esa-sceva/satcom-chunk-collection huggingface dataset:
# Validation of Copernicus Sea Level Altimetry Products in the Baltic Sea and Estonian Lakes
## 2 Material and Methods  
### Validation Scheme  
In this study, five validation strategies (Figure 1), including four field campaigns conducted in 2019, were investigated. For the Sentinel-3 Level-2 products validation, instantaneous sea surface height by altimetry (\(SSH_{SA}\)) was compared to instantaneous SSH from GNSS vessel campaigns (\(SSH_{GNSS}\)), buoy (\(SSH_{buoy}\)) and tide gauge measurements (\(SSH_{TG}\)) which were converted to the same reference system with satellite data by using a geoid model. Ideally, \(SSH_{SA}\approx SSH_{GNSS}\approx SSH_{buoy}\approx SSH_{TG}\); however, the accuracy of the geoid model, tide gauge data, GNSS-data and other factors cause uncertainties (Table 1). Note that the pressure sensor-based tide gauges are affected by a small time-dependent drift. This drift needs to be corrected by employing control readings from the staff gauge. Therefore, the uncertainty of automatic tide gauges remains on 0.01-0.02 m level [15]. The accuracy of the GNSS-derived height depends on several factors, such as the antenna and receiver, the method of measurement and processing. However, the accuracy of GNSS height based on the kinematic measurement method on the vessel should remain within a \(\pm\)0.02 m level as well [16].  
For validation of the Level-3 products, sea-level anomaly of the CMEMS Level-3 product (\(SLA_{3}\)) and the NEMO reanalysis model output (\(SLA_{NEMO}\)) were compared with (i) tide gauges-based sea-level anomaly (\(SLA_{TG}\)) in the Gulf of Finland and the Gulf of Riga, and (ii) buoy-based sea-level anomaly (\(SLA_{buoy}\)) in the Gulf of Riga (Figure 1). More details on the data will be introduced in Sections 2.5 and 2.6.
# An Improved Real-Time Contrasts Control Chart Using Novelty Detection and Variable Importance
## 2 Real-Time Contrast Control Chart
### Fault Isolation Using Variable Importance  
In the original RTC control chart, the cause of a fault can be analyzed by evaluating the importance of variables in the classifier when a fault detection alarm occurs [PERSON] (1984). In this section, we introduce a method for determining the importance of variables proposed by [PERSON] [PERSON] (1984); [PERSON] (1985); [PERSON] (1986). The Random forests algorithm is used to measure the significance contained in the decision tree. A thorough search of every node of every tree in the random forests scored \(m\) selected variables. As a result, we can implicitly consider the importance of each variable to the model with impurity reduction as a measure of relative importance. Variable importance is the degree of impurity reduction. [PERSON] [PERSON] (1984); [PERSON] (1985); [PERSON] (1986) proposed the application of variable importance by using the Gini index of impurity. Equation (7) is described in terms of the Gini index in a random forest.  
\[Gini(v)=\sum_{i=1}^{c}r_{i}(1-r_{i}), \tag{7}\]where \(c\) is the number of classes, \(v\) is a variable as a node, \(r_{i}\) is the ratio of the total data to class \(i\) and \(s_{v}\) means split in node \(v\). The impurity reduction \(\Delta Gini(s_{v},\ v)\) at each node \(v\) reflects the ratios \(w_{L}\) and \(w_{R}\) in that they are proportional to the number of the data for each child node from the parent node \(v\).  
\[\Delta Gini(s_{v},\ v)=Gini(v)-(w_{L}Gini(v_{L})+w_{R}Gini(v_{R})) \tag{8}\]  
The impurity reduction \(\Delta Gini(s_{v},\ v)\) is the difference between the impurity score of node \(v\) and the weighted average of impurity scores of children nodes of node \(v\). Then, in variable \(X_{k}\), the variable importance \(V(X_{k})\) is the average of the impurity reduction \(\Delta Gini(s_{v},\ v)\) for all trees.  
