esa-sceva/satcom-chunk-collection huggingface dataset:
# Temporal Instability Analysis of Injury Severities for Angle and Non-Angle Crashes at Roundabouts
## 7 Summary and Conclusions
\begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Variable** & **Parameter** & **Estimates** & **z-Stat** & **No** & **Minor** & **Severe** \\  & & & **Injury** & **Injury** & **Injury** & **Injury** \\ \hline Constant [SI] & \(-2.91\) & \(-4.67\) & & & & \\ Random parameter (normally distributed) & \(0.92\) & \(1.69\) & \(-0.0151\) & \(0.0111\) & \(0.0040\) \\ Daylight indicator (\(1\) if the light condition was daylight, \(0\) otherwise) [NI] & \((3.06)\) & \((2.00)\) & \(-0.0151\) & \(0.0111\) & \(0.0040\) \\ Heterogeneity in the mean of random parameter & & & & & \\ Daylight indicator (\(1\) if the light condition was daylight, \(0\) otherwise) [NI]: & \(-5.87\) & \(-2.31\) & & & \\ Cystic indicator (\(1\) if cyclists involved in the crash, \(0\) otherwise) & & & & & \\ Temporal characteristics & & & & & \\ Weevelander indicator (\(1\) if a crash occurred during the weekend, \(0\) otherwise) [NI] & \(0.99\) & \(2.34\) & \(0.0200\) & \(-0.0175\) & \(-0.0025\) \\ Environmental characteristics & & & & & \\ Clear indicator (\(1\) if the weather was clear, \(0\) otherwise) [NI] & \(-1.24\) & \(-1.82\) & \(-0.1312\) & \(0.1104\) & \(0.0208\) \\ Clear indicator (\(1\) if the weather was clear, \(0\) otherwise) [MI] & \(-1.52\) & \(-2.47\) & \(0.1493\) & \(-0.1722\) & \(0.0229\) \\ Roadway characteristics & & & & & \\ Paved shoulder indicator (\(1\) if the type of shoulder was paved, \(0\) otherwise) [NI] & \(0.38\) & \(2.05\) & \(0.0157\) & \(-0.0136\) & \(-0.0021\) \\ Spatial characteristics & & & & & \\ Town indicator (\(1\) if a crash occurred in town, \(0\) otherwise) [NI] & \(0.49\) & \(2.15\) & \(0.0082\) & \(-0.0339\) & \(-0.0043\) \\ Town indicator (\(1\) if a crash occurred in town, \(0\) otherwise) [SI] & \(-0.71\) & \(-2.05\) & \(0.0081\) & \(0.0063\) & \(-0.0144\) \\ Vehicle characteristics & & & & & \\ Commercial vehicle indicator (\(1\) if commercial vehicles involved in the crash, \(0\) otherwise) [NI] & \(2.12\) & \(2.94\) & \(0.0104\) & \(-0.0054\) & \(-0.0050\) \\ Commercial vehicle indicator (\(1\) if commercial vehicles involved in the crash, \(0\) otherwise) [SI] & \(2.07\) & \(2.39\) & \(-0.0031\) & \(-0.0016\) & \(0.0047\) \\ O\(\alpha\) observed [SI] & \(0.12\) & \(2.12\) & \(-0.0029\) & \(-0.0016\) & \(0.0045\) \\ Cash characteristics & & & & & \\ Speeding indicator (\(1\) if speeding involved in the crash, \(0\) otherwise) [SI] & \(0.12\) & \(2.12\) & \(-0.0029\) & \(-0.0016\) & \(0.0045\) \\ Number of observations & & & & & \\ Number of estimated parameters & & & & & \\ Log-likelihood at zero (\(LL(\beta)\)) & & & & & \\ Log-likelihood at convergence (\(LL(\beta)\)) & & & & & \\ \(\sigma^{2}=1-LL(\beta)/LL(0)\) & & & & & \\ AIC & & & & & \\ BIC & & & & & \\ \hline \hline \end{tabular} Note: NI = no injury; MI = minor injury; SI = severe injury.  
\end{table} 
Table 8: Model results of mixed logit with heterogeneity in means for non-angle crashes in Florida 2014-2015.
