RESUMEN El uso del sistema GPS contribuye en el mejoramiento de la posición, con la utilización de las estaciones de operación continua podemos llegar a altas precisiones con un mantenimiento de bajo costo, pero aun así todos estos elementos deben de ser analizados para que la red sea óptima. When including with 288 LEO satellites, the overall DOPs (GDOP (geometric DOP), HDOP (horizontal DOP), PDOP (position DOP), TDOP (time DOP), and VDOP) are decreased by about 40%, and the satellite visibility can be increased by 183.99% relative to the Global Positioning System (GPS) constellation. What is more, the inclusion of the polar LEO constellation can significantly improve GNSS service performance. With 5 HEO satellites included in the third-generation BeiDou navigation satellite system (BDS-3), the average VDOP (vertical DOP) of the 30° N–90° N region can be decreased by 16.65%, meanwhile satellite visibility can be increased by 38.76%. HEO satellites can significantly improve constellation geometry distribution quality in the high latitude regions. Results show that QZO satellites perform slightly better in the Northern Hemisphere than IGSO satellites. Applying the EGAPM to evaluate the geometry distribution quality of the hybrid GNSS+ constellation, where highly eccentric orbits (HEO), quasi-zenith orbit (QZO), inclined geosynchronous orbit (IGSO), geostationary earth orbit (GEO), medium earth orbit (MEO), and also low earth orbit (LEO) satellites included, we analyze the overall performance quantities of different constellation configurations. Verified by the reference values derived from precise satellite ephemerides, the accuracy of visible satellite visibility estimation using EGAPM gets an accuracy better than 0.11 on average. Different from conventional methods, requiring real or simulated satellite ephemerides, this new model only uses some basic parameters of one satellite constellation. We proposed an extended geometry and probability model (EGAPM) to analyze the performance of various kinds of (Global Navigation Satellite System) GNSS+ constellation design scenarios in terms of satellite visibility and dilution of precision (DOP) et al. To minimize the error of positioning in forensic cases, we suggest developing a model for GPS application that considers the acceptable degree of error, available equipment, the specificity of the crime scene location and defining a detailed workflow for reducing the error with the averaging method. However, when a sufficient number of fixes is averaged, periodical variations of GPS error less affect accuracy, and error linearly decreases. The results have shown great variations between the actual position and position obtained by GPS through collection time, demonstrating that a single GPS reading is not a reliable tool for establishing an accurate datum point in a forensic context.

In the present simulated case, we have examined the error of establishing a position using a single hand-held GPS unit, as well as the efficiency of reducing the error by averaging multiple coordinates collected at the same spot through the time. However, GPS is prone to multiple errors that occur with a different intensity in different time intervals and degrade the accuracy of the positioning. The Global Positioning System (GPS) is a standard tool for establishing a datum point at the outdoor crime scenes that lack fixed objects or landmarks.

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