EE 570: Location and Navigation
|
|
- Αἴσων Αυγερινός
- 5 χρόνια πριν
- Προβολές:
Transcript
1 EE 570: Locatio ad Navigatio INS Iitializatio Aly El-Osery Electrical Egieerig Departmet, New Mexico Tech Socorro, New Mexico, USA April 25, 2013 Aly El-Osery (NMT) EE 570: Locatio ad Navigatio April 25, / 10
2 Overview Positio, velocity ad attitude drift uless the INS is aided. There are some opportuistic situatios that provide iformatio to the INS to iitialize itself. Two categories of aligmet Coarse Aligmet Fie Aligmet Aly El-Osery (NMT) EE 570: Locatio ad Navigatio April 25, / 10
3 Self-Aligmet 1 Coarse Aligmet: Use kowledge of the gravity vector ad earth rate provided y the three accelerometers, ad the kowledge of the earth rate vector provided y the gyroscopes. 2 Fie Aligmet: Needed i quasi-statioary situatios. Uses the fact that ay positio, velocity chages are cosidered disturaces, ad the kowledge of the gravity vector ad earth rate to estimate the ody s attitude. Latitude eeds to e kow. Aly El-Osery (NMT) EE 570: Locatio ad Navigatio April 25, / 10
4 Coarse Aligmet: Approach 1 f i = C 0 0 = g Oly provides pitch ad roll agles g (+ve) si(θ) cos(θ) si(φ) cos(θ) cos(φ) g Aly El-Osery (NMT) EE 570: Locatio ad Navigatio April 25, / 10
5 Coarse Aligmet: Approach 2 where ( f i, ω i, f i ω ) i = Ĉ C 11 C 12 C 13 Ĉ = C 21 C 22 C 23 C 31 C 32 C 33 ( ) f i, ω i, f i ω i C 11 = C 21 = C 31 = ω x ω ie cos(l ) f x ta(l ) g ω y f ω ie cos(l ) y ta(l ) g ω y f ω ie cos(l ) y ta(l ) g C 12 = f z ω y f y ω z gω ie cos(l ) C 22 = f z ω x + f x ω z gω ie cos(l ) C 32 = f y ω x f x ω y gω ie cos(l ) C 13 = f x g C 23 = f y g C 33 = f z g Must esure that the DCM is properly orthogoalized. Aly El-Osery (NMT) EE 570: Locatio ad Navigatio April 25, / 10
6 Fie Aligmet Use full INS mechaizatio Use equivalet to GPS aided error mechaizatio Setup up measuremets 1 Specific force measuremet 2 Agular rate measuremet δ f i = f i ˆ f i δ ω i = ω i ˆ ω i 3 Positio measuremet: deviatio from iitial positio 4 Velocity measuremet: deviatio from zero Aly El-Osery (NMT) EE 570: Locatio ad Navigatio April 25, / 10
7 Specific force measuremet δ f i = f i ˆ f i = f i (I [ δψ ])C ( f i δ f i ) = [ δψ ]C fi δ f i 0 δψ D δψ E 0 δψ D 0 δψ N 0 + Ĉ δ f i + fd δψ E δψ N 0 g 0 g 0 δψ N g 0 0 δψ E + Ĉ δ f i + fd δψ D = G δψ + Ĉ δ f i + fd Recoordiatize i the ody frame δ f = Ĉ G δψ + δ f i + f d δ f i captures ias-drift (sikig) + Markov,... Aly El-Osery (NMT) EE 570: Locatio ad Navigatio April 25, / 10
8 Specific force measuremet Ĉ δ f i = f i ˆ f i = f i (I [ δψ ])C ( f i δ f i ) = [ δψ ]C fi δ f i 0 δψ D δψ E 0 δψ D 0 δψ N 0 + Ĉ δ f i + fd δψ E δψ N 0 g 0 g 0 δψ N g 0 0 δψ E + Ĉ δ f i + fd δψ D = G δψ + Ĉ δ f i + fd Recoordiatize i the ody frame δ f = Ĉ G δψ + δ f i + f d δ f i captures ias-drift (sikig) + Markov,... Aly El-Osery (NMT) EE 570: Locatio ad Navigatio April 25, / 10
9 Agular Rate Measuremet δ ω i = ω i ˆ ω i = (I +[ δψ ])Ĉ ( ω i + ω ) Ĉ ( ω i δ ω i ) 0 Ω D 0 δψ N Ω D 0 Ω N δψ E + Ĉ δ ω i ω d 0 Ω N 0 δψ D = W δψ + Ĉ δ ω i ω d Recoordiatize i the ody frame δ ω i = Ĉ W δψ + δ ω i ω d δ ω i captures ias-drift (sikig) + Markov,... Aly El-Osery (NMT) EE 570: Locatio ad Navigatio April 25, / 10
10 Agular Rate Measuremet δ ω i = ω i ˆ ω i C = (I +[ δψ ])Ĉ ( ω i + ω ) Ĉ ( ω i δ ω i ) 0 Ω D 0 δψ N Ω D 0 Ω N δψ E + Ĉ δ ω i ω d 0 Ω N 0 δψ D = W δψ + Ĉ δ ω i ω d Recoordiatize i the ody frame δ ω i = Ĉ W δψ + δ ω i ω d δ ω i captures ias-drift (sikig) + Markov,... Aly El-Osery (NMT) EE 570: Locatio ad Navigatio April 25, / 10
11 Agular Rate Measuremet δ ω i = ω i ˆ ω i ˆ ω i = ˆ ω ie = (I +[ δψ ])Ĉ ( ω i + ω ) Ĉ ( ω i δ ω i ) 0 Ω D 0 δψ N Ω D 0 Ω N δψ E + Ĉ δ ω i ω d 0 Ω N 0 δψ D = W δψ + Ĉ δ ω i ω d Recoordiatize i the ody frame δ ω i = Ĉ W δψ + δ ω i ω d δ ω i captures ias-drift (sikig) + Markov,... Aly El-Osery (NMT) EE 570: Locatio ad Navigatio April 25, / 10
12 Agular Rate Measuremet δ ω i = ω i ˆ ω i = (I +[ δψ ])Ĉ ( ω i + ω ) Ĉ ( ω i δ ω i ) 0 Ω D 0 δψ N Dev. from statioarity Ω D 0 Ω N δψ E + Ĉ δ ω i ω d 0 Ω N 0 δψ D = W δψ + Ĉ δ ω i ω d Recoordiatize i the ody frame δ ω i = Ĉ W δψ + δ ω i ω d δ ω i captures ias-drift (sikig) + Markov,... Aly El-Osery (NMT) EE 570: Locatio ad Navigatio April 25, / 10
13 Error State ad Measuremet Matrix x(t) = F(t) x(t)+ w(t) y(t) = H(t) x(t)+ v(t) ( ) T x = δ ψ δ v δ r a g I H = 3 3 I Ĉ G I ĈW I 3 3 Aly El-Osery (NMT) EE 570: Locatio ad Navigatio April 25, / 10
