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Therefore, the CRB of the the matrix natural subspace distance is given by the FIM with respect to the elements of . This fact is made rigorous by the following corobservations. Geodesics on the Grassmann manifold responding to its natural metric are given by the formula [23] (120) is the compact SVD of the tangent vector where at ( , ). For the proper complex case, the transpositions in (120) may be replaced with conjugate transpositions. Furthermore, it may be verified that for the case of geodesics provided in (120) (121) [see also (86) for covariance matrices and footnote 6 for the general case].

Z. Han, “Optimal linear estimation fusion–Part I: Unified fusion rules,” IEEE Trans. Inf. Theory, vol. 49, no. 9, pp. 2192–2208, Sep. 2003. [14] A. Ben-Israel and T. N. E. Greville, Generalized Inverses: Theory and Applications, Second ed. New York: Wiley, 2002. [15] C. K. Chui and G. Chen, Kalman Filtering With Real-Time Applications. New York: Springer-Verlag, 1987. [16] S. Grime and H. F. Durrant-Whyte, “Data fusion in decentralized sensor networks,” Control Eng. Practice, vol. 2, no. 5, pp.

D. degree in applied mathematics from Harvard University, Cambridge, MA, in 1993. From 1986 to 1988, he was a research engineer at ERIM, Ann Arbor, MI, where he developed morphological image processing algorithms. He is currently a senior member of the technical staff at MIT Lincoln Laboratory, Lexington, MA, which he joined in 1993. His research involves algorithms for adaptive signal processing, detection, and tracking to enhance radar and sonar systems performance. He has taught signal processing courses at Harvard and for the IEEE.

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