Sensitivity Functions for Linear Discrete Systems with Applications

z-transform techniques are employed to establish general symmetry and simultaneity properties of the first sensitivity functions of the phase-canonical form of single-input, nth-order, linear, constant, discrete-time, controllable systems. It is demonstrated that computation of the first sensitivity function requires one nth-order model in addition to the system model. This simultaneity property is extended to arbitrary single-input, nth-order, linear, constant, discrete systems. In complete analogy with results presented for continuous systems, symmetry and simultaneity properties may be established for the computation of the /th sensitivity function begin{equation*}^{l}beta^{y} triangleq frac{partial^{l}y_{i}}{partialalpha_{Jl}partialalpha_{Jl-1}cdotspartialalpha_{J2}partialalpha_{J1}}|_{alpha=alpha_{0}} {rm for} substack{i = 1,2,ldots,n\ J_{k} = 1,2,ldots,n\ k = 1,2,ldots,l.}end{equation*} Extension of these results to multi-input systems is also mentioned. The usefulness of the simultaneity property is illustrated by applying the results to the design of a low-sensitivity optimal control law.     

The Effect of Satellite Spin on Two-Way Doppler Rangerate Measurements

The rotation of a spin-stabilized satellite employing a turnstile antenna for reception and retransmission affects two-way Doppler range-rate measurements. Two different types of tracking systems are considered and, in both systems, the range-rate measurement is changed by the amount begin{equation*} |Delta dot{r}| = frac{|1 pm 1/k|}{2} lambda_{t}f_{s} end{equation*} where k is the turn-around ratio of the satellite transponder, Xt is the wavelength of the ground-based transmitter, and fs is the spin rate of the satellite. The positive sign is used if the turnstile antenna elements are connected to give the same polarization for both reception and transmission. If the antenna connections result in different polarizations, the minus sign is used and the magnitude of the effect is reduced.     

Output Probability Density Functions for Cross Correlators Utilizing Sampling Techniques

Sampling techniques provide a practical means of obtaining cross-correlation functions. In this paper, the correlation function is described by sums of the form Z = begin{equation*}Z = Sigma^{N}_{j=1}X_{j}Y_{j}end{equation*}. A general expression is derived for the probability density function of the random variable Z under the condition that Xj and Yj are stationary, jointly Gaussian random processes with nonzero means and unit variances.     

The Least-Square Approximation of Inertial Platform Drift

The drift angle of an inertial platform which is gyro-stabilized with respect to inertial space is equal to the integral of the gyro drift rate. Under controlled laboratory environment the drift angle, denoted by y, may be measured and plotted against time in an interval [0, T]. Without loss in generality, one may take y(0)= 0. A straight line yf can be found, such that the quantity E2 is minimized, where begin{equation*}E^2 = {frac{1}{T}int^{T}_{0}(y-y_f)^{2}}dt.end{equation*} The equation for yf is of the form yf = at + b and, in general, both a and b are nonzero. It is desirable to determine a statistical relationship between the gyro drift rate and the expected value of the minimum E2 for any given interval T. An analysis in this paper determines this relationship and derives a general expression for , where the symbol <*> denotes statistical expectation. It is found that increases linearly with the variance of the gyro drift rate. This general formula is then developed in detail for the case of a first-order Markovian gyro drift. is evaluated numerically and its square root plotted vs. the interval T and the gyro correlation time. The same problem is also solved for the case when yf is constrained to intersect the origin, i.e., when b=0.     

Real-Time Motion Desmearing of Airborne Imagery

This paper considers the real-time ?desmearing? of motion- ?smeared? imagery telemetered from an airborne platform. The specific configuration considered is the direct raster scan readout of a satellite-mounted vidicon. Three types of smearing are considered: 1) linear uniform smearing, 2) linear nonuniform smearing, and 3) nonlinear smearing. The simplest type of smearing, linear uniform, has as its desmearing or inverse filter a circulating delay line (CDL) cascaded with a differentiator. An error analysis of this filter is presented along with an experimental simulation. Linear, non-uniform smearing characterized by the operator begin{equation*}int^{t}_{t-delta(t)}I(tau){ }{dtau}end{equation*} is considered next. Two possible realizations for the inverse filter are discussed as to accuracy and practicality. Finally, an error analysis is performed for the nonlinear smearing that results from a skewing of the raster scan.     

