esa-sceva/satcom-chunk-collection huggingface dataset:
# Intelligent Ship Scheduling and Path Planning Method for Maritime Emergency Rescue
## 4 Experiment and Analysis  
### Route Pre-Planning in the Navigation Planning Stage  
In order to verify the performance of the route pre-planning model in the ship's voyage planning stage, it was compared with the conventional A*algorithm. Taking Sanya Port of China as the planning starting point, the target maritime rescue position of \(109^{\circ}15.4^{\prime}\) E and \(18^{\circ}12.5^{\prime}\) N was selected, and the experiment was carried out in the period when the weather and sea conditions are relatively stable.  
The results are shown in Table 4. The path length of the proposed algorithm is shorter than that of the A* algorithm, which indicates that the navigation route planned by the proposed algorithm can reduce the navigation time and energy consumption and improve the efficiency and economy of navigation. In terms of the number of turns, the proposed algorithm has fewer than the A* algorithm, indicating that the navigation route planned by the algorithm can reduce the difficulty and risk of ship control and improve the stability and safety of navigation. In terms of the average turning Angle, the average turning Angle of the algorithm proposed in this paper is smaller, and the sailing route is smoother. The algorithm has a smaller turning radius and ship inertia, which improves the flexibility and stability of navigation.  
Figure 4: Grid conversion diagram.  
Figure 3: Dataset cropping diagram.
# Application of Machine Learning Models in Optimizing Wastewater Treatment Processes: A Review
## 5 Results
### Comparative Analysis of ML Methods
#### 5.1.1 Applications of Supervised ML Techniques in the Optimization of Treatment Processes
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Technique/Model** & **Application** & **Key Parameters/Output** & **References** \\ \hline \hline \multicolumn{4}{c}{Statistical and Regression Models} \\ k-nearest neighbors (KNN) & Water quality prediction & BOD5, COD, TSS, pH prediction & [41; 52; 69; 76; 77] \\ \hline Partial Least Squares & Data-driven modeling with & COD, NH3-N, multi-collinear & \\ Regression (PLSR) & dimensionality reduction & data & [9; 43] \\ \hline Gaussian Process Regression & Probabilistic regression with & Hydropower production & [18; 42; 49] \\  & uncertainty & prediction & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: _Cont._The algorithms of machine learning listed in Table 5 are well established, having demonstrated successful outcomes in engineering applications. These methods require less computational power and resources, thus enjoying a good deal of interpretability. \begin{table}
\begin{tabular}{c c c c} \hline
**Technique/Model** & **Application** & **Key Parameters/Output** & **References** \\ \hline Adaptive Neuro-Fuzzy (ANFIS) & Interpretable hybrid modeling & Quality classification, total nitrogen & [27; 35; 36; 37; 38; 48; 99] \\ \hline ANFIS-GBO & ANFIS with Gradient-Based Optimization & Total nitrogen prediction, enhanced accuracy & [38] \\ \hline Hybrid Intelligent Systems & Combined multiple AI approaches & Mine water parameter prediction & [48; 71] \\ \hline \end{tabular}
\end{table} 
Table 7: Neuro-fuzzy and hybrid intelligent systems in wastewater treatment optimization. \begin{table}
\begin{tabular}{c c c c} \hline
**Technique/Model** & **Application** & **Key Parameters/Output** & **References** \\ \hline \multicolumn{4}{c}{Bio-inspired Optimization} \\ \hline Genetic Algorithm (GA) & Optimization of neural network parameters & Treatment efficiency optimization & [11; 38] \\ \hline Particle Swarm Optimization (PSO) & Soft sensor parameter optimization & NH4-N prediction, parameter tuning & [5; 76] \\ \hline Salp Swarm Algorithm (SSA) & Bio-inspired optimization for ML parameters & CNN-RBF optimization, enhanced accuracy & [11; 38; 42; 98] \\ \hline \multicolumn{4}{c}{Multi-objective Optimization} \\ \hline NSGA-II & Multi-objective evolutionary optimization & Energy-quality trade-off optimization & [41] \\ \hline Belief Functions + Pareto Front. & Multi-objective optimization with uncertainty & Wastewater recycling quality parameters & [47] \\ \hline \end{tabular}
\end{table} 
Table 8: Optimization-enhanced ML models in wastewater treatment optimization.
