esa-sceva/satcom-chunk-collection huggingface dataset:
# Quantum Antenna as an Open System: Strong Antenna Coupling with Photonic Reservoir
###### Abstract  
We propose a general concept of quantum antenna in the strong coupling regime. It is based on the theory of open quantum systems. Antenna emission into space is considered an interaction with a thermal photonic reservoir. For antenna dynamics modeling, we formulate master equations with a corresponding Lindblad super-operators for the radiation terms. It is shown that strong coupling dramatically changes the radiation pattern of antenna. The total power pattern splits to three partial components, each of which corresponds to a spectral line in Mollow triplet. We analyzed the dependence of splitting on the length of antenna, shift of the phase, and Rabi-frequency. The predicted effect opens a way for implementation of multi-beam electrically tunable antennas, potentially useful in different nano-devices.  
quantum antennas; Rabi-oscillations; photonic reservoir; master equations +
Footnote †: journal: Applied Sciences
# Reducing Model Complexity in Neural Networks by Using Pyramid Training Approaches
## 3 Methodology
### Quantization
#### 3.4.1 Fixed-Point Quantization  
Fixed-point quantization simplifies the representation of weights by using a fixed number of bits for both integer and fractional parts. This method is characterized by the use of a scaling factor, \(2^{k}\), where \(k\) indicates the number of fractional bits. Weights are then quantized by rounding them to the nearest fixed-point value based on this scaling factor. The mathematical formulation is as follows:  
\[Q(x)=\text{Round}(x\times 2^{k})\times 2^{-k} \tag{7}\]  
Fixed-point quantization is particularly beneficial for hardware implementations that support fixed-point arithmetic, leading to more efficient computations than floating-point operations.
## 4 Conclusions  
In the present study, _C. variabilis_ RSM09 was cultured at various CO\({}_{2}\) concentrations ranging from 0.03% to 50% (\(p/v\)), light intensities (3000, 5000, and 7000 Lux), and photoperiods (12:12, 18:6, and 24:0 h L/D) to examine microalgal growth lipid production. The results revealed that the CO\({}_{2}\) concentration of 20% \(v/v\), the light intensity of 5000 Lux, and a photoperiod of 18:6 h L/D were practically suitable for culturing _C. variabilis_ RSM09. Under these conditions, the biomass reached 1.65 \(\pm\) 0.17 g/L with a lipid content of 25.22 \(\pm\) 2.06% wt. According to the FAME profiles, the main fatty acids from _C. variabilis_ RSM09 biomass included palmitic acid, stearic acid, linoleic acid, and linolenic acid. These findings suggest that these suitable conditions can enhance growth, lipid concentration, and the production of key fatty acids suitable for biodiesel production.  
Conceptualization, S.U. and A.C.; methodology, S.U. and A.C.; investigation, S.U. and A.C.; writing--original draft preparation, S.U. and A.C.; writing--review and editing, S.U. and A.C.; funding acquisition, S.U. and A.C. All authors have read and agreed to the published version of the manuscript.  
\begin{table}
\begin{tabular}{l c c c} \hline \hline \multirow{2}{*}{**Fatty Acid**} & \multicolumn{3}{c}{**FAME Composition (\% of Total FAME)**} \\ \cline{2-4}  & **12:12 L/D** & **18:6 L/D** & **24:0 L/D** \\ \hline Lauric (C12:0) & 0.86 & 0.70 & 0.24 \\ Myristic (C14:0) & 0.68 & 0.79 & 0.96 \\ Myristoleic (C14:1) & 0.26 & 0.38 & 0.26 \\ Palmitic (C16:0) & 45.09 & 42.27 & 70.50 \\ Stearic (C18:0) & 4.40 & 4.37 & 5.18 \\ Oleic (C18:1) & 7.82 & 8.26 & 5.23 \\ Linoleic (C18:2) & 18.29 & 21.06 & 8.35 \\ Linolenic (C18:3) & 17.76 & 17.47 & 5.71 \\ Eicosadienoic (C20:2) & 1.82 & 1.37 & 1.79 \\ Eicosapentaenoic (C20:5) & 0.70 & 0.75 & 0.33 \\ Docosadienoic (C22:2) & 0.58 & 0.73 & 0.65 \\ TetexoNanoio (C24:0) & 1.74 & 1.85 & 0.80 \\ Saturated fatty acids (SFAs) & 52.77 & 49.98 & 77.68 \\ Monounsaturated fatty acids (MUFAs) & 8.08 & 8.64 & 5.49 \\ Polyunsaturated fatty acids (PUFAs) & 39.15 & 41.38 & 16.83 \\ \hline \hline \end{tabular}
\end{table}
Table 1: FAME compositions of _C. variabilis_ RSM09 cultivated under different photoperiods.  
