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Mobile Services (ST 2010)Chapter 9: Positioning

Axel Küpper

Service-centric NetworkingDeutsche Telekom Laboratories, TU Berlin

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Mobile ServicesSummer Term 2010

9 Positioning9.1 Fundamentals of Positioning

9.2 Global Positioning System

9.3 Cellular Positioning

9.A Code Division Multiple Access

9.B Circular Lateration

9.C Hyperbolic Lateration

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9.1 Fundamentals of PositioningOverview (I)

Positioning

Process to obtain the spatial position of a target

Various methods differing from each other in a number of features and parameters (quality, overhead,...)

Features of positioning

One or several parameters observed by measurement methods (observables)

Positioning method for position calculation

Descriptive or spatial reference system

Infrastructure

Protocols for coordinating the positioning process

Observables

Reflects the spatial relation of a target relative to a single or a number of fixed points in the surrounding environment

Examples for observables: angles, ranges, range differences, velocity

Fixed point: point of well-known coordinates of a base station, e.g., cellular base station or satellite

Observables are measured by utilizing physical fundamentals of pilot signals (or simply pilots)

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9.1 Fundamentals of PositioningOverview (II)

Derive the target's position by taking into consideration measurement results of observables and coordinates of reference stations

Deliver the target's position with regard to a descriptive reference system (e.g., cell identifier) or a spatial reference system (e.g., WGS-84)

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9.1 Fundamentals of PositioningPositioning Infrastructure

Distributed infrastructure for implementing positioning

Components

Terminal attached to the target person

Reference stations at well-known coordinates

Control units for coordinating positioning

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9.1 Fundamentals of PositioningQuality Parameters (I)

Accuracy

Refers to the closeness of several position fixes to the true but unknown position of a target

The farther away a position fix is from the true position, the lesser is the degree of accuracy and vice versa

Precision

Refers to the closeness of a number of position fixes to their mean value

Yield and Consistency

Yield refers to the ability of a positioning method to obtain position fixes independent of the environment (indoor, rural, urban)

Consistency is a measure for the stability of accuracy in different environments

Overhead

Signaling overhead: reflects the amount of messages exchanged between terminal and infrastructure as well as within the network infrastructure to control positioning

Computational overhead: refers to the waste of processing power that occurs in the control units or databases of the network and at the terminal

Power consumption: battery consumption caused by positioning at the mobile terminal

High degree of accuracy of position fixes usually causes a high overhead and vice versa

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9.1 Fundamentals of PositioningQuality Parameters (II)

Latency

Refers to the time period between a position request and the subsequent delivery of a position response

Important measure: Time to First Fix (TTFF) (which for GPS is in the range of several tens of seconds)

Roll-out costs

Costs for installing a standalone infrastructure for positioning or to extend an existing one

Operating costs

Costs for operating a positioning infrastructure

Indoor positioning: less or no operating costs

Satellite positioning: exhaustive running charges

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9.1 Fundamentals of PositioningPositioning Methods Overview

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9.2 Global Positioning SystemOverview and History

Initial goal of GPS: establish a global, all-weather, continuously available, highly accurate positioning and navigation system for military purposes

Early 1970s: activities on GPS started under the term Navigation Satellite Timing and Ranging System (NAVSTAR)

1978: first of a nominal constellation of 24 satellites was launched

1983: bombardment of a Korean airline flight over the territory of the Soviet Union caused the US to pronounce to open up GPS for civil use

1986: Accident of the Challenger space shuttle (which was responsible for significant delays in the completion of GPS)

1995: GPS was formally declared ready for full operation

2000: Bill Clinton directed to discontinue the Selective Availability feature on a permanent basis

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9.2 Global Positioning SystemGPS Control Segment

Monitor stations

Equipped with GPS receivers for monitoring and tracking the satellites

Control the health of each satellite, their orbits as well as the accuracy of their internal clocks

