Cramer-Rao Analysis
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Cramer-Rao Lower Bound (CRLB) Analysis & Evaluation

Key Benefits:

We are knowledgeable about various historical approaches, their assumptions, their derivation, and their historical evolution.
We have gone through the rigorous supporting mathematics, yet we summarize the results in a clear straightforward manner, expressed as simply as possible.
We are familiar with typical applications utilizing these algorithms and are aware of what application constraints are usually actively in force.

Capabilities:

We have a facility with analytic manipulations that enabled the following:
insights in obtaining new theoretical results at the point were they were needed to expand and improve the existing theory, as conveyed below in references [1], [2], and applied in [3]-[8]. Also see the recent [9] by others that cite us.

Click here to obtain a detailed 266Kilobyte resume for Thomas H. Kerr III emphasizing only Target Tracking for strategic Early Warning Radar (UEWR).

Historical Account of our experience therein:

[1] Kerr, T. H., “A New Multivariate Cramer-Rao Inequality for Parameter Estimation (Application: Input Probing Function Specification),” Proceedings of IEEE Conference on Decision and Control, Phoenix, AZ, pp. 97-103, December 1974.
 
[2] Kerr, T. H., “Status of CR-Like Lower bounds for Nonlinear Filtering,” IEEE Transactions on Aerospace and Electronic Systems, Vol. AES-25, No. 5, pp. 590-601, September 1989 (Authors reply in Vol. AES-26, No. 5, pp. 896-898, September 1990).
 
[3] Kerr, T. H., “Cramer-Rao Lower Bound Implementation and Analysis for NMD Radar Target Tracking,” TeK Associates Technical Report No. 97-101 (for MITRE), Lexington, MA, 26-30 Oct. 1997.

[4] Kerr, T. H., “NMD White Paper on Designated Action Item,” MITRE, Bedford, MA, January 1998.

[5] Kerr, T. H., “Cramer-Rao Lower Bound Implementation and Analysis: CRLB Target Tracking Evaluation Methodology for NMD Radars,” MITRE Technical Report, Contract No. F19628-94-C-0001, Project No. 03984000-N0, Bedford, MA, February 1998.
 
[6] Kerr, T. H., “Developing Cramer-Rao Lower Bounds to Gauge the Effectiveness of UEWR Target Tracking Filters,” Proceedings of AIAA\BMDO Technology Readiness Conference and Exhibit, Colorado Springs, CO, 3-7 August 1998.
 
[7] Kerr, T. H., UEWR Design Notebook-Section 2.3: Track Analysis, TeK Associates, Lexington, MA, (for XonTech, Hartwell Rd, Lexington, MA), XonTech Report No. D744-10300, 29 March 1999.

[8] Kerr, T. H., A Critical View of Some New and Older approaches to EWR Target Tracking: A Summary and Endorsement of Kalman Filter-Related Techniques, a tutorial submitted to IEEE Aerospace and Electronic Systems, Ed. by Peter Willett (in review and expected to appear in 2005).

[9] Hue, C., Le Cadre, J.-P., Perez, P., “Posterior Cramer-Rao Bounds for Multi-Target Tracking,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 42, No. 1, pp. 37-49, January 2006.

[10] Gault, S., Hachem, W., Ciblat, P., “Joint Sampling Clock Offset and Channel Estimation for OFDM Signals: Cramer-Rao Bound and Algorithm, IEEE Trans. on Signal Processing, Vol. 54, No. 5, pp. 1875-1885, May 2006.

[11] Yetik, I. S., Nehorai, A., “Performance Bounds on Image Registration,IEEE Trans. on Signal Processing, Vol. 54, No. 5, pp. 1737-1749, May 2006.

[12] Zou, Q., Lin, Z., Ober, R. J., “The Cramer-Rao Lower Bound for Bilinear Systems,IEEE Trans. on Signal Processing, Vol. 54, No. 5, pp. 1666-1680, May 2006.

[13] Eldar, Y., “Uniformly Improving the Cramer-Rao Bound and Maximum-Likelihood Estimation, IEEE Trans. on Signal Processing, Vol. 54, No. 8, pp. 2943-2956, Aug. 2006.

[14] Brehard, T., Le Cadre, J.-P., “Closed-Form Posterior Cramer-Rao Bounds for Bearings-Only Tracking,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 42, No. 4, pp. 1198-1223, Oct. 2006.

[15] Au-Yueng, C. K., Wong, K. T., “CRB: Sinusoid-Sources' Estimation using Collocated Dipoles/Loops,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 45, No. 1, pp. 94-109, Jan. 2009.

[16] Kay, S., Xu, C., “CRLB via  the Characteristic Function with Application to the K-Distribution,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 44, No. 3, pp. 1161-1168, July 2008.

[17] Smith, S. T., “Statistical Resolution Limits and the Complexified Cramer-Rao Bound,IEEE Trans. on Signal Processing, Vol. 53, No. 5, pp. 1597-1609, May 2005.

[18] Smith, S. T., “Covariance, Subspace, and Intrinsic Cramer-Rao Bounds,IEEE Trans. on Signal Processing, Vol. 53, No. 5, pp. 1610-1630, May 2005.

[19] Gini, F., Regggianini, R., Mengali, U., The Modified Cramer-Rao Lower Bound in Vector Parameter Estimation,IEEE Trans. on Signal Processing, Vol. 46, No. 1, pp. 52-60, Jan. 1998.   

[20] Buzzi, S., Lops, M., Sardellitti, S., “Further Results on Cramer-Rao Bounds for Parameter Estimation in Long-Code DS/CDMA Systems, IEEE Trans. on Signal Processing, Vol. 53, No. 3, pp. 1216- 1221, Mar. 2005.

[21] Branko Ristic, “Cramer Rao Bounds for Target Tracking,International Conference on Sensor Networks and Information Processing, 6 Dec. 2005.

[22] Boers, Y., Driessen, H., “A Note on Bounds for Target Tracking with Pd < 1,” IEEE Trans. on Aerospace and Electronic Systems, Vol. 45, No. 2, pp. 640-646, Apr. 2009.

Gaussian Confidence Region or uncertainty ellipsoid (associated with target tracking) goes from being a pancake (at the horizon) to being a football (after sufficient radar returns have accrued). When knowledge of targets trajectory is sufficiently accurate, then the target can be successfully intercepted.

Tom Kerr and Eli Brookner (Click here to view info about Elis recent book.)

For more about Eli, please click: http://www.raytheon.com/newsroom/feature/ids_brookner06/ 

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http://ieee-aess.org/main/index.php?option=com_content&view=article&id=57&Itemid=66    http://pipl.com/directory/name/Brookner/Eli

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