Navigation is the process of directing a vehicle from one known place to other known place.All navigational techniques involve locating the position of the vehicle being navigated inrelation to the known datum. Tracking of the mobile object whether moving in terrestrialenvironment or in underwater environment is very important activity towards fulfilling itsmission. The process of acquiring/identifying the location of an object of interest is calledpositioning. The example of one of the best known positioning systems is the GlobalPositioning System (GPS). In this chapter, various terrestrial navigation and globalpositioning systems have been described along with various classical under water positioningapproaches. In the underwater environment, avoiding collision of the Autonomousunderwater vehicle (AUV) with floating or fixed objects requires either prior knowledge ofthe operating environment or sensing equipment for evaluating the environment in real time.Having prior knowledge is not feasible for unstructured environments and therefore havingthe sensing equipment is the only viable option. The sensing equipment in this case is thesonar that is mounted on the AUV which scans the area in front and provides the images asthe output. These images are then required to be processed in order to detect the objectscoming in the path of the AUV in order to have safe navigation. Navigation sensor is a deviceused to measure a property from which the navigation system computes its navigationsolution (eg. radio navigation receiver). In the subsequent paragraphs investigation ofunderwater sound wave propagation characteristics and development of sonar range equationare presented.
If the object is located at and the speaker is located at origin, what is the equation for the distance that the sound traveled from the speaker to the object?