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This paper deals with the problem of sensor localization when the localization error is nonlinearly propagated over the sensor network as occurs in Radio Interferometric Positioning System (RIPS). A noise model that takes the location uncertainties of anchor nodes into account in the node localization process has been derived based on a generic nonlinear measurement model that encapsulates the use of many popular node localization techniques. These include circular, parabolic and hyperbolic methods. This development enables the use of a distributed stochastic estimation method for node localization of wireless sensor networks with nonlinear measurements in the presence of anchor node uncertainties. The effectiveness of the derived equivalent noise model is demonstrated via a simulated progressive localization of a mote network using the RIPS measurements.