Fig. 1. Placement of the antenna array, scatterers, and source in the proposed grid configuration.

Fig. 2. Placement of the arbitrary objects and their scattered fields.

Fig. 3. Numerical simulation results for localizing a source existed at the node (0, 0): (a) overlapping plots of along the x axis for all values of where and (b) distribution of the values through the grid.

Fig. 4. Experimental setup.

Fig. 5. Scheme of the designed base station.

Fig. 6. Experimental results of based on the stored fingerprints and the fingerprint related to the node (0, 0): (a) overlapping plots of along the x axis for all values of where and (b) distribution of the values through the grid.

Fig. 7. Experimental results of for localizing a source located at a position close to the node (0, 0): (a) overlapping plots of along the x axis for all values of where and (b) distribution of the values through the grid.

Fig. 8. Distribution of the values.

Fig. 9. Improvement in SNR as the number of used frequencies increases.

Fig. 10. Localizing the ultrasonic source during its movement along an arbitrary trajectory.

Fig. 11. Ultrasonic source localization during its movement along an arbitrary trajectory: (a) source localization at location 1, (b) source localization at location 2, (c) source localization at location 3, and (d) source localization at location 4.