# Dual Residual Denoising Autoencoder with Channel Attention Mechanism for Modulation of Signals
## 4 Dataset
### Dataset Preprocessing  
In order to facilitate the addition of noise and the measurement of the SNR, as well as to accelerate the training of the model and reduce the computational complexity of the data, we normalize the power of the modulation signals generated by MATLAB simulation using the following formulae:  
\[P_{s}=\frac{\sum\limits_{i=1}^{N}|s_{i}|^{2}}{N} \tag{11}\]  
\[N_{s}=\frac{S}{\sqrt{P_{s}}} \tag{12}\]  
where \(s_{i}\) is the initial noise-free modulation signal, \(N\) is the length of the signal, \(P_{s}\) is the signal power, and \(N_{s}\) is the noise-free modulation signal with normalized power. In the training stage of the denoising autoencoder, the signal dataset with 11 different SNR values is made into an IQ data sample with the shape of 2 \(\times\) 1024 for each piece. We split the training set and the values set by the ratio of approximately 8:2, and there are 70,400 pieces of training data and 17,600 pieces of validation data. Then we generate 8800 pieces of test data under the same parameters. The Adaptive Moment Estimation (Adam) optimization algorithm is used to complete model training with 40 training epochs, and the initial learning rate is set to 0.001 while decreasing by 0.1 times every 20 epochs.
# A Direction-Sensitive Microwave Sensor for Metal Crack Detection
## 2 Sensor Design  
### Sensor Geometry  
As depicted in Figure 1, the proposed microwave sensor consists of a rectangular patch resonator and two perpendicular feeding ports. The rectangular patch resonator is excited through feeding ports to realize crack direction detection. An impedance transformation structure is inserted between the feeding port and the rectangular patch resonator to achieve an excellent impedance matching. Additionally, a coupled feeding method is applied to improve the current distribution on the patch resonator.  
The designed sensor is realized with a single-layer substrate F4B (\(\varepsilon_{r}\) = 2.2, tan \(\delta\) = 0.0037 @ 10 GHz) with a thickness of 1 mm. The operation frequency range of the proposed sensor is set from 1.5 GHz to 3 GHz after considering sensor size and fabrication cost. The length \(L\) and width \(W\) of rectangular patch shown in Figure 1 are calculated by Equations (1) and (2), which are expressed as  
\[W=\frac{1}{2f_{r}\sqrt{\mu_{0}\varepsilon_{0}}}\sqrt{\frac{2}{\varepsilon_{r}+ 1}}=\frac{c}{2f_{r}}\sqrt{\frac{2}{\varepsilon_{r}+1}}, \tag{1}\]  
\[L=\frac{1}{2f_{r}\sqrt{\varepsilon_{r}}\sqrt{\mu_{0}\varepsilon_{0}}}-2\Delta L. \tag{2}\]  
where, \(f_{r}\) is the center frequency, \(\mu_{0}\), \(\varepsilon_{0}\) are the magnetic permeability and dielectric constant, respectively, and \(c\) is the light speed. \(\varepsilon_{re}\) is the effective dielectric constant and it can be determined with  
\[\varepsilon_{re}=\frac{\varepsilon_{r}+1}{2}+\frac{\varepsilon_{r}-1}{2} \left[1+12\frac{h}{W}\right]^{-1/2},\;W/h>1. \tag{3}\]  
Figure 1: Geometry of the proposed direction-sensitive microwave sensor.  
Additionally, \(\Delta L\) can be calculated by  
\[\frac{\Delta L}{h}=0.412\frac{(\varepsilon_{re}+0.3)\Big{(}\frac{W}{h}+0.264\Big{)} }{(\varepsilon_{re}-0.258)\Big{(}\frac{W}{h}+0.8\Big{)}} \tag{4}\]  
For the geometry shown in Figure 1, the gap distance \(d\) can be optimized to realize better impedance matching and improve the current distribution on a rectangular patch. In addition, quarter wavelength impedance matching is used to realize impedance transformation.  
The specific sensor geometrical dimensions through simulation and optimization are listed in Table 1. Due to the length and width of the rectangular patch resonator being different, it will result in a resonant frequency difference between two feeding ports.
