Ryoichiro Kaga, Kyushu University; Yasuhiro Yoshimura, Kyushu University; Taku Izumiyama, IHI Corporation
https://doi.org/10.64861/AKXO5842
Keywords: Angles-Only Navigation, Nonsingular Orbital Elements, Relative Orbit Estimation, On-Orbit Servicing, Observability Analysis, Unscented Schmidt Kalman Filter, Covariance Steering
Abstract:
Space-based inspection of non-cooperative objects in geosynchronous Earth orbit (GEO) is increasingly important for space situational awareness (SSA). GEO contains many high-value satellites, making inspection, anomaly response, life-extension support, and relocation of aging assets increasingly relevant. Angles-only navigation (AON) uses only line-of-sight angle measurements from an optical camera and requires neither a range sensor nor cooperative support from the target. It is therefore attractive for spacecraft with limited onboard resources. The primary goal of this research is to establish an accurate and robust AON method for passive relative orbit estimation in GEO. A secondary goal is to examine how the resulting state estimate and covariance can support safe approach planning.
AON in GEO has two main difficulties. First, a line-of-sight measurement does not provide range at a single time. During passive drift without maneuvers, range-scale information must come gradually from the relative dynamics and known perturbations. Its quality depends strongly on the observation geometry and on differential solar radiation pressure (SRP). Second, GEO inspection cases have nearly circular and nearly equatorial orbits, where some classical orbital elements become poorly defined. Together, these conditions can leave large and uneven uncertainty at the end of the observation phase.
The study considers two phases: passive relative orbit estimation and subsequent approach guidance. The central estimation method combines relative modified equinoctial elements (RMEE) with an unscented partial-update Schmidt Kalman filter (UPSKF) to address both GEO difficulties. RMEE remain well defined in nearly circular, nearly equatorial orbits, while the UPSKF limits measurement corrections when range is weakly observable. Its update size is set by a Fisher-information-based measure of observability. During passive observation, the dynamics model includes Earth nonspherical gravity, gravity from the Sun and Moon, and SRP.
The secondary guidance study passes the estimate and covariance directly to a covariance-steering method. The transfer moves the chaser to a stand-off inspection point 2 km from the target while controlling both the mean relative state and its uncertainty. A chance constraint limits the probability of entering a keep-out zone with a radius of 100 m, and each terminal position standard deviation is limited to 100 m. This covariance handoff links navigation and guidance at the design level: the approach begins from the uncertainty reported by the estimator instead of an assumed exact state.
Monte Carlo simulations include an eighth-order Earth gravity model, gravity from the Sun and Moon, and prescribed SRP. We analyze 50 cases with initial position errors up to 33.5 km. This range represents the practical acquisition condition assumed in this study and is comparable to upper-end initialization errors commonly considered in AON studies. After ten orbital periods in a representative geometry, the principal result is that RMEE-UPSKF is the only one of four tested configurations to achieve both a median position error below 1 km and zero divergence. It reduces the median error from 16.3 km to 0.70 km and the sample maximum from 33.5 km to 1.60 km. With the filter fixed to UPSKF, changing from conventional relative orbital elements to RMEE reduces the median final error from 5.24 km to 0.70 km. With the state fixed to RMEE, changing from a conventional unscented Kalman filter (UKF) to UPSKF reduces the median error from 2.71 km to 0.70 km and the divergence rate from 14 percent to zero.
Performance also depends on the observation conditions. In a less informative second geometry, the RMEE-UPSKF median error remains 6.88 km, showing that a filter cannot create information that is absent from the line-of-sight history. Parameter sweeps further show that stronger differential SRP reduces the remaining range-scale error, while larger in-plane and out-of-plane periodic motion improves accuracy by providing more varied viewing directions under the tested conditions. These findings identify the physical and trajectory conditions that support successful passive AON, rather than suggesting that the filter alone guarantees convergence.
At 8.7 orbital periods, the state and covariance initialize guidance for all 50 cases. All designs are feasible under the linear guidance model. Covariance steering gives a median predicted terminal root-mean-square position dispersion of 66.1 m with a median feedforward delta-V of 7.24 m/s. A mean-only two-impulse transfer requires only 3.94 m/s but leaves a dispersion of 349 m and does not meet the terminal uncertainty limit. Nonlinear repropagation of two representative cases shows no entry into the keep-out zone in 200 trials per case. This result is a consistency check for those cases, not a general statistical proof of safety.
The approach phase provides a more informative line-of-sight history. The UPSKF weight has already decreased close to zero and suppresses use of this new information, while switching to the UKF reduces the median position error from 418 m to 1 m. The results therefore support a phase-dependent filter: RMEE-UPSKF during weakly observable passive drift and RMEE-UKF during the controlled approach. The primary contribution is the quantitative demonstration that RMEE-UPSKF-based AON can provide accurate and robust passive relative orbit estimation in GEO under the tested practical initialization range and informative observation conditions. The guidance results show how the estimator-reported covariance can shape subsequent approach planning. The present covariance-steering tests use the true relative state for feedback, so closed-loop guidance using the navigation estimate remains future work. For SSA mission design, these findings can guide observation geometry, handoff time, uncertainty margin, and maneuver budget for inspection of non-cooperative GEO objects using low-cost optical sensors.
Date of Conference: September 15-18, 2026
Track: Conjunction/RPO