14 Challeges There is o mechaism i the aove formulatio to estimate ω d. If it ca e modelled as white oise the the filter will e ale to hadle it. O the other had, if it is correlated type of disturace, additioal measures must e take to accout for it. Aly El-Osery (NMT) EE 570: Locatio ad Navigatio April 25, / 10
EE 570: Location and Navigation
EE 570: Location and Navigation INS Initialization Aly El-Osery Kevin Wedeward Electrical Engineering Department, New Mexico Tech Socorro, New Mexico, USA In Collaboration with Stephen Bruder Electrical
Διαβάστε περισσότεραNavigation Mathematics: Kinematics (Coordinate Frame Transformation) EE 565: Position, Navigation and Timing
Lecture Navigation Mathematics: Kinematics (Coordinate Frame Transformation) EE 565: Position, Navigation and Timing Lecture Notes Update on Feruary 20, 2018 Aly El-Osery and Kevin Wedeward, Electrical
Διαβάστε περισσότεραInertial Navigation Mechanization and Error Equations
Iertial Navigatio Mechaizatio ad Error Equatios 1 Navigatio i Earth-cetered coordiates Coordiate systems: i iertial coordiate system; ECI. e earth fixed coordiate system; ECEF. avigatio coordiate system;
Διαβάστε περισσότεραSUPERPOSITION, MEASUREMENT, NORMALIZATION, EXPECTATION VALUES. Reading: QM course packet Ch 5 up to 5.6
SUPERPOSITION, MEASUREMENT, NORMALIZATION, EXPECTATION VALUES Readig: QM course packet Ch 5 up to 5. 1 ϕ (x) = E = π m( a) =1,,3,4,5 for xa (x) = πx si L L * = πx L si L.5 ϕ' -.5 z 1 (x) = L si
Διαβάστε περισσότεραPhys460.nb Solution for the t-dependent Schrodinger s equation How did we find the solution? (not required)
Phys460.nb 81 ψ n (t) is still the (same) eigenstate of H But for tdependent H. The answer is NO. 5.5.5. Solution for the tdependent Schrodinger s equation If we assume that at time t 0, the electron starts
Διαβάστε περισσότερα1. For each of the following power series, find the interval of convergence and the radius of convergence:
Math 6 Practice Problems Solutios Power Series ad Taylor Series 1. For each of the followig power series, fid the iterval of covergece ad the radius of covergece: (a ( 1 x Notice that = ( 1 +1 ( x +1.
Διαβάστε περισσότεραOutline. Detection Theory. Background. Background (Cont.)
Outlie etectio heory Chapter7. etermiistic Sigals with Ukow Parameters afiseh S. Mazloum ov. 3th Backgroud Importace of sigal iformatio Ukow amplitude Ukow arrival time Siusoidal detectio Classical liear
Διαβάστε περισσότεραEN40: Dynamics and Vibrations
EN40: Dyamics a Vibratios School of Egieerig Brow Uiversity Solutios to Differetial Equatios of Motio for Vibratig Systems Here, we summarize the solutios to the most importat ifferetial equatios of motio
Διαβάστε περισσότεραIIT JEE (2013) (Trigonomtery 1) Solutions
L.K. Gupta (Mathematic Classes) www.pioeermathematics.com MOBILE: 985577, 677 (+) PAPER B IIT JEE (0) (Trigoomtery ) Solutios TOWARDS IIT JEE IS NOT A JOURNEY, IT S A BATTLE, ONLY THE TOUGHEST WILL SURVIVE
Διαβάστε περισσότεραHOMEWORK 4 = G. In order to plot the stress versus the stretch we define a normalized stretch:
HOMEWORK 4 Problem a For the fast loading case, we want to derive the relationship between P zz and λ z. We know that the nominal stress is expressed as: P zz = ψ λ z where λ z = λ λ z. Therefore, applying
Διαβάστε περισσότεραHW 3 Solutions 1. a) I use the auto.arima R function to search over models using AIC and decide on an ARMA(3,1)
HW 3 Solutions a) I use the autoarima R function to search over models using AIC and decide on an ARMA3,) b) I compare the ARMA3,) to ARMA,0) ARMA3,) does better in all three criteria c) The plot of the
Διαβάστε περισσότεραOutline. M/M/1 Queue (infinite buffer) M/M/1/N (finite buffer) Networks of M/M/1 Queues M/G/1 Priority Queue
Queueig Aalysis Outlie M/M/ Queue (ifiite buffer M/M//N (fiite buffer M/M// (Erlag s B forula M/M/ (Erlag s C forula Networks of M/M/ Queues M/G/ Priority Queue M/M/ M: Markovia/Meoryless Arrival process
Διαβάστε περισσότερα[1] P Q. Fig. 3.1
1 (a) Define resistance....... [1] (b) The smallest conductor within a computer processing chip can be represented as a rectangular block that is one atom high, four atoms wide and twenty atoms long. One
Διαβάστε περισσότεραApproximation of distance between locations on earth given by latitude and longitude
Approximation of distance between locations on earth given by latitude and longitude Jan Behrens 2012-12-31 In this paper we shall provide a method to approximate distances between two points on earth
Διαβάστε περισσότερα6.1. Dirac Equation. Hamiltonian. Dirac Eq.
