Relative Impulse Responses (ReIRs) have several applications in speech enhancement, noise suppression and source localization for multi-channel speech processing in reverberant environments. Noise is usually assumed to be white Gaussian during the estimation of the ReIR between two microphones. We show that the noise in this system identification problem is instead dependent upon the microphone measurements and the ReIR itself. We then present modifications that incorporate this new noise model into three prevalent methods: Least Squares, Non-Stationary Frequency Domain and Sparse Bayesian Learning based approaches. We demonstrated improvements with an experimental study using real-world measurements in various noise environments.