## 1 Introduction
### Contributions  
The goal of this work is to propose a variant of the DDIPIC algorithm from [11], named the progressive IPI cancellation (P-IPIC) algorithm, which cancels the IPI by performingresidue cost function (RCF) maximization at each step. The main difference of the proposed algorithm with respect to the DDIPIC is that it operates in two phases: A _search phase_, where a certain number of possible paths are detected and a first rough estimate of the channel parameters is provided, A _refinement phase_, where the found paths are refined, looking for ones declared as false alarms and discarded, until the stopping criterion is met. This procedure allows the correct number of paths to be found while the accuracy of the estimates is improved. The contributions of this work can be summarized as follows:  
* _Progressive IPI cancellation_: Instead of discovering possible paths and performing refinements in each iteration maximizing the observation-based cost function as in [11], we perform maximization of a residue-based cost function (RCF) at each step during the discovery phase. This progressive cancellation of the IPI allows a first channel estimate to be provided, aiming to reduce the residue energy as iteration progress, achieving high accuracy in channel matrix reconstruction.
* _Latency reduction due to single global refinement of the estimates_: The main drawback of the state-of-the-art DDIPIC algorithm is that it performs refinement procedures at each iteration, as discussed in Section 3.5. Progressive IPI cancellation allows the latency to be reduced, since, as discussed above, the algorithm can operate in two distinct phases and a single global refinement is needed.
* _Computational complexity reduction in search phase_: During the iterative search phase, the proposed algorithm looks for new paths by performing a RCF maximization. This allows us to reduce the computational cost since the computation of the RCF does not require matrix inversion. Moreover, the computational cost does not depend on the iteration index. As a consequence, coarse and fine estimation procedures described in Section 3.4 will take less time.
* _Resilience towards high-IPI scenarios_: In the literature, it is commonly assumed to have sufficiently fine delay and Doppler resolutions such that all the propagation paths are resolvable in the DD domain. In some cases, this may not hold, and robust low-complexity channel estimation algorithms must be designed to suit high-IPI scenarios. In this work, we consider both low- and high-IPI regimes, showing that the proposed approach is suitable for both regimes.  
The remainder of this paper is organized as follows. In Section 2, the OTFS signal model is presented. In Section 3, OTFS channel estimation is covered, including the baseline DDIPIC method and our proposed P-IPIC method.
## 6 Conclusions  
In this paper, we explore resource allocation methods that comprehensively consider time-domain, frequency-domain, and spatial-domain multi-dimensional collaboration to achieve optimal network-level user experience in multi-carrier and multi-beam scenarios within the context of 5G and future mobile communication sharing networks. We build an optimization model based on the Shannon theorem. Additionally, an AI-based smart grid technology is introduced to achieve inter-frequency information prediction, enabling the construction of an alternative parameter set for optimization. This scheme predicts inter-frequency RSRP, beam, and spectral efficiency, which are integrated into the optimization algorithm to determine the optimal time-frequency-space resource allocation scheme. Through efficient coordination of multiple frequency bands and inter-beam resources, the  
Figure 17: Average experience rate for different methods in scene 2.  
Figure 18: Average experience rate for network with three carriers.  
potential capability of MU pairing can be released; space resources will be used more rationally. Extensive experiments validate the effectiveness and superiority of the proposed methods. This work contributes to the ongoing efforts to enhance spectrum efficiency and elevate user satisfaction, thereby paving the way for more efficient and user-centric next-generation communication networks.  
Conceptualization, G.L. and L.Z.; methodology, G.L., P.L., L.Z., X.D., C.H. and W.X.; software, L.Z.; validation, X.D. and L.Z.; formal analysis, X.D., P.L. and W.X.; investigation, X.D.; resources, P.L. and C.H.; data curation, L.Z.; writing--original draft preparation, X.D.; writing--review and editing, X.D. and W.X.; visualization, X.D.; supervision, G.L., P.L., C.H. and W.X.; project administration, P.L. and C.H.; funding acquisition, G.L. and W.X. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.
