L-DIT: A dApp for Live Detectability, Identifiability and Trackability for ASOs on the Behavioral Dynamics Blockchain

In this work, we introduce an openly sourced live DIT (L-DIT) rating system, whose primary goal is to formulate an index relying solely on live (real-time) verified publicly available data and to rank all space assets and entities. The proposed rating system is passive, does not depend on sensitive data, takes in real-time data for analysis, and can be applied retrospectively to all ASO.

Where does data from such an effort come from? The data is sourced from the Behavioral and Dynamics Blockchain (BDB) [13]. This is a Space Situational Awareness (SSA) blockchain being developed to record SSA data onto a blockchain. Different space entities including SSA providers, hobbyists, and public SSA efforts (such as SatNOGS) contribute Tracking Data Messages (TDMs) to the chain, which are cross-validated and verified on-chain, before being added to the distributed ledger as blocks. BDB therefore serves as a decentralized provider of ASOs orbital predictions (Two-Line Elements) in a distributed and decentralized manner.

We envision our work to reside as a distributed App (dApp) on the BDB blockchain (See Fig.1). The BDB chain consumes public data along with Tracking Data Messages (TDMs) from various sources including SSA providers and hobbyists, validates and cross-verifies it, and using on-chain consensus provides a single source of truth over which the analysis for O-SSR can be carried out.

With the rise in crowd-sourced space surveillance efforts such as SatNOGs[9] and SatObs[1], more information is being cataloged by hobbyists and is made publicly available. The BDB chain consumes this information and provides a coherent view of the SSA landscape at any given moment.

While we develop BDB, the current version of the dApp presented in this work, incorporates public data from national space agencies released as a part of their public SSA efforts.

The proposed dApp combines individual scores from the detectability (Sec. 3), identifiability (Sec. 4), and trackability (Sec. 5) modules into a single sustainability score, which ranks all ASOs in orbit around the Earth with using public information. Furthermore, individual asset scores contribute to the formulation of entity scores. Utilizing public information about ownership, operators and manufacturers for known assets, average values are computed to form the entity scores, allowing a single number to make comparisons among owners, operators, and manufacturers, expanding the horizon of what was previously not possible in terms of sustainability scores.

The current development of the rating indicates its viability as a basis of comparison for both entities and assets in space using publicly available information. We strongly believe that such an index will guide the community in navigating the uncharted landscape of space safety and sustainability by providing a permissionless, open, and practical rating system.

A decentralized app or dApp is a stack of software that typically operates automatically on a decentralized computing, blockchain network, or distributed ledger system using smart contracts. dApps can be classified into two segments: one that runs on its blockchain and one that integrates with other chains. Smart Contracts are used to maintain data and execute operations on the blockchain network. Complex dApps can have multiple smart contracts. Although the majority (75%) of dApps are made of a single smart contract [15]. Consensus mechanisms are used by dApps to establish consensus on the network. There are several reasons to use a dApp including decentralization, transparency, and security. Moreover, being distributed a dApp offers No downtime and global, uncensorable access to information.

The dApp is implemented of a layer-1 (L1) blockchain that supports smart contracts (See Fig. 1). Data from BDB flows through a bridge to the dApp when the user interacts with it to compute the rating for a particular ASO. This interaction triggers the execution of smart contracts that convert the raw ASO data into L-DIT ratings. The resulting transactions are verified by the underlying L1 chain through its consensus mechanism. At the same time, the resulting L-DIT scores are stored on long-term on-chain storage to serve as a permanent record of the ASOs rating over time.

ASO detectors come in various shapes and sizes and utilize a range of sensing modalities. The two most frequent types of sensors generally used are radar and optical telescopes. Both have complementary strengths. Radar sensors detect ASOs by bouncing radar signals off them. It’s an active sensing mechanism and works as a sender-receiver pair. A transmitter illuminates the target so that a receiver can capture the energy reflected by the target. Radars can determine the position, velocity, size, and shape of an object. On the other hand, optical telescopes equipped with specialized cameras are used for detection by observing satellites passing overhead and utilizing the difference between the ASOs position against the background of stars for detection. This is a passive sensing modality and depends on the light from the sun reflected by the ASO towards the detector, limiting the time during which observations can be made.

