Hose-shaped rescue robots have been developed for searching narrow spaces such as under collapsed buildings. The posture estimation independent of the past history is critical, because conventional inertial-sensor-based posture estimation has two main problems; a cumulative error problem peculiar to inertial sensors, and a sudden posture change problem caused by external forces. For coping with the two problems, we developed a novel posture estimation method by putting an active microphone array, a set of microphones and loudspeakers, on the robot. The method calculates the time difference of arrival (TDOA) of the reference signal emitted from one loudspeaker, and estimates the posture from the distance obtained by TDOA. This concise method still has three problems: (1) external noise, (2) reverberation and reflection, and (3) obstacles. These problems are tackled by (1) TSP signal, (2) GCC-PHAT and a threshold-based onset detection, and (3) rejecting incorrect onset times, respectively. Experiments with simulated sounds and actual recordings demonstrate that the method attains the performance of estimation comparable to that of conventional methods, that is, less than 20 cm of the tip position error. Even without historical data, the method attains the similar performance while conventional methods fail.