This paper presents a cellular LTE and GPS L1 C/A vector tracking software-defined receiver. The architecture of the combined receiver is presented, and the benefits of vector tracking are discussed. A covariance analysis is used to predict the lowest Carrier to Noise power density ratio (C/N0) at which the vector tracking algorithm can operate. The results of the covariance analysis are verified through Monte Carlo simulations of the vector tracking algorithm. Overall, the results of the analysis match well with the Monte Carlo simulation results. Results show that LTE signals can obtain a 2-4 dB-Hz gain over scalar tracking. They also show that positioning performance can possibly be improved in multipath conditions. In addition, it is shown that the survival rate of GPS signals after an outage increases by at least 66% by including just one eNodeB.