When trace elements present in complex matrices are analysed by inductively coupled plasma optical emission spectroscopy (ICP-OES) correction must be made for the background if it overlaps with the desired trace analyte spectrum. However, often this is difficult to achieve because the required pure materials for the complex background matrix cannot be obtained, and hence the standard spectra are unavailable. A chemometrics solution to resolve the overlapping ICP-OES spectra of some such systems (gray systems) is proposed in this paper so as to obviate the need for the background standards. The case considered involves trace calcium in the presence of a large rare-earths background: Pr–Ca, Nd–Ca, Tb–Ca, Ho–Ca and Er–Ca. The application of iterative target transformation factor analysis (ITTFA) is explored to resolve the spectral interferences produced by the ultra-high-purity rare-earth matrices so as to facilitate the determination of the trace calcium. Once the ITTFA method has extracted the required background spectrum, a Kalman filter (KF) procedure is then used for the quantitative determination of the trace element. The calcium results are compared with those estimated by the conventional standard addition method, and improved results are observed. In addition, while in the absence of suitable standards such an approach is essential for the problem of the determination of the trace calcium in the rare-earth matrix described, this method should also be applicable to white systems, thereby often reducing costs of analysis as well as labour associated with the preparation of background material standards.