A SYSTID model for white impulse noise, second edition, volume 2
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Optimal linear filter for continuous time-varying dynamic system, using measurements containing additive white noise
Design of optimal waveforms for optimal estimation or prediction of state of linear dynamical system in presence of Markov and white noise
Statistical properties of PFM effect on white noise Gaussian input
Linear stochastic continuous feedback system with white noise and control input, investigating combined problem of filtering and optimal control
This paper describes a laboratory study of add-on {coustic treatments for a twin-engine, propeller-driven aircraft fuselage. The sound source was a pneumatic-driver, with attached horn to simulate propeller noise distribution, powered by a white noise signal. Treatments included a double-wall, production-line treatment and various fiberglass and lead-vinyl treatments. Insertion losses, space-averaged across six interior microphone positions, were used to evaluate the treatments. In addition, the effects of sound source angle and ambient temperature on interior sound pressure level are presented. The sound source angle is shown to have a significant effect on one-third octave band localized sound pressure level. While changes in ambient temperature are shown to have little effect on one-third octave band localized sound pressure level, the change in narrowband localized sound pressure level may be dramatic.
Optimal control and stability for stochastic systems, viewing linear diffusion models based upon Gaussian-Markov process as finite dimensional linear system driven by white noise
Here, we introduce a data-driven and physics-informed framework for propagating uncertainty in stiff, multiscale random ordinary differential equations (RODEs) driven by correlated (colored) noise. Unlike systems subjected to Gaussian white noise, a deterministic equation for the joint probability density function (PDF) of RODE state variables does not exist in closed form. Moreover, such an equation would require as many phase-space variables as there are states in the RODE system. To alleviate this curse of dimensionality, we instead derive exact, albeit unclosed, reduced-order PDF (RoPDF) equations for low-dimensional observables/quantities of interest. The unclosed terms take the form of state-dependent conditional expectations, which are directly estimated from data at sparse observation times. However, for systems exhibiting stiff, multiscale dynamics, data sparsity introduces regression discrepancies that compound during RoPDF evolution. This is overcome by introducing a kinetic-like defect term to the RoPDF equation, which is learned by assimilating in sparse, low-fidelity RoPDF estimates. Two assimilation methods are considered, namely nudging and deep neural networks, which are successfully tested against Monte Carlo simulations.
Nonstationary colored noise linear shaping filter to transform white noise into nonstationary random process with specified covariance function
Sequential estimation on states of linear systems disturbed by white noise, determining relations between covariance matrices
Steepest descent method extended to trajectory optimization problem for stochastically disturbed systems with application to Euler equation for white noise problem of reentering vehicle
The Kepler Mission launched in June 2009 to commence NASA's first mission to search for potentially habitable, Earth-size planets orbiting Sun-like stars. Kepler discovered explanets via the transit method: searching for minute (100 ppm) drops in brightness lasting 1 - 13 hours corresponding to occasions where the planet crosses the face of its host star from Kepler's point of view. The exquisite precision required to carry out the Kepler mission (20 ppm in 6.5 hours) pushed astronomical time series analysis to the limits, and motivated the development of novel algorithmic approaches. Transit signatures of rocky planets are often dwarfed by the intrinsic stellar variability, which is not white noise, and often is non-stationary, and by instrumental systematic effects, which can include transients and electronic artifacts. Surmounting this challenging regime of weak, temporally compact, periodic signals in observation noise with strong systematics and other sources of variability motivated the development of 1) an overcomplete, non-decimated, wavelet-based matched filter to jointly estimate the properties of the non-stationary, non-white observation noise process, and 2) a multi-scale, maximum a posteriori (msMAP) approach to identifying and removing instrumental systematic effects. After over nine years of observations, the Kepler spacecraft finally ran out of fuel in November 2018, ending its data collection activities. Over 2300 planets were discovered by Kepler in its primary mission, and over 355 have been discovered by K2, the repurposed mission that followed Kepler's primary mission after the loss of a second reaction wheel in May 2013. We have ported the Kepler science pipeline for the Transiting Exoplanet Survey Satellite (TESS) Mission, which began science observations in July 2019, and report initial results and performance of the modified science pipeline.The Kepler and TESS Missions are supported by NASA's Science Mission Directorate.