## 2 Analysis of Ramp Excitation Signal  
Because of the wide spectrum, the step signal is usually used as the excitation signal for the dynamic calibration of sensors. The rise time of step signal from initial value to stable value is 0 s. However, in the actual calibration experiment, it is not feasible to generate step temperature excitation with rise time of 0 s. The excitation signal is generally an approximate step signal with a certain rise time, which is called ramp signal. Assuming that the rise time of ramp signal is \(r\), and the ramp signal can be expressed as  
\[u^{*}(t)=\left\{\begin{array}{ll}t/r,&t<r\\ 1,&t\geq r\end{array}\right.. \tag{1}\]  
The Laplace transform of Equation (1) is  
\[U^{*}(s)=\frac{(1-e^{-rs})}{rs^{2}}. \tag{2}\]  
The frequency response function is  
\[|U^{*}(j\omega)|=\frac{2}{r\omega^{2}}\Big{|}sin\frac{r\omega}{2}\Big{|}. \tag{3}\]  
The ramp signal and its amplitude spectrum are shown in Figure 1. It can be seen from the figure that the larger the rise time of the ramp excitation signal, the smaller the width of the first main lobe of its spectrum. When the first main lobe is used for dynamic calibration, the working frequency of the thermocouple which can be calibrated is narrower. In time domain, the larger the rise time of the ramp excitation signal, the larger the time constant of the thermocouple which can be calibrated. In the existing measurement system of time constant of the thermocouple, such as hot wind tunnel and shock tube, the temperature excitation signal is generally a ramp signal, and the rise time of the slope signal is often unknown or difficult to measure. In time constant measurement, the time constant is obtained from the response signal. If the response signal is considered as the response of step excitation, but it is actually the response of ramp signal, the measurement error of time constant will occur.  
In order to study the effect of ramp excitation signals with different rise times on time constant measurement, assuming that the time constant of the thermocouple is 1 s and the thermocouple model is a first-order lag model with unity gain, the ramp signals with different rise times are used as excitation signals, the time constants are obtained according to the response curves. The results are shown in Table 1. As can be seen from the table, if the measurement error of the time constant is less than 5%, the rise time of the ramp excitation signal should be less than 10% of the time constant. When the time constant of the thermocouple is 10 s and 15 s, the same simulation experiments were carried out, and the results are the same as that in Table 1. Therefore, the relative error of the measurement  
Figure 1: Ramp signal and its amplitude spectrum.  
value of time constant measurement is only related to the ratio of increasing time of ramp signal to time constant of the thermocouple.
# Limitations of Using DAQ Cards for Absolute Vibration Measurement in Hydraulic Machines
## 5 Measurement of Absolute Vibrations of Hydraulics Machines Using DAQ Cards, Measurement Setup
### NI 6033E  
The NI 6033E card from National Instruments (National Instruments Inc., Austin, TX, USA) has the following parameters:  
* resolution: 16 bits;
* number of analog inputs (multiplexed): 64/32 (asymmetric inputs/differential inputs);
* maximum sampling rate (sum of channels used): 100 kHz;
* measurement ranges: \(\pm\)10, \(\pm\)5, \(\pm\)2, \(\pm\)1, \(\pm\)0.5, \(\pm\)0.2, and \(\pm\)0.1 V.  
Table 5 and Figure 9 show the results of the NI 6033E test.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**2 Hz**} & \multicolumn{3}{c}{**1.5 Hz**} & \multicolumn{3}{c}{**1 Hz**} & \multicolumn{3}{c}{**0.5 Hz**} & \multicolumn{3}{c}{**0.25 Hz**} & \multicolumn{3}{c}{**0.1 Hz**} \\ \hline
**Range** & **vrms** & **s-p-p** & **vrms** & **s-p-p** & **vrms** & **s-p-p** & **vrms** & **s-p-p** & **vrms** & **s-p-p** & **vrms** & **s-p-p** \\
**(V)** & **(mm/s)** & **(mm)** & **(mm/s)** & **(mm)** & **(mm/s)** & **(mm)** & **(mm/s)** & **(mm)** & **(mm/s)** & **(mm)** & **(mm/s)** & **(mm)** \\ \hline \(\pm\)10 & 0.097 & 16.82 & 0.113 & 24.60 & 0.137 & 42.37 & 0.184 & 99.67 & 0.197 & 169.27 & 0.225 & 334.61 \\ \(\pm\)5 & 0.047 & 8.35 & 0.056 & 12.58 & 0.070 & 21.95 & 0.088 & 45.58 & 0.096 & 73.33 & 0.106 & 147.96 \\ \(\pm\)2.5 & 0.024 & 4.20 & 0.028 & 5.96 & 0.032 & 9.17 & 0.043 & 21.79 & 0.050 & 40.59 & 0.059 & 108.01 \\ \(\pm\)1.25 & 0.013 & 2.20 & 0.015 & 3.18 & 0.017 & 5.06 & 0.024 & 12.39 & 0.030 & 25.08 & 0.034 & 48.44 \\ \(\pm\)0.625 & 0.008 & 1.39 & 0.009 & 2.04 & 0.011 & 3.21 & 0.015 & 8.4 & 0.018 & 16.3 & 0.021 & 38.04 \\ \(\pm\)0.3125 & 0.006 & 1.06 & 0.007 & 1.48 & 0.009 & 2.74 & 0.014 & 8.31 & 0.017 & 14.96 & 0.021 & 36.63 \\ \(\pm\)0.156 & 0.004 & 0.75 & 0.005 & 1.09 & 0.006 & 1.9 & 0.009 & 5.7 & 0.012 & 10.68 & 0.018 & 53.59 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Vibration measurement results using the IOtech DaqBoard 2000 card for different cut-off frequencies of high-pass filters.  
