2-DIMENSIONAL GEOMETRIC ANALYSIS OF A SIMPLE FREE NETWORK

Abstract. This paper attempts to quantify geometric considerations in observations and observe trends in solutions to free network solutions. The method of investigation will be utilizing 2D observations to determine how each measurement affects the overall solution and the location of the observations relative to the other nodes. A local reference system will be determined using the Gauss-Markov model with constraints by fixing the largest range observation to the y-axis to give a relative orientation. Further solutions will be calculated by fixing additional points to generate multiple least squares solutions relative to the local reference system. The resulting final points will be modeled using the Gauss-mixture model and compared to a simulated dataset generated by adding random error to the observations. Different weight matrices will be tested to demonstrate the effect on the overall solution. These methods were chosen because of prior experimentation by different research groups studying geometric considerations for UAS and ground surveying conditions. The major contribution will be the trends observed in the modeling and the correlation of the fixed local solutions to the geometry of the points.