Cramer Rao Lower Bound Archives - GaussianWaves https://www.gaussianwaves.com/tag/cramer-rao-lower-bound/ Signal Processing for Communication Systems Sat, 02 Jan 2021 08:41:50 +0000 en-US hourly 1 https://wordpress.org/?v=6.7.2 https://i0.wp.com/www.gaussianwaves.com/gaussianwaves/wp-content/uploads/2016/02/cropped-gaussianwaves_logo_120_120.png?fit=32%2C32&ssl=1 Cramer Rao Lower Bound Archives - GaussianWaves https://www.gaussianwaves.com/tag/cramer-rao-lower-bound/ 32 32 163393712 Cramér-Rao Lower Bound (CRLB)-Vector Parameter Estimation https://www.gaussianwaves.com/2014/05/cramer-rao-lower-bound-crlb-for-vector-parameter-estimation/ https://www.gaussianwaves.com/2014/05/cramer-rao-lower-bound-crlb-for-vector-parameter-estimation/#comments Thu, 08 May 2014 07:29:24 +0000 http://www.gaussianwaves.com/?p=5995 Key focus: Applying Cramér-Rao Lower Bound (CRLB) for vector parameter estimation. Know about covariance matrix, Fisher information matrix & CRLB matrix. CRLB for Vector Parameter Estimation 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 that we wish to ... Read more

The post Cramér-Rao Lower Bound (CRLB)-Vector Parameter Estimation appeared first on GaussianWaves.

]]> https://www.gaussianwaves.com/2014/05/cramer-rao-lower-bound-crlb-for-vector-parameter-estimation/feed/ 1 5995 Normalized CRLB – an alternate form of CRLB https://www.gaussianwaves.com/2012/12/normalized-crlb-an-alternate-form-of-crlb-and-its-relation-to-estimator-sensitivity/ https://www.gaussianwaves.com/2012/12/normalized-crlb-an-alternate-form-of-crlb-and-its-relation-to-estimator-sensitivity/#respond Thu, 27 Dec 2012 05:41:32 +0000 http://www.gaussianwaves.com/?p=2676 Key focus: Normalized CRLB (Cramér-Rao Lower bound) is an alternate form of CRLB. Let’s explore how normalized CRLB is related to estimator sensitivity. The variance of an estimate is always greater than or equal to Cramér-Rao Lower Bound of the estimate. The CRLB is in turn given by inverse of Fisher Information. The following equation ... Read more

The post Normalized CRLB – an alternate form of CRLB appeared first on GaussianWaves.

]]> https://www.gaussianwaves.com/2012/12/normalized-crlb-an-alternate-form-of-crlb-and-its-relation-to-estimator-sensitivity/feed/ 0 2676 Cramer Rao Lower Bound for Phase Estimation https://www.gaussianwaves.com/2012/12/cramer-rao-lower-bound-for-phase-estimation/ https://www.gaussianwaves.com/2012/12/cramer-rao-lower-bound-for-phase-estimation/#respond Wed, 05 Dec 2012 06:21:05 +0000 http://www.gaussianwaves.com/?p=2651 Key focus: Derive the Cramer-Rao lower bound for phase estimation applied to DSB transmission. Find out if an efficient estimator actually exists for phase estimation. Problem formulation Consider the DSB carrier frequency estimation problem given in the introductory chapter to estimation theory. A message is sent across a channel modulated by a sinusoidal carrier with ... Read more

The post Cramer Rao Lower Bound for Phase Estimation appeared first on GaussianWaves.

]]> https://www.gaussianwaves.com/2012/12/cramer-rao-lower-bound-for-phase-estimation/feed/ 0 2651 Efficient Estimators by applying CRLB https://www.gaussianwaves.com/2012/12/efficient-estimators-and-crlb/ https://www.gaussianwaves.com/2012/12/efficient-estimators-and-crlb/#respond Tue, 04 Dec 2012 10:07:17 +0000 http://www.gaussianwaves.com/?p=2646 It has been reiterated that not all estimators are efficient. Even not all the Minimum Variance Unbiased Estimators (MVUE) are efficient. Then how do we quantify whether the estimator designed by us is efficient or not? An efficient estimator is defined as the one that is* Unbiased (mean of the estimate = true value of ... Read more

The post Efficient Estimators by applying CRLB appeared first on GaussianWaves.