复合Halpern迭代逼近可数个增生映像的公共零点

设E是严格凸和自反的实Banach空间且其范数是一致Gateaux可微的,K是E中非空闭凸子集,Ai：K→E（i∈N）是m-增生映像且公共不动点集非空,u∈K是给定点,X1∈K是任一初始点,{αn}^∞ n=1、{β}^∞ n=1是[0,1]中的实数列且满足如下条件：（i）lim n→∞αn=0,∑^∞ n=1 αn=∞,∑^∞ n=1｜αn＋1－αn｜〈∞;（ii）lim n→∞βn=0,∑^∞ n=1｜βn＋1－βn｜〈∞。设{Xn}^∞ n=1是由下面复合Halpern格式定义的迭代序列：{yn=βnXn＋（1-βn）SXn,n≥0 Xn＋1=αnu＋（1-αn）yn其中S=∑∞ i=1ξiJAi,JAi=（1＋Ai）^-1（i∈N）,那么{Xn}∞ n=1强收敛于{Ai}i∈N的公共0点。本文的结果改进和推广了Zegeye和Shahzad,Ofoedu以及其他作者的相应结果。     

Signal Sequence Detection Given Noisy, Common Background Image Sets

The optimum processing (likelihood functional) is found for a set of M images {Zm = Sm + Y + Nm}, each the sum of a member Sm of a signal sequence {Sm}, due to an object to be detected and its parameters estimated, a sample function Nm of a noise field {Nm}, and a sample function Y of a common background field {Y}. The noise fields {{Nm}} are independent, zero mean, white Gaussian fields, all independent of the background field {Y}; the latter is assumed to be either 1} completely unknown or of known mean and covariance functions with 2) a certain fluctuation property or 3) Gaussian. Three equivalent forms of the optimum processing are found: 1) a summation of generalized matched filterings of the images, 2) a summation of matched filtering of certain generalized differences of the images, 3) a summation of ?estimator-correlator? type filterings. The detection performance and optimum signal/image selection under the Neyman-Pearson criterion is given and the singularity of the ({{Nm = O}} and M > 1) case noted. It is shown that optimum processor and signal design can completely eliminate any effect of the background on detectability (M > 1). The Cramer-Rao lower bound for the signal parameter estimates meansquare error is given along with an example; optimum signal/image selection in the single parameter case is discussed.     

Seismic Coupling of Short-Period Wind Noise Through Mars’ Regolith for NASA’s InSight Lander

NASA’s InSight lander will deploy a tripod-mounted seismometer package onto the surface of Mars in late 2018. Mars is expected to have lower seismic activity than the Earth, so minimisation of environmental seismic noise will be critical for maximising observations of seismicity and scientific return from the mission. Therefore, the seismometers will be protected by a Wind and Thermal Shield (WTS), also mounted on a tripod. Nevertheless, wind impinging on the WTS will cause vibration noise, which will be transmitted to the seismometers through the regolith (soil). Here we use a 1:1-scale model of the seismometer and WTS, combined with field testing at two analogue sites in Iceland, to determine the transfer coefficient between the two tripods and quantify the proportion of WTS vibration noise transmitted through the regolith to the seismometers. The analogue sites had median grain sizes in the range 0.3–1.0 mm, surface densities of \(1.3\mbox{--}1.8~\mbox{g}\,\mbox{cm}^{-3}\), and an effective regolith Young’s modulus of \(2.5^{+1.9}_{-1.4}~\mbox{MPa}\). At a seismic frequency of 5 Hz the measured transfer coefficients had values of 0.02–0.04 for the vertical component and 0.01–0.02 for the horizontal component. These values are 3–6 times lower than predicted by elastic theory and imply that at short periods the regolith displays significant anelastic behaviour. This will result in reduced short-period wind noise and increased signal-to-noise. We predict the noise induced by turbulent aerodynamic lift on the WTS at 5 Hz to be \(\sim2\times10^{-10}~\mbox{ms}^{-2}\,\mbox{Hz}^{-1/2}\) with a factor of 10 uncertainty. This is at least an order of magnitude lower than the InSight short-period seismometer noise floor of \(10^{-8}~\mbox{ms}^{-2}\,\mbox{Hz}^{-1/2}\).     