Figure 8: Vibration measurements using the IOtech DaqBoard 2000 (IOtech Inc., Cleveland, OH, USA) card depend on the high-pass filter’s cut-off frequency: vibration velocity (**a**) and vibration displacement (**b**).  
The maximum determined vibration velocity reaches a value of 0.114 mm/s for the range of \(\pm\)10 V at a cut-off frequency of 0.1 Hz. The vibration displacements are about 190 \(\upmu\)m for the range of \(\pm\)10 V and a cut-off frequency 0.1 Hz. For the minimum voltage range and this frequency, the value of the vibration displacements is 14 \(\upmu\)m. A value not greater than 1 \(\upmu\)m is achieved for the ranges of \(\pm\)0.1 and \(\pm\)0.2 V at a cut-off frequency 1 Hz. For frequencies above 1 Hz, the displacements are also less than 1 \(\upmu\)m for the range of \(\pm\)0.5 V.
## 3 Results and Discussion
### Visual Inspection  
Let us see Figure 6 (Figure 10 of ref. [2]), where the performance of all models (in Figure 3) was compared for the description of the epidemic data of Germany by GWO.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Cluster** & **Abbreviation** & **Cluster** & **Abbreviation** \\ \hline
**A** & Lgs\_GWO & B & Pow\_PSO \\
**A** & Cop\_GWO & B & Qad\_GA \\
**A** & Exp\_GWO & C & Qad\_GWO \\
**B** & Lgs\_PSO & C & Cub\_PSO \\
**B** & Lin\_GA & C & Cop\_PSO \\
**B** & Lin\_PSO & C & Pow\_GWO \\
**B** & Lin\_GWO & C & Exp\_PSO \\
**B** & Lgt\_GA & D & Lgs\_GA \\
**B** & Lgt\_PSO & E & Qad\_PSO \\
**B** & Lgt\_GWO & E & Cop\_GA \\
**B** & Cub\_GWO & F & Cub\_GA \\
**B** & Pow\_GA & F & Exp\_GA \\ \hline \end{tabular}  
* Notations: Lgs—logistic, Lin—linear, Lgt—logarithmic, Qad—quadratic, Cub—cubic, Cop—compound, Pow—power, and Exp—exponential equations; after underscore: GA—genetic algorithm, PSO—particle swarm optimization, GWO—grey wolf optimizer.  
\end{table}
Table 1: Contains the grouping pattern of algorithm combinations (color coding corresponds to that of Figure 5).  
Figure 5: Sum of ranking differences (SRD) groups the algorithm combinations. (SRD values are scaled between 0 and 100, the smaller the better). Scaled SRD values are plotted on the \(x\) and left \(y\) axes, the right \(y\) axis shows the cumulated relative frequencies of random ranking: black curve. The probability ranges are also given as 5% (XX1), Median (Med), and 95% (XX19). The explanation of capital letters A, B,... F can be found in Table 1.  