6.1. Dirac Equation Ref: M.Kaku, Quantum Field Theory, Oxford Univ Press (1993) η μν = η μν = diag(1, -1, -1, -1) p 0 = p 0 p = p i = -p i p μ p μ = p 0 p 0 + p i p i = E c 2 - p 2 = (m c) 2 H = c p 2
Διαβάστε περισσότεραBiorthogonal Wavelets and Filter Banks via PFFS. Multiresolution Analysis (MRA) subspaces V j, and wavelet subspaces W j. f X n f, τ n φ τ n φ.
Chapter 3. Biorthogoal Wavelets ad Filter Baks via PFFS 3.0 PFFS applied to shift-ivariat subspaces Defiitio: X is a shift-ivariat subspace if h X h( ) τ h X. Ex: Multiresolutio Aalysis (MRA) subspaces
Διαβάστε περισσότεραHomework for 1/27 Due 2/5
Name: ID: Homework for /7 Due /5. [ 8-3] I Example D of Sectio 8.4, the pdf of the populatio distributio is + αx x f(x α) =, α, otherwise ad the method of momets estimate was foud to be ˆα = 3X (where
Διαβάστε περισσότεραPresentation of complex number in Cartesian and polar coordinate system
1 a + bi, aεr, bεr i = 1 z = a + bi a = Re(z), b = Im(z) give z = a + bi & w = c + di, a + bi = c + di a = c & b = d The complex cojugate of z = a + bi is z = a bi The sum of complex cojugates is real:
Διαβάστε περισσότεραLecture 2: Dirac notation and a review of linear algebra Read Sakurai chapter 1, Baym chatper 3
Lecture 2: Dirac notation and a review of linear algebra Read Sakurai chapter 1, Baym chatper 3 1 State vector space and the dual space Space of wavefunctions The space of wavefunctions is the set of all
Διαβάστε περισσότεραEPL 603 TOPICS IN SOFTWARE ENGINEERING. Lab 5: Component Adaptation Environment (COPE)
EPL 603 TOPICS IN SOFTWARE ENGINEERING Lab 5: Component Adaptation Environment (COPE) Performing Static Analysis 1 Class Name: The fully qualified name of the specific class Type: The type of the class
Διαβάστε περισσότεραPartial Trace and Partial Transpose
Partial Trace and Partial Transpose by José Luis Gómez-Muñoz http://homepage.cem.itesm.mx/lgomez/quantum/ jose.luis.gomez@itesm.mx This document is based on suggestions by Anirban Das Introduction This
Διαβάστε περισσότεραw o = R 1 p. (1) R = p =. = 1
Πανεπιστήµιο Κρήτης - Τµήµα Επιστήµης Υπολογιστών ΗΥ-570: Στατιστική Επεξεργασία Σήµατος 205 ιδάσκων : Α. Μουχτάρης Τριτη Σειρά Ασκήσεων Λύσεις Ασκηση 3. 5.2 (a) From the Wiener-Hopf equation we have:
Διαβάστε περισσότεραPARTIAL NOTES for 6.1 Trigonometric Identities
PARTIAL NOTES for 6.1 Trigonometric Identities tanθ = sinθ cosθ cotθ = cosθ sinθ BASIC IDENTITIES cscθ = 1 sinθ secθ = 1 cosθ cotθ = 1 tanθ PYTHAGOREAN IDENTITIES sin θ + cos θ =1 tan θ +1= sec θ 1 + cot
Διαβάστε περισσότεραHomework 3 Solutions
Homework 3 Solutions Igor Yanovsky (Math 151A TA) Problem 1: Compute the absolute error and relative error in approximations of p by p. (Use calculator!) a) p π, p 22/7; b) p π, p 3.141. Solution: For
Διαβάστε περισσότεραHomework 8 Model Solution Section
MATH 004 Homework Solution Homework 8 Model Solution Section 14.5 14.6. 14.5. Use the Chain Rule to find dz where z cosx + 4y), x 5t 4, y 1 t. dz dx + dy y sinx + 4y)0t + 4) sinx + 4y) 1t ) 0t + 4t ) sinx
Διαβάστε περισσότεραThe Simply Typed Lambda Calculus
Type Inference Instead of writing type annotations, can we use an algorithm to infer what the type annotations should be? That depends on the type system. For simple type systems the answer is yes, and
Διαβάστε περισσότεραSOLUTIONS TO MATH38181 EXTREME VALUES AND FINANCIAL RISK EXAM
SOLUTIONS TO MATH38181 EXTREME VALUES AND FINANCIAL RISK EXAM Solutions to Question 1 a) The cumulative distribution function of T conditional on N n is Pr (T t N n) Pr (max (X 1,..., X N ) t N n) Pr (max
Διαβάστε περισσότεραDESIGN OF MACHINERY SOLUTION MANUAL h in h 4 0.