\[V(X_{k})=\frac{1}{ntree}\sum_{t=1}^{ntree}\sum_{v\in D_{t}}\Delta Gini(X_{k},\ v) \tag{9}\]
# Online Deformation Measurement of Laser Repair Substrate Based on Orthogonal Sampling Moire
## 5 Conclusions  
In this paper, an optical deformation measurement system suitable for extreme environment in laser repair was designed. Combined with the cantilever structure specimen, the online detection of the substrate orthogonal deformation field in the repair process was realized using the orthogonal sampling moire method. The main conclusions are as follows:  
1. An optical measurement system suitable for laser repair was designed. Through the combination of various filters, interference of a strong laser, high temperature radiation and liquid metal splash can be filtered out. With the illumination of high-power blue LEDs, the grid line images taken in the cladding process were close to the periodical distribution in sinusoidal shape, which proves the reliability of the high-temperature resistant grating.
2. For cantilever beam components, the orthogonal grid images in the cladding process were recorded by optical measurement system and the orthogonal sampling moire method was used to calculate the displacement field in two directions. The displacement field under different repairing parameters were obtained, and the results show that the scanning path has a significant influence on the deformation in the repair process: compared with the scanning path parallel to the cantilever, when the scanning path is perpendicular to the cantilever, the solidified cladding area lacks tempering, resulting in the gradual accumulation of residual stress and larger residual deformation. In addition, a higher energy density makes the cladding layer thicker and introduces larger residual stress.  
Conceptualization, W.S. and H.X.; Data curation, W.S. and H.X.; Formal analysis, W.S., C.Z. and H.X.; Funding acquisition, H.X.; Investigation, W.S. and H.X.; Methodology, W.S. and H.X.; Project administration, H.X.; Resources, H.X.; Software, W.S. and C.Z.; Supervision, H.X.; Validation, W.S., C.Z. and H.X.; Visualization, C.Z.; Writing--original draft, C.Z.; Writing--review & editing, C.Z. and H.X. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China (grant Nos. 12032013 and 11972209) and the National Key Research and Development Program of China (grant No. 2017 YFB1103900).  
Not applicable.  
The authors declare no conflict of interest.
## 2 Materials and Methods
### Characterization of rGO-Fe\({}_{2}\)O\({}_{3}\)  
rGO-Fe\({}_{2}\)O\({}_{3}\) with 47 wt.% iron oxide was prepared hydrothermally using iron II acetate as iron precursors. In a typical experiment, GO (500 mg) was dispersed in water (100 mL) by probe sonication (CV334, Cole-Parmer, Court Vernon Hills, IL, USA) for 5 min. Iron acetate was dissolved in 100 mL of deionized water and added to the GO suspension under stirring with dropwise addition of NH\({}_{4}\)OH solution to adjust the pH to 10 \(\pm\) 0.1. The mixture was then transferred to 200 mL, Teflon-lined stainless-steel cell, sealed, heated to 80 \({}^{\circ}\)C, and maintained for four hours. After cooling the hydrothermal cell to 25 \({}^{\circ}\)C, the solid product was retrieved via filtration, washed with ethanol, dispersed in water, and freeze-dried (Freeze-Dryer 6 Plus, LABCONCO, Kansas City, MO, USA). The dry sample was calcined at 400 \({}^{\circ}\)C in a tube furnace for 4 h under 40 mL/min Argon flow.  