Although a residual picture would be better, even a layman can judge that all models are inadequate except the logistic one. Why are they aiming to test them? Some of the models are completely worthless (linear, quadratic, cubic, and logarithmic ones), where **negative numbers of infected persons** are predicted. The authors should have paid attention to the positivity constraint. Similarly disappointing is the description of a monotone increasing (concave) curve with a convex one or one that exhibits a minimum. The same statements are valid for all the countries examined. The exponential and logistic functions run together; they are indistinguishable from each other in a visual evaluation. Both models have similar theoretical backgrounds; they can be derived from differential equations. Which one is better and/or adequate? The adequacy can be determined by visual assessment, too. If both models seem to be adequate, then a decision can be made by penalization of models using more fitting parameters: the logistic function uses four, while the exponential has two parameters only. Whether their difference is significant can, and should, be tested by setting null and alternative hypotheses, \(H_{0}\) and \(H_{a}\), respectively. How to do it--will be discussed in the next section.
# A Feature Fusion Model with Data Augmentation for Speech Emotion Recognition
## 3 Proposed Methods
### Mix-Wav  
The Mixup can be demonstrated as:  
\[\mathrm{X_{mix}}=\lambda\mathrm{X_{i}}+(1-\lambda)\mathrm{X_{j}} \tag{1}\]  
Figure 1: Proposed method. Includes data enhancement, feature extraction, global feature selection, feature fusion and classification.  
\[Y_{\rm mix}\ =\lambda Y_{\rm i}+(1\ -\lambda)Y_{\rm j} \tag{2}\]  
The meaning of each variable is as follows:  
* \(X_{\rm i}\) and \(Y_{\rm i}\) are the ith input and label of the data sample;
* \(X_{\rm mix}\) and \(Y_{\rm mix}\) represent the mixed data composed of a pair of original data samples;
* \(\lambda\sim\) Beta \((\alpha,\ \beta),\ \alpha,\ \beta\ \in\ (0,\ \infty),\lambda\) and \(1-\lambda\) are a set of correlation weights used in Figure 2.  
We control the contribution of the two samples to the enhanced sample's weight, typically \(\alpha=\beta\); the hyperparameter \(\alpha\) controls the strength of the interpolation between sample-enhanced samples.  
Mixup has proved its effectiveness in many tasks of speech data augmentation tasks, but its objects are all two-dimensional spectral image features, based on which data augmentation is performed. No work has yet demonstrated the effectiveness of data augmentation on raw audio or one-dimensional sequence data. In many scenarios, we need to enhance the original data. For example, the input of the audio feature processing tool openSMILE [42] is a wav file, which requires the Mixup method to be applied to one-dimensional audio sequence data for data augmentation.  
In response to the above problems, this paper proposes a data augmentation method Mix-wave applied to emotional speech tasks: it inherits the calculation method of Mixup mixed data, and after identifying the mixing between different emotional classes from the sense of hearing, it will cause the problem of inaccurate emotional expression of sound samples. Here it is applied to two audio samples with the same emotional label for calculation, which means \(Y_{\rm i}=Y_{\rm j}\). Only use formula (1) to mix the data of the audio sample. Two audio input samples are weighted and output using weighting coefficients \(\lambda\) and \(1-\lambda\) obeying beta distribution, where \(X_{\rm i}\) and \(X_{\rm j}\) are audio data of the same emotion category.  
Figure 2: Two categories of emotional speech and Mix-wave-enhanced speech. (**a**,**b**) are the emotional speech waveforms of two neutral categories, (**c**) is the audio waveform enhanced with Mix-wave, where \(\lambda\) is 0.9660, so the generated speech (**c**) comes from (**a**) has more ingredients. (**d**–**f**) are the emotional speech of the sad category, using the same weight.
## 3 Spacecraft Dynamics
### Governing Equations of Smart Structures
#### 3.2.1 OPSA Actuators  
This section is devoted to introducing the piezoelectric actuator used in this case study. It was indeed demonstrated [35; 36] that we can obtain a bending control action more effective than piezoelectric patches if a piezoelectric stack actuator (i.e., multilayered piezo operating in \(d_{33}\) mode) is mounted on two L-shaped mechanical frames at a certain distance \(h_{a}\) from the surface of the passive structure. Specifically, the term \"OPSA\" stands for Offset Piezoelectric Stack Actuators, where the offset variable \(h_{a}\) represents the separation between the neutral axis of the beam and the neutral axis of the stack [36].  