Statistical analysis of pulse frequency modulation systems with white noise input
Although ACTS (Advanced Communications Technology Satellite) provides an almost error-free channel during much of the day and under most conditions, there are times when it is not suitable for reliably error-free data communications when operating in the uncoded mode. Because coded operation is not always available to every earth station, measures must be taken in the end system to maintain adequate throughput when transferring data under adverse conditions. The most effective approach that we tested to improve performance was the addition of an 'outer' Reed-Solomon code through use of CCSDS (Consultative Committee for Space Data Systems) GOS 2 (a forward error correcting code). This addition can benefit all users of an ACTS channel including those applications that do not require totally reliable transport, but it is somewhat expensive because additional hardware is needed. Although we could not characterize the link noise statistically (it appeared to resemble uncorrelated white noise, the type that block codes are least effective in correcting), we did find that CCSDS GOS 2 gave an essentially error-free link at BER's (bit error rate) as high as 6x10(exp -4). For users that demand reliable transport, an ARQ (Automatic Repeat Queuing) protocol such as TCP (Transmission Control Protocol) or TP4 (Transport Protocol, Class 4) will probably be used. In this category, it comes as no surprise that the best choice of the protocol suites tested over ACTS was TP4 using CCSDS GOS 2. TP4 behaves very well over an error-free link which GOS 2 provides up to a point. Without forward error correction, however, TP4 service begins to degrade in the 10(exp -7)-10(exp -6) range and by 4x10(exp -6), it barely gives any throughput at all. If Congestion Avoidance is used in TP4, the degradation is even more pronounced. Fortunately, as demonstrated here, this effect can be more than compensated for by choosing the Selective Acknowledgment option. In fact, this option can enable TP4 to deliver some throughput at error rates as high as 10(exp -5).
Here, we present a measurement of the 𝐵-mode polarization power spectrum of the cosmic microwave background anisotropies at 32 ≤ ℓ < 502 for three bands centered at 95, 150, and 220 GHz using data from the SPT-3G receiver on the South Pole Telescope. This work uses SPT-3G observations from the 2019 and 2020 winter observing seasons of a ∼1500 deg 2 patch of sky that directly overlaps with fields observed with the BICEP/Keck family of telescopes and covers part of the proposed Simons Observatory and CMB-S4 deep fields. Employing new techniques for mitigating polarized atmospheric noise, the SPT-3G data demonstrates a white noise level of 9.3 (6.7) μK−arcmin at ℓ ∼500 for the 95 GHz (150 GHz) data, with a 1/ℓ noise knee at ℓ = 128 (182). We fit the observed six auto- and cross-frequency 𝐵-mode power spectra to a model including lensed ΛCDM 𝐵-modes and a combination of Galactic and extragalactic foregrounds. This work characterizes foregrounds in the vicinity of the BICEP/Keck survey area, finding foreground power consistent with that reported by the BICEP/Keck collaboration within the same region and a factor of ∼3 higher power over the full SPT-3G survey area. Using SPT-3G data over the BICEP/Keck survey area, we place a 95% upper limit on the tensor-to-scalar ratio of 𝑟 <0.25 and find the statistical uncertainty on 𝑟 to be 𝜎(𝑟) = 0.067.
We present a measurement of the $B$-mode polarization power spectrum of the cosmic microwave background anisotropies at 32 $\le$$\ell$$<$ 502 for three bands centered at 95, 150, and 220 GHz using data from the SPT-3G receiver on the South Pole Telescope. This work uses SPT-3G observations from the 2019 and 2020 winter observing seasons of a $\sim$1500 deg$^2$ patch of sky that directly overlaps with fields observed with the BICEP/Keck family of telescopes, and covers part of the proposed Simons Observatory and CMB-S4 deep fields. Employing new techniques for mitigating polarized atmospheric noise, the SPT-3G data demonstrates a white noise level of 9.3 (6.7) $\mu$K-arcmin at $\ell \sim 500$ for the 95 GHz (150 GHz) data, with a $1/\ell$ noise knee at $\ell$=128 (182). We fit the observed six auto- and cross-frequency $B$-mode power spectra to a model including lensed $\Lambda$CDM $B$-modes and a combination of Galactic and extragalactic foregrounds. This work characterizes foregrounds in the vicinity of the BICEP/Keck survey area, finding foreground power consistent with that reported by the BICEP/Keck collaboration within the same region, and a factor of $\sim$ 3 higher power over the full SPT-3G survey area. Using SPT-3G data over the BICEP/Keck survey area, we place a 95% upper limit on the tensor-to-scalar ratio of $r < 0.25$ and find the statistical uncertainty on $r$ to be $\sigma(r) = 0.067$.
Examination of (radar) Doppler data which are formed by mi1ing the returning microwave signal with a replica of the transmitted signal, counting the cycles of the beat, and sampling the counter at evenly spaced intervals t sub i. It is shown that the amount of information which can be extracted from a set of data may be larger if the associated noise is perfectly correlated than if it is white, and that the use of the white noise assumption in the filter may result in the loss of some of this information.
The white noise level of space-charge-limited current (SCLC) of holes in a silicon device measured at five temperatures ranging from 113 to 300 K is shown to be proportional to the absolute temperature. This proves experimentally the thermal origin of noise for SCLC in solids.