User:Ouwerbie/Signals & System Engineering

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
 * 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 sinc interpolation using kaiser window. see also Lanczos resampling