In this work, we use the Radar Cross Section (RCS) of an ASO as a measure of its detectability (See Sec. 3.2 for the reasoning). The radar cross section (RCS) quantifies the detectability of an object by ground-based or space-based radar systems. It is defined as the hypothetical area required to intercept and re-radiate an amount of power back to the radar source that is equivalent to the power intercepted by the target. The RCS measures the target’s effectiveness in reflecting radar signals to the receiver. The value of RCS is influenced by several factors including the size, shape, material composition, and the angle of incidence of the radar waves on the target. A higher RCS indicates greater detectability by radar, whereas stealth technology aims to minimize the RCS of objects. RCS is typically expressed in square meters $\text{m}^{2}$ or decibels relative to a square meter (dBsm). The RCS value in dBsm provides a standard reference point for comparing the reflectivity of different objects.

This section provides further details of the proposed detectability metric, how it is derived and the data that is used as input.

Ideally, the observations made by various sensors can been assumed to be independent of each other. However, the work in [11], studied the relationship between RCS and optical magnitude for faint meteors. They show that a linear relationship exists between the measurements made by the two sensors over a range of about 1–9 mag as shown in Fig. 2.

This provides an insight into the correlation that exists between the two sensors, higher detectability in one, is correlated to higher detectability in the other. Therefore, we consider only one sensor for detectability, the RCS, as including both can lead to bias towards more detectable ASOs. Fig.  3 replicates the study in [11] for ASOs closer to Earth, where a similar trend can be seen. For this experiment, the RCS values for ASO were sourced from Celestrack [7] and the visual magnitude data was collected from the nine-channel Mini-MegaTORTORA (MMT-9) optical wide-field monitoring system [6].

Fig. 4 and Fig. 5 provide an overview of the RCS values at various altitudes and inclination respectively. It can be seen that larger ASOs, such as those in GEO and ASOs at lower inclination can be more easily detected. The distribution of $S_{D}$ for all ASOs considered is shown in Fig. 6 and Table. 2 shows the ASO with the highest detectability scores.

The identifiability considered in this work is passive: given a Tracking Data Message (TDM) of an observed ASO, how difficult it is to reliably associate it to a previously known ASO. This assumes that a database of known ASO is available, which is acquired via the BDB chain. To effectively answer whether a TDM can be uniquely assigned to an ASO, we closely follow the clustering-based techniques outlined in [14]. However, the method has not been described in detail in their work. The method presented here is our vision of how clustering similar orbits should be carried out.

Orbits come in various sizes and shapes. It is therefore important to consider a compact representation that encapsulates various aspects of the orbit of an ASO. Such a representational space can then be partitioned into clusters where each cluster contains ASOs with similar orbits.

For this, we consider the angular momentum of an ASO. For an ASO in orbit around a central body (e.g., Earth in our case), the angular momentum $\mathbf{l}$ is given by the cross product of the ASO’s position vector $\mathbf{r}$ and its linear momentum $\mathbf{p}$:

Since the linear momentum $\mathbf{p}$ is equal to the mass of the satellite $m$ times its velocity $\mathbf{v}$, we can write:

For a satellite in a circular orbit, the magnitude of the angular momentum can be simplified further. If $r$ is the radius of the orbit and $v$ is the constant orbital speed, the magnitude of the angular momentum $|l|$ is:

In the case of an elliptical orbit, the expression for angular momentum becomes more complex, as both the radius and velocity of the satellite vary along the orbit. However, the angular momentum remains constant due to the conservation of angular momentum. The direction of the angular momentum vector is perpendicular to the plane of the orbit, following the right-hand rule.