\begin{table}
\begin{tabular}{l l l l l} \hline \hline
**adsorbent** & **Oil Type** & **Oil Conc.**, &
\begin{tabular}{l} **Adsorption** \\ **Ppm** \\ \end{tabular} & **Ref.** \\ \hline Polymeric adsorbent beads & Crude oil & 30 & 301 & [35] \\ Activated carbon & Oilfield PW & 165 & 334 & [36] \\ Metallic hydroxides from white & Crude oil & 1500 & 356 & [37] \\ Bentonite & Oilfield PW & 55 & 378 & [36] \\ Deposited carbon & Oilfield PW & 35 & 386 & [36] \\ Surfactant-modified sepilolite & Crude oil & 3000 & 455 & [38] \\ Graphene aerogel & Diesel-water & 800 & 745 & [34] \\ Graphene nanoplatelets & Diesel & 200 & 805 & [10] \\ Activated carbon nanofiber nonwoven & Crude oil & 10,000 & 1250 & [39] \\ Graphene oxide & Diesel & 200 & 1335 & [9] \\ Thermally reduced graphene & Diesel & 200 & 1554 & [10] \\ Fluorinated graphene & Crude oil & 1000 & 1566 & [40] \\ Ultralight carbon foam & Crude oil & 2020 & 1627 & [41] \\
**rGO-Fe\({}_{2}\)O\({}_{3}\)** & **Diesel** & **200** & **1280** & **This Study** \\ \hline \hline \end{tabular}
\end{table}
Table 1: _Cont._The X-ray diffraction (XRD) patterns of GO and rGO-Fe\({}_{2}\)O\({}_{3}\) were performed using MiniFlex-600 X-ray diffractometer (Rigaku, Tokyo, Japan) with Cu K\(\alpha\) radiation (\(\lambda\) = 0.154 nm). XRD scans (20 from 5 to 60\({}^{\circ}\)) were collected at a scan rate of 1.0\({}^{\circ}\)/min and 0.02\({}^{\circ}\) step size. The adsorbent morphology was analyzed using a scanning electron microscope (SEM) (JCM-6000 PLUS, NeoScope, Joel, Tokyo, Japan). The surface area, pore volume, and pore size were measured via nitrogen adsorption at 80 K (ASAP 2020, Micromerities, Norcross, GA, USA). Thermal gravimetric analysis (TGA) (SDT 600, TA Instruments, New Castle, DE, USA) determined the nanocomposite thermal stability and iron oxide loading. The sample was heated from RT to 650 \({}^{\circ}\)C at 20\({}^{\circ}\)/min under air (20 mL/min).
# Responses of Medicinal and Aromatic Plants to Engineered Nanoparticles +
## 6 Effects of Carbon-Based NPs on Medicinal and Aromatic Plants
### MwCNTs
#### 6.5.4 Genotoxicity  
Uptake of MWCNTs in _Allium cepa_ root cells modified cellular morphology, adversely affected membrane integrity and mitochondrial function, and caused considerable DNA damage, micronucle formation, and chromosome aberration, as well as formation of internucleosomal fragments, which is indicative of apoptotic cell death. Accumulation ofcells in the sub-G\({}_{0}\) phase of the cell cycle, pronounced increases in CpG methylation, and in the levels of 5-methyl-deoxycytidine verified the cyto-genotoxic effect of MWCNT [313].  
The use of MWCNT-COOH as an elicitor of rosmarinic acid and salvianolic acid B in a cell suspension culture prepared from \(\gamma\)-irradiated (70 Gy) _Salvia memorosa_ L callus, which allows to reach >13- and 14-fold higher concentrations of these secondary metabolites than in the control, can be recommended for obtaining these bioactive acids on a larger scale [159] (Table 1).
# The CIPCA-BPNN Failure Prediction Method Based on Interval Data Compression and Dimension Reduction
## 3 Application
### Fault Prediction of UAV Based on CIPCA-BP  
Based on the interval matrix \(P_{m\times q}\) obtained above, a UAV fault diagnosis model can be established through BPNN. From the interval matrix \(P_{m\times q}\), the minimum and maximum values of the interval data are extracted and form the minimum matrixand a maximum matrix \(P_{m\times q}^{\text{max}}\), respectively. Since \(p_{js}\) and \(\overline{p_{j*}}\) come from the same data interval, \(P_{m\times q}^{\text{min}}\) and \(P_{m\times q}^{\text{max}}\) have the same status label vector \(y=\left(s_{1},s_{2},\ldots,s_{m}\right)^{T}\).  
\[P_{m\times q}^{\text{min}}=\left(\begin{array}{cccc}p_{11}&p_{12}&\cdots&p_{1 q}\\ p_{21}&p_{22}&\cdots&p_{2q}\\ \vdots&\vdots&\ddots&\vdots\\ p_{m1}&p_{m1}&\cdots&p_{mq}\end{array}\right)P_{m\times q}^{\text{max}}=\left( \begin{array}{cccc}\overline{p_{11}}&\overline{p_{12}}&\cdots&\overline{p_ {1q}}\\ \overline{p_{21}}&\overline{p_{22}}&\cdots&\overline{p_{2q}}\\ \vdots&\vdots&\ddots&\vdots\\ \overline{p_{m1}}&\overline{p_{m2}}&\cdots&\overline{p_{mq}}\end{array}\right) \tag{9}\]  
Using BPNN to establish fault prediction models for \(\left(P_{m\times q}^{\text{min}},y\right)\) and \(\left(P_{m\times q}^{\text{max}},y\right)\), respectively, the output layer uses linear functions to output the results; consequently, summarize the results of the two models to obtain the final prediction results. The process of CIPCA-BPNN is shown in Figure 2.  