The OSIRIS-REx Thermal Emission Spectrometer (OTES) Instrument

The OSIRIS-REx Thermal Emission Spectrometer (OTES) will provide remote measurements of mineralogy and thermophysical properties of Bennu to map its surface, help select the OSIRIS-REx sampling site, and investigate the Yarkovsky effect. OTES is a Fourier Transform spectrometer covering the spectral range 5.71–100 μm (\(1750\mbox{--}100~\mbox{cm}^{-1}\)) with a spectral sample interval of \(8.66~\mbox{cm}^{-1}\) and a 6.5-mrad field of view. The OTES telescope is a 15.2-cm diameter Cassegrain telescope that feeds a flat-plate Michelson moving mirror mounted on a linear voice-coil motor assembly. A single uncooled deuterated l-alanine doped triglycine sulfate (DLATGS) pyroelectric detector is used to sample the interferogram every two seconds. Redundant ～0.855 μm laser diodes are used in a metrology interferometer to provide precise moving mirror control and IR sampling at 772 Hz. The beamsplitter is a 38-mm diameter, 1-mm thick chemical vapor deposited diamond with an antireflection microstructure to minimize surface reflection. An internal calibration cone blackbody target provides radiometric calibration. The radiometric precision in a single spectrum is \(\leq2.2 \times 10^{-8}~\mbox{W}\,\mbox{cm}^{-2}\,\mbox{sr} ^{-1}/\mbox{cm}^{-1}\) between 300 and \(1350~\mbox{cm}^{-1}\). The absolute integrated radiance error is \(<1\%\) for scene temperatures ranging from 150 to 380 K. The overall OTES envelope size is \(37.5 \times 28.9 \times 52.2~\mbox{cm}\), and the mass is 6.27 kg. The power consumption is 10.8 W average. OTES was developed by Arizona State University with Moog Broad Reach developing the electronics. OTES was integrated, tested, and radiometrically calibrated on the Arizona State University campus in Tempe, AZ.     

用逐步扩阶双递推时域法识别线性振动系统复模态参数

本文给出了从线性振动系统的自由响应识别该系统复模态参数的方法,把自由响应的表达式变为一个自回归方程和一个多项式方程,利用最小二乘递推与逐步扩阶递推的双递推法来进行参数识别。文中讨论了几个应用中的问题,并给出了计算机的模拟计算结果以及越野汽车车架的参数识别试验结果。     

Auroral Substorms: Search for Processes Causing the Expansion Phase in Terms of the Electric Current Approach

Auroral substorms are mostly manifestations of dissipative processes of electromagnetic energy. Thus, we consider a sequence of processes consisting of the power supply (dynamo), transmission (currents/circuits) and dissipations (auroral substorms-the end product), namely the electric current line approach. This work confirms quantitatively that after accumulating magnetic energy during the growth phase, the magnetosphere unloads the stored magnetic energy impulsively in order to stabilize itself. This work is based on our result that substorms are caused by two current systems, the directly driven (DD) current system and the unloading system (UL). The most crucial finding in this work is the identification of the UL (unloading) current system which is responsible for the expansion phase. A very tentative sequence of the processes leading to the expansion phase (the generation of the UL current system) is suggested for future discussions.

1. (1)
   The solar wind-magnetosphere dynamo enhances significantly the plasma sheet current when its power is increased above \(10^{18}~\mbox{erg}/\mbox{s}\) (\(10^{11}\) w).
    
2. (2)
   The magnetosphere accumulates magnetic energy during the growth phase, because the ionosphere cannot dissipate the increasing power because of a low conductivity. As a result, the magnetosphere is inflated, accumulating magnetic energy.
    