DESIGN OF MACHINERY SOLUTION MANUAL -7-1! PROBLEM -7 Statement: Design a double-dwell cam to move a follower from to 25 6, dwell for 12, fall 25 and dwell for the remader The total cycle must take 4 sec
Διαβάστε περισσότεραCongruence Classes of Invertible Matrices of Order 3 over F 2
International Journal of Algebra, Vol. 8, 24, no. 5, 239-246 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/.2988/ija.24.422 Congruence Classes of Invertible Matrices of Order 3 over F 2 Ligong An and
Διαβάστε περισσότεραCHAPTER 48 APPLICATIONS OF MATRICES AND DETERMINANTS
CHAPTER 48 APPLICATIONS OF MATRICES AND DETERMINANTS EXERCISE 01 Page 545 1. Use matrices to solve: 3x + 4y x + 5y + 7 3x + 4y x + 5y 7 Hence, 3 4 x 0 5 y 7 The inverse of 3 4 5 is: 1 5 4 1 5 4 15 8 3
Διαβάστε περισσότεραCHAPTER 101 FOURIER SERIES FOR PERIODIC FUNCTIONS OF PERIOD
CHAPTER FOURIER SERIES FOR PERIODIC FUNCTIONS OF PERIOD EXERCISE 36 Page 66. Determine the Fourier series for the periodic function: f(x), when x +, when x which is periodic outside this rge of period.
Διαβάστε περισσότεραΑπόκριση σε Μοναδιαία Ωστική Δύναμη (Unit Impulse) Απόκριση σε Δυνάμεις Αυθαίρετα Μεταβαλλόμενες με το Χρόνο. Απόστολος Σ.
Απόκριση σε Δυνάμεις Αυθαίρετα Μεταβαλλόμενες με το Χρόνο The time integral of a force is referred to as impulse, is determined by and is obtained from: Newton s 2 nd Law of motion states that the action
Διαβάστε περισσότερα12. Radon-Nikodym Theorem
Tutorial 12: Radon-Nikodym Theorem 1 12. Radon-Nikodym Theorem In the following, (Ω, F) is an arbitrary measurable space. Definition 96 Let μ and ν be two (possibly complex) measures on (Ω, F). We say
Διαβάστε περισσότεραthe total number of electrons passing through the lamp.
1. A 12 V 36 W lamp is lit to normal brightness using a 12 V car battery of negligible internal resistance. The lamp is switched on for one hour (3600 s). For the time of 1 hour, calculate (i) the energy
Διαβάστε περισσότεραSection 8.3 Trigonometric Equations
99 Section 8. Trigonometric Equations Objective 1: Solve Equations Involving One Trigonometric Function. In this section and the next, we will exple how to solving equations involving trigonometric functions.
Διαβάστε περισσότεραOn Generating Relations of Some Triple. Hypergeometric Functions
It. Joural of Math. Aalysis, Vol. 5,, o., 5 - O Geeratig Relatios of Some Triple Hypergeometric Fuctios Fadhle B. F. Mohse ad Gamal A. Qashash Departmet of Mathematics, Faculty of Educatio Zigibar Ade
Διαβάστε περισσότεραSOLUTIONS TO MATH38181 EXTREME VALUES AND FINANCIAL RISK EXAM
SOLUTIONS TO MATH38181 EXTREME VALUES AND FINANCIAL RISK EXAM Solutions to Question 1 a) The cumulative distribution function of T conditional on N n is Pr T t N n) Pr max X 1,..., X N ) t N n) Pr max
Διαβάστε περισσότεραLecture 3: Asymptotic Normality of M-estimators
Lecture 3: Asymptotic Istructor: Departmet of Ecoomics Staford Uiversity Prepared by Webo Zhou, Remi Uiversity Refereces Takeshi Amemiya, 1985, Advaced Ecoometrics, Harvard Uiversity Press Newey ad McFadde,
Διαβάστε περισσότεραDERIVATION OF MILES EQUATION FOR AN APPLIED FORCE Revision C
DERIVATION OF MILES EQUATION FOR AN APPLIED FORCE Revision C By Tom Irvine Email: tomirvine@aol.com August 6, 8 Introduction The obective is to derive a Miles equation which gives the overall response
Διαβάστε περισσότεραANSWERSHEET (TOPIC = DIFFERENTIAL CALCULUS) COLLECTION #2. h 0 h h 0 h h 0 ( ) g k = g 0 + g 1 + g g 2009 =?
Teko Classes IITJEE/AIEEE Maths by SUHAAG SIR, Bhopal, Ph (0755) 3 00 000 www.tekoclasses.com ANSWERSHEET (TOPIC DIFFERENTIAL CALCULUS) COLLECTION # Question Type A.Single Correct Type Q. (A) Sol least
Διαβάστε περισσότεραMatrices and Determinants
Matrices and Determinants SUBJECTIVE PROBLEMS: Q 1. For what value of k do the following system of equations possess a non-trivial (i.e., not all zero) solution over the set of rationals Q? x + ky + 3z
Διαβάστε περισσότεραThe Heisenberg Uncertainty Principle
Chemistry 460 Sprig 015 Dr. Jea M. Stadard March, 015 The Heiseberg Ucertaity Priciple A policema pulls Werer Heiseberg over o the Autobah for speedig. Policema: Sir, do you kow how fast you were goig?