**Funding:** This research was funded by King Mongkut's University of Technology North Bangkok. Contract no. KMUTNB-63-KNOW-015.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.  
**Acknowledgments:** The authors greatly thank the Faculty of Science, Energy and Environment, King Mongkut's University of Technology North Bangkok, Rayong Campus, for their support.  
**Conflicts of Interest:** The authors declare no conflicts of interest.
# State Residualisation and Kron Reduction for Model Order Reduction of Energy Systems
## 2 Power System Modelling
### Grid-Forming Converter
#### 2.1.2 Modelling the Grid-Forming Converter Physical Hardware  
The Equations (24)-(29) represent the RL filter (24) and (25), the C filter (26) and (27), and the DC/AC converter (28) and (29), based upon a DQQ reference frame of the angular frequency \(\omega_{vsm}\) given by the external loop.  
\[\frac{L_{f}}{\omega_{b}}\frac{dic_{cd}}{dt}=v_{cd}-v_{od}-R_{f}i_{cd}+\omega_{ vsm}L_{f}i_{cq}, \tag{24}\]  
\[\frac{L_{f}}{\omega_{b}}\frac{dic_{cq}}{dt}=v_{cq}-v_{qq}-R_{f}i_{cq}-\omega_{ vsm}L_{f}i_{cd}, \tag{25}\]  
\[\frac{C_{f}}{\omega_{b}}\frac{dv_{od}}{dt}=i_{cd}-i_{od}+\omega_{vsm}C_{f}v_{ 0q}, \tag{26}\]  
\[\frac{C_{f}}{\omega_{b}}\frac{dv_{qq}}{dt}=i_{cq}-i_{qq}-\omega_{vsm}C_{f}v_{ 0d}, \tag{27}\]  
\[v_{cd}^{*}=v_{cd}, \tag{28}\]  
\[v_{cq}^{*}=v_{cq}. \tag{29}\]  
Equations (28) and (29) indicate that the DC/AC converter is assumed to be ideal.  
The output voltage and current in (24)-(27) need to be converted to the common DQQ reference frame rotating at a frequency of \(\omega\), with a base capacity of 100 MVA. Given a converter capacity of \(S_{b}\), the conversions are presented as follows.  
\[\frac{100}{S_{b}}\begin{bmatrix}i_{cd}\\ i_{cq}\end{bmatrix}=\begin{bmatrix}\cos(\delta_{vsm})&-\sin(\delta_{vsm})\\ \sin(\delta_{vsm})&\cos(\delta_{vsm})\end{bmatrix}\begin{bmatrix}i_{cd}^{g}\\ i_{cq}^{g}\end{bmatrix}, \tag{30}\]  
\[\begin{bmatrix}v_{od}\\ v_{od}\end{bmatrix}=\begin{bmatrix}\cos(\delta_{vsm})&-\sin(\delta_{vsm})\\ \sin(\delta_{vsm})&\cos(\delta_{vsm})\end{bmatrix}\begin{bmatrix}v_{gd}^{g}\\ v_{0q}^{g}\end{bmatrix}. \tag{31}\]
# Pursuit-Evasion Problem of Unmanned Surface Vehicles in a Complex Marine Environment
## 3 Controller Design of USV
### Heading Control  
In the control strategy, define the angle tracking error as follows:  
\[\widetilde{\psi}=\widetilde{\psi}-\psi_{d} \tag{19}\]  
In order to adopt the first-order sliding mode to converge the heading tracking angle error, it is necessary to obtain the yaw rate error of the USV. The yaw rate error \(\widetilde{r}\) can be obtained by the time derivative of Equation (19):  
\[\widetilde{r}=r-r_{d} \tag{20}\]  
Considering the fast convergence of sliding mode control, the first-order sliding surface is described by the following formula:  
\[S_{qr}=\dot{\widetilde{\psi}}+\lambda_{\varphi}\widetilde{\psi}=r-r_{d}+ \lambda_{\varphi}\widetilde{\varphi} \tag{21}\]  
where \(\lambda_{\varphi r}\) is a positive constant and it represents the sliding mode design variable.  
