Efficient estimation of a normalised correlation function from discrete-time samples

1993 ◽  
Vol 29 (16) ◽  
pp. 1398
Author(s):  
W.J. Szajnowski
Keyword(s):  
Correlation Function ◽  
Discrete Time ◽  
Efficient Estimation

scholarly journals METODE DUAL KANAL UNTUK ESTIMASI KEDALAMAN DI PERAIRAN DANGKAL MENGGUNAKAN DATA SPOT 6 STUDI KASUS : TELUK LAMPUNG (DUAL BAND METHOD FOR BATHYMETRY ESTIMATION IN SHALLOW WATERS DEPTH USING SPOT 6 DATA CASE STUDY: LAMPUNG BAY)

2017 ◽  
Vol 14 (1) ◽  
Author(s):  
Muchlisin Arief ◽  
Syifa Wismayati Adawiah ◽  
Ety Parwati ◽  
Sartono Marpaung
Keyword(s):  
Correlation Function ◽  
Linear Equations ◽  
Depth Estimation ◽  
Efficient Estimation ◽  
Dual Band ◽  
Sensing Technology ◽  
Band Method ◽  
Rms Error ◽  
The Difference ◽  
Dark Pixel

Depth data can be used to produce seabed profile, oceanography, biology, and sea level rise. Remote sensing technology can be used to estimate the depth of shallow marine waters characterized by the ability of light to penetrate water bodies. One image that can estimate the depth is SPOT 6 which has three visible canals and one NIR channel with 6 meter spatial resolution. This study used SPOT 6 image on March 22, 2015. The image was first being  dark pixel atmospheric corrected by making 30 polygons. The originality of this method was to build a correlation between the dark pixel value of red and green channels with the depth of the field measurement results, made on June 3 to 9, 2015. The algorithm  derived experimentally consisted of: thresholding which served to separate the land by the sea and the correlation function. The correlation function was obtained: first correlating the observation value with each band, then calculating the difference of minimum pixel darkness value and minimum for red and green channel was 0.056 and 0.0692. The model was then constructed by using the comparison proportions, so that the linear equations were obtained in two channels: Z (X1, X2) = 406.26 X1 + 327.21 X2 - 28.48. Depth estimation results were for a 5-meter scale, the most efficient estimation with the smallest error relative mean occured in shallow water depth from 20 to 25 meters, while the result of   10 meters scale from 20 to 30 meters and the estimated depth hadsimilar patterns or could be said close to reality. This method was able to detect sea depths up to 25 meters and had a small RMS error of 0.653246 meters. Thus the two-channel method coukd offer a fast, flexible, efficient, and economical solution to map topography of the ocean floor.AbstrakData kedalaman dapat digunakan untuk menghasilkan profil dasar laut, oseanografi, biologi, dan kenaikan muka air laut. Teknologi penginderaan jauh dapat digunakan untuk mengestimasi kedalaman perairan laut dangkal yang ditandai dengan kemampuan cahaya untuk menembus badan air. Salah satu citra yang mampu mengestimasi kedalaman tersebut adalah SPOT 6 yang memiliki tiga kanal visible dan satu kanal NIR dengan resolusi spasial 6 meter. Pada penelitian ini, Citra SPOT-6 yang digunakan adalah 22 Maret 2015. Citra terlebih dahulu dilakukan koreksi atmosferik dark pixel dengan membuat 30 poligon. Originalitas dari metode ini adalah membangun suatu korelasi antara nilai dark pixel kanal merah dan hijau dengan nilai kedalaman hasil pengukuran lapangan yang dilakukan pada 3 sampai dengan 9 Juni 2015. Algoritma diturunkan secara eksperimen yang terdiri dari thresholding yang berfungsi untuk memisahkan daratan dengan lautan dan fungsi korelasi. Fungsi korelasi diperoleh pertama-tama mengkorelasikan nilai pengamatan dengan masing-masing band, kemudian menghitung selisih nilai dark pixel maksimum dan minimum untuk kanal merah dan hijau yaitu 0,056 dan 0,0692. Selanjutnya, dibangun model dengan menggunakan dalil perbandingan sehingga diperoleh persamaan linier dalam dua kanal yaitu: Z(X1,X2) = 406,26 X1 + 327,21 X2 – 28,48. Hasil estimasi kedalaman, untuk skala 5 meter, estimasi yang paling efisien dengan Mean relatif error terkecil terjadi pada kedalaman perairan dangkal dari 20 sampai dengan 25 meter, sedangkan untuk skala 10 meter dari 20 sampai dengan 30 meter dan juga hasil estimasi kedalaman yang diperoleh mempunyai pola kemiripan atau dapat dikatakan mendekati kenyataan. Metode ini mampu mendeteksi kedalaman laut hingga 25 meter dan mempunyai RMS error yang kecil yaitu 0,653246 meter. Dengan demikian, metode dua kanal ini dapat menawarkan solusi cepat, fleksibel, efisien, dan ekonomis untuk memetakan topografi dasar laut.

scholarly journals A FAMILY OF CHAOTIC BILLIARDS WITH VARIABLE MIXING RATES

2005 ◽  
Vol 05 (04) ◽  
pp. 535-553 ◽  
Author(s):  
N. CHERNOV ◽  
H.-K. ZHANG
Keyword(s):  
Correlation Function ◽  
Discrete Time ◽  
Parameter Family ◽  
The Family ◽  
Mixing Rates ◽  
Chaotic Billiards ◽  
Explicit Relation

We describe a one-parameter family of dispersing (hence hyperbolic, ergodic and mixing) billiards where the correlation function of the collision map decays as 1/na (here n denotes the discrete time), in which the degree a ∈ (1, ∞) changes continuously with the parameter of the family, β. We also derive an explicit relation between the degree a and the family parameter β.

The Effect of Partly Missing Covariates on Statistical Power in Randomized Controlled Trials With Discrete-Time Survival Endpoints

Methodology ◽  
2017 ◽  
Vol 13 (2) ◽  
pp. 41-60
Author(s):  
Shahab Jolani ◽  
Maryam Safarkhani
Keyword(s):  
Randomized Controlled Trials ◽  
Discrete Time ◽  
Treatment Effect ◽  
Survival Data ◽  
Controlled Trials ◽  
Missing Covariates ◽  
Indicator Method ◽  
Imputation Methods ◽  
Randomized Controlled ◽  
Baseline Covariates

Abstract. In randomized controlled trials (RCTs), a common strategy to increase power to detect a treatment effect is adjustment for baseline covariates. However, adjustment with partly missing covariates, where complete cases are only used, is inefficient. We consider different alternatives in trials with discrete-time survival data, where subjects are measured in discrete-time intervals while they may experience an event at any point in time. The results of a Monte Carlo simulation study, as well as a case study of randomized trials in smokers with attention deficit hyperactivity disorder (ADHD), indicated that single and multiple imputation methods outperform the other methods and increase precision in estimating the treatment effect. Missing indicator method, which uses a dummy variable in the statistical model to indicate whether the value for that variable is missing and sets the same value to all missing values, is comparable to imputation methods. Nevertheless, the power level to detect the treatment effect based on missing indicator method is marginally lower than the imputation methods, particularly when the missingness depends on the outcome. In conclusion, it appears that imputation of partly missing (baseline) covariates should be preferred in the analysis of discrete-time survival data.

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