Superconvergence relation for a linear combination of amplitudes

Abstract Recently, the internal-linear-combination (ILC) method was investigated extensively in the context of reconstruction of Cosmic Microwave Background (CMB) temperature anisotropy signal using observations obtained by WMAP and Planck satellite missions. In this article, we, for the first time, apply the ILC method to reconstruct the large scale CMB E mode polarization signal, which could probe the ionization history, using simulated observations of 15 frequency CMB polarization maps of future generation Cosmic Origin Explorer (COrE) satellite mission. We find that the clean power spectra, from the usual ILC, are strongly biased due to non zero CMB-foregrounds chance correlations. In order to address the issues of bias and errors we extend and improve the usual ILC method for CMB E mode reconstruction by incorporating prior information of theoretical E mode angular power spectrum while estimating the weights for linear combination of input maps (Sudevan & Saha 2018b). Using the E mode covariance matrix effectively suppresses the CMB-foreground chance correlation power leading to an accurate reconstruction of cleaned CMB E mode map and its angular power spectrum. We compare the performance of the usual ILC and the new method over large angular scales and show that the later produces significantly statistically improved results than the former. The new E mode CMB angular power spectrum contains neither any significant negative bias at the low multipoles nor any positive foreground bias at relatively higher mutlipoles. The error estimates of the cleaned spectrum agree very well with the cosmic variance induced error.

Download Full-text

Partially constrained internal linear combination: A method for low-noise CMB foreground mitigation

Physical Review D ◽

10.1103/physrevd.103.103510 ◽

2021 ◽

Vol 103 (10) ◽

Author(s):

Y. Sultan Abylkairov ◽

Omar Darwish ◽

J. Colin Hill ◽

Blake D. Sherwin

Keyword(s):

Linear Combination ◽

Low Noise

Download Full-text

Single peaked traveling wave solutions to a generalized μ-Novikov Equation

Advances in Nonlinear Analysis ◽

10.1515/anona-2020-0106 ◽

2020 ◽

Vol 10 (1) ◽

pp. 66-75

Author(s):

Byungsoo Moon

Keyword(s):

Linear Combination ◽

Traveling Wave ◽

Wave Solution ◽

Traveling Wave Solutions ◽

Traveling Wave Solution ◽

Wave Solutions ◽

Quadratic Nonlinearities ◽

Novikov Equation

Abstract In this paper, we study the existence of peaked traveling wave solution of the generalized μ-Novikov equation with nonlocal cubic and quadratic nonlinearities. The equation is a μ-version of a linear combination of the Novikov equation and Camassa-Hom equation. It is found that the equation admits single peaked traveling wave solutions.

Download Full-text

New Methodology for Computing the Aircraft’s Position Based on the PPP Method in GPS and GLONASS Systems

Energies ◽

10.3390/en14092525 ◽

2021 ◽

Vol 14 (9) ◽

pp. 2525

Author(s):

Kamil Krasuski ◽

Damian Wierzbicki

Keyword(s):