The Lyapunov function considering heading angle and external disturbance can be expressed as follows:  
\[V_{qr}=\frac{1}{2}S_{\varphi}^{2}+\frac{1}{2}\widetilde{\tau}_{ur}^{2} \tag{22}\]  
By differentiating the above formula, we obtain the following:  
\[\begin{array}{l}\dot{V}_{qr}=S_{\varphi}S_{\varphi}+\widehat{\tau}_{r}^{2} \dot{\widetilde{\tau}}_{r}\\ =S_{\varphi}\big{(}\dot{r}-\dot{r}_{d}+\lambda_{\varphi}(r-r_{d})\big{)}+ \widehat{\tau}_{r}^{2}\dot{\widetilde{\tau}}_{r}\\ =S_{\varphi}\Big{(}\frac{m_{11}-m_{22}}{m_{33}}uv-\frac{d_{33}}{m_{33}}r+\frac {1}{m_{33}}(\tau_{r}+\tau_{ur})-\dot{r}_{d}\Big{)}\\ \quad\quad+S_{\varphi}\big{(}\lambda_{\varphi}(r-r_{d})\big{)}+\widehat{\tau} _{r}^{2}\dot{\widetilde{\tau}}_{r}\end{array} \tag{23}\]To ensure that the pursuer can hunt the target more effectively, the heading angle controller is designed as follows:  
\[\tau_{r}=-m_{33}(\frac{m_{11}-m_{22}}{m_{33}}uv-\frac{d_{33}}{m_{33}}r+\hat{v}_{ \sigma r})+\dot{r}_{d}-\lambda_{\varphi}(r-r_{d})-k_{\tau r}S_{\varphi r} \tag{24}\]  
where \(k_{\tau r}\) is a positive constant and it represents the heading angle gain parameter.  
Substituting the above formula into Formula (24), we obtain the following:  
\[\dot{V}_{\varphi r}=-k_{\tau r}S_{\varphi}^{2}-k_{\tau r}\tilde{\tau}_{\tau}^{ 2}\dot{\tilde{\tau}}_{r}\leq 0 \tag{25}\]  
It can be known that the sliding surface \(S_{\varphi r}\) will converge to zero in finite time and that the heading angle error will also converge to zero, which means \(\underset{t\rightarrow\infty}{\lim}\left(\tilde{\psi},\tilde{\tau}\right)=(0,0)\).
# MPFM-VC: A Voice Conversion Algorithm Based on Multi-Dimensional Perception Flow Matching
## 4 Methods
### Content Perturbation-Based Training Enhancement Method  
Due to distributional discrepancies between the training data and the inference environment, the model may produce degraded audio quality during inference, such as unnatural artifacts or plosive distortions. We counted the probability distribution of the content representation extracted by Sensevoice [46] in the dataset used in this paper. As shown in Figure 5, only about 20% of the 4096 word size was effectively used, and the rest of the representations were redundant representations.  
To improve generalization and robustness, we propose a content perturbation-based training enhancement method. This method is designed to enhance the model's contextual generalization capability and improve its stability in real-world deployment scenarios.  
As illustrated in Figure 6, random perturbations are applied to the input content representations during the training phase to enhance model robustness. Given an input content representation vector \(I_{content}\), a certain proportion of its dimensions are randomly selected and masked. The selected dimensions are replaced with blank tokens, and the perturbation strategy is defined as follows:  
\[I^{\prime}_{content}=M\odot I_{content}+(1-M)\odot I_{blank} \tag{9}\]  
where \(M\in 0,1^{d}\) denotes a binary masking vector, where a subset of elements is randomly set to 0 according to a predefined masking ratio, while the remaining elements are set to 1. \(I_{blank}\) refers to the blank token used for replacement during perturbation, which is generated based on a roulette-wheel sampling strategy. Specifically, the value distribution of the content representation is first estimated from the training data by computing the frequency of each value within the embedding space. Then, values are randomly sampled in proportion to their observed frequencies to construct the blank representation used for masking.  
Through this training strategy, the model is expected to generate high-quality speech even when partial content representations are missing. This enables the model to maintain strong robustness and generalization during inference, particularly in scenarios involving incomplete feature inputs or noise-corrupted conditions, thereby ensuring stable and natural speech synthesis.  
