refinement; Overfitting; Filtering problem (stochastic processes); Least mean squares filter; Similarities between Wiener and LMS; Predictor–corrector method; Kriging
State Estimation, Kalman Filtering: Bayesian inference; Bayesian programming; Maximum likelihood; Maximum likelihood estimation; Best linear unbiased prediction; Observability; State observer; Kalman filter; Alpha_beta_filter; Nonlinear filter; Extended Kalman filter; Symmetry-preserving filter; Bayesian network; Particle filter; Fast Kalman filter; Invariant extended Kalman filter
Sensor & Process Fusion
Aiding
System Control: System analysis; LTI system theory; Laplace transform; Separation principle; State space representation; Full state feedback; Linear-quadratic-Gaussian control
MultiRate Systems: Multi-rate digital signal processing; Downsampling; Upsampling; Interpolation; Sample rate conversion
Angle representations, 3D Attitude, Rotation and Angular velocity, Translation: CORDIC; Transformation matrix; Axis-angle representation; Plane of rotation; Rotation (mathematics); Rotation formalisms in three dimensions; Rotation operator (vector space); Rotation matrix; Precession; Nutation; Rotation; Euler angles; Aircraft principal axes; Givens rotation; Jacobi rotation; Rotation group SO(3); Rodrigues' rotation formula; Euler–Rodrigues formula; Four-dimensional space; Rotations in 4-dimensional Euclidean space; Quaternion; Quaternions and spatial rotation; Conversion between quaternions and Euler angles; Dual quaternion; Moving frame; Lie group; Euclidean group
Inertial Navigation Maths: Inertial frame of reference; Non-inertial reference frame; Rotating reference frame; Angular velocity; Infinitesimal transformation; Gimbal lock; Schuler tuning; Parallel transport
Fictious forces and other effects in a moving frame: Fictitious force; Centrifugal force (rotating reference frame); Coriolis effect; Euler force; Eötvös effect
Matrix Operations: List of matrices; Matrix decomposition; Eigenvalues and eigenvectors; Eigendecomposition of a matrix; Singular-value decomposition; Generalized inverse; Cholesky decomposition; Householder transformation; QR decomposition
Coning & Sculling: Rolling cone motion
Gyroscopes: Gyroscope; Rate integrating gyroscope
Accelerometers: Accelerometer; PIGA accelerometer
Ensemble Domain Implementations: Sample mean and sample covariance; Estimation of covariance matrices; Covariance intersection; Ensemble forecasting; Ensemble Kalman filter
Stochastic Calculus: Stochastic differential equation; Diffusion process; Jump process; Itō calculus; Stratonovich integral
Robust Performance and Robust Stability: Sensitivity (control systems); Robust control; Robust decision making; Robust statistics; Quantitative feedback theory
Modeling and linearisation for observer design: System identification; Nonlinear system; Taylor series; Perturbation theory; Laurent series; Z-transform; Fourier series
Observer mode switching, Bumpless Transfer, KF switching: Sliding mode control
APPLICATIONS Of Inertial Measurement Unit IMU
Guidance and Navigation: Guidance system; Guidance, navigation and control; Gyrocompass; Attitude and heading reference system; Dead reckoning; Earth-centered inertial; Earth's rotation; Latitude; ECEF; Inertial navigation system; LN-3 Inertial Navigation System
GPS INS fusion: Sensor fusion; Global Positioning System; Real Time Kinematic; GPS/INS; Error analysis for the Global Positioning System
GPS extended: GNSS augmentation; GPS augmentation; Assisted GPS; Differential GPS; Wide Area Augmentation System; Local Area Augmentation System; OmniSTAR
Borehole Surveying: Well logging; Logging while drilling; Measurement while drilling; Directional drilling
Precision Farming: Precision agriculture
Dynamic Positioning: Dynamic positioning
People in Engineering: Richard Hamming; Claude Shannon; Ronald Fisher; Malcolm D. Shuster; Jim Williams (analog designer); Bob Pease; Norbert Wiener; Rudolf E. Kálmán; W. Edwards Deming; Jack Kilby; Robert Noyce
BELOW TO BE SORTED and inserted in sequence
MISSING ITEMS
missing Numerical Implementation methods of KF e.g. UD factorisation
missing direct integration of D(RotationMatrix)/dt
missing Numerical Integration Errors in Frequency Domain cf. Hamming
Missing Fixed Point Implementations
missing Coning and Sculling solutions
missing Pseudo Coning
missing Hadamard variance
missing, Error Modeling for Borehole Surveying, precision of estimate.