Διαβάστε περισσότεραL.K.Gupta (Mathematic Classes) www.pioeermathematics.com MOBILE: 985577, 4677 + {JEE Mai 04} Sept 0 Name: Batch (Day) Phoe No. IT IS NOT ENOUGH TO HAVE A GOOD MIND, THE MAIN THING IS TO USE IT WELL Marks:
Διαβάστε περισσότεραST5224: Advanced Statistical Theory II
ST5224: Advanced Statistical Theory II 2014/2015: Semester II Tutorial 7 1. Let X be a sample from a population P and consider testing hypotheses H 0 : P = P 0 versus H 1 : P = P 1, where P j is a known
Διαβάστε περισσότεραEE512: Error Control Coding
EE512: Error Control Coding Solution for Assignment on Finite Fields February 16, 2007 1. (a) Addition and Multiplication tables for GF (5) and GF (7) are shown in Tables 1 and 2. + 0 1 2 3 4 0 0 1 2 3
Διαβάστε περισσότεραDegenerate Perturbation Theory
R.G. Griffi BioNMR School page 1 Degeerate Perturbatio Theory 1.1 Geeral Whe cosiderig the CROSS EFFECT it is ecessary to deal with degeerate eergy levels ad therefore degeerate perturbatio theory. The
Διαβάστε περισσότεραFourier Series. MATH 211, Calculus II. J. Robert Buchanan. Spring Department of Mathematics
Fourier Series MATH 211, Calculus II J. Robert Buchanan Department of Mathematics Spring 2018 Introduction Not all functions can be represented by Taylor series. f (k) (c) A Taylor series f (x) = (x c)
Διαβάστε περισσότεραSCHOOL OF MATHEMATICAL SCIENCES G11LMA Linear Mathematics Examination Solutions
SCHOOL OF MATHEMATICAL SCIENCES GLMA Linear Mathematics 00- Examination Solutions. (a) i. ( + 5i)( i) = (6 + 5) + (5 )i = + i. Real part is, imaginary part is. (b) ii. + 5i i ( + 5i)( + i) = ( i)( + i)
Διαβάστε περισσότερα4.6 Autoregressive Moving Average Model ARMA(1,1)
84 CHAPTER 4. STATIONARY TS MODELS 4.6 Autoregressive Moving Average Model ARMA(,) This section is an introduction to a wide class of models ARMA(p,q) which we will consider in more detail later in this
Διαβάστε περισσότεραOther Test Constructions: Likelihood Ratio & Bayes Tests
Other Test Constructions: Likelihood Ratio & Bayes Tests Side-Note: So far we have seen a few approaches for creating tests such as Neyman-Pearson Lemma ( most powerful tests of H 0 : θ = θ 0 vs H 1 :
Διαβάστε περισσότεραPhysical DB Design. B-Trees Index files can become quite large for large main files Indices on index files are possible.
B-Trees Index files can become quite large for large main files Indices on index files are possible 3 rd -level index 2 nd -level index 1 st -level index Main file 1 The 1 st -level index consists of pairs
Διαβάστε περισσότεραBayesian statistics. DS GA 1002 Probability and Statistics for Data Science.
Bayesian statistics DS GA 1002 Probability and Statistics for Data Science http://www.cims.nyu.edu/~cfgranda/pages/dsga1002_fall17 Carlos Fernandez-Granda Frequentist vs Bayesian statistics In frequentist
Διαβάστε περισσότεραOverview. Transition Semantics. Configurations and the transition relation. Executions and computation
Overview Transition Semantics Configurations and the transition relation Executions and computation Inference rules for small-step structural operational semantics for the simple imperative language Transition
Διαβάστε περισσότεραProbability and Random Processes (Part II)
Probability and Random Processes (Part II) 1. If the variance σ x of d(n) = x(n) x(n 1) is one-tenth the variance σ x of a stationary zero-mean discrete-time signal x(n), then the normalized autocorrelation
Διαβάστε περισσότερα6.3 Forecasting ARMA processes
122 CHAPTER 6. ARMA MODELS 6.3 Forecasting ARMA processes The purpose of forecasting is to predict future values of a TS based on the data collected to the present. In this section we will discuss a linear
Διαβάστε περισσότεραBounding Nonsplitting Enumeration Degrees
Bounding Nonsplitting Enumeration Degrees Thomas F. Kent Andrea Sorbi Università degli Studi di Siena Italia July 18, 2007 Goal: Introduce a form of Σ 0 2-permitting for the enumeration degrees. Till now,
Διαβάστε περισσότεραAdvanced Subsidiary Unit 1: Understanding and Written Response
Write your name here Surname Other names Edexcel GE entre Number andidate Number Greek dvanced Subsidiary Unit 1: Understanding and Written Response Thursday 16 May 2013 Morning Time: 2 hours 45 minutes
Διαβάστε περισσότεραSolutions - Chapter 4
Solutions - Chapter Kevin S. Huang Problem.1 Unitary: Ût = 1 ī hĥt Û tût = 1 Neglect t term: 1 + hĥ ī t 1 īhĥt = 1 + hĥ ī t ī hĥt = 1 Ĥ = Ĥ Problem. Ût = lim 1 ī ] n hĥ1t 1 ī ] hĥt... 1 ī ] hĥnt 1 ī ]
Διαβάστε περισσότεραPP #6 Μηχανικές αρχές και η εφαρµογή τους στην Ενόργανη Γυµναστική