# A Survey on Video Big Data Analytics: Architecture, Technologies, and Open Research Challenges
## 1 Introduction
First, this work presents a consolidated and up-to-date evaluation of VBDA platform architectures and technologies, together with a functional taxonomy of core video analytics tasks and their real-world applications. Second, the paper identifies and synthesizes key open research challenges related to real-time responsiveness, scalability, AI integration, and privacy constraints in large-scale video analytics. Third, this study proposes ViMindXAI as an integrated architectural framework that serves as a reference design for the development of scalable, intelligent, and trustworthy next-generation VBDA platforms. It is important to note that ViMindXAI is currently introduced as a conceptual reference architecture,developed through in-depth analysis of underlying technologies and their capacity to address the practical requirements of modern video big data analytics platforms. Its prototyping and comprehensive performance evaluation are planned as part of future research efforts. To conduct this study, we adopt a survey-based methodology, integrating insights from a broad spectrum of the scholarly literature and real-world implementations across both academic and industrial contexts. An initial corpus of over 350 publications was retrieved from reputable databases, including Scopus, Web of Science, IEEE Xplore, and the ACM Digital Library. A systematic screening process was applied to remove non-peer-reviewed works, studies not directly addressing system architectures or enabling technologies in VBDA, and publications based on outdated technological approaches no longer relevant to current developments. As a result, 157 publications were retained for comprehensive analysis. The majority of these works, focusing on VBDA architectures and core technologies, were published between 2018 and 2025. A substantial portion appeared in high-impact journals and conferences, demonstrating their technical depth, alignment with emerging research directions, and significant contributions to the advancement of VBDA platforms. This systematically selected set of studies ensures that the survey captures both foundational and cutting-edge contributions to the field. The remainder of this paper is organized as follows. Section 2 provides a comprehensive overview of VBDA, detailing architectural paradigms, enabling technologies, and a functional taxonomy of core video processing tasks. Section 3 examines in greater depth VBDA system architectures and foundational technologies, tracing their development and emerging trends from 2018 to 2025. Section 4 introduces the proposed ViMindXAI platform, emphasizing its hybrid architecture, modular design, and AI-driven capabilities for scalable, privacy-preserving video analytics. This section also presents three representative case studies demonstrating the platform's adaptability to diverse real-world scenarios. Section 5 discusses open challenges and outlines future research directions, followed by the conclusion in Section 6.
## 4 Case Study
### Results from Different Construction Scenarios  
In current subsection, the IOT-FML system was tested in four different simulated scenarios at construction sites. In the analyzed scenarios, sensors provided data, JFML received them and the actuators acted based on the output values generated by both the JFML and the FLS for FFH. Additionally, a group of OHS experts evaluated the results provided by the system.  
Due to ethical and safety reasons, experiments in real construction sites were not possible. It is illogical and irresponsible to generate occupational risks in order to test preventive measures. In consequence, the system were only tested using virtual scenarios.
# Artificial Intelligence of Things for Solar Energy Monitoring and Control
## 3 AIoT Applications in PV Systems: A Comprehensive Review
### Applications of AI in PV Systems
#### 3.1.1 Fault Detection and Diagnosis
Integrating lightweight AI models and hybrid techniques could further enhance the effectiveness of sensor-based fault detection in large-scale PV systems. Table 5 provides a comparative analysis of these studies, summarizing their techniques, metrics, strengths, and limitations. \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 \hline
**Study** & **Approach** & **AI Technique** & **Input Data** & **Fault Type Detected** & **Key Metrics** & **Limitations** \\ \hline [PERSON] and [PERSON] [76] & Fault detection and diagnosis & ANN + Analytical Methods & Irradiance, Temperature, Open-circuit voltage, Short-circuit current & Open/Short-circuit Faults, Non-uniform conditions, Inverter faults, MPPT faults & High accuracy, rapid fault detection & Computationally Intensive \\ \hline [PERSON] et al. [77] & Fault detection & ANN + IoT & Irradiance, Temperature & Shading and other faults & Real-time alerts, high accuracy & Requires continuous data connectivity \\ \hline [PERSON] and [PERSON] [78] & Fault detection and diagnosis & DT (C4.5) diagnosis & Ambient temperature, irradiation, power ratio & String fault, short-circuit fault, line-line fault & Detection accuracy: 99.87\%, Fault Diagnostic accuracy: 99.80\% & Limited to the dataset used; real-world performance may vary with different environmental conditions \\ \hline [PERSON] et al. [79] & Fault detection & kNN & Residuals from a simulation model, real measurements from a 9.54-kWp PV system & Open circuit, line-line faults, partial shading & High detection accuracy; robust against conditions; dependent on accurate simulation models \\ \hline [PERSON] et al. [80] & Dust detection & ANN & Optical Sensors & Dust Accumulation & Accuracy: 98.11\% & Limited to dust-related issues \\ \hline [PERSON] et al. [81] & Partial shading detection & ANNBM (MLP) & Irradiance, Temperature & Partial Shading localization & Improved fault localization & Limited generalization to diverse faults \\ \hline [PERSON] et al. [82] & Fault diagnosis & Three-layer ANN & Irradiance, Temperature, voltage, and current of maximum power point & Short Circuit & Accurate fault localization & Memory-intensive for large systems \\ \hline [PERSON] et al. [83] & Fault detection & DA-DCGAN & Pre-recorded PV loop current data & Arc faults & Accuracy: 97.68\% & Dependency on the quality of generated fake data \\ \hline [PERSON] et al. [84] & Fault diagnosis & Modified ANN & open-circuit voltage, voltage, current and power of maximum power & 10 faults: Short circuit, Open degraded modules & High fault detection accuracy & Limited generalization due to reliance on simulated data \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Summary of sensor-based approaches on fault detection.
