There is paper on "Posterior Cramer Rao Bounds for Discrete Time Non-linear Filtering". However, there is difficulty in my understanding part on How some block elements of the posterior information matrices are 0. Kindly anyone help me understand the structure of the matrix.
OR
If possible share some relevant files. I need to understand the details of PCRB derivation for a time-varying parameter.
Thanks in advance.
Dear Ashirwad Ray
These links might be useful, have a look:
1. https://www.intesiscon.com/ficheros/manuales-tecnicos/256-HPE-a00105312en-us-HPE-MSA-1060-2060-2062-Storage-Management-Guide.pdf
2. https://www.delltechnologies.com/asset/en-us/products/storage/industry-market/h17827-dell-emc-unity-operating-environment.pdf
3. https://textranch.com/261785/please-refer-to-the-attached-screenshot/or/please-refer-to-the-screenshot-attached/
4. http://www.ieua.org/wp-content/uploads/2015/07/3PAR-3-2-1-CLI-Reference.pdf
Kind Regards
Qamar Ul Islam
Hello Ashirwad Ray,
I just spotted your question regarding the superb paper on "Posterior Cramér-Rao Bound for Discrete-Time Nonlinear Filtering."
The zero blocks reflect the fact that the stated is assumed to be Markov, i.e., the state is stochastically connected only to its predecessor (and successor, of course), cf. Eq. (19), (22)-(26).
However, for practical applications, you will most likely only want to compute the information submatrix (the Schur complement of J(X_{n+1})) according to the proposed recursion Eq. (21), as doing so does not require the manipulation of large, ever-growing matrices.
I recommend taking a look at the follow-up paper of a former colleague of mine entitled "Cramér-Rao Lower Bound for State-Constrained Nonlinear Filtering" (https://ieeexplore.ieee.org/document/8074758). Therein, the authors provide a sound description not only of the proposed adaption to state-constrained problems but also of Tichavský's original formulation.
Best regards,
Stefan
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