esa-sceva/satcom-chunk-collection huggingface dataset:
## 2 Self-Adaptive Differential Evolution Algorithm with Ensemble of Mutation Strategies
### Ensemble Approach  
In addition to the self-adaptive approach, an ensemble approach [43] is employed in the jDE, so called jEDE. This means that instead of using one type of mutation strategy with fixed parameter setting as in the basic DE, each mutant individual is generated according to different mutation strategies with different parameter settings. In this approach, each dimension has values pool for competition of producing better future offspring according to their success in the past generations. In this paper,following mutation strategies (\(M_{i}\)) are considered as in Equations (8)-(10). In \(M_{1}\), the individuals that formed the mutant population are randomly selected. In \(M_{2}\) and \(M_{3}\), strategies are benefitted from the information of the best solution (xbest) so far.  
\[\text{if }STR_{i}=0\qquad\quad M_{1}:\quad v_{i}^{j,t+1}=x_{k}^{j,t}+ MR_{i}\times\left(x_{l}^{j,t}-x_{m}^{j,t}\right) \tag{8}\]  
\[\text{if }STR_{i}=1\qquad\quad M_{2}:\;v_{ij}^{j,t+1}=x_{best}^{j,t}+ MR_{i}\times\left(x_{l}^{j,t}-x_{m}^{j,t}\right) \tag{9}\]  
\[\text{if }STR_{i}=2\qquad\quad M_{3}:\;v_{i}^{j,t+1}=x_{i}^{j,t}+ MR_{i}\times\left(x_{best}^{j,t}-x_{i}^{j,t}\right)+F\times\left(x_{k}^{j,t}-x_{ l}^{j,t}\right) \tag{10}\]  
where \(k,l,m\) are three randomly selected individuals from the target population such that \((k\
eq l\
eq m\
eq i\in(1,..,NP))\) and \(j=1,..,D\). \(MR_{i}>0\) is a mutation scale factor, in our jEDE, it is generated by using self-adaptive procedure. \(STR_{i}\) is the strategy used in each population to choose different mutation strategies. The pseudo code of the jEDE is given in Algorithm 1.  
```
1:Set parameters \(\text{g}=0\), \(\text{NP}=100\), \(M_{\text{max}}=4\)
2:Establish initial population randomly
3:\(\text{P}\delta=\left\{x_{1}^{g},..,x_{NP}^{g}\right\}\) with \(x_{l}^{g}=\left\{x_{1}^{g},..,x_{iD}^{g}\right\}\)
4:Assign a mutation strategy to each individual randomly
5:\(M_{i}=rand()\%M_{\text{max}}\) for \(i=1,..,NP\)
6:Evaluate population and find \(x_{best}^{g}\)
7:\(f(\text{P}\delta)=\left\{\left(x_{1}^{g}\right),..,f\left(x_{NP}^{g}\right)\right\}\)
8:Assign CR\(\text{I}\) = 0.5 and F\(\text{I}\) = 0.9 to each individual
9:Repeat the following for each individual \(x_{i}^{g}\)
10:Obtain \(v_{i}^{g}=M_{i}\left(x_{i}^{g}\right)\)
11:Obtain \(u_{i}^{g}=CR\left(x_{i}^{g},v_{i}^{g}\right)\)
12:Obtain \(x_{i}^{g}=\begin{cases}u_{i}^{g}&\text{if }f\left(u_{i}^{g}\right)\leq f\left(x_{i}^{g-1} \right)\\ x_{i}^{g-1}&\text{otherwise}\end{cases}\)
13:If \(\left(u_{i}^{g}\right)>f\left(x_{i}^{g-1}\right)\), \(M_{i}=rand()\%M_{\text{max}}\)
14:If \(f\left(x_{i}^{g}\right)\leq f\left(x_{best}^{g}\right)\), \(x_{best}^{g}=x_{i}^{g}\)
15:Update \(F_{i}^{g}\) and \(\text{CR}_{i}^{g}\)
16:If the stopping criterion is not met, go to Lines 9-15
17:Else stop and return \(\pi_{best}\)
```  
**Algorithm 1** The self-adaptive differential evolution algorithm with ensemble of mutation strategies.
## 2 Framework for Coordinated Operation  
### Coordination of Interdependent Electricity and Natural Gas Systems (IENS): An Overview  
Due to the increasing interdependence between power grids and natural gas networks, it may be unreasonable, or physically infeasible, to model and optimize the two energy systems separately in practice. Different coordination strategies are as follows:  
* From the perspective of the macro scope of the energy system model, the models can be classified from four aspects: comprehensive evaluation, energy economy, power system planning, and energy system planning [34]. They have different methods, different ranges of use and different fields of application. Energy modeling tools such as LEAP, EnergyPlan, MASSAGE, MARKAL/TIMES have been designated for sustainable energy planning analysis [35]. The main methods of energy system modeling are top-down and bottom-up. The combination of these models leads to a hybrid energy model.