PP #6 Μηχανικές αρχές και η εφαρµογή τους στην Ενόργανη Γυµναστική Υπολογισµός Γωνιών (1.2, 1.5) (2.0, 1.5) θ 3 θ 4 θ 2 θ 1 (1.3, 1.2) (1.7, 1.0) (0, 0) " 1 = tan #1 2.0 #1.7 1.5 #1.0 $ 310 " 2 = tan #1
Διαβάστε περισσότερα2 Composition. Invertible Mappings
Arkansas Tech University MATH 4033: Elementary Modern Algebra Dr. Marcel B. Finan Composition. Invertible Mappings In this section we discuss two procedures for creating new mappings from old ones, namely,
Διαβάστε περισσότεραBessel function for complex variable
Besse fuctio for compex variabe Kauhito Miuyama May 4, 7 Besse fuctio The Besse fuctio Z ν () is the fuctio wich satisfies + ) ( + ν Z ν () =. () Three kids of the soutios of this equatio are give by {
Διαβάστε περισσότεραInstruction Execution Times
1 C Execution Times InThisAppendix... Introduction DL330 Execution Times DL330P Execution Times DL340 Execution Times C-2 Execution Times Introduction Data Registers This appendix contains several tables
Διαβάστε περισσότεραUniform Convergence of Fourier Series Michael Taylor
Uniform Convergence of Fourier Series Michael Taylor Given f L 1 T 1 ), we consider the partial sums of the Fourier series of f: N 1) S N fθ) = ˆfk)e ikθ. k= N A calculation gives the Dirichlet formula
Διαβάστε περισσότεραΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΤΜΗΜΑ ΠΛΗΡΟΦΟΡΙΚΗΣ. ΕΠΛ342: Βάσεις Δεδομένων. Χειμερινό Εξάμηνο Φροντιστήριο 10 ΛΥΣΕΙΣ. Επερωτήσεις SQL
ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΤΜΗΜΑ ΠΛΗΡΟΦΟΡΙΚΗΣ ΕΠΛ342: Βάσεις Δεδομένων Χειμερινό Εξάμηνο 2013 Φροντιστήριο 10 ΛΥΣΕΙΣ Επερωτήσεις SQL Άσκηση 1 Για το ακόλουθο σχήμα Suppliers(sid, sname, address) Parts(pid, pname,
Διαβάστε περισσότεραChapter 6: Systems of Linear Differential. be continuous functions on the interval
Chapter 6: Systems of Linear Differential Equations Let a (t), a 2 (t),..., a nn (t), b (t), b 2 (t),..., b n (t) be continuous functions on the interval I. The system of n first-order differential equations
Διαβάστε περισσότερα3.4 SUM AND DIFFERENCE FORMULAS. NOTE: cos(α+β) cos α + cos β cos(α-β) cos α -cos β
3.4 SUM AND DIFFERENCE FORMULAS Page Theorem cos(αβ cos α cos β -sin α cos(α-β cos α cos β sin α NOTE: cos(αβ cos α cos β cos(α-β cos α -cos β Proof of cos(α-β cos α cos β sin α Let s use a unit circle
Διαβάστε περισσότεραMean-Variance Analysis
Mean-Variance Analysis Jan Schneider McCombs School of Business University of Texas at Austin Jan Schneider Mean-Variance Analysis Beta Representation of the Risk Premium risk premium E t [Rt t+τ ] R1
Διαβάστε περισσότεραCalculating the propagation delay of coaxial cable
Your source for quality GNSS Networking Solutions and Design Services! Page 1 of 5 Calculating the propagation delay of coaxial cable The delay of a cable or velocity factor is determined by the dielectric
Διαβάστε περισσότεραΠρόβλημα 1: Αναζήτηση Ελάχιστης/Μέγιστης Τιμής
Πρόβλημα 1: Αναζήτηση Ελάχιστης/Μέγιστης Τιμής Να γραφεί πρόγραμμα το οποίο δέχεται ως είσοδο μια ακολουθία S από n (n 40) ακέραιους αριθμούς και επιστρέφει ως έξοδο δύο ακολουθίες από θετικούς ακέραιους
Διαβάστε περισσότεραHomework 4.1 Solutions Math 5110/6830
Homework 4. Solutios Math 5/683. a) For p + = αp γ α)p γ α)p + γ b) Let Equilibria poits satisfy: p = p = OR = γ α)p ) γ α)p + γ = α γ α)p ) γ α)p + γ α = p ) p + = p ) = The, we have equilibria poits
Διαβάστε περισσότερα2. THEORY OF EQUATIONS. PREVIOUS EAMCET Bits.
EAMCET-. THEORY OF EQUATIONS PREVIOUS EAMCET Bits. Each of the roots of the equation x 6x + 6x 5= are increased by k so that the new transformed equation does not contain term. Then k =... - 4. - Sol.
Διαβάστε περισσότεραLast Lecture. Biostatistics Statistical Inference Lecture 19 Likelihood Ratio Test. Example of Hypothesis Testing.
Last Lecture Biostatistics 602 - Statistical Iferece Lecture 19 Likelihood Ratio Test Hyu Mi Kag March 26th, 2013 Describe the followig cocepts i your ow words Hypothesis Null Hypothesis Alterative Hypothesis
Διαβάστε περισσότεραVolume of a Cuboid. Volume = length x breadth x height. V = l x b x h. The formula for the volume of a cuboid is
Volume of a Cuboid The formula for the volume of a cuboid is Volume = length x breadth x height V = l x b x h Example Work out the volume of this cuboid 10 cm 15 cm V = l x b x h V = 15 x 6 x 10 V = 900cm³
Διαβάστε περισσότεραC.S. 430 Assignment 6, Sample Solutions
C.S. 430 Assignment 6, Sample Solutions Paul Liu November 15, 2007 Note that these are sample solutions only; in many cases there were many acceptable answers. 1 Reynolds Problem 10.1 1.1 Normal-order
Διαβάστε περισσότεραJ. of Math. (PRC) Shannon-McMillan, , McMillan [2] Breiman [3] , Algoet Cover [10] AEP. P (X n m = x n m) = p m,n (x n m) > 0, x i X, 0 m i n. (1.