Uplink stations

Transmit control data to the satellites

Master control station

Processes control data received from monitor stations

Calculates clock corrections and satellite ephemerides

Correction of satellite orbits, clock keeping, signal encryption

Assembles set of control data for each satellite

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9.2 Global Positioning SystemGPS Satellite Constellation

Satellite constellation: number and positionsof satellites in space

Constellation has been arranged in a way that any point on the Earth's surface iscovered by at least four satellites

GPS consists of nominally 24 satellites (but more of them are launched in order to be ableto immediately replace malfunctioning ones)

Satellites circulate the Earth on six orbits with nominally four satellites per orbit

Orbits are equally spaced 60° apart from each other and have an inclination angle of 55°

Orbit altitude: 20,200 km with regard to mean sea level

Satellites repeat the same ground track exactly twice each sidereal day

Sidereal day: corresponds to the time it takes for the Earth to turn 360° and lasts 23h, 56 min and 4.09s

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9.2 Global Positioning SystemPilot Signals and Spreading Codes (I)

GPS Positioning: terminal-based - circular lateration - timing measurements by code phase ranging

GPS receiver measures ranges to the satellites and must know the satellites' position at the time the ranges are measured

GPS pilot signals

Carry two different ranging codes that are used for measuring the signal traveling time

Carry a navigation message, which contains assistance data like satellite orbits, clock corrections, and system parameters

Demodulated carriers of signals are generated as multiples of the fundamental frequency f0=10.23 MHz of the satellites' clocks

L1 carrier: fL1=f0154=1575.42 MHz (civil signal)

L2 carrier: fL2=f0120=1227.6 MHz (military signal)

L5 carrier: additional civil signal that will be available after GPS modernization in a few years

Use of spread spectrum technology in GPS …

… because spread signals are less susceptible to distortion and jamming than conventional narrowband signals (improving reliability of GPS service)

… as multiple access scheme for GPS satellites

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9.2 Global Positioning SystemPilot Signals and Spreading Codes (II)

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9.2 Global Positioning SystemPilot Signals and Spreading Codes (III)

C/A code

Provide moderate level of accuracy

Used for civil purposes

Modulated onto the L1 carrier

Consists of 1023 chips and is repeated every millisecond

Requires 1 MHz bandwidth

Each chip has a length of 300 m

Entire C/A code repeats itself every 300 km between satellite and receiver

P-code

Yields much better accuracy than C/A codes

Can only be interpreted by military applications

Modulated onto L1 and L2 carriers

Very long code consisting of approx. 1014 chips

Entire P-code does not repeat for 38 weeks

Requires 10.23 MHz bandwidth

Simultaneously modulated onto L1 and L2 carriers

P-code is shared between all satellites in that each satellite is assigned a certain one-week segment of it

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9.2 Global Positioning SystemPilot Signals and Spreading Codes (IV)

Before modulation, C/A code is mixed with navigation message with a spreading factor of 20,000, resulting in a data rate of 50 bps

C/A code and P-code are modulated onto L1 carrier using binary PSK and shifted by 90°from each other

L2-carrier is modulated by P-code only, also by using binary PSK

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9.2 Global Positioning SystemNavigation Message (I)

Navigation message is transmitted in a frame structure

Frame consists of 5 subframes, each with a length of 300 bits

Frame transmissions are continuously repeated every 30 s

TLM (telemetry)

Indicates the beginningof a new subframe andused for synchronizationpurposes

Carries information aboutrecent operations performedon the transmitting satellite(e.g., upload of new ephemeris)

HOW (handover word)

Time-of-week (TOW) of subsequent sequence(required for synchronizationwith P-code)

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9.2 Global Positioning SystemNavigation Message (II)

Ephemeris

Contains all information needed by the receiver to compute the exact satellite position in space when performing measurements

Keplerian parameters

Valid reference time

Satellite's angle velocity

Correction parameters that describe the perturbing forces on the satellite

Does not reflect the satellite position at the time of transmission, but refers to a certain reference time from which the receiver can then estimate the current position

