Why BLUE : We have discussed Minimum Variance Unbiased Estimator (MVUE) in one of the previous articles. Following points should be considered when applying MVUE to an estimation problem MVUE…

# Category: Estimation Theory

Background: The various estimation concepts/techniques like Maximum Likelihood Estimation (MLE), Minimum Variance Unbiased Estimation (MVUE), Best Linear Unbiased Estimator (BLUE) – all falling under the umbrella of classical estimation –…

The agenda for the subsequent series of articles is to introduce the notion of autocorrelation, AutoCorrelation Function (ACF), Partial AutoCorrelation Function (PACF) , using ACF and PACF in system identification.…

Read More AutoCorrelation (Correlogram) and persistence – Time series analysis

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If a time series data is assumed to be following an Auto-Regressive (AR(N)) model of given form, $$x[n] + a_1 x[n-1] + a_2 x[n-2] + … + a_N x[n-N] =…

As discussed in the previous post, the ARMA model is a generalized model that is a mix of both AR and MA model. Given a signal \(x[n]\), AR model is…

Read More Comparing AR and ARMA model – minimization of squared error

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Signal models are used to analyze stationary univariate time series. The goal of signal modeling is to estimate the process from which the desired signal is generated. Though the concept…

Read More LTI system models for random signals – AR, MA and ARMA models

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CRLB for scalar parameter estimation was discussed in previous posts. The same concept is extended to vector parameter estimation. Consider a set of deterministic parameters \(\mathbb{\theta}=[ \theta_1, \theta_2, …, \theta_p]^{T}…

Read More Cramer Rao Lower Bound (CRLB) for Vector Parameter Estimation

Introducing The Kalman Filter – Ramsey Faragher PDF Text: click here PDF Text: click here

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Any \( n \times n\) positive definite matrix \( A \) can be factored as $$ A=LL^T $$ where \( L \) is \(n \times n\) lower triangular matrix. The lower…

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It is often required to check if a given matrix is positive definite or not. Three methods to check the positive definiteness of a matrix were discussed in a previous…

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