An Analytical Method for 3-D Target Localization Based on a Four-Element Ultrasonic Sensor Array With TOA Measurement

A new analytical method for 3-D target localization based on a four-element ultrasonic sensor array is proposed. In the sensor array, with the consideration of good real-time performance, one ultrasonic sensor (the reference ultrasonic sensor) works both as a transmitter and as a receiver, while the other three sensors work as receivers. A basic target localization model is developed. The necessary and sufficient condition of the proposed method to obtain the unique and analytical solution is analyzed. It is proved that if and only if the four ultrasonic sensors are not in the same plane, the four-element ultrasonic sensor array can obtain a unique and analytical solution. In addition, with the consideration of the stability and the complexity of the analytical solution, a practical four-element ultrasonic sensor array configuration is proposed, which is characterized in that the reference ultrasonic sensor is at the origin, the other three ultrasonic sensors are on the three coordinate axes, respectively, and the distances from the three ultrasonic sensors to the reference ultrasonic sensor are equal. 3-D target localization experiments are carried out. The experimental results verify the effectiveness of the proposed method and the localization performance is satisfactory. The proposed sensor array can realize the 3-D localization with the advantages of simple construction and less computation.