A signal processing algorithm for the estimation of the trajectory of a mobile transmitter in a wireless network, based on RSSI measurements, was proposed in [A. Almudevar, “Approximate calibration-free trajectory reconstruction in a wireless network,” IEEE Trans. Signal Process., vol. 56, no. 7, pp. 3081-3088, 2008]. The problem of explicit transmission source location estimation is bypassed, producing instead an estimation of the trajectory shape which does not require a translation of RSSI measurements into transmission distance estimates. It was proven for the case of k=3 receivers that the resulting mapping of the source to an estimation region is 1-1 and continuous while preserving directionality and providing robustness to measurement distortion. The purpose of this correspondence is to extend these results to the general k ≥ 3 case. The method is demonstrated using a commercial RSSI home monitoring system using k=4 receivers.