Linear Combination ◽

Research Method ◽

High Efficiency ◽

Satellite System ◽

Weighting Scheme ◽

Measurement Technology ◽

Dual Frequency ◽

Weighted Mean ◽

Mean Error ◽

The Mean

In the field of air navigation, there is a constant pursuit for new navigation solutions for precise GNSS (Global Navigation Satellite System) positioning of aircraft. This study aims to present the results of research on the development of a new method for improving the performance of PPP (Precise Point Positioning) positioning in the GPS (Global Positioning System) and GLONASS (Globalnaja Nawigacionnaja Sputnikovaya Sistema) systems for air navigation. The research method is based on a linear combination of individual position solutions from the GPS and GLONASS systems. The paper shows a computational scheme based on the linear combination for geocentric XYZ coordinates of an aircraft. The algorithm of the new research method uses the weighted mean method to determine the resultant aircraft position. The research method was tested on GPS and GLONASS kinematic data from an airborne experiment carried out with a Seneca Piper PA34-200T aircraft at the Mielec airport. A dual-frequency dual-system GPS/GLONASS receiver was placed on-board the plane, which made it possible to record GNSS observations, which were then used to calculate the aircraft’s position in CSRS-PPP software. The calculated XYZ position coordinates from the CSRS-PPP software were then used in the weighted mean model’s developed optimization algorithm. The measurement weights are a function of the number of GPS and GLONASS satellites and the inverse of the mean error square. The obtained coordinates of aircraft from the research model were verified with the RTK-OTF solution. As a result of the research, the presented solution’s accuracy is better by 11–87% for the model with a weighting scheme as a function of the inverse of the mean error square. Moreover, using the XYZ position from the RTKLIB program, the research method’s accuracy increases from 45% to 82% for the model with a weighting scheme as a function of the inverse of the square of mean error. The developed method demonstrates high efficiency for improving the performance of GPS and GLONASS solutions for the PPP measurement technology in air navigation.

Download Full-text

Comparisons of CODE and CNES/CLS GPS satellite bias products and applications in Sentinel-3 satellite precise orbit determination

GPS Solutions ◽

10.1007/s10291-021-01164-5 ◽

2021 ◽

Vol 25 (4) ◽

Author(s):

Bingbing Duan ◽

Urs Hugentobler

Keyword(s):

Linear Combination ◽

Orbit Determination ◽

Fractional Part ◽

Precise Orbit Determination ◽

Satellite Orbit ◽

Satellite Orbits ◽

Satellite Clock ◽

Analysis Center ◽

Wide Lane ◽

Total Difference

AbstractTo resolve undifferenced GNSS phase ambiguities, dedicated satellite products are needed, such as satellite orbits, clock offsets and biases. The International GNSS Service CNES/CLS analysis center provides satellite (HMW) Hatch-Melbourne-Wübbena bias and dedicated satellite clock products (including satellite phase bias), while the CODE analysis center provides satellite OSB (observable-specific-bias) and integer clock products. The CNES/CLS GPS satellite HMW bias products are determined by the Hatch-Melbourne-Wübbena (HMW) linear combination and aggregate both code (C1W, C2W) and phase (L1W, L2W) biases. By forming the HMW linear combination of CODE OSB corrections on the same signals, we compare CODE satellite HMW biases to those from CNES/CLS. The fractional part of GPS satellite HMW biases from both analysis centers are very close to each other, with a mean Root-Mean-Square (RMS) of differences of 0.01 wide-lane cycles. A direct comparison of satellite narrow-lane biases is not easily possible since satellite narrow-lane biases are correlated with satellite orbit and clock products, as well as with integer wide-lane ambiguities. Moreover, CNES/CLS provides no satellite narrow-lane biases but incorporates them into satellite clock offsets. Therefore, we compute differences of GPS satellite orbits, clock offsets, integer wide-lane ambiguities and narrow-lane biases (only for CODE products) between CODE and CNES/CLS products. The total difference of these terms for each satellite represents the difference of the narrow-lane bias by subtracting certain integer narrow-lane cycles. We call this total difference “narrow-lane” bias difference. We find that 3% of the narrow-lane biases from these two analysis centers during the experimental time period have differences larger than 0.05 narrow-lane cycles. In fact, this is mainly caused by one Block IIA satellite since satellite clock offsets of the IIA satellite cannot be well determined during eclipsing seasons. To show the application of both types of GPS products, we apply them for Sentinel-3 satellite orbit determination. The wide-lane fixing rates using both products are more than 98%, while the narrow-lane fixing rates are more than 95%. Ambiguity-fixed Sentinel-3 satellite orbits show clear improvement over float solutions. RMS of 6-h orbit overlaps improves by about a factor of two. Also, we observe similar improvements by comparing our Sentinel-3 orbit solutions to the external combined products. Standard deviation value of Satellite Laser Ranging residuals is reduced by more than 10% for Sentinel-3A and more than 15% for Sentinel-3B satellite by fixing ambiguities to integer values.

