Second and Third Order Ionospheric Effects on GNSS Positioning: A Case Study in Brazil

The Global Positioning System (GPS) transmits signals in two frequencies. It allows the correction of the first order ionospheric effect by using the ionosphere free combination. However, the second and third order ionospheric effects, which combined may cause errors of the order of centimeters in the GPS measurements, still remain. In this paper the second and third order ionospheric effects, which were taken into account in the GPS data processing in the Brazilian region, were investigated. The corrected and not corrected GPS data from these effects were processed in the relative and precise point positioning (PPP) approaches, respectively, using Bernese V5.0 software and the PPP software (GPSPPP) from NRCAN (Natural Resources Canada). The second and third order corrections were applied in the GPS data using an in-house software that is capable of reading a RINEX file and applying the corrections to the GPS observables, creating a corrected RINEX file. For the relative processing case, a Brazilian network with long baselines was processed in a daily solution considering a period of approximately one year. For the PPP case, the processing was accomplished using data collected by the IGS FORT station considering the period from 2001 to 2006 and a seasonal analysis was carried out, showing a semi-annual and an annual variation in the vertical component. In addition, a geographical variation analysis in the PPP for the Brazilian region has confirmed that the equatorial regions are more affected by the second and third order ionospheric effects than other regions.

RINEX_HO: second- and third-order ionospheric corrections for RINEX observation files

When GNSS receivers capable of collecting dual-frequency data are available, it is possible to eliminate the first-order ionospheric effect in the data processing through the ionosphere-free linear combination. However, the second- and third-order ionospheric effects still remain. The first-, second- and third-order ionospheric effects are directly proportional to the total electron content (TEC), although the second- and third-order effects are influenced, respectively, by the geomagnetic field and the maximum electron density. In recent years, the international scientific community has given more attention to these kinds of effects and some works have shown that for high precision GNSS positioning these effects have to be taken into consideration. We present a software tool called RINEX_HO that was developed to correct GPS observables for second- and third-order ionosphere effects. RINEX_HO requires as input a RINEX observation file, then computes the second- and third-order ionospheric effects, and applies the corrections to the original GPS observables, creating a corrected RINEX file. The mathematical models implemented to compute these effects are presented, as well as the transformations involving the earth's magnetic field. The use of TEC from global ionospheric maps and TEC calculated from raw pseudorange measurements or pseudoranges smoothed by phase is also investigated.

Higher order ionospheric effects in GNSS positioning in the European region

After removal of the Selective Availability in 2000, the ionosphere became the dominant error source for Global Navigation Satellite Systems (GNSS), especially for the high-accuracy (cm-mm) demanding applications like the Precise Point Positioning (PPP) and Real Time Kinematic (RTK) positioning.The common practice of eliminating the ionospheric error, e. g. by the ionosphere free (IF) observable, which is a linear combination of observables on two frequencies such as GPS L1 and L2, accounts for about 99% of the total ionospheric effect, known as the first order ionospheric effect (Ion1). The remaining 1% residual range errors (RREs) in the IF observable are due to the higher - second and third, order ionospheric effects, Ion2 and Ion3, respectively. Both terms are related with the electron content along the signal path; moreover Ion2 term is associated with the influence of the geomagnetic field on the ionospheric refractive index and Ion3 with the ray bending effect of the ionosphere, which can cause significant deviation in the ray trajectory (due to strong electron density gradients in the ionosphere) such that the error contribution of Ion3 can exceed that of Ion2 (Kim and Tinin, 2007).The higher order error terms do not cancel out in the (first order) ionospherically corrected observable and as such, when not accounted for, they can degrade the accuracy of GNSS positioning, depending on the level of the solar activity and geomagnetic and ionospheric conditions (Hoque and Jakowski, 2007). Simulation results from early 1990s show that Ion2 and Ion3 would contribute to the ionospheric error budget by less than 1% of the Ion1 term at GPS frequencies (Datta-Barua et al., 2008). Although the IF observable may provide sufficient accuracy for most GNSS applications, Ion2 and Ion3 need to be considered for higher accuracy demanding applications especially at times of higher solar activity.This paper investigates the higher order ionospheric effects (Ion2 and Ion3, however excluding the ray bending effects associated with Ion3) in the European region in the GNSS positioning considering the precise point positioning (PPP) method. For this purpose observations from four European stations were considered. These observations were taken in four time intervals corresponding to various geophysical conditions: the active and quiet periods of the solar cycle, 2001 and 2006, respectively, excluding the effects of disturbances in the geomagnetic field (i.e. geomagnetic storms), as well as the years of 2001 and 2003, this time including the impact of geomagnetic disturbances. The program RINEX_HO (Marques et al., 2011) was used to calculate the magnitudes of Ion2 and Ion3 on the range measurements as well as the total electron content (TEC) observed on each receiver-satellite link. The program also corrects the GPS observation files for Ion2 and Ion3; thereafter it is possible to perform PPP with both the original and corrected GPS observation files to analyze the impact of the higher order ionospheric error terms excluding the ray bending effect which may become significant especially at low elevation angles (Ioannides and Strangeways, 2002) on the estimated station coordinates.

