esa-sceva/satcom-chunk-collection huggingface dataset:
# Predicting the Gap in the Day-Ahead and Real-Time Market Prices Leveraging Exogenous Weather Data
## 2 Learning Algorithms and Methodologies
### Random Forest Algorithm  
The Random Forest is an ensemble learning algorithm. It combines multiple weak models to build a strong predictor by taking advantage of methods called bagging and decision trees. The goal of the decision tree algorithm is to build a tree-like structure from the existing data points, where each leaf will only contain labels from the same class. The algorithm will split the dataset into roughly two halves until the leaves are pure. To find the best split that will keep the tree compact, the impurity function is minimized. In the case of regression tasks, usually the squared loss, as given in (7), is used as an impurity function, while classification problems employ the Gini impurity, as presented in (8).  
\[L(D)=\frac{1}{|D|}\sum_{(x,y)\in D}(y-\tilde{y}_{D})^{2} \tag{7a}\] \[\text{where}\;\tilde{y}_{D}=\frac{1}{|D|}\sum_{(x,y)\in D}y \tag{7b}\]  
Given a dataset, \(D=\{(x_{1},y_{1}),\ldots,(x_{n},y_{n})\}\), with \(c\) distinct categories, where \(D_{k}\) is all the inputs with the label \(k\), the squared loss impurity outputs the average squared difference of the actual value and the average prediction, while the Gini impurity measures the homogeneity of the classes.  
\[G(D)=\sum_{k=1}^{c}p_{k}(1-p_{k}) \tag{8a}\] \[\text{where}\;p_{k}=\frac{|D_{k}|}{|D|} \tag{8b}\]  
Decision trees learn the exact patterns in the training set, so they do not generalize well enough, so they are prone to overfitting. The Random Forest uses bagging to decrease the high variance caused by decision trees. Bagging generates datasets \(D_{1},\ldots,D_{m}\) from the existing data points, \(D\). The created datasets are the replicated datasets, each consisting of \(k\) features drawn at random but with replacements from the original dataset [30]. The new datasets are equal in size to the original dataset and have approximately the same probability distribution.  
The Random Forest consists of large number of decision trees, \(h(x,D_{m})\), from \(D_{1},\ldots,D_{m}\), where \(D_{m}\) is an independent, identically distributed vector [31]. In the case of classification tasks, the majority vote acquired from all the decision trees will be the prediction, and for regression purposes, the average of all the predictors will be the output. Moreover, the RF algorithm has only two hyper-parameters, \(m\) and \(k\). Based on empirical evidence, a good choice for \(k\) is \(k=\sqrt{d}\), where \(d\) is the total number of features in the dataset, and increasing the size of \(m\) will only benefit the model.  
The RF algorithm performs feature selection and generates uncorrelated decision trees by choosing a random set of features to build each decision tree. In addition, by averaging the results from each decision tree that the model builds, it also averages variance as well. Consequently, the RF can balance the bias-variance trade-off well. Thus, in this paper, the RF algorithm is utilized to select the most important features.
# Detecting Traffic Incidents Using Persistence Diagrams
## 1 Introduction
### Survey of Literature  
Detecting incidents in traffic data is important for the safety and welfare of society [2]. Significant efforts have been made to automate incident detection [5; 6; 7; 8]. Traditional automatic incident detection data sources include radar sensors [9], video cameras [10], probes [11]. Loop detectors are also a very common source of traffic data [3; 12], which is the source of the traffic data analyzed in our method.  
Detecting incidents in traffic data can be formulated as an anomaly detection problem. Approaches in this formulation include: dynamic clustering [13] or Support Vector Machines [14] to detect anomalous trajectories, autoencoders to learn regularity of video sequences [15], motion reconstruction [16], and convolutional neural networks to predict congestion in traffic networks [17]. In this paper, we also view incident detection as an anomaly detection problem, with our approach using TDA to identify outliers. For an overview of anomaly detection, see [18].  