Figure 2: Complete-information-based principal component analysis–back-propagation neural network (CIPCA-BPNN) fault diagnosis process. The sample state of the same flight is the same (\(y\) is the same). In the modeling stage, the data used are the data of many flights, and the \(y\) of different states will be different.
## 3 Results
### CAC Score  
CAC score distributions obtained by Horos and LIFEx were not Gaussian (\(p\) < 0.001 for both), and not comparable in shape (\(p\) = 0.002). [PERSON]'s concordance correlation coefficient was 0.998 (95% CI: 0.997-0.998). Figure 2 shows the boxplots of the measurements of the CAC score achieved by Horos and LIFEx.  
Figure 3 reports the Bland-Altman plot of the CAC score. The mean difference among the measurements increased from 8 to 78 by the mean values of the measured CAC score (intercept = \(-\) 0.050; slope = 0.054; \(p\) < 0.001). According to the observed linear relationship, lower and upper limits of agreement were shifted \(\pm\) 1.96 times the residual standard deviation (SD = 20.5) of the regression. The Bland-Altman plot shows an increasing difference in measurement by two software programs as the score increases.  
Figure 4 shows a comparison between the ROI and the CAC score obtained by Horos and LIFEx software in two patients. The volumes turned out to be equal between the two software programs, while the CAC scores calculated by Horos were overestimated with respect to LIFEx.  
\begin{table}
\begin{tabular}{l c} \hline \hline
**Patients**, \(n\) & **40** \\ \hline Male gender, \(n\) (\%) & 19 (47) \\ Age (years) & 54 \(\pm\) 22 \\ \({}^{18}\)F-FCH PET/CT, \(n\) (\%) & 26 (65) \\ \({}^{18}\)F-FDG PET/CT, \(n\) (\%) & 14 (35) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Clinical characteristics of overall patient population.  
\begin{table}
\begin{tabular}{l c c} \hline \hline  & **Horos Software** & **LIFEx Software** \\ \hline CAC score & 155 \(\pm\) 331 & 147 \(\pm\) 314 \\ Vascular age (years) & 60 \(\pm\) 20 & 60 \(\pm\) 20 \\ CAD risk according to CAC & & \\ score & & \\ Low, \(n\) (\%) & 19 (47) & 16 (40) \\ Moderate, \(n\) (\%) & 16 (40) & 19 (47) \\ High, \(n\) (\%) & 5 (12) & 5 (12) \\ Muscle mass (cm\({}^{2}\)) & 132 \(\pm\) 37 & 131 \(\pm\) 37 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Imaging findings in the overall patient population according to Horos and LIFEx evaluation.  
CVA was computed for 31 of 40 patients with age > 39 years (mean, 65 \(\pm\) 11 years). CVA was 60 \(\pm\) 20 years for both Horos and LIFEx. These distributions were in agreement (\(p\) = 0.99), while the Bland-Altman plot showed three measurements out of 95% CI (\(-\)0.9 to 1.3 years).
# A Novel Inductor-Based Non-Dissipative Equalizer
## 2 Proposed Equalizer Scheme
### Equalization Principle  
As shown in Figure 4, the NIBNDE is applied to four series connected batteries for illustrating the equalization principle. The battery \(B_{2}\) is assumed to have the highest voltage, \(V_{B2}\), and \(B_{1}\) is assumed to have the lowest voltage, \(V_{B1}\). The average voltage \(V_{arg}\) of the four cells is calculated by  
Figure 3: Structure of equalizer. (**a**) The multiple switch-inductors equalizer (MSIE). (**b**) The novel inductor-based non-dissipative equalizer (NIBNDE).  
