P Stoica and T Soderstrom. Statistical analysis of MUSIC and subspace rotation estimates of sinusoidal frequencies. IEEE Transactions on Signal Processing, 39:8:1836--1847, August 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....methods of Section 6. it has been shown that TLS ESPRIT and LS ESPRIT are asymptotically equiv alent [64, 118] although for small N TLS ESPRIT has slightly better em pirical performance. It has also been shown that TLS ESPRIT is in general asymptotically less accurate that MUSIC [120], although comparing the two algorithms is somewhat unfair since they rely on a different set of assumptions about the sensor array. In particular, MUSIC requires much more informa tion about the array, and hence its superior performance is to be expected. A recent non asymptotic comparison ....

....of the form (44) can yield performance equivalent to MUSIC in such cases, but it requires a weighting matrix W quite different from that of WSF. In the context of system identification, theoretical studies comparing several Matrix Pencil and Orthogonal Vector methods have been carried out in [81, 133, 120, 68, 72] for the harmonic retrieval problem. As already noted above, in this problem the noise matrix has a Hankel structure, and its columns cannot be regarded as being independent. This fact makes the analysis somewhat more difficult, although some results have been obtained. For example, the conclusion ....

[Article contains additional citation context not shown here]

P. Stoica and T. SSderstrSm, "Statistical analysis of MUSIC and sub- space rotation estimates of sinusoidal frequencies," IEEE Trans. Signal Processing, vol. 39, pp. 1836-1847, Aug. 1991. 83

....that the modified MUSIC estimator proposed in [1] is identical to the special case = 1 and a particular weighting. This is shown in Appendix A. 4 Analysis The asymptotic analysis is derived from a Taylor expan sion of the cost function around the true value and exten sions of the analysis in [6] is used. The derivation is carried out with the assumption of a full rank I in [7] and the re sult is E k where , 2 (Re(Tr(UEnEn) 1 , 1 II = H Es) JUk . For alternative 1 the following expression is obtained, 5 A Numerical Example To compare the performance of the ....

P. Stoica and T S0derstr0m, "Statistical Analysis of MUSIC and Subspace Rotation Estimates of Sinusoidal Frequencies" IEEE Transactions on Signal Processing, vol. 39, pp. 1836-1847, August 1991.

....corresponding to k , and define the error as k = k Gamma k : 50) We shall make one simplification, namely to assume that W r = I. The reason is that in [9, 10] it is shown that this weighting does not influence the variance of the IV ESP estimated poles. Following [40] see also [24]) we can then relate the error in the estimated system poles to the subspace estimate as k f k Q s Q T s Gamma :k ; 51) where denotes o p (1= p N) approximation 5 , Gamma :k is the k th column of Gamma fl and f k = f Gamma 1 g y k: J 2 Gamma J 1 k ) 52) 5 ....

P. Stoica and T. Soderstrom. "Statistical Analysis of MUSIC and Subspace Rotation Estimates of Sinusoidal Frequencies". IEEE Trans. ASSP, ASSP-39:1836--1847, Aug. 1991.

....of [4] 1] J k;MU ( Tr n U k ( H k ( E n E n H k ( o ; 3) where U k 2 C (i 1) Theta(i 1) is the k th user s Hermitian weighting matrix. 2 Asymptotic Analysis In this section an asymptotic analysis of the algorithm is presented. The analysis is based on [5]. In Section 2.1 the analysis of the algorithm with overlapped vector samples is found and as a special case of this, the result for the non overlapped version is found in Section 2.2. 2.1 Alternative 2 (Overlap) First, a few definitions and preliminary results are summarized. Since the data and ....

P. Stoica and T. Soderstrom, "Statistical Analysis of MUSIC and Subspace Rotation Estimates of Sinusoidal Frequencies" IEEE Transactions on Signal Processing, vol. 39, pp. 1836--1847, August 1991.

....zeros of size p Theta l. One important difference between the alternatives is that the first has an uncorrelated noise sequence which yields a simple analysis and compact expressions of the asymptotic performance, 12] Alternative 2 has correlated noise samples which complicates the analysis, [13]. On the other hand, since (2) has more samples the convergence of the estimated covariance matrix is in general faster. One might argue that since the covariance matrix is zero for jlj 2 increasing i beyond 2 would not be necessary. However, since the new sequences still are correlated, ....

....results, all the proposed algorithms are shown to be near far resistant and yields substantially improved performance compared to the previously proposed modified MUSIC estimator. A Asymptotic Analysis In this appendix an asymptotic analysis of the algorithm is presented. The analysis is based on [13]. In Section A.1 the analysis of the algorithm with overlapped vector samples is found and as a special case of this, the result for the non overlapped version is found in Section A.2. A.1 Alternative 2 (Overlap) First, a few definitions and preliminary results are summarized. Since the data and ....

P. Stoica and T. Soderstrom, "Statistical Analysis of MUSIC and Subspace Rotation Estimates of Sinusoidal Frequencies" IEEE Transactions on Signal Processing, vol. 39, pp. 1836--1847, August 1991.

.... fi 2 i b M ik M k ; k = 1; n: 38) Equation (37) could also be found by using results in [20] on the first order expansion of the projection matrix P = b S b S , together with results on the derivatives of a non normalized version of the MUSIC cost function (31) see [21]) We chose to give the derivation above as it is also valid for the WSF algorithm, as will be indicated below. 4.3 The ESPRIT Algorithm The ESPRIT algorithm [22] assumes the fact that the array can be partitioned into two subsets. The two sub arrays are identical except for a translational shift ....