## 2 Design of LQ Optimal Controllers
### Half-Car Model and Derivation of State-Space Equation
\begin{split}\mathbf{p}\triangleq\begin{bmatrix}z_{c}\\ \theta_{c}\end{bmatrix},\;\mathbf{z}_{s}\triangleq\begin{bmatrix}z_{sf}\\ z_{sr}\end{bmatrix},\;\mathbf{z}_{u}\triangleq\begin{bmatrix}z_{uf}\\ z_{ur}\end{bmatrix},\;\mathbf{z}_{r}\triangleq\begin{bmatrix}z_{rf}\\ z_{ru}\end{bmatrix},\;\mathbf{z}\triangleq\begin{bmatrix}\mathbf{p}\\ z_{u}\end{bmatrix},\;\mathbf{f}\triangleq\begin{bmatrix}f_{f}\\ f_{r}\end{bmatrix},\;\mathbf{G}\triangleq\begin{bmatrix}1&1\\ -l_{f}&l_{r}\end{bmatrix}\\ \mathbf{x}\triangleq\begin{bmatrix}\mathbf{z}\\ \mathbf{z}\end{bmatrix},\;\mathbf{w}\triangleq\mathbf{z}_{r}\;,\;\mathbf{u} \triangleq\begin{bmatrix}u_{f}\\ u_{r}\end{bmatrix}\end{split} , \tag{6}\]  
\[\mathbf{M}_{s}\equiv\text{diag}\big{(}m_{s},I_{y}\big{)},\;\mathbf{M}_{u} \equiv\text{diag}\Big{(}m_{uf},m_{ur}\Big{)}\]  
\[\mathbf{K}_{s}\equiv\text{diag}\Big{(}k_{sf},k_{sr}\Big{)},\;\mathbf{B}_{s} \equiv\text{diag}\Big{(}b_{sf},b_{sr}\Big{)},\;\mathbf{K}_{t}\equiv\text{diag }\Big{(}k_{tf},k_{tr}\Big{)}\]  
\[\mathbf{f}=-\mathbf{K}_{s}(\mathbf{z}_{s}-\mathbf{z}_{u})-\mathbf{B}_{s}\big{(} \dot{\mathbf{z}}_{s}-\dot{\mathbf{z}}_{u}\big{)}+\mathbf{u}, \tag{7}\]  
\[ \begin{cases}\mathbf{M}_{s}\ddot{\mathbf{p}}=\mathbf{G}\mathbf{f}\;\Rightarrow \;\begin{bmatrix}m_{s}\ddot{z}_{c}\\ l_{y}\ddot{\theta}_{c}\end{bmatrix}=\begin{bmatrix}1&1\\ -l_{f}&l_{r}\end{bmatrix}\begin{bmatrix}f_{f}\\ f_{r}\end{bmatrix}=\mathbf{G}\mathbf{f}\\ \mathbf{M}_{u}\ddot{\mathbf{z}}_{u}=-\mathbf{f}-\mathbf{K}_{t}(\mathbf{z}_{u}- \mathbf{z}_{r})\end{cases} , \tag{8}\]  
\[\mathbf{z}_{s}=\mathbf{G}^{T}\mathbf{p}\;\Leftrightarrow\;\mathbf{p}=\Big{(} \mathbf{G}^{T}\Big{)}^{-1}\mathbf{z}_{s}, \tag{9}\]  