* In IENS, due to the uncertainty of natural gas supply, the balance of supply and demand in power system may be affected for security and economic purposes. Power system researchers have incorporated natural gas transmission constraints into the unit commitment problem of security constraints [12; 23; 24]. The uncertainty of natural gas supply and the variability of natural gas price are also considered in reference [36] to study the impact of natural gas supply shortage on the optimal dispatch of power system.
* In the natural gas optimization problem, the time-varying gas consumption of gas generating units is simulated to explore the influence of large gas generating units [37; 38; 39] on the daily operation efficiency of natural gas network.
* For sequence optimization of power grid and natural gas network [38; 39], this model cannot guarantee global optimality of the IENS.
* The collaborative optimization of IENS considers the power grid and natural gas network as a whole to minimize the total cost associated with the two energy systems. It can achieve the best solution for the whole IENS [40; 41; 42]. In addition, considering that power grid and natural gas network may belong to different system operators and information exchange may be restricted by policies, researchers explore decentralized algorithms to obtain high-quality coordination solutions of IENS, while maintaining decision independence and information privacy of the two systems [43; 44; 45]
* IENS should be considered from operational and long-term planning aspects [46]. Co-planning of power and natural gas networks can be proposed at system level [47] and local level [48]. The integration of natural gas and power sectors usually needs to study the interaction between them and Resource Co-optimization from the perspective of central planners [49]. The mathematical model used in the joint planning of electric power and natural gas shows that some relationships are nonlinear and nonconvex [50]. The most common problem in this paper is MINLP model [51]. Inorder to solve the complexity of the model, various techniques of linear and convex reconstruction/relaxation [52] and decomposition method [53] are proposed.
# Analysis of Security Issues and Countermeasures for the Industrial Internet of Things
### Contributions  
The business, cultural, technological, and personal advantages are expected to rise significantly by IIoT commerce and support. This includes smarter cities, creative infrastructure, intelligent communications and information sharing platforms, smart healthcare systems, energy-saving uses, autonomous supply chain management, and smart transportation [40]. However, protecting IIoT systems is challenging due to the security, privacy, and trust issues that constrain the convenience of a digital world into the physical world. Apart from the security, privacy, and trust concerns, the scale of the number of different devices, administrations, services, resource-constrained nature of the devices, and the curtailment of well-known standards and design considerations for an IIoT system further makes it difficult to enforce traditional security approaches within it [26]. Therefore, the baseline security requirements must be robust and scalable. This paper is motivated by the following research questions: (1) Are the current security requirements enough to develop a secure IIoT system? (2) What are the potential threats and attacks that are primary concerns for a seamless IIoT application that operates in a multi-organizational heterogeneous network environment? (3) How can one design dynamic security mechanisms for managing authentication, authorization, and access control seamlessly over billions of interconnected entities in an IIoT system? The goals of this paper are two-fold: (1) to discuss the various security issues of an IIoT system (note, we use the term security issue to represent attacks, threats, and the potential vulnerabilities), and (2) to use an IIoT layered architecture to demonstrate the various threats and attacks specific to each layer. The significant contributions of this paper can be summarized as follows:  
* We review the existing IIoT security issues in a systematic way. We consider broader aspects of an IIoT system (e.g., integration of IoT, Industry 4.0, and various communication and networking issues related to multi-organizational communications) and list a set of security issues for the IIoT systems.
* We discuss an example use case of IIoT architecture based on layers and examine the identified security issues in each layer. We provide a detailed discussion of the potential countermeasures against these security issues. It helps to understand the system-specific security needs in an IIoT architecture at a more fine-grained level.
* We discuss a set of unique open research issues and list the future research directions that require further study to ensure the security of an IIoT system at scale.