The angular momentum quantifies the various orbital parameters (velocity, mass, distance, orbital plane) conveniently into a vector $\mathbf{l}\in\mathcal{R}^{3}$, which can be used for clustering to find ASOs with similar orbital characteristics. To find ASOs with similar characteristics, we use bisecting k-means clustering [2] to cluster all ASO in distinct subsets. When a new ASO is observed, its computed angular momentum is assigned to the nearest cluster center. The number of other ASOs present in the assigned cluster determines the identifiability score of the observer ASO. If the cluster size is larger, it is generally considered difficult to identify which of the ASOs in the cluster corresponds to the current observation, making it less identifiable. The smaller the size of the matched cluster, the more identifiable the ASO is considered. More specifically, the identifiability score for a cluster ($C_{I}$) of size $N$ is given by

We first present the results for the k-means clustering which shows the number of clusters (empirically found to be 60). The results are shown in Fig. 8 where each cluster is represented using a different color. The clustering leads to a few large clusters (low identifiability) and many smaller clusters (high identifiability). The smallest cluster contains only three orbits and are visualized in Fig. 9. This demonstrated the efficacy of the angular momentum space as a viable representation for clustering.

The most and least identifiable ASO are given in Table. 5 and Table. 5.

Trackability is a function of the observing sensor network as it enables the opportunities for the detection of ASOs. We therefore formulate the trackability of an ASO based on how frequently and for how long it is observed by a simulated sensor network (See Fig. 11 for locations). To simulate noise and intermittent failures of sensors, we compute the detectability score using a Monte Carlo simulation. Monte Carlo simulation is a computational technique that uses random sampling and statistical modeling to estimate the possible outcomes of a complex system. The choice of distribution can impact the simulation’s accuracy, bias, variance, and the level of detail captured.

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  The dependence on sensor distribution refers to how the placement or arrangement of these sensors affects the behavior and characteristics of the simulated system.

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  The sensors or the array of sensors distributed globally aren’t always available for tracking an object in space, various objects are being tracked across various locations at the same/ different times of the day.

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  Taking a subset of locations for simulating the passes to calculate various parameters and then taking their average across several runs gives us a better representation of the real-time system, tracking objects across multiple locations.

The trackability of a satellite is determined using three parameters -

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  The average pass duration of a satellite is the average amount of time a satellite is visible during each orbit as it passes over a particular location on the Earth’s surface. This duration is the difference between the rise and the set time. In this case, we used this as a criterion to determine the average amount of time it is visible during each pass across several different locations on Earth chosen randomly from a list of actual positions of ground stations.

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  The average interval duration for a satellite refers to the average time between consecutive passes over a location or how frequently a satellite revisits that particular location on Earth. A shorter interval means frequent revisits. To keep things consistent, we have inverted the values after normalizing them to make the values close to one represent more frequent passes over a particular location.

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  The average ground coverage during a satellite pass is the percentage of ground stations from where it can be detected or tracked. To simulate a dynamic ground station network, a subset of locations was used within a Monte Carlo simulation, during each trial.

The scores obtained are min-max normalized to get a value within the range of 0 to 1, with 0 representing the lowest and 1 representing the highest.

When discussing satellites and their pass times in terms of “rise” and “set”, we are typically referring to how they appear from the perspective of an observer on the Earth’s surface.

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  Satellite Rise and Set:

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    Rise: The moment when a satellite becomes visible above the horizon as it moves along its orbital path. This is when it transitions from being below the observer’s horizon to being visible in the sky.

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    Set: The moment when a satellite disappears below the horizon as it continues along its orbit. This is when it transitions from being visible in the sky to being obstructed by the Earth’s curvature.

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  Factors Affecting Rise/Set Time:

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    Orbital Inclination: Satellites with higher inclinations will appear to rise and set more towards the poles for observers at mid-latitudes.

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    Observer’s Latitude: Observers closer to the poles may experience longer periods of visibility (continuous pass) for polar orbiting satellites.

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    Satellite Altitude: Higher altitude satellites will appear to move more slowly across the sky, affecting the duration between rise and set.

Satellites in GEO do not have a ’rise’ and ’set’ time like LEO/MEO satellites. They are positioned to appear stationary in the sky relative to an observer’s location on the ground. This steady position allows for continuous visibility and is advantageous for applications requiring constant coverage over a specific area. Unlike geostationary satellites, geosynchronous satellites may have slight north-south motion as they orbit the Earth.

The 10 most trackable ASO are given in Table. 6 and the distribution for all ASOs is shown in Fig. 10