Vol. 35 ( 205 ) No. 4 J. of Math. (PRC), (, 243002) : a.s. Marov Borel-Catelli. : Marov ; Borel-Catelli ; ; ; MR(200) : 60F5 : O2.4; O236 : A : 0255-7797(205)04-0969-08 Shao-McMilla,. Shao 948 [],, McMilla
Διαβάστε περισσότερα22 .5 Real consumption.5 Real residential investment.5.5.5 965 975 985 995 25.5 965 975 985 995 25.5 Real house prices.5 Real fixed investment.5.5.5 965 975 985 995 25.5 965 975 985 995 25.3 Inflation
Διαβάστε περισσότεραRG Tutorial xlc3.doc 1/10. To apply the R-G method, the differential equation must be represented in the form:
G Tuorial xlc3.oc / iear roblem i e C i e C ( ie ( Differeial equaio for C (3 Thi fir orer iffereial equaio ca eaily be ole bu he uroe of hi uorial i o how how o ue he iz-galerki meho o fi ou he oluio.
Διαβάστε περισσότεραHigher Derivative Gravity Theories
Higher Derivative Gravity Theories Black Holes in AdS space-times James Mashiyane Supervisor: Prof Kevin Goldstein University of the Witwatersrand Second Mandelstam, 20 January 2018 James Mashiyane WITS)
Διαβάστε περισσότεραTridiagonal matrices. Gérard MEURANT. October, 2008
Tridiagonal matrices Gérard MEURANT October, 2008 1 Similarity 2 Cholesy factorizations 3 Eigenvalues 4 Inverse Similarity Let α 1 ω 1 β 1 α 2 ω 2 T =......... β 2 α 1 ω 1 β 1 α and β i ω i, i = 1,...,
Διαβάστε περισσότεραNotes on the Open Economy
Notes on the Open Econom Ben J. Heijdra Universit of Groningen April 24 Introduction In this note we stud the two-countr model of Table.4 in more detail. restated here for convenience. The model is Table.4.
Διαβάστε περισσότεραNote: Please use the actual date you accessed this material in your citation.
MIT OpenCourseWare http://ocw.mit.edu 6.03/ESD.03J Electromagnetics and Applications, Fall 005 Please use the following citation format: Markus Zahn, 6.03/ESD.03J Electromagnetics and Applications, Fall
Διαβάστε περισσότεραFREE VIBRATION OF A SINGLE-DEGREE-OF-FREEDOM SYSTEM Revision B
FREE VIBRATION OF A SINGLE-DEGREE-OF-FREEDOM SYSTEM Revisio B By Tom Irvie Email: tomirvie@aol.com February, 005 Derivatio of the Equatio of Motio Cosier a sigle-egree-of-freeom system. m x k c where m
Διαβάστε περισσότεραStrain gauge and rosettes
Strain gauge and rosettes Introduction A strain gauge is a device which is used to measure strain (deformation) on an object subjected to forces. Strain can be measured using various types of devices classified
Διαβάστε περισσότερα1 String with massive end-points
1 String with massive end-points Πρόβλημα 5.11:Θεωρείστε μια χορδή μήκους, τάσης T, με δύο σημειακά σωματίδια στα άκρα της, το ένα μάζας m, και το άλλο μάζας m. α) Μελετώντας την κίνηση των άκρων βρείτε
Διαβάστε περισσότεραProblem 7.19 Ignoring reflection at the air soil boundary, if the amplitude of a 3-GHz incident wave is 10 V/m at the surface of a wet soil medium, at what depth will it be down to 1 mv/m? Wet soil is
Διαβάστε περισσότεραΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 6/5/2006
Οδηγίες: Να απαντηθούν όλες οι ερωτήσεις. Ολοι οι αριθμοί που αναφέρονται σε όλα τα ερωτήματα είναι μικρότεροι το 1000 εκτός αν ορίζεται διαφορετικά στη διατύπωση του προβλήματος. Διάρκεια: 3,5 ώρες Καλή
Διαβάστε περισσότεραCHAPTER 12: PERIMETER, AREA, CIRCUMFERENCE, AND 12.1 INTRODUCTION TO GEOMETRIC 12.2 PERIMETER: SQUARES, RECTANGLES,
CHAPTER : PERIMETER, AREA, CIRCUMFERENCE, AND SIGNED FRACTIONS. INTRODUCTION TO GEOMETRIC MEASUREMENTS p. -3. PERIMETER: SQUARES, RECTANGLES, TRIANGLES p. 4-5.3 AREA: SQUARES, RECTANGLES, TRIANGLES p.