Topological data analysis has been used previously in the context of traffic data: [19] uses TDA as a model for tracking vehicles and [20] uses TDA to understand individual travel behaviors. TDA has also been used previously for anomaly detection in [21; 22]. TDA provides a framework for studying the \"shape\" of data in geometric and topological terms rather than a solely statistical framework [23; 24; 25].  
TDA has been an extremely successful tool in applied algebraic topology across a multitude of applications, including analysis of neural networks [26; 27], data dimension reduction techniques [28; 29], anomaly detection [21; 22] biological studies [30], viral evolution [31], the study of blood flow through brain arteries [32], and tracking vehicles [19]. TDA has been applied previously to study time-series data in a variety of settings [33; 34]. Existing applications include to financial data [35; 36; 37], medical signal (EEG) analysis [38; 39] and general techniques including sliding-window methods [40; 41; 42; 43]. Most of these methods rely on a Takens-style embedding to transform time-series data into point-cloud data [44; 45]. In contrast, our method does not require such an embedding.  
Our algorithm is motivated by the intuition that if we take a data set of vectors that represent typical behavior and one of the vectors were replaced with an anomalous observation, the topology of the data set would be significantly altered. This intuition is supported by randomized persistence diagrams [46; 47]. For example, [48] finds that samples from a manifold corrupted by noise with a Gaussian distribution will not in general significantly deviate from the persistence diagram of the underlying manifold, but other distributions could. Further results in [49] emphasize this by showing that extending the stability results for noise with a Gaussian distribution in [48] to other noise distributions should not \"be expected\".
# Ensemble Clustering in GPS Velocities: A Case Study of Turkey
## 2 Data and Methodology
### Consensus Functions
#### 2.4.1 Hybrid Bipartite Graph Formulation  
HBGF is a kind of clustering ensemble model which transforms the combination problem into a hypergraph partitioning problem. It was first introduced by [PERSON] and [PERSON] [47]. This method models the clusters and the data points in the same graph simultaneously [53]. This method creates a bipartite graph with no edges between vertexes that are both instances or clusters. There is an edge between two nodes only if one node represents a cluster and the other node corresponds to an object belonging to that cluster. Then, traditional graph partition techniques such as the METIS algorithm [54] or spectral clustering [43] are applied to obtain this consensus partition.
## 2 Materials and Methods
### Confusion Matrix Calculation
\begin{table}
\begin{tabular}{p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt}} \hline
**Cluster** & **Models** & **Accuracy** & **Precision** & **Sensitivity** & **Characteristics** \\ \hline
1 & 5 & 85\% & 49\% & 85\% & Exceptional performance, highest in all metrics. Possible optimistic bias. \\ \hline
2 & 8, 6, 9 & 70–75\% & 35–39\% & 67–71\% & Moderate to high performance. Biased towards sensitivity. \\ \hline
3 & 4, 3 & 55–60\% & 24–26\% & 55–60\% & Moderate performance. Relatively sensitive but less than Cluster 2. \\ \hline
4 & 1, 7 & 45–50\% & 19–20\% & 45–50\% & Moderate, balanced performance across all metrics. Generalist models. \\ \hline
5 & 2 & 30\% & 15\% & 32\% & Lowest performance. Possible pessimistic bias. \\ \hline \end{tabular}
\end{table} 
Table 4: Summary of the clustering analysis. Figure 3: On the left, evolution of the Calinski-Harabasz index when exploring from 2 to 7 possible clusters. On the right, 3D graphical representation of the clusters. The numbers indicate the model, while each cluster is represented by a different (arbitrary) colour. The number in the right panel corresponds to the models: OH (1), MM (2), NM (3), TM (4), CS (5), Llama (6), Palm (7), CGPT (8) and Claude (9). The third group consists of models TS (4) and NM (3), both with moderate accuracy (60% and 55%, respectively), precision (26% and 24%, respectively) and sensitivity (60% and 55%, respectively). Like the second group, these models share the characteristics of being relatively sensitive in identifying true positives, but less than the second group. The fourth group includes models OH (1) and Palm (7). In both cases, these are models with moderate values for all three parameters. In particular, OH shows moderate accuracy (50%) and precision (20%), but relatively high sensitivity (50%). It correctly identifies true positives, but also generates a considerable number of false positives. On the other hand, Palm has a slightly lower accuracy (45%), precision (19%) and sensitivity (45%) than OH but with the same profile. In both cases, a balanced performance is observed across all metrics with no extreme tendencies towards pessimism or optimism, making them generalist models. Finally, the fifth group consists only of model MM (2), which has the lowest accuracy (30%), precision (15%) and sensitivity (32%) of all models. This model appears to be pessimistic as it predicts fewer true positives and has a higher number of false positives and false negatives, which might overestimate the severity of the conditions due to its cautious approach.
