The future of deep space exploration depends upon technological advancement towards improving spacecraft's autonomy and versatility. This study aims to examine the feasibility of autonomous orbit determination using advanced accelerometer measurements. The objective of this research is to ascertain specific sensor requirements to meet pre-defined mission navigation error budgets. Traditional inertial navigation (dead reckoning and external aiding) is not considered. Instead, measurements from pairs of advanced, highly sensitive accelerometers (e.g., cold atom accelerometers) are used onboard to determine gravity field gradients, which are then correlated to onboard gravity maps and used to determine orbital information. Linear Covariance Theory helps to efficiently conduct an error budget analysis of the system. This error budget analysis helps to determine the effect of specific error sources in the sensor measurements, thereby providing information to rank and compare relevant sensor parameters and determine an optimal sensor configuration for a given space mission. The procedure is repeated to evaluate different accelerometer configurations and sensor parameters.