Normalized CRLB – an alternate form of CRLB

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 concisely summarizes the above point.

The Fisher Information can be re-written as

Thus the variance of the estimate can be written as

Consider an incremental change in , that is, . This causes the PDF to change from . We wish to answer the following question : How sensitive is to that change ? Sensitivity (denoted by ) is given by the ratio of change in to the change in .

Letting

From Calculus,

Thus the sensitivity is given by,

The variance of the estimate can now be put in the following form.

The above expression is the normalized version of CRLB. It can be interpreted that the normalized CRLB is equal to the inverse of mean square sensitivity.

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Mathuranathan

Mathuranathan Viswanathan, is an author @ gaussianwaves.com that has garnered worldwide readership. He is a masters in communication engineering and has 12 years of technical expertise in channel modeling and has worked in various technologies ranging from read channel, OFDM, MIMO, 3GPP PHY layer, Data Science & Machine learning.

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