Equation (1). The equalization circuit will be activated when the voltage gap between \(V_{B2}\) and \(V_{avg}\) exceeds the equalization threshold (see Equation (2)). Figure 4 presents the two consecutive stages of the equalization principle [20].  
\[V_{avg}=\frac{V_{B1}+V_{B2}+V_{B3}+V_{B4}}{4} \tag{1}\]  
\[V_{B2}-V_{avg}<3\mathrm{mV} \tag{2}\]  
Stage 1: Charge \(L_{1}\)  
As shown in Figure 4a, in a pulse-width modulation (PWM) cycle, when \(S_{2}\) and \(S_{2b}\) are turned on, cell \(B_{2}\) charge inductor \(L_{1}\), \(i_{L1}\) increases [19].  
\[V_{B2}=R_{on}i_{L1}+L\frac{di_{L1}}{dt}+V_{D}\ \ 0<t\leq t_{on} \tag{3}\]  
where \(R_{on}\) represents the total loop resistance when \(S_{2}\) and \(S_{2b}\) are turned on, \(L\) represents the inductance value of \(L_{1}\), \(i_{L1}\) represents the inductor current of \(L_{1}\), \(V_{D}\) represents the forward voltage of the body diode of the MOSFET and \(t_{on}\) represents the turn-on time of \(S_{2}\) and \(S_{2b}\).  
The general solution of Equation (3) is:  
\[i_{L1}=\frac{V_{B2}-V_{D}}{R_{on}}-\frac{V_{B2}-V_{D}}{R_{on}}e^{-t\frac{R_{on }}{L}}=\frac{V_{B2}-V_{D}}{R_{on}}\Big{(}1-e^{-t\frac{R_{on}}{L}}\Big{)}\ \ 0<t\leq t_{on} \tag{4}\]  
When \(t=t_{on}\), the circuit current \(i_{L1}\) reaches the maximum value \(i_{p}\), that is:  
\[i_{L1}=i_{p}=\frac{V_{B2}-V_{D}}{R_{on}}\Big{(}1-e^{-t_{on}\frac{R_{on}}{L}} \Big{)},\ \ \ t=t_{on} \tag{5}\]  
Stage 2: Discharge \(L_{1}\)  
As shown in Figure 4b, when \(t>t_{on}\), \(S_{2}\) and \(S_{2b}\) are turned off, and \(L_{1}\) charges \(B_{1}\) to transfer energy from cell \(B_{2}\) to cell \(B_{1}\):  
\[L\frac{di_{L1}}{dt}=V_{B1}+V_{D}+R_{off}i_{L1}\ \ \ \ t_{on}<t\leq t_{d} \tag{6}\]  
The general solution of Equation (6) is:  
\[i_{L1}=i_{p}e^{-(t-t_{on})\frac{R_{off}}{L}}-\frac{V_{B1}+V_{D}}{R_{off}} \bigg{(}1-e^{-(t-t_{on})\frac{R_{off}}{L}}\bigg{)}\ \ \ t_{on}<t\leq t_{d} \tag{7}\]  
where \(R_{off}\) represents the total loop resistance when \(S_{2}\) and \(S_{2b}\) are turned off and \(t_{d}\) represents the moment when the inductor current is reduced to zero [21; 22].
## 2 Multipath Modelling and Mathematic Tools for Analysis
### Covariance Function  
The covariance function is a method used to describe the spatial correlation between data points, where the covariance between any two measured values can be represented as the function \(C(d)\), and \(d\) represents the distance between the two points. Assuming there are two points, \(x_{i}\) and \(x_{j}\), in the spatial domain with a distance of \(d_{ij}\), their covariance can be expressed as  
\[C\big{(}x_{i},x_{j}\big{)}=C\big{(}d_{ij}\big{)} \tag{10}\]  
The function \(C(d)\) decreases as the distance \(d\) increases, attaining its maximum value at zero distance and approaching zero as the distance tends to infinity. Commonly used covariance functions that satisfy these conditions include the Gaussian function, Markov's function, the Hirvonen function, and so on [31]. [PERSON]'s function can be expressed by  
\[C(d)=C_{0}e^{-d/d_{0}} \tag{11}\]  
where \(C_{0}\) represents the covariance at zero distance, \(d_{0}\) is the coefficient of the covariance function, and \(d\) is the distance between two points.  