\[ \begin{cases}\mathbf{M}_{s}\ddot{\mathbf{p}}=-\mathbf{G}\mathbf{K}_{s}\Big{(} \mathbf{G}^{T}\mathbf{p}-\mathbf{z}_{u}\Big{)}-\mathbf{G}\mathbf{B}_{s}\Big{(} \mathbf{G}^{T}\dot{\mathbf{p}}-\dot{\mathbf{z}}_{u}\Big{)}+\mathbf{G}\mathbf{ u}\\ \mathbf{M}_{u}\ddot{\mathbf{z}}_{u}=\mathbf{K}_{s}\Big{(}\mathbf{G}^{T}\mathbf{ p}-\mathbf{z}_{u}\Big{)}+\mathbf{B}_{s}\Big{(}\mathbf{G}^{T}\dot{\mathbf{p}}-\dot{ \mathbf{z}}_{u}\Big{)}-\mathbf{u}-\mathbf{K}_{t}(\mathbf{z}_{u}-\mathbf{z}_{r} \Big{)}\end{cases} , \tag{10}\]  
\[\mathbf{A}\equiv \begin{bmatrix}\mathbf{0}_{4\times 4}&\mathbf{I}_{4\times 4}\\ \mathbf{M}^{-1}\mathbf{K}&\mathbf{M}^{-1}\mathbf{B}\end{bmatrix} ,\;\mathbf{B}_{1 }\equiv \begin{bmatrix}\mathbf{0}_{4\times 2}\\ \mathbf{M}^{-1}\mathbf{L}\end{bmatrix} ,\;\mathbf{B}_{2}\equiv \begin{bmatrix} \mathbf{0}_{4\times 2}\\ \mathbf{M}^{-1}\mathbf{U}\end{bmatrix} , \tag{13}\]  
\[\dot{\mathbf{x}}=\mathbf{A}\mathbf{x}\mathbf{+B}_{1}\mathbf{w}\mathbf{+B}_{2} \mathbf{u}. \tag{14}\]
###### Abstract  
A fast and low-complexity blind chromatic dispersion (CD) estimation method is proposed by a stepwise optimal order search of fractional Fourier transform (FrFT) in coherent optical communications. The method can track the cumulative dispersion over time in future dynamic and flexible scenarios. The validity of the FrFT method is verified by analogy to the field of CD estimation from the energy concentration property of the chirp signal, and the estimation equation of the CD value is obtained by parameter transformation. Numerical simulations have been carried out in the CD range of 1600 ps/nm to 32,000 ps/nm for 28 GBaud PM-QPSK and 14 GBaud PM-16 QAM signals. The results show that the proposed algorithm achieves a high CD estimation accuracy with an average estimation error of less than 50 ps/nm within the 4096 sampling points and an order search interval of 0.0001. The effects of the polarization mode dispersion, optical signal-to-noise ratio and nonlinearity on CD estimation performance are discussed. In addition, the stepwise optimal order search method can achieve the purpose of greatly reducing the computational complexity under the premise of ensuring the accuracy of CD estimation.  