Comparing lock-in ranges and transient responses of second- and third-order phase-locked loops in master-slave clock distribution networks

The distribution of clock signals throughout the nodes of a network is essential for several applications. in control and communication with the phase-locked loop (PLL) being the component for electronic synchronization process. In systems with master-slave (MS) strategies, the PLLs are the slave nodes responsible for providing reliable clocks in all nodes of the network. As PLLs have nonlinear phase detection, double-frequency terms appear and filtering becomes necessary. Imperfections in filtering process cause oscillations around the synchronous state worsening the performance of the clock distribution process. The behavior of one-way master-slave (OWMS) clock distribution networks is studied and performances of first- and second-order filter processes are compared, concerning lock-in ranges and responses to perturbations of the synchronous state. (c) 2007 Elsevier GmbH. All rights reserved.

Tunable compensation of second and third order dispersion by non-uniformly strained chirped fibre Bragg grating

A novel fibre grating device is demonstrated with tuneable chromatic dispersion slope. The tuning range is 70 to 190 ps/nm and 0 to 25 ps/nm2 for the second and third order dispersion, respectively.

Efeitos de segunda e terceira ordem da ionosfera no posicionamento GNSS no Brasil

O Sistema de Posicionamento Global (GPS) transmite seus sinais em duas freqüências, o que permite eliminar matematicamente os efeitos de primeira ordem da ionosfera através da combinação linear ionosphere free. Porém, restam os efeitos de segunda e terceira ordem, os quais podem provocar erros da ordem de centímetros nas medidas GPS. Esses efeitos, geralmente, são negligenciados no processamento dos dados GPS. Os efeitos ionosféricos de primeira, segunda e terceira ordem são diretamente proporcionais ao TEC presente na ionosfera, porém, no caso dos efeitos de segunda e terceira ordem, comparecem também o campo magnético da Terra e a máxima densidade de elétrons, respectivamente. Nesse artigo, os efeitos de segunda e terceira ordem da ionosfera são investigados, sendo que foram levados em consideração no processamento de dados GPS na região brasileira para fins de posicionamento. Serão apresentados os modelos matemáticos associados a esses efeitos, as transformações envolvendo o campo magnético da Terra e a utilização do TEC advindo dos Mapas Globais da Ionosfera ou calculados a partir das observações GPS de pseudodistância. O processamento dos dados GPS foi realizado considerando o método relativo estático e cinemático e o posicionamento por ponto preciso (PPP). Os efeitos de segunda e terceira ordem foram analisados considerando períodos de alta e baixa atividade ionosférica. Os resultados mostraram que a não consideração desses efeitos no posicionamento por ponto preciso e no posicionamento relativo para linhas de base longas pode introduzir variações da ordem de poucos milímetros nas coordenadas das estações, além de variações diurnas em altitude da ordem de centímetros.

Influência da ionosfera no posicionamento GPS: estimativas dos resíduos no contexto de duplas diferenças e eliminação dos efeitos de 2ª e 3ª ordem

Pós-graduação em Ciências Cartográficas - FCT

Effects of instruction on first, second and third grade children's ability to decenter when assessed on discrimination between contrasting musical characteristics

This experimental study sought to determine the effect of instruction on the abilities of first through third grade children to single and double discriminate contrasting musical characteristics. Six samples were used. The experimental variable consisted of four sessions designed to teach children to distinguish between fast/slow and smooth/choppy musical excerpts. Subjects were tested on their single/double discrimination abilities following the treatment sessions. Results show that first and second grade experimental groups scored significantly higher on single discrimination items than their control groups. On the double discrimination accuracy section the experimental second, third and control first graders were significantly higher than their counter-groups. These findings demonstrated that the four treatment sessions have a profound effect on first and second grade children's abilities to make single discriminations. They also show that success in making double discriminations may depend more on the individual subjects. Further investigation would be beneficial.

The impact of labour market status on second and higher-order births. A comparative study of Denmark, Italy, Spain and United Kingdom

This paper investigates the effects of women‘s labour force participation on fertility, as well as the effects of the combined labour force participation of both members of a couple. It specifically focuses on such dimensions as unemployment, earnings, temporary contracts and part-time jobs, and it shows that their effects differ in accordance with national institutions and labour market regulations. Event-history methods and a longitudinal sample of the European Community Household Panel are used in the analyses, concerning the years 1993-2000. The results show that labour market insecurity of one or both members of a couple has a particularly strong impact in reducing birth rates in the Southern European countries studied. The more conventional model of men’s employment combined with housewifery has a positive impact on second or higher order births in United Kingdom, Spain and Italy, while in Denmark the effect is the opposite. These differences are consistent with different national models of combining parental responsibilities and participation by gender across the life course.