Figure 5: Word probability distribution map with 4096 word size.  
Figure 6: Content perturbation-based training enhancement method.
# Repurposing Historic Drugs for Neutrophil-Mediated Inflammation in Skin Disorders
### Neurophilic Dermatoses
#### 1.3.1 Sweet Syndrome  
Also known as acute febrile neutrophil dermatosis, Sweet syndrome is characterized by the sudden onset of painful, erythematosus plaques and nodules. The pathogenesis of Sweet syndrome remains incompletely understood. However, its frequent association with infections suggests a potential pathogenic role for bacterial antigens or antigen-antibody complexes. Additionally, its co-occurrence with arthritis and Sjogren's syndrome, along with the rapid response to corticosteroids, indicates the involvement of immune mechanisms. Although no specific guidelines exist for treating Sweet syndrome, systemic corticosteroids are generally the first-line treatment [5].  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Treatment** & **Effect** & **Mechanism** \\ \hline \multirow{3}{*}{Dapsone} & \multirow{3}{*}{Anti-neutrophilic properties} & Modulation of neutrophil chemotaxis \\  & & Inhibition of myeloperoxidase reducing oxidative stress \\  & & Amelioration of neutrophil-mediated damage \\ \hline \multirow{3}{*}{Colchicine} & \multirow{3}{*}{Anti-neutrophilic properties} & Inhibition of neutrophil chemotaxis \\  & & Inhibition of neutrophil degranulation \\  & & Modulation of the inflammatory cascade \\  & & Inhibition of MMPs \\  & & Binding zinc or calcium ions in the enzyme structure \\  & & Inhibition of bacterial breakdown products, \\ Tetracycline & Anti-inflammatory activity & Reduced production of pro-inflammatory cytokines (IL-1\(\beta\), IL-8, TNF), \\  & & Inhibition of leukocyte migration, \\  & & Reduced NO by inhibiting iNOS activity \\  & & \multicolumn{1}{c}{} \\  & & \multicolumn{1}{c}{} \\  & & \multicolumn{1}{c}{} \\  & & \multicolumn{1}{c}{} \\  & & \multicolumn{1}{c}{} \\  & & \multicolumn{1}{c}{} \\ \end{tabular}
\begin{tabular}{c} Inhibition of neutrophil chemotaxis \\ Inhibition of neutrophil degranulation \\ Modulation of the inflammatory cascade \\ Binding zinc or calcium ions in the enzyme structure \\ Inhibition of bacterial breakdown products, \\ Reduced production of pro-inflammatory cytokines (IL-1\(\beta\), IL-8, TNF), \\ Inhibition of leukocyte migration, \\ Reduced NO by inhibiting iNOS activity \\ ROS scavenging and preventing oxidative damage to cell structures \\ through the phenolic ring \\ Decreased caspase expression, \\ Altered mitochondrial membrane potential, \\ Inhibition of cytochrome C release, affecting the intrinsic pathway \\ of apoptosis \\ \hline \hline \end{tabular} Abbreviations: iNOS, inducible nitric oxide synthase; MMP, metalloproteinases; NO, nitric oxide; ROS, reactive oxygen species.  
\end{table}
Table 2: Effects and mechanisms of action of anti-neutrophilic drugs.
# Influence of Silane-Modified Coal Gangue Ceramsite on Properties of Ultra-High-Performance Concrete
## 3 Results and Discussion
### Working Performance  
The modified aggregate is substituted for the unmodified aggregate in UHPC on a mass-ratio basis, and according to the replacement ratio, the original ratio and substitution ratio are labeled as M0, M20, M40, M60, M80, and M100. In accordance with the relevant standard GBT2419-2005 [41], the fluidity of each ratio was measured, and the average flow diameter was recorded, as illustrated in Figure 8, and the influence of modified aggregate on the working performance of UHPC was analyzed.  
From Figure 8, it is evident that as the content of modified aggregate rises, the fluidity of the UHPC gradually improves, demonstrating that the SCA effectively enhances the UHPC's workability. The fluidity of M0 is only 148 mm, while when the mass substitution rate of modified aggregate hits 100%, the fluidity reaches 205 mm, marking a 38.51% increase. In contrast to the UHPC system incorporating unmodified CGC and steel fibers studied by [PERSON] et al. [42] (flowability of approximately 180 mm), the use of SCA-modified CGC in this study significantly boosts the flowability of the UHPC, thereby ensuring favorable workability.  
