Estimation theory has been developed over centuries. There are several approaches to utilizing this theory; in this chapter, these approaches are classified into three types. Type I includes the oldest two methods, the least squares (LS) and moment methods; both of these methods are non-optimal estimators. The least squares method was introduced by Carl Friedrich Gauss. Least squares problems f...

The Best Linear Unbiased Estimator (BLUE) has widely been used in atmospheric and oceanic data assimilation (DA). However, when the errors from data (observations and background forecasts) have non-Gaussian probability density functions (pdfs), the BLUE differs from the absolute Minimum Variance Unbiased Estimator (MVUE), minimizing the mean square a posteriori error. The non-Gaussianity of err...

An estimator is said to be unbiased if b(θ̂) = 0. If multiple unbiased estimates of θ are available, and the estimators can be averaged to reduce the variance, leading to the true parameter θ as more observations are available. Placing the unbiased restriction on the estimator simplifies the MSE minimization to depend only on its variance. The resulting estimator, called the Minimum Variance Unb...

Estimating the speed of aerial user equipment (UE) is critically important to provide reliable mobility management for cellular-connected unmanned vehicles (UAVs) since this can enhance quality service. The 3GPP standard uses number handovers made by a UE during predefined time period estimate and state efficiently. In paper, we introduce an approximation probability mass function handover coun...

An analog minimum-variance unbiased estimator (MVUE) over an asymmetric wireless sensor network is studied. Minimisation of variance is cast into a constrained non-convex optimisation problem. An explicit algorithm that solves the problem is provided. The solution is obtained by decomposing the original problem into a finite number of convex optimisation problems with explicit solutions. These ...

Vibrations of blade and tower have important impact for wind turbine. This paper presents a active controller design to suppress blade edgewise vibrations under aerodynamic load and gravitational load.Treating the sum of aerodynamic load input in edgewise direction and gravitational load as unknown disturbance input,a stochastic disturbance accommodating control(SDAC) approach is proposed to de...

SUMMARY The linear Gauss–Markov model for waveform-based moment tensor inversion often relies on the overdetermined least-squares method. It needs a proper stochastic of observables accurate and precise estimates unknown parameters. Furthermore, estimating level distribution random errors in observed waveforms is challenging due to assessing minimum-variance unbiased estimator (MVUE). Hence, ac...

We propose an algebraic combinatorial method for solving large sparse linear systems of equations locally that is, a method which can compute single evaluations of the signal without computing the whole signal. The method scales only in the sparsity of the system and not in its size, and allows to provide error estimates for any solution method. At the heart of our approach is the so-called reg...