3. (3)
   When the power reaches \(3\mbox{--}5\times 10^{18}~\mbox{erg}/\mbox{s}\) (\(3\mbox{--}5\times 10^{11}\) w) for about one hour and the stored magnetic energy reaches \(3\mbox{--}5\times10^{22}\) ergs (\(10^{15}\) J), the magnetosphere begins to develop perturbations caused by current instabilities (the current density \({\approx}3\times 10^{-12}~\mbox{A}/\mbox{cm}^{2}\) and the total current \({\approx}10^{6}~\mbox{A}\) at 6 Re). As a result, the plasma sheet current is reduced.
    
4. (4)
   The magnetosphere is thus deflated. The current reduction causes \(\partial B/\partial t > 0\) in the main body of the magnetosphere, producing an earthward electric field. As it is transmitted to the ionosphere, it becomes equatorward-directed electric field which drives both Pedersen and Hall currents and thus generates the UL current system.
    
5. (5)
   A significant part of the magnetic energy is accumulated in the main body of the magnetosphere (the inner plasma sheet) between 4 Re and 10 Re, because the power (Poynting flux \([ \boldsymbol{E} \times \boldsymbol{B} ])\) is mainly directed toward this region which can hold the substorm energy.
    
6. (6)
   The substorm intensity depends on the location of the energy accumulation (between 4 Re and 10 Re), the closer the location to the earth, the more intense substorms becomes, because the capacity of holding the energy is higher at closer distances. The convective flow toward the earth brings both the ring current and the plasma sheet current closer when the dynamo power becomes higher.
    

This proposed sequence is not necessarily new. Individual processes involved have been considered by many, but the electric current approach can bring them together systematically and provide some new quantitative insights.

     

Large-scale Bright Fronts in the Solar Corona: A?Review of?��EIT waves��

??EIT waves?? are large-scale coronal bright fronts (CBFs) that were first observed in 195 Å images obtained using the Extreme-ultraviolet Imaging Telescope (EIT) onboard the Solar and Heliospheric Observatory (SOHO). Commonly called ??EIT waves??, CBFs typically appear as diffuse fronts that propagate pseudo-radially across the solar disk at velocities of 100?C700 km?s^?1 with front widths of 50?C100 Mm. As their speed is greater than the quiet coronal sound speed (c _s ??200 km?s^?1) and comparable to the local Alfvén speed (v _A ??1000 km?s^?1), they were initially interpreted as fast-mode magnetoacoustic waves ( $v_{f}=(c_{s}^{2} + v_{A}^{2})^{1/2}$ ). Their propagation is now known to be modified by regions where the magnetosonic sound speed varies, such as active regions and coronal holes, but there is also evidence for stationary CBFs at coronal hole boundaries. The latter has led to the suggestion that they may be a manifestation of a processes such as Joule heating or magnetic reconnection, rather than a wave-related phenomena. While the general morphological and kinematic properties of CBFs and their association with coronal mass ejections have now been well described, there are many questions regarding their excitation and propagation. In particular, the theoretical interpretation of these enigmatic events as magnetohydrodynamic waves or due to changes in magnetic topology remains the topic of much debate.     

Dust Phenomena Relating to Airless Bodies

Airless bodies are directly exposed to ambient plasma and meteoroid fluxes, making them characteristically different from bodies whose dense atmospheres protect their surfaces from such fluxes. Direct exposure to plasma and meteoroids has important consequences for the formation and evolution of planetary surfaces, including altering chemical makeup and optical properties, generating neutral gas and/or dust exospheres, and leading to the generation of circumplanetary and interplanetary dust grain populations. In the past two decades, there have been many advancements in our understanding of airless bodies and their interaction with various dust populations. In this paper, we describe relevant dust phenomena on the surface and in the vicinity of airless bodies over a broad range of scale sizes from \(\sim10^{-3}~\mbox{km}\) to \(\sim10^{3}~\mbox{km}\), with a focus on recent developments in this field.     

