Design of a planar array of sensors for 3D location using genetic algorithms

Ultrasonic pulse echo systems are widely used to detect and locate targets within a specific region. A classical direction-of-arrival technique is the so-called triangulation method. This scheme uses the geometrical information provided by the time-of-flight measurements. Based on this information the bearing of the oncoming energy to a planar array of sensors can be computed. The cosine director of the target can be written as function of the time-of-flight readings, receiving elements position and speed of sound in the medium of propagation. There are two important sources of error in the cosine director calculation: random and the systematic types. A formulation based on the random error of the cosine director leads to a combinatorial expression as a function of receiver positions. Then to minimise the random error, an optimum receivers position must be computed, by evaluating this combinatorial expression. Genetic algorithms, using sub-set and binary representation, were developed to evaluate and to find optimum position of the receivers, producing minimum random errors.