The bending moment generated by the actuator about the local \(z\)-axis in Figure 10 on the controlled flexible structure can be represented [34] as  
\[M_{a}=\frac{n\ d_{33}A_{pz}E_{pz}}{l_{pz}}h_{a}\varphi^{a}=c_{pz}h_{a}\varphi^ {a} \tag{18}\]  
where \(d_{33}\) is the piezoelectric coefficient, \(\varphi^{a}\) is the actuation voltage, and \(A_{pz}\), \(E_{pz}\), \(l_{pz}\), and \(n\) are the area, Young modulus, length, and number of layers of the stack device, respectively. The complete derivation of Equation (18) can already be found in the work from [PERSON] et al. [36] and [PERSON] [34]. By referring to Equation (17), the influence vector of one actuator in the local finite element reference frame--i.e., the forces and moments that the actuator exerts on the passive structure degrees of freedom can be written as follows:  
\[\left(K_{u\varphi}^{a}\right)^{e}=c_{pz}[1,0,0,0,0,-h_{a},-1,0,0,0,0,h_{a}] \tag{19}\]  
where the apex \(e\) indicates that the vector is referred to one finite element. Consequently, the electro-mechanical coupling matrix in the global 3D body reference frame can be assembled  
Figure 10: Two-nodes FEM element.  
by multiplying rotation matrix \(R_{i}^{e\to g}\) (from the local to the global reference systems) by the local coupling matrix \(\left(K_{u\varphi}^{a}\right)^{e}\) as  
\[\mathbf{K}_{u\varphi}^{a}=\begin{bmatrix}0&\dots&0\\ \mathbf{R}_{1}^{e\to g}\Big{(}K_{u\varphi}^{a}\Big{)}_{1}^{e}&\dots&\vdots\\ \vdots&\dots&\mathbf{R}_{N_{a}}^{e\to g}\Big{(}K_{u\varphi}^{a}\Big{)}_{N_{a}}^{e} \\ 0&\dots&0\end{bmatrix} \tag{20}\]  
where \(K_{u\varphi}^{a}eR^{N_{d}\times N_{a}}\), with \(N_{d}\) number of the finite element model degrees of freedom and \(N_{a}\) number of actuators. In detail, each column of the matrix \(\mathbf{K}_{u\varphi}^{a}\) describes the effect of one smart device on the structure and can be regarded as the influence vector \({b_{a}}^{T}\) presented in Equation (11).  
The capacitance matrix of the element [34] is given as follows  
\[\left(\mathbf{K}_{\varphi\varphi}^{a}\right)^{e}=-\frac{A_{pz}\chi_{33}n^{2}}{l_{ pz}}h_{a} \tag{21}\]  
The global capacitance matrix can be assembled under the same logic of the electromechanical coupling term. The properties of the selected actuator stack are listed in Table 4.
# A Survey of Precision Formation Relative State Measurement Technology for Distributed Spacecraft
## 2 Research Status of the Precision Formation of Distributed Spacecraft Project
### CanX-4/CanX-5  
CanX-4/CanX-5 [15] is a Canadian Space Agency-funded formation project developed by the University of Toronto, Canada, comprising two spacecraft in formation at a distance of 500-1000 m, as shown in Figure 6. Its mission is the verification of the autonomous formation flight technology in sub-meter-precision spacecraft. CanX-4 and CanX-5 are identical cubic micro-nanosatellites with a mass of 7 kg. The satellite altitude system consists of a three-axis magnetometer, three rate gyros, six sun-sensors, and three orthogonally mounted reaction wheels. The satellites are equipped with four 5-mN cold gas thrusters (sulfur hexafluoride) oriented in a single direction for orbital maneuvers. The formation satellites are configured with GPS receivers to transmit status information and use the S-band inter-satellite link to transmit status information, with a measurement accuracy of 10 cm.  
Figure 5: Space orbit schematic of LISA.  
Figure 6: Schematic diagram of the CanX-4/CanX-5 formation flight.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Payloads** & **Measurement Accuracy** & **Function** \\ \hline K-band ranging system (KBR) & 1 \(\mu\)m/s & Measuring changes in the Earth’s gravity field \\ Super STAR accelerometer & 1 nm/s\({}^{2}\) & Measuring non-gravity-induced acceleration \\ Star sensor & 0.1 mrad & Spacecraft altitude measurement \\ BLACKJACK GPS receiver & 1 mm & Spacecraft relative state determination \\ Laser backward reflector & 1 mm & Auxiliary GPS for precision orbiting \\ \hline \hline \end{tabular}
\end{table}
Table 3: Payloads performance of GRACE.