chromatic dispersion estimation; fractional Fourier transform; stepwise optimal order search; coherent optical communications 2022, 9, 223. [[https://doi.org/10.3390/photonics9040223](https://doi.org/10.3390/photonics9040223)]([https://doi.org/10.3390/photonics9040223](https://doi.org/10.3390/photonics9040223))
## 6 In Situ Investigation of Full-Scale Construction of Arch-Shaped Steel Sheets
### Multi-Camera DIC System with Distributed Field of View  
In order to cover the localization of points corresponding to the numerically predicted maximum displacements (caused by environmental loads), the measurements system consisted of three 3D DIC setups (six cameras in total). Each FOV of 3D DIC setup covered the area of 2.5 \(\times\) 1.5 m and distance between neighboring AOIs was approximately 4 m. In order to perform the measurements in distributed FOV, the dedicated multi-camera DIC system was developed. This system and is described in detail in [16]. The multi-camera DIC system used in these measurements comprised six 5 MPx (2448 \(\times\) 2048) Pointgrey cameras equipped with 8 mm focal length lenses. The cameras were connected to the control computer in order to synchronize the data acquisition procedure. The calibration procedure comprised two steps. In the first step, each 3D DIC system was calibrated with utilization of a standard chessboard calibration target. In the second calibration step, the transformation of individual coordinate systems of separate 3D DIC systems into a common coordinate system has been determined, with the additional support of a laser tracker [26]. Geometrical transformations were determined by using multiple positions of a fiducial marker, which was sequentially placed in the FOV of each 3D DIC setups. The 3D positions of the marker in local coordinate systems were determined with the use of three-dimensional computer vision algorithms [18]. Simultaneously, the positions of the marker in the global coordinate system were determined by a laser tracker. A global coordination system was related to the foundations of the building. Transformation parameters (rotation: Rx; Ry; Rz and translation: Tx; Ty; Tz) between local and global coordinate systems were obtained by using the singular value  
Figure 9: The comparison of load (**a**) U, (**b**) V, (**c**) W displacement functions obtained for numerical models and experimental data (results for referential points).  
decomposition (SVD) method [27]. The obtained accuracy of displacement measurements in each 3D DIC setup was below 0.3 mm (detailed description of calculation of displacement error is presented in [16]).  
A multi-camera DIC system was placed on the 6 m high and 10 m wide buildings' temporary scaffolding (Figure 10), and the measurements were carried out for a few months (from March to October 2016). Therefore, the temperature influence on displacements of measurement setup was noticeable. In order to neutralize this influence, the displacements of the 3D DIC systems as a function of temperature, caused by the thermal expansions of aluminum scaffolding were measured by means of a laser tracker. The correction obtained was included in the results of displacement measurements. The temperature inside the hall was measured using a weather station.
## 4 Sensitivity
### Functional Sensitivity  
The functional sensitivity covers the relationship between the physical measurand to be detected and the frequency detuning of the micromechanical resonator. In the case of the magnetic field sensor used in this article to illustrate the results, the functional sensitivity is referred to as the magnetic sensitivity  
\[S_{\text{mag}}(B_{\text{bias}})=\frac{\partial f_{\text{res}}}{\partial B_{ \text{x}}} \tag{21}\]  
with the physical dimension Hz/T. For other types of resonant sensors, the functional sensitivity could have, for example, the physical dimensions of Hz/K (temperature sensor), Hz/N (force sensor), or Hz/kg (mass sensor). Note that the functional sensitivity only depends on the sensor's initial state, here set by the constant magnetic bias \(B_{\text{bias}}\).
# A New GNSS Single-Epoch Ambiguity Resolution Method Based on Triple-Frequency Signals
## 2 Mathematical Model
The detailed methodology will be introduced in the next section. The solution of Equation (7) can be obtained by minimizing Equation (8):  
\[\min||L-BN-AX||^{2}_{QL},\quad N\in Z^{n},X\in R^{n} \tag{8}\]  
where \(||*||^{2}_{QL}=(*)^{T}Q_{L}{}^{-1}(*)\) and \(Q_{L}\) is the variance-covariance (VC) matrix of observation vector \(L\). In general, the fixed solution can be divided into three steps. In the first step, the integer constraints on the ambiguities are simply ignored. The unconstrained least-squares solution is referred to as the float solution of \(\hat{N}\), \(\hat{X}\) and the corresponding variance-covariance matrix, as follows  
\[\left[ \begin{array}{c}\hat{N}\\ \hat{X}\end{array} \right],\quad\left[ \begin{array}{cc}Q_{\hat{N}}&Q_{\hat{N }\hat{X}}\\ Q_{\hat{X}\hat{N}}&Q_{\hat{X}}\end{array} \right] \tag{9}\]  
In the second step, the integer ambiguity estimation \(\tilde{\text{N}}\) is computed from the \"float\" ambiguity, subject to \(\min||\hat{N}-\tilde{\text{N}}||^{2}_{Q_{\hat{N}}}\). This can be efficiently done using the LAMBDA method. Finally, a fixed solution is obtained by  
\[\tilde{X}=\hat{X}-Q_{\hat{X}\hat{N}}Q_{\hat{N}}{}^{-1}\big{(}\hat{N}-\tilde{ \text{N}}\,\big{)} \tag{10}\]