Please note all the sources used are appropriately cited. If you use this document cite it as well. Citation: TBD

Please note all the sources used are appropriately cited. If you use this document cite it as well. Citation: TBD

Introduction into Inertial Navigation Systems Pavel Pačes

Prerequisites Subjects: Aircraft sensors systems (Přístrojové systémy letadel) Navigation (Navigace)

Content Introduction Requirements Inertial Measurement Systems Sensors

Area Navigation (RNAV) Instrument Flight Rules (IFR) Navigation Beacons 1970, and later Inercial Reference Systems

Navigation Land navigation Very high frequency Omnidirectional Radio range (VOR) Distance Measuring Equipment (DME) Over ocean Inertial Measurement Systems (INS)

Precision System precision Definition of airspace and obstacle clearance Delays New method of defining equipment requirements => Performance-based Navigation (PBN)

Current Status Performance based Navigation Area Navigation (RNAV) Required Navigation Performance (RNP) related to Actual Navigation Performance (ANP) Differences: the requirement for on-board performance monitoring and alerting What about service assurance? => RNAV (coexistence of both systems)

Source [4]

Performance Based Navigation RNAV (Area Navigation) umožňuje letadlu vybrat vhodnou trasu za využití soustavy navigračních prostředků (majáky, GPS, INS) šetří se čas, délka dráhy a doba letu. Nejde to použít všude, je nutné definovat požadavky (na vybavení, posádku, letadlo, ) Required navigation performance Rozdíly se stírají poslední dobou (od 1990) jsou i RNAV systémy vybavované funkcí performance monitoring and alerting = tj. vše je RNAV.

RAIM RAIM Receiver Autonomous Integrity Monitor Poskytuje varování v případě, že systém není možné použít pro navigaci. U GPS je kontrola například použitím několika čtveřic viditelných satelitů.

RNP Lepší spolehlivost a funkce garantující funkčnost zařízení. Přesnější navigace Menší rozestupy mezi letadly Navigace pouze pomocí RNP systému Problém je cena, ale předpokládá se, že v budoucnosti se budou využívat už jen RNP systémy.

RNAV requirements continuous indication of aircraft position relative to track to be displayed to the pilot flying on a navigation display situated in his primary field of view; display of distance and bearing to the active (To) waypoint; display of ground speed or time to the active (To) waypoint; navigation data storage function; and appropriate failure indication of the RNAV system including its sensors.

RNAV Lateral Navigation Navigation Accuracy path definition error (PDE), flight technical error (FTE) and navigation system error (NSE) Total System Error (TSE) => σ = sqrt(σ PDE + σ FTE + σ NSE )

RNAV Longitudinal navigation Position along a track It is not considered important Except, e.g. Descent points Designation RNAV X whre X is a number in nautical miles representing 95% probability of aircraft operation within lateral distance from a path

RNP Used in specific airspaces Permitting closer route spacing Offer significant safety, operational and efficiency benefits

RNP designation An RNP of 0.3 means the aircraft navigation system must be able to calculate its position to within a circle with a radius of 0.3 nautical mile

What is it for? Nose reduction along a path Source [3]

What is it for? Precise approach over a a river no noise polution of residential areas Source [5]

Airplanes categories (SBAS) Landing minimums

Source [4] RNP-0.3 required

What do we have? Precision? System Precision [m] Loran, GPS 9-180 DECCA 200 Transit, Tacan 400 INS (after 1 hour) 650 VOR/DME & Doppler 900 Omega 2200

Inertial Navigation System (INS) Includes A computer and a module containing Accelerometers, Gyroscopes or Other devices It is necessary to provide its position and velocity (GPS, FMS, etc.) and then it calculates its own position, velocity and orientation by integration from motion sensors.

Definice Polohové úhly Théta, pitch podélný sklon Phi, roll příčný náklon Psi, yaw, headind, azimuth - kurz + + +

Sensors Mechanical gyroscopes rotating mass Accelerometers movement of a mass point transferred on electric signal Micro Electro Mechanical Structures (MEMS)

Porovnání MEMS a RLG Křivky výkonnosti RLG1308 a MEMS Gyro

Coordinate Frames Body frame North-East-Down (NED) Navigation frame Earth Centered xxx Frame Image source [7]

Roll, Pitch and Yaw Coordinate sysems C Target Original, or C To From Euler angles singularity problem => Use quaternions Covariance matrix = measure of trust in measurement

INS Systems Gimbaled platform Gimbaled frame with an inertial center gyro Strap-down systems Image source [Wiki] Image source [8]

Gimbaled platform

Gimbaled frame with an inertial center gyro

Strap-down system

Strap-down systems alignment Image source [8]

INS algorithms Examples Flat Earth Non-rotating Earth Rotating Earth

Strap-down system

Flat Earth Image source [7]

Non-rotating Earth

Rotating spherical Earth navigator

GPS system coupling A Tightly coupled

Other system

Gravitační pole Nerovnoměrné rozložení se kterým se musí počítat. Závislost na: Geografické lokaci Výšce

Schulerovo kyvadlo Kyvadlo s dobou kyvu 84.4 min takové jehož délka je stejná jako délka poloměru země. Unikátní vlastností je, že vektor vedoucí ze závaží kyvadla do bodu uchycení (počátku) zůstává stále vertikální vzhledem k povrchu navzdory jakémukoliv pohybu jeho počátku (závěsu). V inerciálních systémech je zaváděno jako jeden z výpočetních bloků. Zavádí se jako změna úhlu, která závisí na rychlosti pohybu v horizontální rovině dělená poloměrem země.

Schuler pendulum v/ R R 6378 km -1 v 10 m.s 1.5679e 6 Kompletní oscilace T l 2.. =6.28. 637,8 km 84.4377 min g

Sensor Fusion Magnetometers GPS systems Pressure Reference System Image source [8]

In-flight alignment and system precision Image source [8]

AHRS Altitude heading and reference system low-cost INS A magnetometer unit

AHRS INS Magnetometer

Aircraft instalation

Characterization of sensors Is the sensor good for INS? Alan Variance movement of an average value in time

Errors

Raw data

Allan Variance

Literatura 1. Establishment of Area Navigation Routes (RNAV), http://www.epa.gov/epa-impact/2003/may/day-09/i11638.htm 2. Navigation Systems - Level 3 Area Navigation http://www.allstar.fiu.edu/aero/rnav.htm 3. Space Communication and Aviation Navigation: The United States Moves towards Performance-Based Navigation http://spacejournal.ohio.edu/issue9/aviation_navigation.html 4. RNP - What is it? http://www.overtheairwaves.com/airwaves/vol2-5a.htm 5. Example of the RNP River approach to Brisbane runway 01-03/08 http://www.airservicesaustralia.com/media/pressreleases/pr3_08.asp 6. Airbus, getting to grips with modern navigation 7. Stovall, Sherryl H. Basic Inertial Navigation. California : Naval Air Warfare Center, Weapons Division, 1997. NAWCWPNS TM 8128. 8. Weed, Doug, a další. GPS Align In Motion of civilian strapdown INS. Development, Honeywell Commerzial Aviation Products, Honeywell Interantional. Picastaway : IEEE, 2004. stránky 184-192. 0-7803-8416-4/04.