From the discussion in Sec. 2, it can be seen that the calculation of CRB must exploit the initial location parameter estimate. These parameter estimates can be obtained by using various methods proposed in Ref. ^{26}. Moreover, for the convenience of comparison, we need to calculate the CRB of the robust MMSE-based method. Similar to the derivation of that in Ref. ^{22}, based on the model shown in Ref. ^{21}, the elements of Fisher information matrix for the robust MMSE-based method can be represented as follows: Display Formula
$F11=({[(B\u02d9*A)+(B*A\u02d9)]H[I+(R\Phi \u2297P\u22121)RHc]\u22121(R\Phi \u2297P\u22121)[(B\u02d9*A)+(B*A\u02d9)]})\u2299(\beta *\beta T)$(26)
Display Formula$F12=diag(\beta *){(B\u02d9*A+B*A\u02d9)H[I+(R\Phi \u2297P\u22121)RHc]\u22121(R\Phi \u2297P\u22121)(B*A)}$(27)
Display Formula$F22=(B*A)H[I+(R\Phi \u2297P\u22121)RHc]\u22121(R\Phi \u2297P\u22121)(B*A)$(28)
Display Formula$A=[a(\theta 1),a(\theta 2),\u2026,a(\theta K)],B=[b(\theta 1),b(\theta 2),\u2026,b(\theta K)],\beta =[\beta 1,\beta 2,\u2026,\beta K]T$(29)
Display Formula$A\u02d9=[\u2202a(\theta 1)\u2202\theta 1\cdots \u2202a(\theta K)\u2202\theta K],B\u02d9=[\u2202b(\theta 1)\u2202\theta 1\cdots \u2202b(\theta K)\u2202\theta K],$(30)
where $Ht=\u2211k=1K\beta ka(\theta k)bT(\theta k)\Phi $, the other parameter is the same as the illustration in Sec. 2. Insertion of Eqs. (26)–(28) into Eq. (2), then we can calculate the CRB for the robust MMSE-based method proposed in Ref. ^{21}.