The enhanced workability primarily stems from the hydrophobicity imparted to the ceramsite aggregate surface through SCA modification. Given a constant water-cement ratio, as the proportion of modified aggregate in the UHPC increases, the amount of free water that the aggregate can absorb gradually decreases, so more free water exists between cementitious materials and aggregate [22], ultimately resulting in improved workability of the UHPC.
# Use of Dairy and Plant-Derived Lactobacillus as Starters for Cherry Juice Fermentation
## 3 Results
### Sugars and Organic Acid Metabolism  
Sugar in cherry juice was mainly fructose, glucose and sucrose. Generally, their microbial metabolism was limited (Figure 2, Table S1). As an example, fructose, the most concentrated sugar, was only partially metabolized, especially after storage by _L. plantarum_ strains (\(p<0.05\)). Microbial fermentation did not change glucose concentration, but it was only metabolized during storage; whereas sucrose significantly decreased in all fermented samples. Lactic acid was the main end product in all fermentations, reaching the highest amount when _L. plantarum_ POM1 was used as starter (9.47 \(\pm\) 0.32 mg/mL). Malolactic fermentation occurred, leading to total degradation of malic acid, in particular when strains of dairy origin were used. Only one strain, _L. plantarum_ C1, did not convert malic acid (Figure 2 and Table S1). Tartaric acid metabolism was observed after fermentation and storage, especially by _L. plantarum_ strains (\(p<0.05\), reduction of 92%), but it was also observed in _L. rhamn_s and _L. paracasei_ (Figure 2, group A2 and B Table S1). No significant differences were observed for citric acid among fermented and unfermented samples (Figure 2 and Table S1).  
Figure 1: Principal component analyses. (**A**) Score plot obtained from the analysis of unfermented (control) and fermented (_L. plantarum_, _L. rhamn_s and _L. paracasei_) cherry juice. Each sample is identified by the strain number and the time of incubation. For example, 1 LE1_48h is used for strain _L. plantarum_ 1 LE1 after fermentation. (**B**) Loading plot is based on sugars, organic acids, and volatile and phenolic compounds. Abbreviations are the same as used in Table S1 for organic acids (A) and sugars (S), Table S2 for volatile compounds (V), and Table S4 for polyphenols (P).  
Figure 2: Sugars and organic acid metabolism. Hierarchical clustering and heat map performed on sugars and organic acids detected in fermented juice with _L. plantarum_ (C1, 1 LE1, POM1 and 285), _L. rhamn_s (2360) and _L. paracasei_ (4186) and unfermented juice (30 \({}^{\circ}\)C and 37 \({}^{\circ}\)C) after fermentation (48 h) and storage (14 days). A scale ranging from a maximum of 4 (blue) and a minimum of \(-\)4 (pink) was used.
## 3 Results  
### Behavioral Performance  
Participants showed a large variance in their behavioral accuracy performance (NR off: mean = 75.82%, median = 76.36%, SD = 8.75%; NR 1: mean = 79.03%, median = 80.00%, SD = 9.38%; NR 2: mean = 73.09%, median = 72.73%, SD = 8.15%). A one-way repeated-measures ANOVA showed the significant effect of NR on behavioral accuracy (\(F_{2,58}\) = 6.00, \(p\) = 0.004). Post hoc analysis with Bonferroni corrections indicated that although performances from NR 1 and NR 2 were significantly different (\(t\)(29) = 3.46, adjusted \(p\) = 0.003), none of the NR conditions were different from NR-off conditions (NR 1 vs. NR off: \(t\)(29) = 1.87, adjusted \(p\) = 0.20, NR 2 vs. NR off: \(t\)(29) = \(-\)1.59, adjusted \(p\) = 0.35). These results are consistent with the literature, which reported no enhancement in behavioral performance with NR processing (e.g., [PERSON], [PERSON] [5], [PERSON] and [PERSON] [55]). However, Figure 4 revealed a large individual variance in performance _change_ due to NR; 17 people (57%) had better or the same performance when NR 1 was provided, as opposed to 11 people (37%) when NR 2 was provided. Note that 9 out of those 11 people (about 82%) also showed increased performance when NR 1 was given, suggesting that the same underlying individual characteristics might affect performance changes in both conditions. Indeed, NR 1-driven accuracy changes (NR 1 minus NR off) and NR 2-driven accuracy changes (NR 2 minus NR off) were highly correlated (\(r\) = 0.58, \(p\) < 0.001) among all participants. The following section discusses how the variance in NR-driven accuracy change (\(\Delta\)accuracy) correlated with cortical and subjective measures of individual noise tolerance.