]]> https://www.gaussianwaves.com/2012/12/efficient-estimators-and-crlb/feed/ 0 2646 Applying Cramer Rao Lower Bound (CRLB) to find a Minimum Variance Unbiased Estimator (MVUE) https://www.gaussianwaves.com/2012/11/applying-cramer-rao-lower-bound-crlb-to-find-a-minimum-variance-unbiased-estimator-mvue/ https://www.gaussianwaves.com/2012/11/applying-cramer-rao-lower-bound-crlb-to-find-a-minimum-variance-unbiased-estimator-mvue/#respond Thu, 29 Nov 2012 08:53:01 +0000 http://www.gaussianwaves.com/?p=2629 It was mentioned in one of the earlier articles that CRLB may provide a way to find a MVUE (Minimum Variance Unbiased Estimators). Theorem: There exists an unbiased estimator that attains CRLB if and only if, Here \( ln \; L(\mathbf{x};\theta) \) is the log likelihood function of x parameterized by \(\theta\) – the parameter ... Read more

The post Applying Cramer Rao Lower Bound (CRLB) to find a Minimum Variance Unbiased Estimator (MVUE) appeared first on GaussianWaves.

]]> https://www.gaussianwaves.com/2012/11/applying-cramer-rao-lower-bound-crlb-to-find-a-minimum-variance-unbiased-estimator-mvue/feed/ 0 2629 Cramér-Rao Lower Bound (CRLB)-Scalar Parameter Estimation https://www.gaussianwaves.com/2012/11/cramer-rao-lower-bound-for-scalar-parameter-estimation/ https://www.gaussianwaves.com/2012/11/cramer-rao-lower-bound-for-scalar-parameter-estimation/#comments Tue, 20 Nov 2012 13:44:09 +0000 http://www.gaussianwaves.com/?p=2614 Key focus: Discuss scalar parameter estimation using CRLB. Estimate DC component from observed data in the presence of AWGN noise. Consider a set of observed data samples and is the scalar parameter that is to be estimated from the observed samples. The accuracy of the estimate depends on how well the observed data is influenced ... Read more

The post Cramér-Rao Lower Bound (CRLB)-Scalar Parameter Estimation appeared first on GaussianWaves.

]]> https://www.gaussianwaves.com/2012/11/cramer-rao-lower-bound-for-scalar-parameter-estimation/feed/ 1 2614 Cramér-Rao Lower Bound: Introduction https://www.gaussianwaves.com/2012/11/cramer-rao-lower-bound-introduction/ https://www.gaussianwaves.com/2012/11/cramer-rao-lower-bound-introduction/#comments Mon, 19 Nov 2012 07:02:18 +0000 http://www.gaussianwaves.com/?p=2605 Key concept: Cramér-Rao bound is the lower bound on variance of unbiased estimators that estimate deterministic parameters. Introduction The criteria for existence of having an Minimum Variance Unbiased Estimator (MVUE) was discussed in a previous article. To have an MVUE, it is necessary to have estimates that are unbiased and that give minimum variance (compared ... Read more

The post Cramér-Rao Lower Bound: Introduction appeared first on GaussianWaves.

]]> https://www.gaussianwaves.com/2012/11/cramer-rao-lower-bound-introduction/feed/ 2 2605 Minimum-variance unbiased estimator (MVUE) https://www.gaussianwaves.com/2012/08/minimum-variance-unbiased-estimators-mvue/ https://www.gaussianwaves.com/2012/08/minimum-variance-unbiased-estimators-mvue/#respond Wed, 29 Aug 2012 10:00:04 +0000 http://www.gaussianwaves.com/?p=2170 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

The post Minimum-variance unbiased estimator (MVUE) appeared first on GaussianWaves.

]]> https://www.gaussianwaves.com/2012/08/minimum-variance-unbiased-estimators-mvue/feed/ 0 2170