Estimation Theory Archives - GaussianWaves

Hidden Markov Models (HMM) – Simplified !!!

Mathuranathan — Tue, 17 Mar 2020 05:08:35 +0000

Markov chains are useful in computing the probability of events that are observable. However, in many real world applications, the events that we are interested in are usually hidden, that is we don’t observe them directly. These hidden events need to be inferred. For example, given a sentence in a natural language we only observe the ... Read more

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Markov Chains – Simplified !!

Mathuranathan — Fri, 06 Mar 2020 07:11:37 +0000

Key focus: Markov chains are a probabilistic models that describe a sequence of observations whose occurrence are statistically dependent only on the previous ones. ● Time-series data like speech, stock price movements.● Words in a sentence.● Base pairs on the rung of a DNA ladder. States and transitions Assume that we want to model the ... Read more

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Generate color noise using Auto-Regressive (AR) model

Mathuranathan — Wed, 04 Dec 2019 07:16:19 +0000

Key focus: Learn how to generate color noise using auto regressive (AR) model. Apply Yule Walker equations for generating power law noises: pink noise, Brownian noise. Auto-Regressive (AR) model An uncorrelated Gaussian random sequence can be transformed into a correlated Gaussian random sequence using an AR time-series model. If a time series random sequence is ... Read more

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Generating colored noise with Jakes PSD: Spectral factorization

Mathuranathan — Thu, 17 Oct 2019 06:16:55 +0000

The aim of this article is to demonstrate the application of spectral factorization method in generating colored noise having Jakes power spectral density. Before continuing, I urge the reader to go through this post: Introduction to generating correlated Gaussian sequences. In spectral factorization method, a filter is designed using the desired frequency domain characteristics (like ... Read more

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Generate correlated Gaussian sequence (colored noise)

Mathuranathan — Tue, 15 Oct 2019 06:43:03 +0000

Key focus: Colored noise sequence (a.k.a correlated Gaussian sequence), is a non-white random sequence, with non-constant power spectral density across frequencies. Introduction Speaking of Gaussian random sequences such as Gaussian noise, we generally think that the power spectral density (PSD) of such Gaussian sequences is flat.We should understand that the PSD of a Gausssian sequence ... Read more

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BLUE estimator

Mathuranathan — Fri, 04 Jul 2014 09:48:48 +0000

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 is the optimal estimator Finding a MVUE requires full knowledge of PDF (Probability Density Function) of the underlying process. Even if the PDF is known, ... Read more

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Linear Models – Least Squares Estimator (LSE)

Mathuranathan — Tue, 17 Jun 2014 09:07:09 +0000

Key focus: Understand step by step, the least squares estimator for parameter estimation. Hands-on example to fit a curve using least squares estimation 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 – require assumptions/knowledge ... Read more

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AutoCorrelation (Correlogram) and persistence – Time series analysis

Mathuranathan — Mon, 02 Jun 2014 11:02:05 +0000

The agenda for the subsequent series of articles is to introduce the idea of autocorrelation, AutoCorrelation Function (ACF), Partial AutoCorrelation Function (PACF) , using ACF and PACF in system identification. Introduction Given time series data (stock market data, sunspot numbers over a period of years, signal samples received over a communication channel etc.,), successive values ... Read more

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Yule Walker Estimation and simulation in Matlab

Mathuranathan — Tue, 27 May 2014 10:11:22 +0000

If a time series data is assumed to be following an Auto-Regressive (AR(N)) model of given form, the natural tendency is to estimate the model parameters a1,a2,…,aN. Least squares method can be applied here to estimate the model parameters but the computations become cumbersome as the order N increases. Fortunately, the AR model co-efficients can ... Read more

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Solving ARMA model – minimization of squared error

Mathuranathan — Fri, 23 May 2014 03:01:44 +0000

Key focus: Can a unique solution exists when solving ARMA (Auto Regressive Moving Average) model ? Apply minimization of squared error to find out. 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 easiest ... Read more

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