# Multi-Spacecraft Tracking and Data Association Based on Uncertainty Propagation
## 2 Problem Formulation  
### State Model  
Consider a space-based multi-spacecraft tracking problem. As shown in Figure 1, in this scenario, an observer and several targets are involved. The grey lines denote the \(x\)-axis, the \(y\)-axis, and the \(z\)-axis of the Earth-centered inertial coordinate. The red line and the blue line represent the orbits of the target and the observer, respectively. The inter-spacecraft inertial line-of-sight (LOS) is taken as the mean of the measurement. The inertial LOS information can be obtained by combining several sensors, i.e., a camera measuring the LOS with respect to the camera coordinate system and a star sensor measuring inertial attitude. The LOS measurement is chosen to validate the performance of the proposed method in an owe-observation condition.  
The motion of the observer and targets are governed by an Earth-centered dynamic, which is given as follows [6; 40]:  
\[\dot{\mathbf{x}}=\left[\begin{array}{c}\dot{\mathbf{r}}\\ \dot{\mathbf{v}}\end{array}\right]=\mathbf{f}(\mathbf{x})=\left[\begin{array}{c}\mathbf{v}\\ -\frac{\mu_{e}}{\|\mathbf{r}\|^{3}}\mathbf{r}+\mathbf{a}_{\mathbf{I}_{2}}(\mathbf{r})\end{array}\right] \tag{1}\]  
where \(\mathbf{x}=[\mathbf{r};\mathbf{v}]=[x,y,z,\dot{x},\dot{y},\dot{z}]^{T}\) denotes the state of the spacecraft; \(\mathbf{f}(\mathbf{x})\) is the continuous dynamic equation; \(\mu_{e}\) is the gravitational constant of the Earth; \(\mathbf{a}_{\mathbf{I}_{2}}(\mathbf{r})\) represents the perturbation acceleration of the \(J_{2}\) term:  
\[\mathbf{a}_{\mathbf{I}_{2}}(\mathbf{r})=-\frac{3}{2}\mu_{e}J_{2}\frac{R_{E}^{2}}{\|\mathbf{r} \|^{5}}\left[\begin{array}{c}x\left(1-5z^{2}/\|\mathbf{r}\|^{2}\right)\\ y\left(1-5z^{2}/\|\mathbf{r}\|^{2}\right)\\ z\left(3-5z^{2}/\|\mathbf{r}\|^{2}\right)\end{array}\right] \tag{2}\]  
In Equation (2), \(R_{e}\) is the radius of the Earth; \(J_{2}\) is the even zonal harmonic coefficient of Earth which identifies the oblateness effect.  
The discrete format of continuous dynamic in Equation (1) is given as:  
\[\mathbf{x}(t_{k+1})=\mathbf{F}(\mathbf{x}(t_{k}),\Delta t_{k}) \tag{3}\]  
where \(\Delta t_{k}=t_{k+1}-t_{k}\) is the propagating interval between two successive epochs \(t_{k}\) and \(t_{k+1}\); \(\mathbf{F}(\mathbf{x}(t_{k}),\Delta t_{k})\) is the corresponding discrete-time nonlinear transformation, which can be obtained by integrating Equation (1).  
Figure 1: An illustration of the LOS-based tracking framework.  
