Emmanuel Delande, CNES; Yvan Gary, CNES; Agustina Gascue, European Space Agency (ESA); Valentin Baral, CNES
https://doi.org/10.64861/JDUJ6418
Keywords: Heterogeneous data, Sensor network, Orbit determination, WRMS
Abstract:
We focus in this paper the influence of a mixture of sensors with widely different data rates, when their measurements are combined in a single Orbit Determination (OD) step with a Least-Square Method (LSM). It is customary to balance out contributions of individual sensors in a LSM process through subsampling of higher-data-rate units, though the justification for this operation is lacking, and its implementation rarely follows a principled approach.
This paper has two objectives: first, to analyze the conditions in which mixing sensors with various data-rates in a single LSM may be detrimental to the output estimate, then, to propose a simple algorithmic solution to balance the contributions of various sensors to the LSM process without requiring explicit sub-sampling of collected data.
Our initial conjecture is that discrepancies in data rate should not affect negatively the LSM process unless modeling mismatches are present in the estimation pipeline. In particular, if a sensor’s observation process is perfectly modeled in the LSM, we surmise that the information gain of an increasing pool of measurements should not accrue indefinitely, but it should not decrease either. Yet, modeling mismatches in a LSM pipeline may also arise from the objects dynamics: since the information collected from each sensor measurement is transported to the epoch where the output estimate is computed, sensor information gain may be poorly accounted for into the LSM output if the dynamics lack realism, and this effect can be magnified in the presence of high-data-rate sensors.
In order to illustrate the phenomena above, we set up a simulation test bench where we can control modeling mismatches between the ground truth and the models used by the LSM. We then compare the output estimate (mean + covariance) against the object’s true state, exploiting in particular p-value-based statistical tests to assess the consistency of the covariance information. As expected, we show that when neither sensor models nor object dynamics are plagued by modeling mismatches, increasing the data-rate does not reduce the quality of the output estimate – quite the opposite. However, we show that the covariance realism decreases with the volume of sensor data when either the sensor model, or the object dynamics, or both, are corrupted. This shows, in particular, that having perfect confidence in a sensor model exploited in the LSM does not guarantee that any volume of measurement data stemming from that sensor can be processed safely in the OD step. This in turn suggests that culling the volume of measurements from high-data-rate units may be beneficial to the OD step in an operational context; it may mitigate, to the very least, the detrimental effects arising from the limited fidelity of the orbital propagator exploited in the LSM algorithm.
Finally, we introduce a simple parametrization of the LSM process in order to control a priori the effect of the measurements of a particular sensor. Each sensor is given a confidence factor, a scalar between 0 and 1 reflecting one’s confidence in the sensor model exploited in the LSM pipeline (e.g. noise covariance matrix). The LSM equations are then rigorously adapted so that the influence of a sensor decreases with the value of its confidence factor, and the sensor is completely discarded – regardless of its volume of data – if its factor is set to zero. The parametrization is then illustrated on the simulated scenarios described above.
Date of Conference: September 15-18, 2026
Track: Space Domain Awareness