Emission source localization and sensor registration using received signal strength (RSS) measurements is investigated. Previous studies for RSS localization assume that the sensors receiving signals are bias free, which is not the case in practice. This issue is taken into consideration in this paper for the localization problem. To avoid non-convexity of the global optimization problem for the traditional maximum likelihood (ML) or least squares (LS) estimation, we present novel semidefinite programming methods, linear least squares (LLS) and constrained LS (CLS) methods by approximating and linearizing the original model. The methods are divided into two types: URSS and DRSS. The former estimates the source location and sensor bias simultaneously while the latter estimates the sensor bias after localizing the source. Numerical examples show that our proposed methods have good performance. Some of them are close to the Cramer-Rao Lower Bound (CRLB).