The autonomous unmanned vehicles (AUV) are the important tools of the underwater investigations. The high accuracy of AUV navigation is one of the important conditions of the effective AUV work. The AUV navigation is based on the use of the several wide spread methods. One of the most useful of them is single beacon navigation also called the synthetic or dynamic long base method. To use this method one must measure the distance between maneuvering AUV and single beacon on different time intervals and use the obtained estimates together with the estimates of the AUV course and speed for the AUV positioning. The method was firstly announced in 1995 but by the now it is considered as one of the most useful method for AUV navigation. The purpose of the work is the synthesis of the maximum likelihood single beacon navigation algorithm and its accuracy investigation.
Autonomous underwater vehicles (AUV) are a promising tool for studying and development the World ocean [Kim, Eustice, 2015; Millar, Mackay, 2015; Newman, Leonard, Rikoski, 2003; Scherbatyuk, Dubrovin, 2012].
One of the main demands brought to AUVs to fulfill there tasks is precision navigation in three-dimensional underwater space.
To navigate AUV the following methods are used [Kinsey, Eustice, Whitcomb, 2006]:
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inertial navigation method (INM) which uses on-board navigational devices, including inertial navigation system (INS), hydroacoustic (absolute) lag (HL), which measures the speed of AUV in the longitudinal and transverse directions relative to the bottom, and a depth sensor (DS). This method must be referred as basic because all other methods are in addition to it. The advantage of inertial method is full autonomy, and the disadvantage is steady increasing position error with the time of underwater motion, due to gyro drift and low accuracy of AUV speed measurement in the deep sea;
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satellite navigation method (SNM), which consists in determining the coordinates of AUV using a GPS satellite navigation system (SNS). The advantage of this method is the high precision of coordinates determination, and the disadvantage is the need for the surfacing of AUV, which is associated with a high energy consumption and the loss of time of the mission;
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long base method (LBM) consisting in determining the AUV coordinates by simultaneous measuring its distance to several (at least three) beacons which coordinates are known with high accuracy, and resolving the relevant system of equations. Beacons can be fixed (usually on bottom) and moving (typically drifting). In last case their coordinates are determined using the SNS. For this purpose special buoys called GPS Intelligent Buoys (GIBs) are often used [Desset, Damus, Morash, Bechaz, 2003; Thomas, 1998]. The advantage of the long-base method is the high precision (up to tens of centimeters) of the AUV coordinates determination [Kebkal, Kebkal, Kebkal, 2014]. The disadvantages of this method are obvious: it requires an expensive equipment of AUV navigation area, and the size of this area, as a rule, does not exceed 10 km;