## 5 Simulation Analysis
### Simulation Results and Analysis of Fusion Algorithm
#### 5.2.1 The Necessity of Algorithm Fusion  
Although the DWA algorithm has good real-time obstacle avoidance performance, it easily falls into local optimum and fails at path planning when facing concave obstacles, as shown in Figure 8a. This is prevented after merging the improved A* algorithm, as shown in Figure 8b.  
As shown in Figure 8, the blue triangle represents the starting point, the blue circle represents the destination point, the red solid line represents the actual travel path, and the green arrowhead represents the current travel direction.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Algorithm** & **Path Length (m)** & **Turning Times** & **Total Turning Angle** \\ \hline Traditional A* & 72.33 & 20 & 900.0 \\ [21] & 75.84 & 28 & 1260.0 \\ [8] & 70.49 & 14 & 410.0 \\ This study improves A* & 72.00 & 9 & 435.3 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Performance indicators of 50 \(\times\) 50 raster maps.  
As shown in Figure 7(a), using the DWA algorithm alone prevents the AGV from being driven out of concave obstacles and makes it fall into local optimization, failing to reach the target point; On the contrary, in Figure 7(b), the improved A* algorithm in the hybrid algorithm provides key nodes for the DWA algorithm as local target points so that the AGV can avoid concave obstacles and reach the target point smoothly.
## 3 Antibiotics Having Direct Interactions with tRNAs
### Cleavage of tRNAs  
Colicins are antibacterial toxins secreted out into the extracellular medium by members of the enterobacteriaceae family, such as _E. coli_ (about 30% of _E. coli_ contain them). They are produced as a tool to decrease competition from other bacteria living side by side in the same environment [60]. Several different types of colicins exist and they kill the target cell by various mechanisms, such as DNase activity, RNase activity, depolarization of the cytoplasmic membrane, and inhibition of murein synthesis. Of these, colicins E5 and D are RNases and enzymatically target specific tRNAs and cleave them. This results in the depletion the levels of tRNA required for aminoacylation, consequently impairing protein synthesis and causing cell death.  
Figure 2: Chemical structures of RNase P inhibitor (neomycin B) and inhibitors that directly interact with tRNA (tobramycin, pentamidine and purpuromycin).  
Colicin E5 RNase targets tRNAs specific for tyrosine, histidine, asparagine and aspartic acid by cleaving anticodon QUN that contains the hyper-modified queuosine nucleotide (Q) at the wobble position 34 [61]. On the other hand, colicin D affects all four isoacceptor tRNAs of arginine at the anticodon loops at positions 38 and 39 [61]. Both the colicin E5 and D exhibit their effect _in vivo_ as well as _in vitro_. In addition to the nuclease activity by colicin E5 and D, there exists another type of nuclease called PrrC [61]. These are produced by a clinical strain of _E. coli_ in response to a T4 phage infection. PrrC is a suicidal nuclease since it cleaves its own lysine tRNA as a result of the phage infection [62] and it does so at the anticodon loop of tRNA\({}^{\text{Lys}}\)[63]. Thus the modes of substrate recognition by these colicins and their cleavage sites are different. Yet, they achieve the same physiological function of cleaving the tRNAs [62]. This is intriguing since all colicins possess a similar mechanism of entry into the cell. Further investigation in the mode of action of colicins is needed before use as a treatment for infections.
# Optimized Sonar Broadband Focused Beamforming Algorithm
## 2 Broadband Focused Beamforming Algorithm  
Let the incident signal be \(s(t)\) and the received broadband signal of the M array for:  
\[x_{m}(t)=s(t-\tau_{m})+n_{m}(t),\qquad m==1,\cdots,M\quad, \tag{1}\]  
where \(n_{m}(t)\) is the additive noise of the \(m\)th array element, the output of each sensor is divided into \(K\)th non-overlapping blocks, and each block contains \(l\) sampling points. The FFT transform of L points is applied to each data block, the data in frequency domain is acquired from \(l\) frequency sub-bands, and each frequency sub-band contains a \(K\) data snapshot. The \(l\)th frequency sub-band data in the frequency domain represented in matrix form are:  
\[X_{k}(f_{l})=A_{l}(\varphi,\theta)s(f_{l})+n_{k}(f_{l}),\quad\ k=1,\cdots,K;l=1,\cdots,L\enspace, \tag{2}\]  
where \(A_{l}(\varphi,\theta)\) is the steering vector of the \(l\)th frequency sub-band signal corresponding to the direction of \((\varphi,\theta)\), \(\varphi\) is the pitching angle, and \(\theta\) is the azimuth angle.  