Download Full-text

Wide range and highly linear signal processed systematic humidity sensor array using Methylene Blue and Graphene composite

Scientific Reports ◽

10.1038/s41598-021-95977-6 ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Muhammad Umair Khan ◽

Gul Hassan ◽

Rayyan Ali Shaukat ◽

Qazi Muhammad Saqib ◽

Mahesh Y. Chougale ◽

...

Keyword(s):

Methylene Blue ◽

Linear Combination ◽

Linear Function ◽

Humidity Sensor ◽

Sensor Array ◽

Combination Method ◽

Humidity Sensing ◽

Sensing Applications ◽

Wide Range ◽

Graphene Flakes

AbstractThis paper proposes a signal processed systematic 3 × 3 humidity sensor array with all range and highly linear humidity response based on different particles size composite inks and different interspaces of interdigital electrodes (IDEs). The fabricated sensors are patterned through a commercial inkjet printer and the composite of Methylene Blue and Graphene with three different particle sizes of bulk Graphene Flakes (BGF), Graphene Flakes (GF), and Graphene Quantum Dots (GQD), which are employed as an active layer using spin coating technique on three types of IDEs with different interspaces of 300, 200, and 100 µm. All range linear function (0–100% RH) is achieved by applying the linear combination method of nine sensors in the signal processing field, where weights for linear combination are required, which are estimated by the least square solution. The humidity sensing array shows a fast response time (Tres) of 0.2 s and recovery time (Trec) of 0.4 s. From the results, the proposed humidity sensor array opens a new gateway for a wide range of humidity sensing applications with a linear function.

Download Full-text

A Model Reconstruction Method of Blade Repair Based on Linear Combination

International Journal of Precision Engineering and Manufacturing ◽

10.1007/s12541-020-00449-y ◽

2021 ◽

Vol 22 (3) ◽

pp. 383-394

Author(s):

Baohai Wu ◽

Hai Zheng ◽

Ying Zhang ◽

Ming Luo ◽

Dinghua Zhang

Keyword(s):

Linear Combination ◽

Reconstruction Method ◽

Model Reconstruction ◽

Blade Repair

Download Full-text

Demographic Variables, Delay Discounting Models and Dysfunctional Personality Traits as Predictors of Financial Risk-Tolerance Among Community-Dwelling Italian Adults

Journal of Interdisciplinary Economics ◽

10.1177/02601079211032117 ◽

2021 ◽

pp. 026010792110321

Author(s):

Antonella Somma ◽

Rebecca Sergi ◽

Chiara Pagliara ◽

Clelia Di Serio ◽

Andrea Fossati

Keyword(s):

Personality Traits ◽

Linear Combination ◽

Delay Discounting ◽

Financial Risk ◽

Short Form ◽

Demographic Variables ◽

Risk Tolerance ◽

Community Dwelling ◽

Self Report ◽

Financial Risk Tolerance

To evaluate the effect of demographic variables, delay discounting and dysfunctional personality traits on financial risk tolerance (FRT), 281 community-dwelling adults were administered the Italian translations of the Risk-Tolerance Scale (RTS), Monetary Choice Questionnaire, Probability Discounting Questionnaire, and Personality Inventory for DSM-5-Short Form (PID-5-SF) self-report questionnaires through an online platform. Hierarchical robust regression results showed that the linear combination of demographic variables (gender and active worker status), delay discounting measures and selected PID-5-SF trait scale scores (i.e., Attention Seeking and Risk Taking) explained roughly 39% of the RTS total score. As a whole, our findings underscore the role of demographic characteristics, dysfunctional personality traits and delay discounting in FRT expression. As a result, FRT is likely to represent the linear combination of several factors that should be assessed in order to understand FRT and prevent erroneous choices among lay investors.

Download Full-text