Pulsar Timing and Its Application for Navigation and Gravitational Wave Detection

Pulsars are natural cosmic clocks. On long timescales they rival the precision of terrestrial atomic clocks. Using a technique called pulsar timing, the exact measurement of pulse arrival times allows a number of applications, ranging from testing theories of gravity to detecting gravitational waves. Also an external reference system suitable for autonomous space navigation can be defined by pulsars, using them as natural navigation beacons, not unlike the use of GPS satellites for navigation on Earth. By comparing pulse arrival times measured on-board a spacecraft with predicted pulse arrivals at a reference location (e.g. the solar system barycenter), the spacecraft position can be determined autonomously and with high accuracy everywhere in the solar system and beyond. We describe the unique properties of pulsars that suggest that such a navigation system will certainly have its application in future astronautics. We also describe the on-going experiments to use the clock-like nature of pulsars to “construct” a galactic-sized gravitational wave detector for low-frequency (\(f_{GW}\sim 10^{-9} \text{--} 10^{-7}\) Hz) gravitational waves. We present the current status and provide an outlook for the future.     

Estimations of the Seismic Pressure Noise on Mars Determined from Large Eddy Simulations and Demonstration of Pressure Decorrelation Techniques for the Insight Mission

The atmospheric pressure fluctuations on Mars induce an elastic response in the ground that creates a ground tilt, detectable as a seismic signal on the InSight seismometer SEIS. The seismic pressure noise is modeled using Large Eddy Simulations (LES) of the wind and surface pressure at the InSight landing site and a Green’s function ground deformation approach that is subsequently validated via a detailed comparison with two other methods: a spectral approach, and an approach based on Sorrells’ theory (Sorrells, Geophys. J. Int. 26:71–82, 1971; Sorrells et al., Nat. Phys. Sci. 229:14–16, 1971). The horizontal accelerations as a result of the ground tilt due to the LES turbulence-induced pressure fluctuations are found to be typically \(\sim 2 \mbox{--} 40~\mbox{nm}/\mbox{s}^{2}\) in amplitude, whereas the direct horizontal acceleration is two orders of magnitude smaller and is thus negligible in comparison. The vertical accelerations are found to be \(\sim 0.1\mbox{--}6~\mbox{nm}/\mbox{s}^{2}\) in amplitude. These are expected to be worst-case estimates for the seismic noise as we use a half-space approximation; the presence at some (shallow) depth of a harder layer would significantly reduce quasi-static displacement and tilt effects.We show that under calm conditions, a single-pressure measurement is representative of the large-scale pressure field (to a distance of several kilometers), particularly in the prevailing wind direction. However, during windy conditions, small-scale turbulence results in a reduced correlation between the pressure signals, and the single-pressure measurement becomes less representative of the pressure field. The correlation between the seismic signal and the pressure signal is found to be higher for the windiest period because the seismic pressure noise reflects the atmospheric structure close to the seismometer.In the same way that we reduce the atmospheric seismic signal by making use of a pressure sensor that is part of the InSight Auxiliary Payload Sensor Suite, we also the use the synthetic noise data obtained from the LES pressure field to demonstrate a decorrelation strategy. We show that our decorrelation approach is efficient, resulting in a reduction by a factor of \(\sim 5\) in the observed horizontal tilt noise (in the wind direction) and the vertical noise. This technique can, therefore, be used to remove the pressure signal from the seismic data obtained on Mars during the InSight mission.     

Particle acceleration by magnetic reconnection and shocks during current loop coalescence in solar flares

This article reviews recent development of the theory of current loop coalescence and shock waves, giving particular attention to particle acceleration caused by these processes. First, explosive reconnection driven by the current loop coalescence and associated particle acceleration are studied by theoretical and magnetohydrodynamic simulation methods and the results are compared with observations of solar flares; this model gives a good explanation for the quasi-periodic structure of some solar flare bursts. Next follows a discussion of particle acceleration in association with fast magnetosonic shock waves. It is shown theoretically and by relativistic particle simulation that a quasi-perpendicular shock wave can accelerate trapped ions in the direction perpendicular to the ambient magnetic field up to speeds much greater than the Alfvén speed, . When the ambient magnetic field is rather strong ( _{ce pe} ), both ions and electrons can be accelerated to relativistic energies. For both the nonrelativistic and relativistic cases, the time needed for the acceleration is very short; it is for the ions. These results are compared with the rapid and simultaneous acceleration of ions and electrons in the impulsive phase of solar flares.     