Διαβάστε περισσότεραΑΚΑ ΗΜΙΑ ΕΜΠΟΡΙΚΟΥ ΝΑΥΤΙΚΟΥ ΜΑΚΕ ΟΝΙΑΣ ΣΧΟΛΗ ΜΗΧΑΝΙΚΩΝ ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ
ΑΚΑ ΗΜΙΑ ΕΜΠΟΡΙΚΟΥ ΝΑΥΤΙΚΟΥ ΜΑΚΕ ΟΝΙΑΣ ΣΧΟΛΗ ΜΗΧΑΝΙΚΩΝ ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ ΘΕΜΑ : ΣΥΣΤΗΜΑΤΑ ΣΤΑΘΕΡΟΠΟΙΗΣΗΣ ΠΛΟΙΩΝ ΣΠΟΥ ΑΣΤΗΣ : ΑΛΑΤΙΝΗΣ ΑΛΕΞΑΝ ΡΟΣ ΕΠΙΒΛΕΠΩΝ ΚΑΘΗΓΗΤΗΣ : ΠΑΠΑΣΤΑΜΟΥΛΗΣ ΑΘΑΝΑΣΙΟΣ NEA ΜΗΧΑΝΙΩΝΑ
Διαβάστε περισσότεραOrdinal Arithmetic: Addition, Multiplication, Exponentiation and Limit
Ordinal Arithmetic: Addition, Multiplication, Exponentiation and Limit Ting Zhang Stanford May 11, 2001 Stanford, 5/11/2001 1 Outline Ordinal Classification Ordinal Addition Ordinal Multiplication Ordinal
Διαβάστε περισσότεραΜΕΤΑΠΤΥΧΙΑΚΗ ΔΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ «ΘΕΜΑ»
ΠΑΝΕΠΙΣΤΗΜΙΟ ΑΙΓΑΙΟΥ ΣΧΟΛΗ ΑΝΘΡΩΠΙΣΤΙΚΩΝ ΕΠΙΣΤΗΜΩΝ ΤΜΗΜΑ ΕΠΙΣΤΗΜΩΝ ΤΗΣ ΠΡΟΣΧΟΛΙΚΗΣ ΑΓΩΓΗΣ ΚΑΙ ΤΟΥ ΕΚΠΑΙΔΕΥΤΙΚΟΥ ΣΧΕΔΙΑΣΜΟΥ Π.Μ.Σ. «ΠΕΡΙΒΑΛΛΟΝΤΙΚΗ ΕΚΠΑΙΔΕΥΣΗ» ΜΕΤΑΠΤΥΧΙΑΚΗ ΔΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ «ΘΕΜΑ» «Εφαρμογή
Διαβάστε περισσότεραDurbin-Levinson recursive method
Durbin-Levinson recursive method A recursive method for computing ϕ n is useful because it avoids inverting large matrices; when new data are acquired, one can update predictions, instead of starting again
Διαβάστε περισσότεραΕργαστήριο Ανάπτυξης Εφαρμογών Βάσεων Δεδομένων. Εξάμηνο 7 ο
Εργαστήριο Ανάπτυξης Εφαρμογών Βάσεων Δεδομένων Εξάμηνο 7 ο Procedures and Functions Stored procedures and functions are named blocks of code that enable you to group and organize a series of SQL and PL/SQL
Διαβάστε περισσότεραderivation of the Laplacian from rectangular to spherical coordinates
derivation of the Laplacian from rectangular to spherical coordinates swapnizzle 03-03- :5:43 We begin by recognizing the familiar conversion from rectangular to spherical coordinates (note that φ is used
Διαβάστε περισσότεραPolicy Coherence. JEL Classification : J12, J13, J21 Key words :
** 80%1.89 2005 7 35 Policy Coherence JEL Classification : J12, J13, J21 Key words : ** Family Life and Family Policy in France and Germany: Implications for Japan By Tomoko Hayashi and Rieko Tamefuji
Διαβάστε περισσότεραEcon 2110: Fall 2008 Suggested Solutions to Problem Set 8 questions or comments to Dan Fetter 1
Eon : Fall 8 Suggested Solutions to Problem Set 8 Email questions or omments to Dan Fetter Problem. Let X be a salar with density f(x, θ) (θx + θ) [ x ] with θ. (a) Find the most powerful level α test
Διαβάστε περισσότεραSolutions to the Schrodinger equation atomic orbitals. Ψ 1 s Ψ 2 s Ψ 2 px Ψ 2 py Ψ 2 pz
Solutions to the Schrodinger equation atomic orbitals Ψ 1 s Ψ 2 s Ψ 2 px Ψ 2 py Ψ 2 pz ybridization Valence Bond Approach to bonding sp 3 (Ψ 2 s + Ψ 2 px + Ψ 2 py + Ψ 2 pz) sp 2 (Ψ 2 s + Ψ 2 px + Ψ 2 py)
Διαβάστε περισσότεραv(t) 10 V + - R L C + -
ÕÛÎËÛË Ο διακόπτης στο κύκλωµα του Σχήµατος -, είναι κλειστός για µεγάλο χρονικό διάστηµα, στα πλαίσια εργαστηριακού πειράµατος. Ένας φοιτητής βλέποντας ότι η πηγή τάσης είναι µόνο 0 V, ακουµπά απρόσεκτα
Διαβάστε περισσότεραEcon Spring 2004 Instructor: Prof. Kiefer Solution to Problem set # 5. γ (0)
Cornell University Department of Economics Econ 60 - Spring 004 Instructor: Prof. Kiefer Solution to Problem set # 5. Autocorrelation function is defined as ρ h = γ h γ 0 where γ h =Cov X t,x t h =E[X
Διαβάστε περισσότερα1.8 Paul Mother Wavelet Real Part Imaginary Part Magnitude.6.4 Amplitude.2.2.4.6.8 1 8 6 4 2 2 4 6 8 1 t .8.6 Real Part of Three Scaled Wavelets a = 1 a = 5 a = 1 1.2 1 Imaginary Part of Three Scaled Wavelets
Διαβάστε περισσότερα«Χρήσεις γης, αξίες γης και κυκλοφοριακές ρυθμίσεις στο Δήμο Χαλκιδέων. Η μεταξύ τους σχέση και εξέλιξη.»
ΕΘΝΙΚΟ ΜΕΤΣΟΒΙΟ ΠΟΛΥΤΕΧΝΕΙΟ ΣΧΟΛΗ ΑΓΡΟΝΟΜΩΝ ΚΑΙ ΤΟΠΟΓΡΑΦΩΝ ΜΗΧΑΝΙΚΩΝ ΤΟΜΕΑΣ ΓΕΩΓΡΑΦΙΑΣ ΚΑΙ ΠΕΡΙΦΕΡΕΙΑΚΟΥ ΣΧΕΔΙΑΣΜΟΥ ΔΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ: «Χρήσεις γης, αξίες γης και κυκλοφοριακές ρυθμίσεις στο Δήμο Χαλκιδέων.
Διαβάστε περισσότερα