Cramér-rao bounds for multiple near field sources location under unknown gain/phase response

In this paper the Cramer-Rao bound (CRB) for the estimation of nearfield source location under unknown gain/phase responses is analyzed. We first derive the CRB under the special case of single source and then extend to more general case of multiple sources. For single-source scenario we show that the CRB can be segmented into two parts, which separately corresponds to gain responses and phase responses. For multiple-sources scenario, we show that the CRB can be recursively calculated based on the single-source CRB expressions. The CRB expressions of multiple-sources scenario are in closed-form and only involve matrix multiplications. We show that with the increase in the number of incident sources, CRB increases.