# Fusion of Land-Based and Satellite-Based Localization Using Constrained Weighted Least Squares
## 2 Measurement Models
### TDOA Measurement Model for Land-Based Station  
The signals emitted by the source are forwarded by satellites to the ground station, which receives the signals sent by all the satellites and can obtain the TDOAs. Figure 2 shows the schematic diagram of the satellite forwarding the signal to the ground station.  
Satellite are in high-speed motion and thus the positions are also in error, so the satellite positions are modeled as measurements with errors: \(\mathbf{s}_{N_{1}+j}=\mathbf{s}_{N_{1}+j}^{o}+\delta\mathbf{s}_{N_{1}+j^{\prime}}\), \(1\leq j\leq N_{2}\), \(\delta\mathbf{s}_{N_{1}+j}=\left[\delta\mathbf{s}_{N_{1}+jx},\delta\mathbf{s}_{N_{1}+jy}, \delta\mathbf{s}_{N_{1}+jz}\right]^{\mathrm{T}}\) is the random  
Figure 2: Schematic diagram of a satellite relaying the source signal.  
position vector is obtained as \(\mathbf{s}_{t}=\mathbf{s}_{t}^{o}+\mathbf{n}_{s}\), where \(\mathbf{s}_{t}^{o}=\left[\left(\mathbf{s}_{N_{1}+1}^{o}\right)^{\mathrm{T}},\left(\mathbf{s} _{N_{1}+2}^{o}\right)^{\mathrm{T}},...,\left(\mathbf{s}_{N_{1}+N_{2}}^{o}\right)^{ \mathrm{T}}\right]^{\mathrm{T}}\).  
\(\mathbf{n}_{\mathrm{s}}=\left[\left(\delta\mathbf{s}_{N_{1}+1}\right)^{\mathrm{T}} \left(\delta\mathbf{s}_{N_{1}+2}\right)^{\mathrm{T}},...,\left(\delta\mathbf{s}_{N_{1} +N_{2}}\right)^{\mathrm{T}}\right]^{\mathrm{T}}\) with the covariance matrix \(\mathbf{Q}_{s}\).  
From Figure 2, the propagation length can be expressed as  
\[r_{j}^{o}=||\mathbf{u}-\mathbf{s}_{N_{1}+j}^{o}||_{2}+||\mathbf{s}_{N_{1}+j}^{o}-\mathbf{t}||_{ 2},1\leq j\leq N_{2} \tag{10}\]  
Taking the first satellite as the reference satellite, the TDOA can be obtained as  
\[\tau_{i1}^{o}=\frac{1}{c}(r_{i}^{o}-r_{1}^{o}),2\leq i\leq N_{2} \tag{11}\]  
where \(c\) is the signal propagation velocity and is a known constant. Thus, the TDOA shown in (11) can be converted to the range difference of arrival (RDOA) shown in (12):  
\[r_{i1}^{o}=||\mathbf{u}-\mathbf{s}_{N_{1}+i}^{o}||_{2}-||\mathbf{u}-\mathbf{s}_{N_{1}+1}^{o}|| _{2}+||\mathbf{s}_{N_{1}+i}^{o}-\mathbf{t}||_{2}-||\mathbf{s}_{N_{1}+1}^{o}-\mathbf{t}||_{2},2 \leq i\leq N_{2} \tag{12}\]  
The measurement vector of RDOA is denoted as  
\[\mathbf{r}=\left[r_{21},r_{31},...,r_{N_{2}1}\right]^{\mathrm{T}}=\mathbf{r}^{o}+\mathbf{ n}_{\mathbf{r}}\in\mathbb{R}^{(N_{2}-1)\times 1} \tag{13}\]  
where \(\mathbf{n}_{\mathbf{r}}=\left[\delta r_{21},\delta r_{31},...,\delta r_{N_{2}1}\right] ^{\mathrm{T}}\) is the measurement noise with the covariance matrix \(\mathbf{Q}_{\mathbf{r}}\).