navka smartphone rtk - cycle slip and ambiguity robust ... · georeferencing on smartphones and...

3rd GNSS Raw Measurements TF WS Jäger/Diekert GSA Prague, 26-06-2019

NAVKA Smartphone RTK - Cycle Slip and Ambiguity

Robust GNSS Algorithms & Software for GNSS

Raw Data on the Smartphone

Reiner Jäger1) and Julia Diekert2)

1), 2) Hochschule Karlsruhe Technik & Wirtschaft (HSKA) - University Applied Sciences

1) Faculty for Informationmanagement and Media (IMM)

Head of Laboratory on GNSS and Navigation

Projectleader Institute for Applied Research (IAF)

Honorary Professor Siberian State University of Geosystems and Technologies

2) Laboratory on GNSS and Navigation

RaD

www.dfhbf.de, www.goca.info, www.moldpos.eu

www.geozilla.de, www.navka.de

Email: [email protected]

http://www.dfhbf.de/

http://www.goca.info/

http://www.moldpos.eu/

http://www.navka.de/


DGNSS-Positioning

Using Classical Amgbiguity

Function Method (AFM)

and

Redesigned AF (RAF)


Observation Equations and Euler-Theorem

Observation Equations

λRi,t = xs − x 2 + ys − y 2 + zs − z 2

t− Ni ∙ λ + Di,t ∙ λ

λRi,t

λ−1

λ∙ xs − x 2 + ys − y 2 + zs − z 2

t

xi

= − Ni + Di,t

yi

Euler-Theorem: eiz = cos 𝑧 + 𝑖 ∙ sin 𝑧

Euler-Theorem applied to the right side of Observation Equations

𝑧 =: 2π ∙

yi𝑦𝑖𝑒𝑙𝑑𝑠

൞cos 𝑧 = cos 2π ∙ yi = cos −2π ∙ Ni + Di,t = −1

sin 𝑧 = sin 2π ∙ yi = sin −2π ∙ Ni + Di,t = 0


Classical Ambiguity Function Method

Using the observation Equations on the left side of Euler-Theorem

1

𝑛∙𝑚

ei∙(2π∙xi) =

1

𝑛∙𝑚

ei∙2π∙(

λRi,t

λ−1λ∙ xs−x

2+ ys−y2+ zs−z

2t)= n ∙ m

3D Grid

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Postprocessing!


Anwendung

Übereinstimmung

100 %

0 %

XYZ

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Ambiguity-Resolution on GNSS-Processing

Parameter Estimation Procedures


Ambiguity-Resolution on GNSS-Processing

Parameter Estimation Procedures

QIF equals L3 („QIF-L3“) without an external

Iono-Model. QIF-L3 or full QIF are appropriate

for the Redesigned Ambiguity Function (RAF)


Redesigend Ambiguity Function Method (RAF)

With expection values for Observations and Parameters

cos (2π/λ ∙ 𝜎𝑙𝑖,𝑡 ∙ 1/ 𝜎𝑙

𝑖,𝑡 ∙ (෨λRi,t− xs − 𝑥 2 + ys − 𝑦 2 + zs − ǁ𝑧 2

t) − 1 = 0

sin (2π/λ ∙ 𝜎𝑙𝑖,𝑡 ∙ 1/ 𝜎𝑙

𝑖,𝑡 ∙ (෨λRi,t − xs − 𝑥 2 + ys − 𝑦 2 + zs − ǁ𝑧 2

t= 0

Using the nonlinear Observation on the right side of Euler Theorem

cos 2π ∙ (λRi,t

λ−1

λ∙ xs − x 2 + ys − y 2 + zs − z 2

t)

xi

− 1

sin 2π ∙ (λRi,t

λ−

1

λ∙ xs − x 2 + ys − y 2 + zs − z 2

t)

xi


Redesigned Ambiguity Function Method (RAF)

