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In geodesy and geoinformation science, as well as in many other technical disciplines, it is often not possible to directly determine the desired target quantities. Therefore, the unknown parameters must be linked with the measured values by a mathematical model which consists of the functional and the stochastic models. The functional model describes the geometrical–physical relationship between the measurements and the unknown parameters. This relationship is sufficiently well known for most applications. With regard to the stochastic model, two problem domains of fundamental importance arise: 1. How can stochastic models be set up as realistically as possible for the various geodetic observation methods and sensor systems? 2. How can the stochastic information be adequately considered in appropriate least squares adjustment models? Further questions include the interpretation of the stochastic properties of the computed target values with regard to precision and reliability and the use of the results for the detection of outliers in the input data (measurements). In this Special Issue, current research results on these general questions are presented in ten peer-reviewed articles. The basic findings can be applied to all technical scientific fields where measurements are used for the determination of parameters to describe geometric or physical phenomena.

History of engineering & technology --- EM-algorithm --- multi-GNSS --- PPP --- process noise --- observation covariance matrix --- extended Kalman filter --- machine learning --- GNSS phase bias --- sequential quasi-Monte Carlo --- variance reduction --- autoregressive processes --- ARMA-process --- colored noise --- continuous process --- covariance function --- stochastic modeling --- time series --- elementary error model --- terrestrial laser scanning --- variance-covariance matrix --- terrestrial laser scanner --- stochastic model --- B-spline approximation --- Hurst exponent --- fractional Gaussian noise --- generalized Hurst estimator --- very long baseline interferometry --- sensitivity --- internal reliability --- robustness --- CONT14 --- Errors-In-Variables Model --- Total Least-Squares --- prior information --- collocation vs. adjustment --- mean shift model --- variance inflation model --- outlierdetection --- likelihood ratio test --- Monte Carlo integration --- data snooping --- GUM analysis --- geodetic network adjustment --- stochastic properties --- random number generator --- Monte Carlo simulation --- 3D straight line fitting --- total least squares (TLS) --- weighted total least squares (WTLS) --- nonlinear least squares adjustment --- direct solution --- singular dispersion matrix --- laser scanning data

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• Reference Manager
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In geodesy and geoinformation science, as well as in many other technical disciplines, it is often not possible to directly determine the desired target quantities. Therefore, the unknown parameters must be linked with the measured values by a mathematical model which consists of the functional and the stochastic models. The functional model describes the geometrical–physical relationship between the measurements and the unknown parameters. This relationship is sufficiently well known for most applications. With regard to the stochastic model, two problem domains of fundamental importance arise: 1. How can stochastic models be set up as realistically as possible for the various geodetic observation methods and sensor systems? 2. How can the stochastic information be adequately considered in appropriate least squares adjustment models? Further questions include the interpretation of the stochastic properties of the computed target values with regard to precision and reliability and the use of the results for the detection of outliers in the input data (measurements). In this Special Issue, current research results on these general questions are presented in ten peer-reviewed articles. The basic findings can be applied to all technical scientific fields where measurements are used for the determination of parameters to describe geometric or physical phenomena.

History of engineering & technology --- EM-algorithm --- multi-GNSS --- PPP --- process noise --- observation covariance matrix --- extended Kalman filter --- machine learning --- GNSS phase bias --- sequential quasi-Monte Carlo --- variance reduction --- autoregressive processes --- ARMA-process --- colored noise --- continuous process --- covariance function --- stochastic modeling --- time series --- elementary error model --- terrestrial laser scanning --- variance-covariance matrix --- terrestrial laser scanner --- stochastic model --- B-spline approximation --- Hurst exponent --- fractional Gaussian noise --- generalized Hurst estimator --- very long baseline interferometry --- sensitivity --- internal reliability --- robustness --- CONT14 --- Errors-In-Variables Model --- Total Least-Squares --- prior information --- collocation vs. adjustment --- mean shift model --- variance inflation model --- outlierdetection --- likelihood ratio test --- Monte Carlo integration --- data snooping --- GUM analysis --- geodetic network adjustment --- stochastic properties --- random number generator --- Monte Carlo simulation --- 3D straight line fitting --- total least squares (TLS) --- weighted total least squares (WTLS) --- nonlinear least squares adjustment --- direct solution --- singular dispersion matrix --- laser scanning data --- EM-algorithm --- multi-GNSS --- PPP --- process noise --- observation covariance matrix --- extended Kalman filter --- machine learning --- GNSS phase bias --- sequential quasi-Monte Carlo --- variance reduction --- autoregressive processes --- ARMA-process --- colored noise --- continuous process --- covariance function --- stochastic modeling --- time series --- elementary error model --- terrestrial laser scanning --- variance-covariance matrix --- terrestrial laser scanner --- stochastic model --- B-spline approximation --- Hurst exponent --- fractional Gaussian noise --- generalized Hurst estimator --- very long baseline interferometry --- sensitivity --- internal reliability --- robustness --- CONT14 --- Errors-In-Variables Model --- Total Least-Squares --- prior information --- collocation vs. adjustment --- mean shift model --- variance inflation model --- outlierdetection --- likelihood ratio test --- Monte Carlo integration --- data snooping --- GUM analysis --- geodetic network adjustment --- stochastic properties --- random number generator --- Monte Carlo simulation --- 3D straight line fitting --- total least squares (TLS) --- weighted total least squares (WTLS) --- nonlinear least squares adjustment --- direct solution --- singular dispersion matrix --- laser scanning data

