Cassini orbit change detection

The efficient analysis of any framework entails the empirical observations reference in the time domain. The proposed approach is an amalgamated framework, which can specify trajectory modifications among the mission of the C-H expedition.

The analysis of trajectories gives the opportunity to acquire information, not just about the spacecraft motion, but allows gaining a better view about far objects. Our framework captures the trajectories as inputs and analyses them temporally and spatially depending on the number and timing of that samples beside the spacecraft velocity. The input to the proposed model are sequence of sample ID i {1,…, N – 1

= 393,976}, sampling intervals ∆ti = ti+1 – ti, modification of the coordinates (∆xi, ∆yi,

∆zi) and modification of the velocity components (∆vx,i, ∆vy,i, ∆vz,i) among the last 13.2 project years of the studied time interval. The input is a 7 x (N – 1) type matrix, which conforms to the formula below:

where the column vectors X_i have following elements:

To provide an illustration of the change that is happening within Cassini velocity, we represent the Cassini spacecraft maneuver around the time moment of Saturn Orbit Insertion (SOI).

During the insertion process, an engine firing was initiated to decrease Cassini velocity. The maneuver of SOI took roughly 90 minutes, allowing the spacecraft to be caught via gravity of Saturn and enter an orbit in 5 months period. Fig. 3 gives details of the SOI process.

The trajectory in a smaller distance scale is a helicoid with an ellipse in cross-section view to the Saturn orbit. It should be mentioned that no coordinate data values exist in the NASA database small vicinity around the SOI. The red circle is the starting moment of the interval. The diamond mark on Fig. 4 represents the insertion point (SOI) of the Cassini around Saturn. The difference of consecutive position values is

Fig. 3. Large-scale trajectory of Cassini around SOI process

high before SOI because just very rare data were saved into the NASA database in this period.

Data capturing were executed in different phases and sub-phases of the project. Each sub-phase has several sequences where each sequence has a number of observations depending on the decision of project leaders. An observation contains a set of samplings where the set size depends on technological events of the spacecraft or astronomical conditions around Saturn.

First possible metric to detect modification of the trajectory is the velocity of the angle modification ∆ϕi between consecutive velocity vectors vi and vi+1. This metric is given by the following formula:

Second possible metric is modification in time of the velocity vector given by the Fig. 4. Distance from the Sun during SOI process

following formula:

If ≥ Thϕ or ai ≥ Tha we consider dissimilarity in the time series and we name it as complex event in the trajectory. The corresponding sampling indexes are saved in sets Iϕ and Ia respectively. To determine the thresholds Thϕ and Tha we used dependence of the cardinality of sets Iϕ and Ia on the magnitude of these thresholds.

Based on the two conditions mentioned has been identified EC = 324 extreme cases, corresponding to the trajectory modifications of the Cassini orbiter (Fig. 5.).

The physical position of Complex Event Detections (CED, right plot), the Sun, first and last sample analysed are marked with star, circle and square characters, respectively. We mention that majority of manoeuvres were executed in the first mission, named Prime of the Cassini interplanetary project.

5. Conclusions

The adopted detection technique has the ability to take a paramount part in change detection of the spacecraft orbiter trajectory. Consequently, carefully choose the most suitable representative quantitative detection approach would be the pivotal procedure among the change detection process. We are providing a novel approach that can increase the veracity of the change in time detection solutions. Tiny variations within the pre-encounter trajectory may cause extraordinarily various post-encounter trajectories based on the faced distance and velocity. Deterministic method is required to find the right threshold values in the next research phase.

Acknowledgement

This work was supported by the construction EFOP-3.6.3-VEKOP-16-2017-00002. The project was supported by the European Union, co-financed by the European Social Fund. The paper has been supported by the QoS-HPC-IoT Laboratory, as well.

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