Almanac

Subset of each satellite's ephemeris and clock data

Contains Keplerian elements and angle velocity, but no correction parameters

Helps to speed up the tart-up time of GPS receivers since it enables to obtain a rough overview of the current satellite constellation when the receiver is turned on

Ionospheric data

Parameters of the ionospheric delay used by the GPS receiver to reduce the timely impacts of a signal when passing the ionosphere

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9.2 Global Positioning SystemNavigation Message (III)

Almanac and ionospheric data represent too much data to be carried in a single frame

Transmission is distributed over 25 consecutive frames (masterframe)

Within a masterframe, subframes 1, 2, and 3 are repeated in each frame, while subframes 4 and 5 carry only portions of the almanac

Masterframe has a duration of 12.5 minutes

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9.2 Global Positioning SystemGPS Positioning Services

Standard Positioning Service (SPS)

Positioning and timing service focusing on the civilian user

Based on C/A code transmitted at the L1 carrier

Initially designed to accomplish a predictable accuracy of 100m horizontally and 156m vertically

Precise Positioning Service (PPS)

Positioning, timing, and velocity service for military purposes

Based on C/A and P-code transmissions on both carriers

Predicted accuracy is within at least 22m horizontally and 27.7m vertically

Usage restricted to authorized users (U.S. and allied military)

Selective Availability (SA)

Intentional degradation of accuracy of SPS users on a global basis

Developed as it turned out after GPS went into operation that SPS users achieved a much higher accuracy than initially intended

Accomplished by falsifying the orbit data of satellites carried in the navigation messages and by manipulating the satellites' clock frequency

Discontinued in May 2000

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9.2 Global Positioning SystemPositioning Step 1 – Identification of Satellites

GPS receiver must in the first step determine the satellites to be used for range measurements

5 to 10 satellites are typically in the visible horizon of a receiver

Identification procedure depends on the state of the receiver

Cold start-up (40-60s)

Receiver has no information about its last position and no valid almanac

Receiver must listen to the transmission on the L1 carrier and auto-correlate the received C/A codes with the entire C/A code space

Warm start-up (30-40s)

Receiver knows its last position and has almanac

Receiver can roughly estimate current satellite constellation

Hot start-up (5-15s)

Receiver has valid ephemeris, which allows to determine current satellite constellation very accurately

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9.2 Global Positioning SystemPositioning Step 2 – Ranging

Code phase ranging for SPS and PPS

Dual-frequency ranging: PPS uses code phase ranging on both carriers and can thus adjust much better to ionospheric refraction

Carrier phase ranging can be applied optionally, but is very time consuming and thus not applicable for real-time application like LBSs

Range measurements must be made to at least four satellites for applying circular lateration in 3D

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9.2 Global Positioning SystemPositioning Step 3 – Position Calculation

Ranges measured to satellites are pseudoranges and are subject to errors

For correcting errors, navigation message contains coefficients of a correction formula, which the receiver applies on the measured ranges to achieve more accurate results

Coordinates of the satellites at the time of measurements can be derived from Keplerian elements transmitted in the navigation message

Time offset between receiver time and GPS time is modeled as an additional unknown in the system of equations for circular lateration:

In the last step, derived ECEF-coordinates are translated into LLA coordinates based on a selected datum (default is WGS-84)

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9.2 Global Positioning SystemDifferential GPS (I)

Principle

Observe and measure pilot signals from the satellites at a well-known position (reference station) and determine the difference between the measured range and an approximation of the true range derived from the known position of observation

Derived difference then serves as a correction value for GPS receivers staying close by

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9.2 Global Positioning SystemDifferential GPS (II)

Calculation of the range between the known position (xrs, yrs, zrs) of the reference station and the position (Xi, Yi, Zi) of the ith satellite:

Difference between the calculated range ci,rs and the measured range pi,rs:

with ti,rs being the time offset and i,rs representing the range difference resulting from error sources like ionospheric refraction