Analysis of nonlinear diffusion equations of second and fourth order

Wegen der fortschreitenden Miniaturisierung von Halbleiterbauteilen spielen Quanteneffekte eine immer wichtigere Rolle. Quantenphänomene werden gewöhnlich durch kinetische Gleichungen beschrieben, aber manchmal hat eine fluid-dynamische Beschreibung Vorteile: die bessere Nutzbarkeit für numerische Simulationen und die einfachere Vorgabe von Randbedingungen. In dieser Arbeit werden drei Diffusionsgleichungen zweiter und vierter Ordnung untersucht. Der erste Teil behandelt die implizite Zeitdiskretisierung und das Langzeitverhalten einer degenerierten Fokker-Planck-Gleichung. Der zweite Teil der Arbeit besteht aus der Untersuchung des viskosen Quantenhydrodynamischen Modells in einer Raumdimension und dessen Langzeitverhaltens. Im letzten Teil wird die Existenz von Lösungen einer parabolischen Gleichung vierter Ordnung in einer Raumdimension bewiesen, und deren Langzeitverhalten studiert.

Ultrasound feedback and motivational interviewing targeting smoking cessation in the second and third trimesters of pregnancy.

INTRODUCTION: Cigarette smoking during pregnancy is associated with poor maternal and child health outcomes. Effective interventions to increase smoking cessation rates are needed particularly for pregnant women unable to quit in their first trimester. Real-time ultrasound feedback focused on potential effects of smoking on the fetus may be an effective treatment adjunct, improving smoking outcomes. METHODS: A prospective randomized trial was conducted to evaluate the efficacy of a smoking cessation intervention consisting of personalized feedback during ultrasound plus motivational interviewing-based counseling sessions. Pregnant smokers (N = 360) between 16 and 26 weeks of gestation were randomly assigned to one of three groups: Best Practice (BP) only, Best Practice plus ultrasound feedback (BP+US), or Motivational Interviewing-based counseling plus ultrasound feedback (MI+US). Assessments were conducted at baseline and end of pregnancy (EOP). RESULTS: Analyses of cotinine-verified self-reported smoking status at EOP indicated that 10.8% of the BP group was not smoking at EOP; 14.2% in the BP+US condition and 18.3% who received MI+US were abstinent, but differences were not statistically significant. Intervention effects were found conditional upon level of baseline smoking, however. Nearly 34% of light smokers (< or =10 cigarettes/day) in the MI+US condition were abstinent at EOP, followed by 25.8% and 15.6% in the BP+US and BP conditions, respectively. Heavy smokers (>10 cigarettes/day) were notably unaffected by the intervention. DISCUSSION: Future research should confirm benefit of motivational interviewing plus ultrasound feedback for pregnant light smokers and explore mechanisms of action. Innovative interventions for pregnant women smoking at high levels are sorely needed.

Influence of unilateral maxillary first molar extraction treatment on second and third molar inclination in Class II subdivision patients.

OBJECTIVE To assess the maxillary second molar (M2) and third molar (M3) inclination following orthodontic treatment of Class II subdivision malocclusion with unilateral maxillary first molar (M1) extraction. MATERIALS AND METHODS Panoramic radiographs of 21 Class II subdivision adolescents (eight boys, 13 girls; mean age, 12.8 years; standard deviation, 1.7 years) before treatment, after treatment with extraction of one maxillary first molar and Begg appliances and after at least 1.8 years in retention were retrospectively collected from a private practice. M2 and M3 inclination angles (M2/ITP, M2/IOP, M3/ITP, M3/IOP), constructed by intertuberosity (ITP) and interorbital planes (IOP), were calculated for the extracted and nonextracted segments. Random effects regression analysis was performed to evaluate the effect on the molar angulation of extraction, time, and gender after adjusting for baseline measurements. RESULTS Time and extraction status were significant predictors for M2 angulation. M2/ITP and M2/IOP decreased by 4.04 (95% confidence interval [CI]: -6.93, 1.16; P  =  .001) and 3.67 (95% CI: -6.76, -0.58; P  =  .020) in the extraction group compared to the nonextraction group after adjusting for time and gender. The adjusted analysis showed that extraction was the only predictor for M3 angulation that reached statistical significance. M3 mesial inclination increased by 7.38° (95% CI: -11.2, -3.54; P < .001) and 7.33° (95% CI: -11.48, -3.19; P  =  .001). CONCLUSIONS M2 and M3 uprighting significantly improved in the extraction side after orthodontic treatment with unilateral maxillary M1 extraction. There was a significant increase in mesial tipping of maxillary second molar crowns over time.

