Future cislunar missions built around NASA’s Gateway will rely increasingly on autonomous navigation architectures that use inter-spacecraft measurements to support both absolute and relative orbit determination. We are interested in spacecraft-to-spacecraft absolute and relative tracking, where the goal is to estimate the absolute states of two spacecraft with respect to a common reference point or system barycenter, together with their relative state, using only relative measurements between spacecraft and without assuming that either trajectory is known a priori. In this setting, spacecraft flying on nearby periodic and quasi-periodic orbits (QPOs) about a Gateway-like near rectilinear halo orbit (NRHO) provide a natural platform for autonomous navigation, but they also introduce strong nonlinear coupling in both the dynamics and the measurement geometry.

In this work we will systematically relate NRHO–QPO and QPO–QPO configurations to estimation behavior across a range of filters to map how absolute and relative performance varies with orbit selection, measurement set, and the level of nonlinear geometric coupling present in the relative motion. The results are expected to clarify how QPOs can be used as a design tool for introducing beneficial nonlinearity, complementing along-track phase shifts on a common NRHO. Ultimately, this work is intended to inform the design of future cislunar formations and constellations that rely on relative-only measurements for autonomous spacecraft-to-spacecraft absolute and relative navigation around Gateway and in cislunar space.

In earlier work, we examined a single strongly nonlinear two-spacecraft configuration in the Circular Restricted Three-Body Problem (CR3BP) and compared several filters for spacecraft-to-spacecraft tracking using relative-only sensing. One spacecraft was on a 9:2 NRHO near perilune and the other was initialized on a bounded QPO near apolune, placing the vehicles on opposite sides of the Moon and creating large separation and strong nonlinearity in the inter-spacecraft measurements. That study implemented a second-order Extended Kalman Filter (EKF) and compared it to the conventional EKF and the Unscented Kalman Filter (UKF) under optical-only and radar-only measurement models. The results, based on a single representative scenario, indicated that explicitly modeling second-order effects in both the dynamics and the measurements can be important for accuracy and stability when estimating absolute and relative states from relative-only measurements in such regimes.

More recently, we analyzed a lead–follower formation in which two spacecraft shared the same 9:2 NRHO and the phase separation was varied while the underlying orbit was held fixed. Using relative-only measurements and a second-order EKF, we explored how changing the phase separation alters the balance between absolute and relative navigation performance. The results showed that increasing along-track separation improves geometric diversity for absolute state recovery but can degrade relative accuracy, and that phase shifts on a single NRHO do not always fully exploit the nonlinear coupling required for absolute state observability. These findings suggest that formation design should consider the choice of orbit families, not just along-track phase, as a means of shaping the nonlinear structure of the relative motion.

Here, we extend these studies to formations that combine a Gateway-like NRHO with nearby QPOs, as well as formations composed of two QPOs, in the Earth–Moon CR3BP. We consider two-spacecraft configurations in which one vehicle follows an NRHO and the other occupies a QPO with tunable amplitude, inclination, and out-of-plane structure, together with cases where both spacecraft are placed on distinct QPOs. These NRHO–QPO and QPO–QPO geometries are expected to introduce richer curvature, asymmetry, and out-of-plane motion in the relative dynamics than pure phase shifts on a common NRHO, and therefore to offer additional ways to strengthen absolute-from-relative information content. Within this framework, we investigate a range of filtering approaches with an emphasis on understanding how filter performance and robustness depend on formation geometry and measurement type.