Reference station calculates

and transmits it to close-by mobile GPS receivers (for example, via GSM/GPRS or UMTS)

Mobile GPS receiver corrects each measured pseudorange pi,mr by the related correction term:

Assumption: errors in the pseudoranges are temporally and spatially correlated if the observations are made in the same local region

Reference station and mobile GPS-receiver should not be separated from each other by distances larger than 60-70 km

Within this distance, ranges observed by reference station and GPS receiver usually experience tropospheric, ionospheric, multipath, and noise errors of similar magnitude

Thus, i,sr and i,mr cancel out each other:

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9.3 Cellular PositioningOverview of LCS Architecture

Location Service (LCS): GSM/UMTS term for positioning method

LCS architecture: extension of existing GSM/UMTS architecture for enabling LCS

Mobile Location Center (MLC): control and coordination of positioning

Serving MLC (SMLC): control of positioning in the access network

Gateway MLC (GMLC): interconnectivity to external LCS clients

Location Measurement Unit (LMU): Timing synchronization of base stations

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9.3 Cellular PositioningProximity Sensing and CEllID

Easiest and most widespread positioning method

Based on the limited range of coverage of radio, infrared, or ultrasound signals

Position of a target is derived from the coordinates of the serving base station

GSM and UMTS: Cell-Id, Cell-of-Origin (CoO), or Cell Global Identity (CGI)

Indoor: WLAN hotspot area, RFID range, ...

Problem (if implemented as terminal-based approach): mapping of cell-identifiers onto geographic coordinates

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9.3 Cellular PositioningProximity Sensing and CEllID with Timing Advance

Timing Advance (TA): corresponds to the distance between terminal and base station with an accuracy of approx. 500 m

Estimated position corresponds to a ring around the base station (omnidirectional antennas) or the part of a ring (sectorized antennas)

Terminal is only “heard” by one base station at a time, why lateration based on the TA parameter is not possible

Network-based: position is estimated by the network

Cell-Id only specified in combination with TA parameter (pure Cell-Id methods applied today are based on proprietary solutions)

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9.3 Cellular PositioningSignaling Flow for CellID

Busy mode: cell and TA are known to the network and can be requested from the serving BSC

Idle mode: no connection exists and the terminal must be paged

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9.3 Cellular PositioningEnhanced Observed Time Difference (I)

Enhanced Observed Time difference (EOTD) or Downlink Time Difference of Arrival (DL-TDoA)

Based on hyperbolic lateration

Terminal-based positioning method

Requires terminals with special firmware

Geometric Time Difference (GTD):

GTD=(d2-d1)/v

with v: velocity of light

Problem: No synchronization of GSM and UTRAN FDD Node B’s

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9.3 Cellular PositioningEnhanced Observed Time Difference (II)

Solution: Measure not only the time intervals between arrival of signal bursts at the terminal, but also the time offset between emission at the base stations

Real Time Difference (RTD): time offset between emission of signal bursts at the base stations

Observed Time Difference (OTD): time offset between arrival of signal bursts at the terminal

GTD=OTD-RTD

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9.3 Cellular PositioningEnhanced Observed Time Difference (III)

OTD values are derived by the terminal

Radio Interface Timing (RIT) measurements: determination of RTD values by a Location Measurement Unit (LMU)

Measures RTD relative to a selected base station clock (GSM/UMTS time), or

Measures RTD relative to GPS time (preferred and more accurate way, but requires GPS equipment)

Incoming signal bursts from surrounding base stations are timestamped and RTD values are calculated against a selected reference base station

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9.3 Cellular PositioningEnhanced Observed Time Difference (IV)

1. SMLC requests LMU to perform RIT measurements for a particular set of base stations

2. LMU returns measured RTDs

3. SMLC requests terminal to measure OTDs (and optionally calculate its position) and passes assistance data to the terminal

4. Terminal sends measured OTDs and/or calculated position

Alternative for Steps 3 and 4:

Assistance data is periodically broadcast (maybe encrypted)