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The classical Melnikov method provides information on the behavior of deterministic planar systems that may exhibit transitions, i.e. escapes from and captures into preferred regions of phase space. This book develops a unified treatment of deterministic and stochastic systems that extends the applicability of the Melnikov method to physically realizable stochastic planar systems with additive, state-dependent, white, colored, or dichotomous noise. The extended Melnikov method yields the novel result that motions with transitions are chaotic regardless of whether the excitation is deterministic or stochastic. It explains the role in the occurrence of transitions of the characteristics of the system and its deterministic or stochastic excitation, and is a powerful modeling and identification tool. The book is designed primarily for readers interested in applications. The level of preparation required corresponds to the equivalent of a first-year graduate course in applied mathematics. No previous exposure to dynamical systems theory or the theory of stochastic processes is required. The theoretical prerequisites and developments are presented in the first part of the book. The second part of the book is devoted to applications, ranging from physics to mechanical engineering, naval architecture, oceanography, nonlinear control, stochastic resonance, and neurophysiology.

Differentiable dynamical systems. --- Chaotic behavior in systems. --- Stochastic systems. --- Systems, Stochastic --- Stochastic processes --- System analysis --- Chaos in systems --- Chaos theory --- Chaotic motion in systems --- Differentiable dynamical systems --- Dynamics --- Nonlinear theories --- System theory --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Affine transformation. --- Amplitude. --- Arbitrarily large. --- Attractor. --- Autocovariance. --- Big O notation. --- Central limit theorem. --- Change of variables. --- Chaos theory. --- Coefficient of variation. --- Compound Probability. --- Computational problem. --- Control theory. --- Convolution. --- Coriolis force. --- Correlation coefficient. --- Covariance function. --- Cross-covariance. --- Cumulative distribution function. --- Cutoff frequency. --- Deformation (mechanics). --- Derivative. --- Deterministic system. --- Diagram (category theory). --- Diffeomorphism. --- Differential equation. --- Dirac delta function. --- Discriminant. --- Dissipation. --- Dissipative system. --- Dynamical system. --- Eigenvalues and eigenvectors. --- Equations of motion. --- Even and odd functions. --- Excitation (magnetic). --- Exponential decay. --- Extreme value theory. --- Flow velocity. --- Fluid dynamics. --- Forcing (recursion theory). --- Fourier series. --- Fourier transform. --- Fractal dimension. --- Frequency domain. --- Gaussian noise. --- Gaussian process. --- Harmonic analysis. --- Harmonic function. --- Heteroclinic orbit. --- Homeomorphism. --- Homoclinic orbit. --- Hyperbolic point. --- Inference. --- Initial condition. --- Instability. --- Integrable system. --- Invariant manifold. --- Iteration. --- Joint probability distribution. --- LTI system theory. --- Limit cycle. --- Linear differential equation. --- Logistic map. --- Marginal distribution. --- Moduli (physics). --- Multiplicative noise. --- Noise (electronics). --- Nonlinear control. --- Nonlinear system. --- Ornstein–Uhlenbeck process. --- Oscillation. --- Parameter space. --- Parameter. --- Partial differential equation. --- Perturbation function. --- Phase plane. --- Phase space. --- Poisson distribution. --- Probability density function. --- Probability distribution. --- Probability theory. --- Probability. --- Production–possibility frontier. --- Relative velocity. --- Scale factor. --- Shear stress. --- Spectral density. --- Spectral gap. --- Standard deviation. --- Stochastic process. --- Stochastic resonance. --- Stochastic. --- Stream function. --- Surface stress. --- Symbolic dynamics. --- The Signal and the Noise. --- Topological conjugacy. --- Transfer function. --- Variance. --- Vorticity.