In this paper, the subscripts 'O' and 'T' are to distinguish between the observer and targets, i.e., \(\mathbf{x}_{O}=[\mathbf{r}_{O};\mathbf{v}_{O}]\) denotes the orbit state of the observer and \(\mathbf{x}_{Ti}=[\mathbf{r}_{Ti};\mathbf{v}_{Ti}]\) represents the state of the \(i\)-th target.
## 3 Problem Description and Mathematical Models  
### Problem Description  
In this paper, the multiobjective multi-AGV routing planning mathematical model JIT-RMOVRPTW was constructed. The VRP in the assembly workshop is described as follows: \(i,j\) indicates the identification of workstations; \(i,j\in V,V=\{0,1,\ldots,n\}\) represents the set of workstations; and when \(i\) or \(j\) is 0, it represents the raw material library. There are \(K\) AGVs with the same performance in the raw material library. Each of them has a maximum load capacity of \(Q\) and an average travel speed of \(v\). The maximum travel distance of the AGV is unlimited. Materials are delivered by material carts, which are pulled by the tail hook of the AGV. Each AGV can transport up to \(R\) carts. The cart has a maximum capacity of \(Q_{r}\). There are \(N\) workstations in the assembly workshop, and a total of \(M\) materials are needed. The correspondence between workstations and materials is known, the information about the materials is known, and \(q_{i}\) is the total number of material boxes required for the workstation \(i\). The position of each workstation is known, and \(d_{ij}\) is the distance between stations. AGVs are dispatched to deliver \(M\) materials to \(N\) workstations. In AGV delivery, disturbed by random events such as traffic jams, the transportation time is uncertain, and the disturbance time is defined as \(t_{i}^{\sim}\). In the JIT-RMOVRPTW, the traditional time window \([a_{i},b_{i}]\) is canceled, and materials need to be delivered on time by the deadline \(JIT_{i}\). The materials of each workstation require \(s_{i}\) to be unloaded. \(s_{i}\) is the unloading time, determined by the number of boxes of materials to be delivered to the station.  
The VRP problem in the assembly workshop is based on the following assumptions:  
(1) There is only one raw material library in the entire workshop, and the raw material library is able to meet the material requirements of all the workstations.  
(2) The material demand at each station is less than the load capacity of the AGV, and the unloading time of the AGV at each station is known.  
(3) All the AGVs depart from the same raw material library and must return to the raw material library after unloading the transported material.  
(4) AGV acceleration and deceleration, charging, etc., are not considered during vehicle operation.  
(5) Materials are placed in standard material boxes, and the material requirements of each workstation cannot be split. The AGV transports materials through the material carts. The boxes of the materials required for the same workstation are loaded in the same material cart, which is not mixed with other workstation materials.
# LoRa Communication Using TVWS Frequencies: Range and Data Rate
## 3 LoRa Radio Propagation Model
### Propagation Models
Setting some typical parameter values for simplicity, the indoor path loss \(L_{p_{in}}\) can be calculated as  
\[L_{p_{in}}=49+50 log_{10}(d_{in}) \tag{11}\]  
where \(L_{p}(d_{0})\) is taken as 40 dB at a distance \(d_{0}\) = 1 m, path loss exponent \(n\) = 5 for indoor obstructed paths, and wall loss and interaction loss are taken as 6 and 3 dB, respectively, assuming an indoor office scenario [22; 23]. The communication range \(d_{in}\) can be computed from (11) as given in  
\[d_{in}=10^{(L_{p_{in}}-49)/50} \tag{12}\]
# Wireless Mesh Networking: An IoT-Oriented Perspective Survey on Relevant Technologies
## 2 Preliminaries on Routing Protocols for Ad-hoc Networks  
Key features of a mesh network, both wired and wireless, are flexibility and self-organizing capability. To build multi-hop routes and to define the network topology, a mesh network needs a routing protocol to rely on. Such protocol can be derived from routing protocols for ad hoc networks, that can be in turn classified as _proactive_ and _reactive_ protocols. _Proactive_ routing protocols are characterized by the fact that each node is in charge of maintaining single or multiple routing tables to represent the entire network topology (or a portion of it). Therefore, proactive routing protocols are known as \"table-driven\", meaning that routing information for each tuple of nodes are continously updated, thus maintaining the routing table updated. Generally, proactive routing protocols are used for networks with a small number of nodes. One of the most known proactive routing protocol examples is represented by the Destination Sequence Distance Vector (DSDV) protocol [4].  
