**Time deviation** (**TDEV**),^{ [1] } also known as , is the time stability of phase *x* versus observation interval *τ* of the measured clock source. The time deviation thus forms a standard deviation type of measurement to indicate the time instability of the signal source. This is a scaled variant of frequency stability of Allan deviation. It is commonly defined from the modified Allan deviation, but other estimators may be used.

*Time variance* (*TVAR*) also known as is the time stability of phase versus observation interval tau. It is a scaled variant of modified Allan variance.

TDEV is a metric often used to determine an aspect of the quality of timing signals in telecommunication applications and is a statistical analysis of the phase stability of a signal over a given period. Measurements of a reference timing signal will refer to its TDEV and maximum time interval error (MTIE) values, comparing them to specified masks or goals.

The most common estimator uses the modified Allan variance

where . The 3 in the denominator normalizes TVAR to be equal to the classical variance if the deviations in x are random and uncorrelated (white-noise).

or TDEV, which is the square-root of TVAR, may be derived from MDEV modified Allan deviation

**Autocorrelation**, sometimes known as **serial correlation** in the discrete time case, is the correlation of a signal with a delayed copy of itself as a function of delay. Informally, it is the similarity between observations of a random variable as a function of the time lag between them. The analysis of autocorrelation is a mathematical tool for finding repeating patterns, such as the presence of a periodic signal obscured by noise, or identifying the missing fundamental frequency in a signal implied by its harmonic frequencies. It is often used in signal processing for analyzing functions or series of values, such as time domain signals.

In statistics, a **normal distribution** or **Gaussian distribution** is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is

In statistics, the **standard deviation** is a measure of the amount of variation of a random variable expected about its mean. A low standard deviation indicates that the values tend to be close to the mean of the set, while a high standard deviation indicates that the values are spread out over a wider range.

In probability theory and statistics, **variance** is the expected value of the squared deviation from the mean of a random variable. The standard deviation is obtained as the square root of the variance. Variance is a measure of dispersion, meaning it is a measure of how far a set of numbers is spread out from their average value. It is the second central moment of a distribution, and the covariance of the random variable with itself, and it is often represented by , , , , or .

The **Allan variance** (**AVAR**), also known as **two-sample variance**, is a measure of frequency stability in clocks, oscillators and amplifiers. It is named after David W. Allan and expressed mathematically as . The **Allan deviation** (**ADEV**), also known as **sigma-tau**, is the square root of the Allan variance, .

**Pink noise**, **1⁄f noise** or **fractional noise** or **fractal noise** is a signal or process with a frequency spectrum such that the power spectral density is inversely proportional to the frequency of the signal. In pink noise, each octave interval carries an equal amount of noise energy.

In probability theory, a **log-normal** (or **lognormal**) **distribution** is a continuous probability distribution of a random variable whose logarithm is normally distributed. Thus, if the random variable X is log-normally distributed, then *Y* = ln(*X*) has a normal distribution. Equivalently, if Y has a normal distribution, then the exponential function of Y, *X* = exp(*Y*), has a log-normal distribution. A random variable which is log-normally distributed takes only positive real values. It is a convenient and useful model for measurements in exact and engineering sciences, as well as medicine, economics and other topics (e.g., energies, concentrations, lengths, prices of financial instruments, and other metrics).

In statistics, the **mean squared error** (**MSE**) or **mean squared deviation** (**MSD**) of an estimator measures the average of the squares of the errors—that is, the average squared difference between the estimated values and the actual value. MSE is a risk function, corresponding to the expected value of the squared error loss. The fact that MSE is almost always strictly positive is because of randomness or because the estimator does not account for information that could produce a more accurate estimate. In machine learning, specifically empirical risk minimization, MSE may refer to the *empirical* risk, as an estimate of the true MSE.

In statistics, **Spearman's rank correlation coefficient** or **Spearman's ρ**, named after Charles Spearman and often denoted by the Greek letter (rho) or as , is a nonparametric measure of rank correlation. It assesses how well the relationship between two variables can be described using a monotonic function.

The **standard error** (**SE**) of a statistic is the standard deviation of its sampling distribution or an estimate of that standard deviation. If the statistic is the sample mean, it is called the **standard error of the mean** (**SEM**). The standard error is a key ingredient in producing confidence intervals.

In statistics, **propagation of uncertainty** is the effect of variables' uncertainties on the uncertainty of a function based on them. When the variables are the values of experimental measurements they have uncertainties due to measurement limitations which propagate due to the combination of variables in the function.

In signal processing, **cross-correlation** is a measure of similarity of two series as a function of the displacement of one relative to the other. This is also known as a *sliding dot product* or *sliding inner-product*. It is commonly used for searching a long signal for a shorter, known feature. It has applications in pattern recognition, single particle analysis, electron tomography, averaging, cryptanalysis, and neurophysiology. The cross-correlation is similar in nature to the convolution of two functions. In an autocorrelation, which is the cross-correlation of a signal with itself, there will always be a peak at a lag of zero, and its size will be the signal energy.

**Dilution of precision** (**DOP**), or **geometric dilution of precision** (**GDOP**), is a term used in satellite navigation and geomatics engineering to specify the error propagation as a mathematical effect of navigation satellite geometry on positional measurement precision.

In statistics and signal processing, a **minimum mean square error** (**MMSE**) estimator is an estimation method which minimizes the mean square error (MSE), which is a common measure of estimator quality, of the fitted values of a dependent variable. In the Bayesian setting, the term MMSE more specifically refers to estimation with quadratic loss function. In such case, the MMSE estimator is given by the posterior mean of the parameter to be estimated. Since the posterior mean is cumbersome to calculate, the form of the MMSE estimator is usually constrained to be within a certain class of functions. Linear MMSE estimators are a popular choice since they are easy to use, easy to calculate, and very versatile. It has given rise to many popular estimators such as the Wiener–Kolmogorov filter and Kalman filter.

A **cyclostationary process** is a signal having statistical properties that vary cyclically with time. A cyclostationary process can be viewed as multiple interleaved stationary processes. For example, the maximum daily temperature in New York City can be modeled as a cyclostationary process: the maximum temperature on July 21 is statistically different from the temperature on December 20; however, it is a reasonable approximation that the temperature on December 20 of different years has identical statistics. Thus, we can view the random process composed of daily maximum temperatures as 365 interleaved stationary processes, each of which takes on a new value once per year.

In estimation theory and decision theory, a **Bayes estimator** or a **Bayes action** is an estimator or decision rule that minimizes the posterior expected value of a loss function. Equivalently, it maximizes the posterior expectation of a utility function. An alternative way of formulating an estimator within Bayesian statistics is maximum a posteriori estimation.

In statistical signal processing, the goal of **spectral density estimation** (**SDE**) or simply **spectral estimation** is to estimate the spectral density of a signal from a sequence of time samples of the signal. Intuitively speaking, the spectral density characterizes the frequency content of the signal. One purpose of estimating the spectral density is to detect any periodicities in the data, by observing peaks at the frequencies corresponding to these periodicities.

**Location estimation** in **wireless sensor networks** is the problem of estimating the location of an object from a set of noisy measurements. These measurements are acquired in a distributed manner by a set of sensors.

The **modified Allan variance (MVAR)**, also known as mod *σ _{y}*

In probability theory, an **exponentially modified Gaussian distribution** describes the sum of independent normal and exponential random variables. An exGaussian random variable *Z* may be expressed as *Z* = *X* + *Y*, where *X* and *Y* are independent, *X* is Gaussian with mean *μ* and variance *σ*^{2}, and *Y* is exponential of rate *λ*. It has a characteristic positive skew from the exponential component.

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