Terminal can carry out positioning autonomously (without explicit request from the SMLC)

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9.3 Cellular PositioningEnhanced Observed Time Difference (V)

Problem: RTDs derived by an LMU are actually observed RTDs, because they are subject to the propagation delay like OTDs

To get actual RTDs, remove time portions from the observed RTDs that is caused by the propagation delay

Exact coordinates of monitored base stations and LMU must be known in order to determine the distances between them

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9.3 Cellular PositioningEnhanced Observed Time Difference (VI)

Mode of Operation

Terminal-based: terminal performs OTD measurements and calculates position

Terminal-assisted: terminal performs OTD measurements only and returns results to the SMLC for calculating the position in the network

Reference and neighbor base stations

Prescribe the pairs of base stations for which to measure OTDs

Measurement support data

RTD values for reference and neighbor base stations (in case of terminal-based mode)

Expected OTD: estimation of OTD by SMLC in order to speed up measurement process

Base station coordinates

Desired response time and accuracy

Maximum response time after which the terminal should have finished the measurements (terminal-assisted mode)

Minimum level of accuracy for position calculation (terminal-based mode)

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9.3 Cellular PositioningEnhanced Observed Time Difference (VII)

Explicit position request Requires dedicated point-to-

point signaling between terminal and SMLC

Autonomous position estimation by the terminal

Requires broadcast of assistance data

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9.3 Cellular PositioningAssisted GPS (I)

Motivation

Reduce GPS sensor startup time

Increase accuracy by DGPS

Consume less handheld power than conventional GPS

Assumption

Network of GPS reference stations whose receivers have clear views to the sky and can operate continuously

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9.3 Cellular PositioningAssisted GPS (II)

Mobile-assisted A-GPS Position calculation is done in the network

Network transmits short assistance data to the terminal GPS time Visible satellite list Doppler shift Code phase search window

Terminal performs measurements and returns results to the network for position estimation

Mobile-based A-GPS

Position calculation is done by the terminal

Network transmits extended assistance data to the terminal

GPS time

Reference location

Satellite ephemeris and clock corrections

D-GPS data

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9.A Code Division Multiple Access Overview

All channels transmit simultaneously in the same frequency range

Signals of different channels are summedup during transmission and must beseparated from each other by code

Chipping sequence (or spreading code)

Sequence of chips unambiguously assigned to a channel

Must be known to sender and receiver

Data is encoded with the chipping sequence by multiplication

Receiver applies chipping sequence on the received added signal and derives the original data after integration

Chip

Value of +1 or -1 (in bipolar notation)

Much shorter than a bit

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9.A Code Division Multiple Access Spreading and De-Spreading of Signals (I)

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9.A Code Division Multiple Access Spreading and De-Spreading of Signals (II)

Chip rate Cc is a multiple of the bit rate Cb

Data encoded with a chipping sequence is spread over a much larger frequency range compared to a signal derived from pure data (follows from the coherence between data rate and bandwidth)

CDM/CDMA is a spread spectrum technique

Spreading factor: relation between the chip and bit length (i.e., it defines the number of chips used for encoding a single bit)

Spread signal has the same amount of power as the despread signal, but this power is equally distributed over the much larger frequency band

Smaller amount of power per frequency (power spectral density)

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9.A Code Division Multiple Access Autocorrelation and Cross-correlation (I)

Spreading codes must have good correlation properties in order to be suitable for CDM/CDMA

Correlation: measure for determining how much similarity one set of data has with another

Autocorrelation

Defines the correlation of a chip sequence ci of N chips with regard to n shifts of itself:

Important measure for achieving synchronization between sender and receiver

A chipping sequence has a good autocorrelation if

Receiver monitors the incoming signal and applies the autocorrelation function

If the result shows a peak, the beginning of the code is detected and sender and receiver aresynchronized

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9.A Code Division Multiple Access Autocorrelation and Cross-correlation (II)

Cross-Correleation

Defines the correlation of two chip sequencesci and cj, both consisting of N chips, withregard to n shifts:

Low cross correlation betweendifferent chipping sequences isessential in order to properly separatethe different channels from the composedsignal at the receiver

The more similar a pair of chipping sequences is, the more difficult it is to reconstruct the original data

Orthogonality

Two chipping sequences show zero cross correlation

Only exists if unshifted versions of chipping sequences are matched

Problem in CDMA systems, where different senders are not synchronized and any combination of shifted sequences overlay during transmission

Autocorrelation of the same sequence

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9.B Circular Lateration2D versus 3D

Circular lateration in 2D

Range ri between the ith base station:

with (Xi, Yi) being the known coordinates of the ith base station with respect to ECEF and (x,y) the target's unknown position

Circular lateration in 3D

Range ri between the ith base station:

with (Xi, Yi, Zi) being the known coordinates of the ith base station with respect to ECEF and (x,y,z) the target's unknown position

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9.B Circular LaterationError Potential

Measured pseudoranges pi deviate from the actual ranges ri by an error due to inaccurate clock synchronization, refraction, and multipath propagation:

Consequence: circles (spheres) do not intersect at a certain point, but span an area of some size

System of equations is in most cases inconsistent and has no unique solution

To achieve a result different mathematical approaches can be used

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9.B Circular LaterationPosition Calculation (I)

Approximation of the target's position by an iterative process of least square fits

Start with an estimation of the target's position

Calculate a correction vector that can be applied to the estimated position

Function of the pseudorange to the ith base station expressed by a Taylor series:

For calculating the position fix, only the first order expansion is determined:

Taylor series

Describe a function f at a certain point by a power series:

I: interval

a: inner point of I

f: function with derivatives up to the order of (n+1) on I

Rn(x,a): remainder after n+1 terms

x I

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9.B Circular LaterationPosition Calculation (II)

Solution of the partial differentials:

Because the coordinates of the ith base station as well as the target's estimated position are known, the coefficients ai, bi, ci are numerically known, too:

corresponds to the pseudorange between the estimated position and the position of the respective base station and is therefore numerically known

System of linear equations:

with pi being the difference between this pseudorange and the observed pseudorange

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9.B Circular LaterationPosition Calculation (III)

In matrix notation:

A: contains the partial differentials

b: deviation of the observed pseudorange from the range based on the estimated position

x: searched correction vector of the estimated position

In the best case, the system of equations has a unique solution, which can be obtained by calculating

Problem: in most cases, system of equations is overdetermined (more equations than unknowns) and is based estimations and inaccurate observations -> no unique solution exists

Solution: least square fit for approximating a solution

Idea of least square fit

Minimize the sum of the squares of the residual between the fitted function and the measurement data

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9.B Circular LaterationPosition Calculation (IV)

Compose the squared Euclidian distance of the residual vector :

Condition of the least square fit: minimize the squared Euclidian distance of the residual vector

by building the derivative and setting it to zero:

Solving the following equations for yields the correction for the previously estimated position:

Correction is applied to the estimated position and linearization (Taylor Series) and least square fit are repeated

Iterative process stops if the calculated correction values fall below a predefined threshold

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9.C Hyperbolic LaterationOverview

Hyperbolic lateration is based on range differences

Hyperbola

Set of all points for which the difference in the range to two fixed points is constant

Fixed points are denoted as foci and are given by a pair of two base stations

Observable: range difference between the target and a number of base stations

Target's position is given by the intersection of hyperbolas (in 2D) or hyperboloids (in 3D) defined by the range differences

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9.C Hyperbolic LaterationError Potential and Position Calculation

System of equations for hyperbolic lateration in 3D:

Error potential because of inaccurate determination of range differences:

Linearization of non-linear system of equations by using a Taylor series (see circular lateration)

Coefficients of the resulting design matrix:

with

Note: range differences are usually measured with regard to a selected reference base station, indicated here by i=1

Approximation of the solution by applying a least square fit (in analogy to circular lateration)