At the opposite, _reactive_ routing protocols build multi-hop routes only upon specific requests and are thus characterized by a reduced overhead. They are based on the concept of flooding and involve three main phases: (i) route discovery, needed to find a possible existing route toward an unknown destination; (ii) route maintenance, used to detect link breaks and to find alternative routes; and (iii) an incremental search method to limit the number of links traversed when routing discovery is enabled. In this kind of networks, nodes that are not actively involved in communication flows do not generate any control or routing information traffic. Moreover, a route is maintained alike as long as it is needed by the source node. Among all available reactive routing protocols, the well-known ones are represented by the Dynamic Source Routing (DSR) protocol [5] and the Ad hoc On-Demand Distance Vector Routing Protocol (AODV) [6].
## 1 Introduction  
China's BeiDou Navigation Satellite System (BDS) has evolved from the first phase of a demonstration system (BDS-1) to the second phase of a regional navigation satellite system (BDS-2) and is currently in construction of the third phase of a global navigation system (BDS-3) [1]. Before formal deployment of BDS-3 constellation, a demonstration system with five BDS-3 experimental satellites, including two Inclined Geosynchronous Orbit (IGSO) satellites (i.e., I1-S and I2-S) and three Medium Earth Orbit (MEO) satellites (i.e., M1-S, M2-S, and M3-S), have been established from March 2015 to February 2016 to carry out in-orbit test and verification for the new payloads, new designed signals, and new techniques [1; 2; 3]. The first two operational satellites for BDS-3 were successfully launched on 5 November 2017, which marked the official start of the establishment of BDS-3 [2]. By the end of 2018, China has successfully launched a total of 19 BDS-3 operational satellites, including 18 MEO satellites in operation and one Geostationary Earth Orbit (GEO) satellite under in-orbit test, to complete a primary system for providing global services [4]. Currently (early May 2019), 20 operational BDS-3 satellites have been launched (as listed in Table 1) [5]. BDS-3 is expected to complete its full constellation with 30 satellites, including 3 GEO, 3 IGSO, and 24 MEO, to provide positioning and navigation services for global users by 2020 [1; 4]. In order to improve the interoperability with other satellite navigation systems, in addition to the backward BDS-2 compatible B11 (1561.098 MHz) and B3I (1268.520 MHz) signals, the BDS-3 satellites (both experimental and operational) are also capable of broadcasting new BIC (1575.42 MHz), B2a (1176.45 MHz), and B2b (1207.14 MHz) open service navigation signals (as listed in Table 2) that overlap with the GPS L1/L5 and Galileo E1/E5a/E5b signals [1; 4; 6]. During the past two years, the characteristics of these new signals from BDS-3 experimental satellites has been intensively investigated in various aspects, including signal carrier-to-noise density ratio (\(C\)/\(N_{0}\)), pseudorange multipath effects, triple-frequency carrier phase ionosphere-free and geometry-free combination, together with precision of code and carrier phase observations, etc. [7; 8; 9; 10; 11]. Their results demonstrated that the observational quality of the new-generation B1C/B2a/B2b signals from BDS-3 experimental satellites is comparable to their GPS/Galileo counterparts. Moreover, the performance of precise orbit determination, satellite clocks, precise point positioning, and relative positioning were also evaluated using observations from BDS-3 experimental satellites or together with BDS-2 satellites [2; 7; 8; 12; 13; 14; 15]. Recently, several researchers have further presented their initial evaluation results for the new navigation signals transmitted by eight BDS-3 operational satellites, and similar results are also achieved as the experimental satellites [2; 3; 16].