The focusing matrix should ensure the following equation is satisfied during focus transformation [10]:  
\[T(f_{j})A(f_{j},\theta)=A(f_{0},\theta),\quad\ j=1,2,\cdots,J\enspace, \tag{3}\]  
where \(f_{j}\) is any narrowband frequency within the scope of broadband, \(f_{0}\) is the focusing frequency, \(A(f_{j},\theta)\) is the steering vector of the \(j\)th frequency sub-band signal, and \(T(f_{j})\) is the focusing matrix.  
In this paper, the focusing matrix was determined using the rotation signal subspace (RSS) method [11]. The optimal focusing matrix is determined by the following equation [10]:  
\[\left\{\begin{array}{c}\min\|A(f_{0},\theta)-T(f_{j})A(f_{j},\theta)\|_{F}^ {2}(j=1,2,\cdots,J)\\ T^{H}(f_{j})T(f_{j})=I\end{array}\right., \tag{4}\]  
where \(\|\bullet\|_{F}\) is the Frobenius norm, and the solution of Equation (4) is:  
\[T(f_{j})=V(f_{j})U^{H}(f_{j})(j=1,2,\cdots,J).\]  
\(U(f_{j})\) and \(V(f_{j})\) are the left and the right singular vectors of the matrix \(A(f_{j},\theta)A^{H}(f_{0},\theta)\), respectively. The fitting errors still exist from the formula \(\left\|A(f_{0},\theta)-T(f_{j})A(f_{j},\theta)\right\|_{F}^{2}\), and the errors are associated with the focusing frequency.
# CuInSe\({}_{2}\)-Based Near-Infrared Photodetector
## 2 Materials and Methods
### Measurement Details  
The surface morphology of the synthesized CISe layers was characterized by scanning electron microscopy (SEM, S-4700, Hitachi, Tokyo, Japan). For crystallographic analysis, \(X\)-ray diffraction patterns were recorded using an \(X\)-ray diffractometer (XRD, X'Pert PRO, Malvern Panalytical, Malvern, UK) with a Cu target (1.5406 A) and a 1.4 kW power \(X\)-ray generator. The Raman Spectra of CISe layers were obtained using a Raman spectroscopy system (LabRam HR800, Horiba Jobin-Yvon, Bensheim, Germany) equipped with a 512 nm and 325 nm excitation laser operated at room temperature. The topographical study was performed using atomic force microscopy (AFM, XE-100, Park Systems, Suwon, South Korea) in non-contact mode with a PPP-NCHR tip (Si). Its force constant and scanning rates were 42 N/m and 0.3 Hz, respectively. The overall Cu/In composition ratio of the CuInSe thin films were confirmed by X-ray fluorescence measurements (XRF, X-Strata980, Malvern Panalytical, Malvern, UK). The refractive index and extinction coefficient of the CISe layer was measured using an Ellipsometer (Elli-SE, Ellipso Technology, Suwon, South Korea). External quantum efficiency (EQE) was measured using an incident photon-to-electron conversion efficiency measurement system (QEX7 series, PV Measurements Inc., Boulder, CO, USA) under a 75 W xenon lamp light source (UXL-75 XE, Ushio, Tokyo, Japan). The wavelength of the laser diode used for optical illumination was 1064 nm. The incident optical power was measured using an optical power sensor (1930F-IG, Newport, Irvine, CA, USA). The nominal spot size of the illuminated light that passed through the fiber was \(<\)9 \(\mu\)m. Dark current and photocurrent were measured using a semiconductor parameter analyzer (HP 4155A, Agilent, Santa Clara, CA, USA).
# Evidence of Carbon Uptake Associated with Vegetation Greening Trends in Eastern China
## 2 Data and Methods
### Trends in Regional Vegetation Indices
#### 2.1.2 Growing Period Identification  
Vegetation indices are widely used to characterize phenology [55; 56; 57]. We adopted an exponential and logistical smoothing function [57] to fit EVI time series to quantify the beginning and end of strong vegetation activity as the growing period (GP), shown in Equation (1).  