Solar Wind Turbulence and the Role of Ion Instabilities

Solar wind is probably the best laboratory to study turbulence in astrophysical plasmas. In addition to the presence of magnetic field, the differences with neutral fluid isotropic turbulence are: (i) weakness of collisional dissipation and (ii) presence of several characteristic space and time scales. In this paper we discuss observational properties of solar wind turbulence in a large range from the MHD to the electron scales. At MHD scales, within the inertial range, turbulence cascade of magnetic fluctuations develops mostly in the plane perpendicular to the mean field, with the Kolmogorov scaling $k_{\perp}^{-5/3}$ for the perpendicular cascade and $k_{\|}^{-2}$ for the parallel one. Solar wind turbulence is compressible in nature: density fluctuations at MHD scales have the Kolmogorov spectrum. Velocity fluctuations do not follow magnetic field ones: their spectrum is a power-law with a ?3/2 spectral index. Probability distribution functions of different plasma parameters are not Gaussian, indicating presence of intermittency. At the moment there is no global model taking into account all these observed properties of the inertial range. At ion scales, turbulent spectra have a break, compressibility increases and the density fluctuation spectrum has a local flattening. Around ion scales, magnetic spectra are variable and ion instabilities occur as a function of the local plasma parameters. Between ion and electron scales, a small scale turbulent cascade seems to be established. It is characterized by a well defined power-law spectrum in magnetic and density fluctuations with a spectral index close to ?2.8. Approaching electron scales, the fluctuations are no more self-similar: an exponential cut-off is usually observed (for time intervals without quasi-parallel whistlers) indicating an onset of dissipation. The small scale inertial range between ion and electron scales and the electron dissipation range can be together described by $\sim k_{\perp}^{-\alpha}\exp(-k_{\perp}\ell_{d})$ , with α?8/3 and the dissipation scale ? _d close to the electron Larmor radius ? _d ?ρ _e . The nature of this small scale cascade and a possible dissipation mechanism are still under debate.     

复合Halpern迭代逼近一族m-增生映像公共零点

在严格凸的Banach空间E中,介绍了一种新的复合迭代方法强收敛到一族m-增生映像公共零点。K是E中非空闭凸子集,假定E的每个非空闭凸子集上的非扩张映像都存在不动点,Ai：K→E（i=1,2,…,r）是一族m-增生映像,{xn}是由复合Halpem格式定义的迭代序列,证明了当n→∞时,{xn}强收敛于方程Aix=0（i=1,2,…,r）的公共解,改进和推广了Zegeye和Shahzad等人的相应结果。     

An Investigation of the Mechanical Properties of Some Martian Regolith Simulants with Respect to the Surface Properties at the InSight Mission Landing Site

In support of the InSight mission in which two instruments (the SEIS seismometer and the \(\mbox{HP}^{3}\) heat flow probe) will interact directly with the regolith on the surface of Mars, a series of mechanical tests were conducted on three different regolith simulants to better understand the observations of the physical and mechanical parameters that will be derived from InSight. The mechanical data obtained were also compared to data on terrestrial sands. The density of the regolith strongly influences its mechanical properties, as determined from the data on terrestrial sands. The elastoplastic compression volume changes were investigated through oedometer tests that also provided estimates of possible changes in density with depth. The results of direct shear tests provided values of friction angles that were compared with that of a terrestrial sand, and an extrapolation to lower density provided a friction angle compatible with that estimated from previous observations on the surface of Mars. The importance of the contracting/dilating shear volume changes of sands on the dynamic penetration of the mole was determined, with penetration facilitated by the \(\sim1.3~\mbox{Mg/m}^{3}\) density estimated at the landing site. Seismic velocities, measured by means of piezoelectric bender elements in triaxial specimens submitted to various isotropic confining stresses, show the importance of the confining stress, with lesser influence of density changes under compression. A power law relation of velocity as a function of confining stress with an exponent of 0.3 was identified from the tests, allowing an estimate of the surface seismic velocity of 150 m/s. The effect on the seismic velocity of a 10% proportion of rock in the regolith was also studied. These data will be compared with in situ data measured by InSight after landing.