missing INS error propagation, Borehole Surveying Systems Error Models: Multivariate normal distribution; Multivariate stable distribution; Chi distribution
missing Gyro While Drill
missing, attitude dilution of precision
missing Wander azimuth and other specifc navigation frames
missing KF observability
missing multirate systems for data processing
missing Robust Estimation, Robust KF
missing Rate Random Walk RRW, Angular Random Walk ARW definition wrt to standard noise models
missing quantisation noise
missing 3 parameter quaternion plus sign
Attitude Estimation and Initial Alignment
missing, Attitude Estimation Direct Method
missing davenport q-method for attitude determination
missing SVD based attitude determination
missing QUEST Attitude estimator as solution to wahba's problem
missing Attitude estimation indirect method: Gyrocompassing, Azimuth Alignment enhanced by horizontal force
missing Observability of RIMU systems
missing Redundant Inertial Measurement Systems RIMU
missing, optimally skewed sensor arrays
missing Impact of cross axis sensitivity and sensor misalignment cf. James Farrell
missing Fisher Information and information Matrix: Fisher information; Formation matrix; Observed information; Cramér–Rao bound
missing literature reference
missing INS Transport Rates
missing Complementary Filter
missing Dimension Analysis, PI theorem
missing Akima spline fit
missing Numerical Methods: Hermitian matrix; Hankel matrix
Control Engineering, Dynamics of Systems: Ergodic theory; Control engineering; Dynamical systems theory; Control theory; Optimal control; Bode plot; Nichols plot; Bode's sensitivity integral; Nyquist plot; Linear phase; Minimum phase; Holonomic (robotics); Holonomic constraints; Nonholonomic system; Bicycle and motorcycle dynamics; Falling cat problem; Parallel parking problem
Stuff to be sorted
´Careful not to overlap with JARGON from Statistics: Filter bank; Generalized least squares; Partial least squares regression; Iteratively reweighted least squares; Loss function; Geometric median; Regression validation; Mean and predicted response; Errors and residuals; Goodness of fit; Studentized residual; Portal:Statistics; Confidence region; Ellipsoid; Errors-in-variables models; Efficient estimator; Fisher consistency; Consistent estimator; Polar decomposition; Outlier; Cross-covariance; List of uncertainty propagation software; Uncertainty quantification; Experimental uncertainty analysis; Automatic differentiation; Digital filter; Recursive filter; Moving average; Laplace distribution; Nonuniform sampling; Phase margin; Signal reconstruction; Group delay and phase delay; Phase distortion; Waveform; Angle; Geodetic datum; Discretization; Stochastic simulation; Discrete event simulation; Time-scale calculus; Resonance; Electrical impedance; Q factor; Mean-preserving spread; Correlation and dependence; Numerical differentiation; Finite difference; Padé approximant; Stencil (numerical analysis); Five-point stencil; Newton polynomial; Polynomial interpolation; Polynomial regression; Spline (mathematics); Discrete spline interpolation; Cubic Hermite spline; Collocation method; Trigonometric interpolation; Chebfun; Lagrange polynomial; Singular value; Singular value decomposition; Verification and validation; Curve fitting; Smoothing; Autoregressive–moving-average model; Exponential smoothing; Local regression; Quantification of margins and uncertainties; Decimation (signal processing); Comb filter; Chebyshev filter; Butterworth filter; Differentiator; Recurrence relation; Holonomic function; Orthogonal polynomials; Kernel (statistics); Kernel method; Spectral theory; Spectrum of a matrix; Spectral radius; Integrator; Gramian matrix; Controllability Gramian; Observability Gramian; Controllability; State-space