Mach bands and multiscale models of spatial vision:the role of first, second, and third derivative operators in encoding bars and edges

Ernst Mach observed that light or dark bands could be seen at abrupt changes of luminance gradient in the absence of peaks or troughs in luminance. Many models of feature detection share the idea that bars, lines, and Mach bands are found at peaks and troughs in the output of even-symmetric spatial filters. Our experiments assessed the appearance of Mach bands (position and width) and the probability of seeing them on a novel set of generalized Gaussian edges. Mach band probability was mainly determined by the shape of the luminance profile and increased with the sharpness of its corners, controlled by a single parameter (n). Doubling or halving the size of the images had no significant effect. Variations in contrast (20%-80%) and duration (50-300 ms) had relatively minor effects. These results rule out the idea that Mach bands depend simply on the amplitude of the second derivative, but a multiscale model, based on Gaussian-smoothed first- and second-derivative filtering, can account accurately for the probability and perceived spatial layout of the bands. A key idea is that Mach band visibility depends on the ratio of second- to first-derivative responses at peaks in the second-derivative scale-space map. This ratio is approximately scale-invariant and increases with the sharpness of the corners of the luminance ramp, as observed. The edges of Mach bands pose a surprisingly difficult challenge for models of edge detection, but a nonlinear third-derivative operation is shown to predict the locations of Mach band edges strikingly well. Mach bands thus shed new light on the role of multiscale filtering systems in feature coding. © 2012 ARVO.

Correlation between placental thickness in the second and third trimester and fetal weight

PURPOSE: To investigate relationship between placental thickness during the second and third trimesters and placental and birth weights. METHODS: From January 2011 to June 2012, a total of 250 singleton pregnant women presented at our antenatal clinic were enrolled in this prospective study. All recruited women were assessed at the 1st trimester screening for baseline demographic and obstetric data. The placental thickness was measured trans-abdominally by placing the ultrasound transducer perpendicularly to the plane of the placenta, in the area of the cord insertion at second and third trimester. Pearson's correlation analysis was used to establish the degree of relationship between placental thickness and birth and placental weights. RESULTS: Of 250 recruited participants, 205 women were able to complete the study. The mean age of cases was 26.4±5.1. Values of mean birth and placental weights were 305.56±657.0 and 551.7±104.8 grams respectively. Ultrasonographic measures of placental thickness in second and third trimester and changes between them were 21.68±4.52, 36.26±6.46 and 14.67±5.67 mm respectively. There was a significant positive correlation between placental thickness and birth weight in the second and third trimesters (r=0.15, p=0.03; r=0.14, p=0.04 correspondingly). CONCLUSION: According to our study, birth weight has a positive relation with both second and third trimester placental thickness; however, placental thickness change could not predict low birth weight.

Uterine Doppler velocimetry of the uterine arteries in the second and third trimesters for the prediction of gestational outcome

PURPOSE: The aim of this longitudinal study was to investigate the value of uterine artery Doppler sonography during the second and third trimesters in the prediction of adverse pregnancy outcome in low-risk women. METHODS: From July 2011 to August 2012, a total of 205 singleton pregnant women presenting at our antenatal clinic were enrolled in this prospective study and were assessed for baseline demographic and obstetric data. They underwent ultrasound evaluation at the time of second and third trimesters, both included Doppler assessment of bilateral uterine arteries to determine the values of the pulsatility index (PI) and resistance index (RI) and presence of early diastolic notch. The endpoint of this study was assessing the sensitivity, specificity, positive predictive value (PPV) and negative predictive value (NPV) of Doppler ultrasonography of the uterine artery, for the prediction of adverse pregnancy outcomes including preeclampsia, stillbirth, placental abruption and preterm labor. RESULTS: The mean age of cases was 26.4±5.11. The uterine artery PI and RI values for both second (PI: 1.1±0.42 versus 1.53±0.59, p=0.002; RI: 0.55±0.09 versus 0.72±0.13, p=0.000 respectively) and third-trimester (PI: 0.77±0.31 versus 1.09±0.46, p=0.000; RI: 0.46±0.10 versus 0.60±0.14, p=0.010 respectively) evaluations were significantly higher in patients with adverse pregnancy outcome than in normal women. Combination of PI and RI >95th percentile and presence of bilateral notch in second trimester get sensitivity and specificity of 36.1 and 97% respectively, while these measures were 57.5 and 98.2% in third trimester. CONCLUSIONS: According to our study, it seems that uterine artery Doppler may be a valuable tool for the prediction of a variety of adverse outcomes in second and third trimesters.