## 4 ARP Routing Protocol Design
### Queue Management
#### 4.2.1 Message's Survival Time  
We assume each data message has a field to record its survival time. When a message is generated, its survival time is initialized to be zero. In order to update the survival time, each sensor maintains a timer. Once the timer expires, the stored message's survival time are increased. Moreover, let's consider a sensor, which is transmitting a data message j to a nearby sensor node \(\Psi\)z. Since the propagation time between two adjacent nodes with short distance could be ignored, thus the receiver would insert the message to its own queue directly without any modification to the value of survival time. If a source message has transmitted to its next hop and it is inserted into node's queue again, its survival time is also assumed to be equal to the value before transmitting.
# Simplified Derivative-Based Carrierless PPM Using VCO and Monostable Multivibrator
## 4 Performance Analysis
### FM-PWM Error Analysis  
Under the same assumptions as the signal-to-noise analysis for both the integrator control and PLL previously, the PPM signal contaminated with noise is first compared. This comparison results in a time error \(\Delta t\), which in turn causes a frequency disturbance \(\Delta f\), where the relationship is defined by Equation (44).  
\[\pm\Delta f=\frac{1}{T\pm\Delta t}-\frac{1}{T}=\mp\frac{\Delta t}{T(T\pm\Delta t)} \tag{44}\]  
Under the condition that \(T\) is very much greater than \(\Delta t\) (\(T\gg\Delta t\)), \(\Delta f\) is approximated by Equation (45). Then, the PDF of AWGN in terms of the frequency-domain noise is generated in Equation (46), where Equation (45) is slightly adjusted to be \(\Delta t\cong\Delta fT^{2}\).  
\[\Delta f\cong\Delta t/T^{2} \tag{45}\]  
\[f(\Delta f)=\left(1/\sqrt{2\pi\sigma_{n}^{2}}\right)e^{-\left(s\Delta fT^{2} \right)^{2}/2\sigma_{n}^{2}} \tag{46}\]  
Subsequently, Equation (28), adapted from [PERSON] et al. [19], is rewritten in terms of frequency expression aligned with Equation (45) and rearranged, as shown by Equation (47). This is done to obtain the term of noise signal \(n_{o}\). At the same time, the information signal \(m(t)\) is superseded by the noise signal \(n_{o}\).  
\[\frac{AT_{p}}{T_{i}}=AT_{p}kn_{0}\to AT_{p}\Delta f=AT_{p}kn_{0}\to\Delta f= kn_{0} \tag{47}\]  
After determining the relationship of the noise signal \(n_{o}\), the PDF of AGWN in this quasi-FM-PWM approach is derived by substituting \(n_{o}\) into Equation (46), resulting in Equation (48). The power corresponding to Equation (48) is computed, yielding \(N_{FM-PWM}=\frac{N_{o}}{\left[ST^{2}k_{h_{o}}\right]^{2}}\).  
\[f(n_{0})=\left(1/\sqrt{2\pi\sigma_{n}^{2}}\right)e^{-\left(sT^{2}k_{h_{o}} \right)^{2}/2\sigma_{n}^{2}}=\left(1/\sqrt{2\pi\sigma_{n}^{2}}\right)e^{-\left( n_{o}\right)^{2}/\left(\frac{N_{o}}{\left|T^{2}k_{o}^{2}\right|^{2}}\right)} \tag{48}\]  
To gauge the effect of noise, the signal-to-noise ratio using the same PPM information signal in conjunction with this noise in terms of power is calculated and expressed by Equation (49).  
\[\frac{S_{m}}{N_{FM-PWM}}=\left(k_{p}^{2}\overline{m^{2}(t)}\right)/\left( \frac{N_{o}}{\left[ST^{2}k\right]^{2}}\right)=\frac{S^{2}T^{4}k^{3}k_{p}^{2} \overline{m^{2}(t)}}{N_{o}} \tag{49}\]