Furthermore, when the observed values are numerical data, the empirical covariance function (ECVF) can be computed and expressed numerically [24], which is commonly employed in practice for LSC. It can be written as  
\[\left\{\begin{array}{l}C_{0}=\frac{1}{m}\sum_{i=1}^{m}l_{i}l_{i}\\ C(d_{k})=\frac{1}{m_{k}}\sum_{i<j}l_{i}l_{j}\end{array}\right. \tag{12}\]  
where \(C_{0}\) is the variance when distance d equals zero, \(d_{k}\) is the distance between two points \(i\) and \(j\), \(m\) is the number of point pairs at distance \(d_{k}\), and the terms \(l_{i}\) and \(l_{j}\) represent the multipath values at points \(i\) and \(j\), respectively.  
In this study, we computed the covariance at various distance intervals using the ECVF. The procedure for obtaining the ECVF can be referenced from [PERSON] et al. [24]. Next, we employed Markov's function to fit the covariance coefficients, and the parameters \(C_{0}\) and \(d_{0}\) in Equation (11) are derived.
## 5 Discussions  
For the results presented so far, only the IGS final products are applied and the PPP and POP approaches are all processed in post mode. As the POP approach is independent of the external clock information, it can be seen that it is possible to use different types of IGS products, including the ultra-rapid (observed and predicted orbits and clocks). The accuracy of the ultra-rapid (predicted)  
Figure 11: Statistics of the distances between the three antennas derived from the five types of solutions. It is seen that the POP fixed solutions generate the best baseline results.  
Figure 10: The number of DD observations used in the processing for the three baselines. During 20:00–21:00, the number is 6 and is not beneficial for the calculation of DD solutions.  
satellite clock is 3 ns, the requirement for real-time PPP applications cannot be satisfied. Fortunately, the IGS Real-Time Pilot Project (RTPP) ([[http://www.rtigs.net](http://www.rtigs.net)]([http://www.rtigs.net](http://www.rtigs.net))) makes it possible to obtain real-time orbits with an accuracy of 5 cm and a clock accuracy of 0.3 ns which is almost the same accuracy as the IGS ultra-rapid (observed) products (3 cm for orbit and 0.15 ns for clock). Therefore, the POP approach can perform better than PPP when applied in real-time applications since it is independent of the real-time clocks. This becomes significant when applied in airborne gravimetry as the gravity results calculated from the GNSS solutions and the gravity measurements can be investigated in real-time.
