Three Satellite Navigation in an Urban Canyon using a Chip-Scale Atomic Clock

It is widely known that at least four pseudorange measurements are required to solve for a GPS receiver's 3-d position and clock bias. In GPS degraded environments, such as urban canyons, typically less than four satellites are available, so in order to provide the user with a full navigation solution, some type of augmentation to the GPS receiver is required. With the advances in the size, weight, and power (SWAP) characteristics of miniature frequency standards, it is now feasible to integrate a chip-scale atomic clock (CSAC) in a GPS receiver. Due to the high degree of frequency stability of the CSAC, the clock bias is predictable, and thus only three satellites are needed for a full navigation solution. A review of current literature on the use of clock-aiding in GPS receivers did not turn up research on using clock-aiding for navigation in urban canyon environments with multipath effects. The contribution of this paper in this regard is that it will present theoretical analysis along with data demonstrating the use of a CSAC as the core of the GPS receiver in an urban canyon environment. More specifically, this paper analyzes the benefits of using a CSAC to aid the GPS receiver navigation solution when navigating with three satellites using two performance metrics: 1) the solution's dilution of precision (DOP) and 2) the mean squared error (MSE) of the solution. The navigation solution's DOP is compared via two estimators: the least squares (LS) estimator and weighted least squares (WLS) estimator. The clock bias is predicted using two different predictors: 1) Kalman and 2) least squares.