Linear Models – Least Squares Estimator (LSE)

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

Estimator Bias

Estimator bias: Systematic deviation from the true value, either consistently overestimating or underestimating the parameter of interest. Estimator Bias: Biased or Unbiased Consider a simple communication system model where a transmitter transmits continuous stream of data samples representing a constant value – ‘A’. The data samples sent via a communication channel gets added with White … Read more

Minimum-variance unbiased estimator (MVUE)

As discussed in the introduction to estimation theory, the goal of an estimation algorithm is to give an estimate of random variable(s) that is unbiased and has minimum variance. This criteria is reproduced here for reference In the above equations f0 is the transmitted carrier frequency and is the estimated frequency based on a set … Read more

Estimation Theory : an introduction

Key focus: Understand the basics of estimation theory with a simple example in communication systems. Know how to assess the performance of an estimator. A simple estimation problem : DSB-AM receiver In Double Side Band – Amplitude Modulation (DSB-AM), the desired message is amplitude modulated over a carrier of frequency f0. The following discussion is … Read more