## 4 Establishing the Data Fusion Kalman Filter Equations
### Measurement Equation
\begin{split}&\mathbf{Z}_{i}\approx\delta{\mathbf{p}}_{p_{1}}^{n}-\delta{ \mathbf{p}}_{p_{1}}^{n}+\left[\begin{array}{cc}0&-\frac{\delta{\mathbf{p}}_{p_{1}}^{n }}{(R_{M}+\frac{{\mathbf{p}}_{1}^{n}}{R_{1}})^{2}}&0\\ -\frac{\delta{\mathbf{p}}_{p_{1}}^{n}\sec{l_{p_{1}}^{n}}}{(R_{N}+\frac{{\mathbf{p}}_{1} }{R_{1}})^{2}}+\frac{\sec^{2}{l_{p_{1}}^{n}}\sin{l_{p_{1}}^{n}}\Delta{l_{p_{1} }^{n}}}{(R_{N}+\frac{{\mathbf{p}}_{1}}{R_{1}})}&0\\ 0&0&0\end{array}\right]\mathbf{C}_{p_{1}}^{n^{\prime}}\cdot\mathbf{r}_{i}^{p_{1}}\\ +\left[\begin{array}{cc}0&\frac{1}{R_{M}+\frac{{\mathbf{p}}_{1}}{R_{1}}}&0\\ \frac{\sec{l_{p_{1}}^{n}}}{R_{N}+\frac{{\mathbf{p}}_{1}}{R_{1}}}&0&0\\ 0&0&1\end{array}\right]\mathbf{C}_{p_{1}}^{n^{\prime}}\cdot\delta{\mathbf{r}}_{i}^{p_{1 }}-(\mathbf{C}_{p_{1}}^{n^{\prime}}\cdot\mathbf{r}_{i}^{p_{1}}\times)\left[\begin{array} []{cc}0&\frac{1}{R_{M}+\frac{{\mathbf{p}}_{1}}{R_{1}}}&0\\ \frac{\sec{l_{p_{1}}^{n}}}{R_{N}+\frac{{\mathbf{p}}_{1}}{R_{1}}}&0&0\\ 0&0&1\end{array}\right]\phi\end{split}  \tag{32}\]  
Therefore, the measurement matrix can be established as:  
\[ \begin{split}\mathbf{H}=\left[\begin{array}{cc}\mathbf{H}_{SRINS_{12}} &\mathbf{H}_{r}&\mathbf{O}_{3\times 6}&\mathbf{H}_{SRINS_{2}}&\mathbf{O}_{3\times 24}\\ \mathbf{H}_{SRINS_{13}}&\mathbf{O}_{3\times 24}&\mathbf{H}_{r}&\mathbf{O}_{3\times 6}&\mathbf{H}_{SRINS_{3}} \end{array}\right]\end{split}  \tag{33}\]  
\[ \begin{split}&\mathbf{H}_{SRINS_{2}}=\left[\begin{array}{cc}\mathbf{O}_ {3\times 6}&-\mathbf{I}_{3\times 3}&\mathbf{O}_{3\times 6}\end{array}\right]\\ &\mathbf{H}_{SRINS_{3}}=\left[\begin{array}{cc}\mathbf{O}_{3\times 6}&-\mathbf{I}_{3 \times 3}&\mathbf{O}_{3\times 6}\end{array}\right]\\ &\mathbf{H}_{SRINS_{3}}=\left[\begin{array}{cc}\mathbf{O}_{3\times 6}&-\mathbf{I}_{3 \times 3}&\mathbf{O}_{3\times 6}\end{array}\right]\\ &\mathbf{H}_{SRINS_{3}}=\left[\begin{array}{cc}\mathbf{O}_{3\times 6}&-\mathbf{I}_{3 \times 3}&\mathbf{O}_{3\times 6}\end{array}\right]\\ &\mathbf{H}_{pi}=\left[\begin{array}{cc}1&0&-\frac{(\mathbf{C}_{p_{1}}^{n^{\prime}} \cdot\mathbf{r}_{i}^{p_{1}})}{(R_{M}+\frac{{\mathbf{p}}_{1}}{R_{1}})^{2}}\\ \frac{\sec^{2}{l_{p_{1}}^{n}}\sin{l_{p_{1}}^{n}}(\mathbf{C}_{p_{1}}^{n^{\prime}} \cdot\mathbf{r}_{i}^{p_{1}})}{(R_{N}+\frac{{\mathbf{p}}_{1}}{R_{1}})}&1&-\frac{(\mathbf{C}_{p _{1}}^{n^{\prime}}\cdot\mathbf{r}_{i}^{p_{1}})}{(R_{N}+\frac{{\mathbf{p}}_{1}}{R_{1}}) ^{2}}\\ 0&0&1\end{array}\right]\end{split} \]  
\[ \begin{split}&\mathbf{H}_{\phi i}=-(\mathbf{C}_{p_{1}}^{n^{\prime}}\cdot \mathbf{r}_{i}^{p_{1}}\times)\left[\begin{array}{cc}0&\frac{1}{R_{M}+\frac{{\mathbf{ p}}_{1}}{R_{1}}}&0\\ \frac{1}{(R_{N}+\frac{{\mathbf{p}}_{1}}{R_{1}})\cos{l_{p_{1}}^{n}}}&0&0\\ 0&0&1\end{array}\right]\end{split} \]  
where \((\mathbf{C}_{p_{1}}^{n}\cdot\mathbf{r}_{i}^{p_{1}})_{x}\) represents the component of \(\mathbf{C}_{p_{1}}^{n}\cdot\mathbf{r}_{i}^{p_{1}}\) in the \(x\)-axis direction; \((\mathbf{C}_{p_{1}}^{n}\cdot\mathbf{r}_{i}^{p_{1}})_{y}\) represents the component of \(\mathbf{C}_{p_{1}}^{n}\cdot\mathbf{r}_{i}^{p_{1}}\) in the \(y\)-axis direction.