\[y(t)=\frac{c}{1+e^{a+bt}}+d \tag{1}\]  
where \(t\) is time in days, \(y(t)\) is the EVI value at time \(t\), \(a\) and \(b\) are fitting parameters, and \(c\) and \(d\) were used to constrain the range of EVI values. The spatial/temporal resolution of EVI used here is in \(1\times 1\) degree/16-day. The start/end of GP for each grid cell can be defined as minimum/maximum value of derivation of the curvature of the function fitted to either the early season data or the late season data separately (Figure 2, the period between two red dashed lines). We excluded grid cells with poorly constrained GP from our analysis including those starting after July, ending before April, or extending for longer than 12 months as these are unrealistic results. The start, end, and length of the GP in each grid cell used for the trend analysis shown in Figure S1. The GP length retrieved in EC was \(149\pm 36\) days, which started from day of year \(126\pm 27\) and went to day of year \(275\pm 16\) with longer GP lengths in the south and shorter in the north (Figure S1).  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Name** & **Sources** & **Time Res.** & **Space Res.** & **Period** & **Reference** \\ \hline NDVI/EVI & MOD13C1 v6 & 16 days & 0.05 deg. & & [38] \\ NDVI & GIMMS 3g & 15 days & 1/12 deg. & & [39] \\ LAI & MCD15A3H v6 & 4 days & 500 m & 2003.01–2016.12 & [40] \\ LAI & NOAA CDR v4 & 1 day & 0.05 deg & & [41] \\ GPP & MOD17A2H v6 & 8 days & 500 m & & [42] \\ \hline \multirow{4}{*}{Global maps of XCO\({}_{2}\)} & SCIMACHY & & & 2003.01–2009.05 & [43; 44] \\  & BESD-XCO\({}_{2}\), COSAT & 8 days & 1 deg. & 2009.06–2014.08 & [45] \\  & ACOS-XCO\({}_{2}\) & & & 2014.09–2016.05 & [46] \\  & OCO-2 XCO\({}_{2}\) & & & & \\ \hline XCO\({}_{2}\)/CO\({}_{2}\) flux & CarbonTracker 2017 & 3 h & \(2\times 3/1\times 1\) deg. & & [47] \\ XCO\({}_{2}\)/CO\({}_{2}\) flux & MACC-III & 3 h & \(1.875\times 3.75\) deg. & 2003.01–2016.12 & [48] \\ XCO\({}_{2}\) & GEOS-Chem V11.4 & 3 h & \(2\times 2.5/0.5\times 0.625\) deg. & & [49] \\ \hline TCCP & AVHRR VCF & Yearly & 0.05 deg & & [50] \\ Fossil fuel CO\({}_{2}\) Emission & ODLACK 2017 & monthly & 1 deg. & 2003.01–2016.12 & [51] \\ LST & MCD11C2 v6 & 8 days & 0.05 deg. & & [52] \\ Precipitation & TRMM 3B42 & 3 h & 0.25 deg. & & [53] \\ \hline \hline \end{tabular}
\end{table}
Table 1: Datasets used in this study.
# Robust Clustering Routing Method for Wireless Sensor Networks Considering the Locust Search Scheme
## 5 Experiments and Simulation
### Throughput  
The throughput measures the number of packets that have been sent to the base station. It is desirable to send the largest number of packages throughout the life of the network. This measure is illustrated in Figure 7. The throughput is inherent to the number  
Figure 5: Total residual energy.  
of alive sensor nodes transmitting data packets in every round, which means that the collection of information is more significant.  
Figure 7 clearly shows that the proposed protocol has the highest throughput. The number of packets sent to the base station reaches 1200 for the LS-II, while the LEACH protocol sends less than 1000. These results are as expected since the proposed method extends the life of the network, and therefore, the amount of gathered data is improved.