P. Stoica and T. S oderstr om, "Statistical analysis of MUSIC and subspace rotation estimates of sinusoidal frequencies," IEEE Transactions on Signal Processing, vol. 39, pp. 1836--1847, August 1991.

....Shift Invariant methods of Section 6. it has been shown that TLS ESPRIT and LS ESPRIT are asymptotically equivalent [64, 118] although for small N TLS ESPRIT has slightly better empirical performance. It has also been shown that TLS ESPRIT is in general asymptotically less accurate that MUSIC [120], although comparing the two algorithms is somewhat unfair since they rely on a different set of assumptions about the sensor array. In particular, MUSIC requires much more information about the array, and hence its superior performance is to be expected. A recent non asymptotic comparison between ....

....of the form (44) can yield performance equivalent to MUSIC in such cases, but it requires a weighting matrix W quite different from that of WSF. In the context of system identification, theoretical studies comparing several Matrix Pencil and Orthogonal Vector methods have been carried out in [81, 133, 120, 68, 72] for the harmonic retrieval problem. As already noted above, in this problem the noise matrix has a Hankel structure, and its columns cannot be regarded as being independent. This fact makes the analysis somewhat more difficult, although some results have been obtained. For example, the conclusion ....

[Article contains additional citation context not shown here]

P. Stoica and T. Soderstrom, "Statistical analysis of MUSIC and subspace rotation estimates of sinusoidal frequencies," IEEE Trans. Signal Processing, vol. 39, pp. 1836--1847, Aug. 1991.

....rootMUSIC and similar large sample performance. 1. Introduction Estimating frequencies from uniformly sampled data has been an active research area for decades. A number of, so called, high resolution algorithms or eigenstructure methods have been presented and analyzed in the literature, e.g. [4, 6, 7, 8]. One disadvantage with these subspace based methods is that it is difficult to incorporate knowledge of the source correlation into the eigendecomposition. In this paper we propose an estimator which combines ideas from subspace and covariance matching methods. The objective is to find a ....

P. Stoica and T. Soderstrom. Statistical Analysis of MUSIC and Subspace Rotation Estimates of Sinusoidal Frequencies. IEEE Trans. on Signal Processing, SP-39(8):1836--1847, August 1991.

....Shift Invariant methods of Section VI, it has been shown that TLS ESPRIT and LS ESPRIT are asymptotically equivalent [64, 118] although for small N TLS ESPRIT has slightly better empirical performance. It has also been shown that TLSESPRIT is in general asymptotically less accurate that MUSIC [120], although comparing the two algorithms is somewhat unfair since they rely on a different set of assumptions about the sensor array. In particular, MUSIC requires much more information about the array, and hence its superior performance is to be expected. A recent non asymptotic comparison between ....

....of the form (44) can yield performance equivalent to MUSIC in such cases, but it requires a weighting matrix W quite different from that of WSF. In the context of system identification, theoretical studies comparing several Matrix Pencil and Orthogonal Vector methods have been carried out in [68, 72, 81, 120, 133] for the harmonic retrieval problem. As already noted above, in this problem the noise matrix has a Hankel structure, and its columns cannot be regarded as being independent. This fact makes the analysis somewhat more difficult, although some results have been obtained. For example, the conclusion ....

[Article contains additional citation context not shown here]

P. Stoica and T. Soderstrom, "Statistical analysis of MUSIC and subspace rotation estimates of sinusoidal frequencies," IEEE Trans. Signal Processing, vol. 39, pp. 1836--1847, Aug. 1991.

....that the modified MUSIC estimator proposed in [1] is identical to the special case i = 1 and a particular weighting. This is shown in Appendix A. 4 Analysis The asymptotic analysis is derived from a Taylor expansion of the cost function around the true value and extensions of the analysis in [6] is used. The derivation is carried out with the assumption of a full rank H in [7] and the result is E Phi ( k Gamma k ) 2 Psi = ff Gamma RefTrfU k Psi k E n E n Psi k gg Delta 2 ; where ff = 1 2 M 2 Re ae i Gamma1 X l= Gamma(i Gamma1) M Gamma ....

P. Stoica and T. Soderstrom, "Statistical Analysis of MUSIC and Subspace Rotation Estimates of Sinusoidal Frequencies" IEEE Transactions on Signal Processing, vol. 39, pp. 1836--1847, August 1991.

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P Stoica and T Soderstrom. Statistical analysis of MUSIC and subspace rotation estimates of sinusoidal frequencies. IEEE Transactions on Signal Processing, 39:8:1836--1847, August 1991.

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Preprint. Stoica, P. and T. Soderstrom (1991). "`Statistical Analysis of MUSIC and Subspace Rotation Estimates of Sinusoidal Frequencies"'. IEEE Trans. ASSP ASSP-39, 1836--1847.

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P. Stoica and T. Soderstrom, "Statistical Analysis of MUSIC and Subspace Rotation Estimates of Si- nusoidal Frequencies", IEEE Trans. ASSP, ASSP39: 1836--1847, Aug. 1991.

No context found.

P. Stoica and T. Soderstrom, "Statistical analysis of MUSIC and subspace rotation estimates of sinusoidal frequencies," IEEE Trans. on Signal Processing, vol. SP-39, no. 8, pp. 1836--1847, August 1991.

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