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www.sea-technology.com March 2015 / st 29 In contrast, analyzing the GAPS acoustic tracking data results in a different picture. Density shifts in the water column can refract sound waves and can cause tracking errors or even a complete loss of signal (LOS). Due to this, the GAPS data show less consistency than the vehicle data. However, when the vehicle is on the surface and receives a GPS signal, both the vehicle and the GAPS data match re- markably well. As GPS is a reliable positioning source it can thus be concluded that GAPS is reliable as well, but outliers need to be removed. One particular feature of the GAPS data became impor- tant during the development of the algorithm. As previously mentioned, GAPS also calculates the depth of a tracked object. Obviously unrealistic positions frequently go along with depth values that seem to be unrealistic as well. In contrast to the position data, the parameter "depth" can be compared to a reliable source that is permanently avail- able during the dive: the depth sensor of the vehicle. Due to the close correlation described before and assuming that the AUV's depth sensor is correct, a comparison of the two depth data sets (GAPS + AUV) can serve as a flter criterion to identify outliers in the GAPS position data. The Algorithm The entire correction process can be divided into four different phases that gradually yield an improvement of the result. In phase one (Index: P1), only the raw AUV data (Index: P0) are processed. The function of the algorithm is exem- plarily depicted by correcting the latitude value. The difference between the last INS-determined position (AUV Lat INS ) and the frst GPS-determined position (AUV Lat GPS ) roughly represents orientation and extent of the spatial drift the INS experienced during the dive. For this frst phase of the correction process, a constant drift of the INS and there- fore a linear increase of the navigation error are assumed. Thus, with N total representing the total number of navigation updates exclusively based on the INS and N total t represent- ing the number of AUV navigation updates at a time t, this yields to: In phase two, the algorithm starts processing the GAPS data and removes outliers. It takes advantage of the close correlation between unrealistic position and depth values, which was described before. Derived from the GAPS and AUV depth data, a tolerance scale z tol is defned to identify outliers in the GAPS data set. For every time step, two different depth values (GAPS + AUV) are available. In this pair of variates, d 1 represents the shallower value and d 2 the deeper value. With two flter co- effcients and the damping exponent x, the tolerance scale z tol can be expressed as: The frst flter coeffcient defnes the initial extent of the tolerance scale. The second flter coeffcient with the damp- ing exponent restricts the size of z tol , which otherwise would increase with depth. The tolerance scale z tol represents the maximum differ- ence between the two depth values d 1 and d 2 . If the dif- ference of a specifc pair exceeds the respective value of z tol , the associated GAPS position is considered to be invalid and thus ignored in the further process. In this particular case the two flter coeffcients had the values 5.0 and 0.9, respectively. Using this method, a relatively coarse flter, which is un- able to eliminate outliers completely, is applied to the data. For this particular dive, roughly 75 percent of the GAPS data was accepted as valid. In phase three of the correction process (Index: P3), the algorithm determines locations that the AUV "most likely" passed during the dive. Following the naming convention used for spline functions, these special locations are further referred to as "knots." In order to identify these knots, the basic assumption was that the longer a period of consecutive tracking results is not interrupted by an LOS, the more reliable the position data are. For this reason, the algorithm looks for sequences with