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Signals & System Engineering2[edit]

For Inertial Measurement and Navigation Systems[edit]

Jaap Overschie
Signal Processing
Signal (electrical engineering)
Signal processing
Errors, Uncertainty & Covariance
Measurement uncertainty
Covariance matrix
Expected value
Location parameter
Squared deviations
Variance decomposition of forecast errors
Accuracy and precision
Signal-to-noise ratio
Coefficient of variation
Probability density function
Error Compounding, Additive or Multiplicative
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
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
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
Time series & Spectral Analysis
Fourier transform
Discrete Fourier transform
Fast Fourier transform
Spectral density
Spectral density estimation
Window function
Spectral leakage
Bartlett's method
Welch's method
Complex logarithm
Noise Characteristics
Noise (electronics)
List of noise topics
White noise
Colors of noise
Phase noise
Flicker noise
Random walk
Brownian noise
Autoregressive model
Noise spectral density
Allan Variance
Allan variance
Modified Allan variance
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
Wiener process
Ornstein–Uhlenbeck process
Wiener filter
Estimation & Least Squares
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
Whitening transformation
Bayesian inference
Regularization (mathematics)
Tikhonov regularization
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
Principal component analysis
Independent component analysis
Recursive least squares filter
Iterative refinement
Filtering problem (stochastic processes)
Least mean squares filter
Similarities between Wiener and LMS
Predictor–corrector method
State Estimation, Kalman Filtering
Maximum likelihood
Best linear unbiased prediction
State observer
Kalman filter
Nonlinear filter
Extended Kalman filter
Symmetry-preserving filter
Bayesian network
Particle filter
Fast Kalman filter
Invariant extended Kalman filter
Sensor & Process Fusion
System Control
System analysis
LTI system theory
Laplace transform
Separation principle
State space representation
Full state feedback
Linear-quadratic-Gaussian control
Numerical Integration, Numerical Methods and Analysis
Numerical integration
Truncation error (numerical integration)
Rectangle method
Riemann sum
Trapezoidal rule
Simpson's rule
Numerical methods for ordinary differential equations
Euler method
Runge–Kutta methods
List of Runge–Kutta methods
Energy drift
Symplectic integrator
Semi-implicit Euler method
List of numerical analysis topics
List of numerical analysis software
List of numerical libraries
List of information graphics software
MultiRate Systems
Multi-rate digital signal processing
Sample rate conversion
Angle representations, 3D Attitude, Rotation and Angular velocity, Translation
Transformation matrix
Axis-angle representation
Plane of rotation
Rotation (mathematics)
Rotation formalisms in three dimensions
Rotation operator (vector space)
Rotation matrix
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
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
Rate integrating gyroscope
PIGA accelerometer
Ensemble Domain Implementations
Sample mean and sample covariance
Estimation of covariance matrices
Covariance intersection
Data assimilation
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
Modeling and linearisation for observer design
System identification
Nonlinear system
Taylor series
Perturbation theory
Laurent series
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
Attitude and heading reference system
Dead reckoning
Earth-centered inertial
Earth's rotation
Inertial navigation system
LN-3 Inertial Navigation System
GPS INS fusion
Sensor fusion
Global Positioning System
Real Time Kinematic
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
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
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 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
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
Stuff to be sorted
Filter bank
Generalized least squares
Partial least squares regression
Loss function
Iteratively reweighted least squares
Geometric median
Regression validation
Mean and predicted response
Errors and residuals
Goodness of fit
Studentized residual
Confidence region
Hankel matrix
Errors-in-variables models
Efficient estimator
Fisher consistency
Consistent estimator
Polar decomposition
List of uncertainty propagation software
Uncertainty quantification
Experimental uncertainty analysis
Automatic differentiation
Digital filter
Recursive filter
Moving average
Laplace distribution
Nonuniform sampling
Nyquist plot
Nichols plot
Quantitative feedback theory
Bode plot
Bode's sensitivity integral
Phase margin
Signal reconstruction
Group delay and phase delay
Minimum phase
Linear phase
Phase distortion
Geodetic datum
Stochastic simulation
Discrete event simulation
Time-scale calculus
Electrical impedance
Q factor
Mean-preserving spread
Canonical correlation
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
Lagrange polynomial
Singular value
Singular value decomposition
Verification and validation
Curve fitting
Autoregressive–moving-average model
Exponential smoothing
Local regression
Quantification of margins and uncertainties
Decimation (signal processing)
Comb filter
Chebyshev filter
Butterworth filter
Recurrence relation
Holonomic function
Orthogonal polynomials
Kernel (statistics)
Kernel method
Spectral theory
Spectrum of a matrix
Spectral radius
Gramian matrix
Controllability Gramian
Observability Gramian
State-space representation
Control theory
Control engineering
Phase portrait
Phase space
Dynamical systems theory
Filter (signal processing)
Levenberg–Marquardt algorithm
Nelder–Mead method
Conjugate gradient method
Nonlinear conjugate gradient method
Iterative method
Matrix splitting
Root-finding algorithm
List of operator splitting topics
Cauchy's integral theorem
Methods of contour integration
Lebesgue integration
Pathological (mathematics)
Monte Carlo method
Quasi-Monte Carlo method
Markov chain Monte Carlo
Markov chain
Brownian motion
Ergodic hypothesis
Ergodic process
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
Regression toward the mean
Martingale (probability theory)
Noisy-channel coding theorem
Poisson distribution
Hofstadter's law
Ergodic theory
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
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
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)
Discrete cosine transform
Hilbert space
Fourier analysis
Orthonormal basis
Cartesian coordinate system
Lp space
Mean absolute error
Random field
Regression analysis
Correlation function
Covariance mapping
Generalized canonical correlation
Differential equation
Spectral theorem
Multiplier (Fourier analysis)
Homomorphic filtering
Conformal map
Transient (acoustics)
Likelihood ratio
Likelihood function
Conditional probability
Frequentist inference
German tank problem
Bayes factor
Blind deconvolution
Hidden Markov model
Recursive Bayesian estimation
Optimal control
Dynamic Bayesian network
Variational Bayesian methods
Generalized filtering
Expectation–maximization algorithm
MM algorithm
Mixture model
Nonholonomic system
Holonomic constraints
Falling cat problem
Holonomic (robotics)
Bicycle and motorcycle dynamics
Parallel parking problem
Pfaffian constraint
Udwadia–Kalaba equation
Parallel curve
Grey box model
Black box
Wiener deconvolution
Cascaded integrator–comb filter
Nearest-neighbor interpolation
Instantaneous phase
Gram–Schmidt process
Numerical analysis
Analysis of algorithms
Inner product space
Arnoldi iteration
Hermitian matrix
Condition number
Well-posed problem
Coherence (signal processing)
Pearson correlation coefficient
Scaled correlation