representation; Phase portrait; Phase space; Filter (signal processing); Levenberg–Marquardt algorithm; Nelder–Mead method; Conjugate gradient method; Nonlinear conjugate gradient method; Preconditioner; Iterative method; Matrix splitting; Root-finding algorithm; List of operator splitting topics; Cauchy's integral theorem; Methods of contour integration; Antiderivative; Lebesgue integration; Pathological (mathematics); Monte Carlo method; Quasi-Monte Carlo method; Markov chain Monte Carlo; Markov chain; Brownian motion; Ergodic hypothesis; Ergodic process; Ergodicity; Law of large numbers; Central limit theorem; Central limit theorem for directional statistics; Taylor expansions for the moments of functions of random variables; Law of the iterated logarithm; Martingale (probability theory); Noisy-channel coding theorem; Poisson distribution; Hofstadter's law; Overengineering; Planning fallacy; Markov process; Variance-stabilizing transformation; Examples of Markov chains; Continuous stochastic process; Continuous-time Markov chain; Metropolis–Hastings algorithm; Gibbs sampling; Gaussian process; Brownian bridge; Fractional Brownian motion; Pink noise; Crest factor; Clipping (signal processing); Dynamic range; Form factor (electronics); Johnson–Nyquist noise; Quantum 1/f noise; Shot noise; Autoregressive fractionally integrated moving average; Riemann integral; Heteroscedasticity; Homoscedasticity; Factor analysis; Jordan normal form; Canonical form; Angles between flats; Matrix similarity; Additive white Gaussian noise; Type I and type II errors; Hilbert transform; Envelope (waves); Group velocity; Phase velocity; Wave; Impulse response; Quadrature filter; Analytic signal; Noise floor; Burst noise; Moving target indication; Karhunen–Loève theorem; Mean squared error; Random variable; Orthogonal functions; Covariance function; Uncorrelated random variables; Independence (probability theory); Statistic; Discrete cosine transform; Hilbert space; Fourier analysis; Orthonormal basis; Cartesian coordinate system; Lp space; Mean absolute error; Variogram; Random field; Autocorrelation; Cross-correlation; Regression analysis; Correlation function; Covariance mapping; Generalized canonical correlation; Differential equation; Multiplier (Fourier analysis); Homomorphic filtering; Conformal map; Transient (acoustics); Likelihood ratio; Likelihood function; Conditional probability; Frequentist inference; Fiducial inference; Decision theory; German tank problem; Bayes factor; Blind deconvolution; Hidden Markov model; Recursive Bayesian estimation; Dynamic Bayesian network; Variational Bayesian methods; Generalized filtering; Expectation–maximization algorithm; MM algorithm; Mixture model; Pfaffian constraint; Udwadia–Kalaba equation; Parallel curve; Grey box model; Black box; Cybernetics; Wiener deconvolution; Deconvolution; Cascaded integrator–comb filter; Nearest-neighbor interpolation; Bandlimiting; Instantaneous phase; Gram–Schmidt process; Numerical analysis; Tortuosity; Analysis of algorithms; Inner product space; Arnoldi iteration; Condition number; Well-posed problem; Coherence (signal processing); Pearson correlation coefficient; Scaled correlation; Statistical inference; Statistics; Eigenvalue perturbation; Data fusion; Data wrangling; Information integration; Integrative level; Data assimilation; Image fusion; Convolutional neural network; Design of experiments; Graphical model; Monty Hall problem; List of people in systems and control; Lists of engineers; List of systems engineers; List of systems scientists; List of systems engineering universities; List of information graphics software
missing windowed sync interpolation using kaiser window. see also Lanczos resampling

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