# Target Localization via Integrated and Segregated Ranging Based on RSS and TOA Measurements
## 2 Problem Formulation
### R-GTRS Algorithm
 \tag{22}\]  
Since both RSS and TOA short-distance links are trusted more than the remote ones, due to their multiplicative and additive factors [1], the authors in [14] enhanced the localization accuracy, by introducing weights in (22), defined as \(\mathbf{w}=[\hat{w}_{i},\hat{w}_{i}]^{T}\), where \(\hat{w}_{i}=1-\tilde{d}_{i}/\sum_{i=1}^{N}\tilde{d}_{i}\), \(\tilde{w}_{i}=1-\tilde{d}_{i}/\sum_{i=1}^{N}\tilde{d}_{i}\), with \(\hat{d}_{i}=d_{0}10^{\frac{\tilde{\eta}_{0}-\tilde{\eta}_{\max}/2}{10\tilde{ \eta}}}\) being a _mean_ ML estimate of the distance from (1a). In addition, because (22) is highly non-convex, it was not tackled directly, but it was rather substituted by  
\[ \begin{split}&\underset{x}{\text{minimize}}\sum_{i=1}^{N}\hat{w}_{i} \left(\frac{\upsilon_{i}^{2}\|\mathbf{x}-\mathbf{a}_{i}\|^{2}-\mu}{2\upsilon_{i}\tilde {d}_{i}}\right)^{2}+\sum_{i=1}^{N}\hat{w}_{i}\left(\frac{\upsilon_{i}^{2}\|\bm {x}-\mathbf{a}_{i}\|^{2}-\eta}{2\upsilon_{i}\tilde{d}_{i}}\right)^{2}\\ &+\sum_{i=1}^{N}\hat{w}_{i}\left(\frac{d_{i}^{2}-\|\mathbf{x}-\mathbf{a}_ {i}\|^{2}}{2\tilde{d}_{i}}\right)^{2}+\sum_{i=1}^{N}\hat{w}_{i}\left(\frac{( \tilde{d}_{i}-\frac{\beta_{\max}}{2})^{2}-\|\mathbf{x}-\mathbf{a}_{i}\|^{2}}{2\tilde{ d}_{i}}\right)^{2}.\end{split}  \tag{23}\]  
Then, by expanding the squared norm terms in the numerators of (23), the proposed joint hybrid localization algorithm can be written as  
\[\underset{\mathbf{\theta}=[\mathbf{x}^{T},\|\mathbf{x}\|^{2}]^{T}}{\text{minimize}}\left\{ \|\widetilde{\mathbf{W}}\left(\widetilde{\mathbf{A}}\mathbf{\theta}-\widetilde{\mathbf{q}} \right)\|^{2}\ :\ \mathbf{\theta}^{T}\mathbf{D}\mathbf{\theta}+2\mathbf{f}^{T}\mathbf{\theta}=0\right\}, \tag{24}\]  
\(\widetilde{\mathbf{W}}=\text{diag}([\mathbf{w}_{1}^{T},\mathbf{w}_{2}^{T}])\), \(\mathbf{w}_{1}=[w_{1i},w_{1i}]^{T}\), \(w_{1i}=\frac{\sqrt{\mathbf{w}_{1}}}{2\upsilon_{i}\tilde{d}_{i}}\) and \(\mathbf{w}_{2}=[w_{2i},w_{2i}]^{T}\), \(w_{2i}=\frac{\sqrt{\mathbf{w}_{1}}}{2\tilde{d}_{i}}\) for \(i=1,...,N\),  
\[\widetilde{\mathbf{A}}= \begin{bmatrix}\vdots&\vdots\\ -2\upsilon_{i}^{2}\mathbf{a}_{i}^{T}&\upsilon_{i}^{2}\\ \vdots&\vdots\\ -2\upsilon_{i}^{2}\mathbf{a}_{i}^{T}&\upsilon_{i}^{2}\\ \vdots&\vdots\\ 2\mathbf{a}_{i}^{T}&-1\\ 2\mathbf{a}_{i}^{T}&-1\\ 2\mathbf{a}_{i}^{T}&-1\\ \vdots&\vdots\end{bmatrix} ,\widetilde{\mathbf{q}}= \begin{bmatrix}\vdots\\ \mu-\upsilon_{i}^{2}\|\mathbf{a}_{i}\|^{2}\\ \vdots\\ \eta-\upsilon_{i}^{2}\|\mathbf{a}_{i}\|^{2}\\ \vdots\\ \|\mathbf{a}_{i}\|^{2}-d_{i}^{2}\\ \vdots\\ \|\mathbf{a}_{i}\|^{2}-(\tilde{d}_{i}-\frac{\beta_{\max}}{2})^{2}\\ \vdots\end{bmatrix} .\]
# 3D Point Cloud Generation Based on Multi-Sensor Fusion
## 2 Filtering and Smoothing Theory  
We proposed a method of three-dimensional point cloud generation based on multi-sensor fusion for the rapid accumulation of inertial navigation positioning and attitude determination errors in tunnels and other scenes without GNSS signals. This method used a few control points, constrained inertial navigation and odometer data through RTS smoothing algorithm, and generated three-dimensional point cloud data by fusion. In this section, we first analyze the inertial navigation position update and error equation and introduce the RTS smoothing algorithm.