Homogenization and Introduction of Homogenized Observations

cos (2π/λ ∙ 𝜎𝑙𝑖,𝑡 ∙ ( ҧሚ𝜆𝑅

𝑖,𝑡 − xs − 𝑥 2 + ys − 𝑦 2 + zs − ǁ𝑧 2t/ 𝜎𝑙

𝑖,𝑡) − 1 = 0

sin (2π/λ ∙ 𝜎𝑙𝑖,𝑡 ∙ ( ҧሚ𝜆𝑅


𝑖,𝑡) = 0

cos (2π/λ ∙ 𝜎𝑙𝑖,𝑡 ∙ ( ҧ𝜆𝑅

𝑖,𝑡+ തɛ𝑅


𝑖,𝑡) − 1 = 0

sin (2π/λ ∙ 𝜎𝑙𝑖,𝑡 ∙ ( ҧ𝜆𝑅

𝑖,𝑡+ തɛ𝑅


𝑖,𝑡) = 0

L1-Norm-Estimation (Robustness) – Strict Approach

σ | ҧ𝑣𝑅𝑖,𝑡|=Min| ො𝐱 with Side-conditions

cos (2π/λ ∙ 𝜎𝑙𝑖,𝑡 ∙ ( ҧ𝜆𝑅

𝑖,𝑡+ ഥ𝑣𝑅


𝑖,𝑡) − 1 = 0

sin (2π/λ ∙ 𝜎𝑙𝑖,𝑡 ∙ ( ҧ𝜆𝑅

𝑖,𝑡+ഥ𝑣𝑅


𝑖,𝑡) = 0

Robust RTK Adjustment


PREGON-X: PREcise Positioning and

Georeferencing on Smartphones and Tablets

• Development of LowCost External Hardware

• L1/L2 ublox F9-ZED

• Bluetooth LE for communication to Smartphone

• Implementation of Robust Positioning

Algorithms especially for Smartphones

and Tablets, i.e.

• Implementation of the RAF Method into

RTKLIB (Takasu 2009)

• as L2 Norm estimation and Robust L1 Norm estimation

• additional integration of smartphone IMU data, camera data and a

laser for the estimation of a full navigation state

• Datum Transformation


PREGON-X: PREcise Positioning and

Georeferencing on Smartphones and Tablets

Transition from External GNSS to Internal GNSS

• using same GNSS Algorithms, integrated into SmartphoneRTK,

developed by NAVKA Team (Karlsruhe University of Appl. Sciences)

• Realtime stream plugin integrated into Google GnssLogger

• Both for prototype and educational purpose


Exemplary Results

Smartphone Static Tests on Rooftop

• open sky environment

• reference measurements on pillar with known ETRF89 coordinates

• two smartphones (Samsung S9, Huawei P10)

• L1/L2 receiver with

geodetic antenna

• 30 min samples


Exemplary Results for SmartphonesLambda Algorithm with Kalman Filter (Static) RTKLIB

• DGNSS of the Samsung S9 with a nearby base station

• Difference to average position

• yellow = float solution, green = fixed solution

no fix in 20 minutes,

but convergence after

10 minutes

Stddev Smartphone

(float solution):

2D: 0.48 m

Height: 0.54 m


Exemplary Results for Smartphones

Smartphone Samsung Galaxy 9 on ETRF89 reference point

• Systematic error in E-W of approx. 0.5 m from multipath


Comparison of Lambda vs. RAFUsing L1/L2 GPS receiver

• Measurement sample was below a tree

• Obstructed sky view resulted in cycle slips and unstable ambiguity

fixing for real time measurements

• Redesignded Ambiguity Function (RAF) unaffected by cycle

slips. Only needs good approximate position on half wavelength

accuracy.To be achieved for L1/L2c or E1/E5a by introducing a

widelane (86 cm wave) into the RAF QIF parameter estimation

Lambda with KalmanFilter (RTKLIB) Redesigned Ambiguity Function (RAF)


Comparison of Lambda vs. RAF

Using same smartphone data as before

• RAF by L1-norm stable and „ready for positioning“ from the start. No

initial fixing and no ambiguity refixing times in between are wasted.

• RAF noise (right) is non systematic. From the single positions a high

precise solution can be computed by a sequential L1-adjustment.

Lambda with KalmanFilter (RTKLIB) Redesigned Ambiguity Function (RAF)


Summary and Outlook

Redesigned Ambiguity Function (RAF) as robust GNSS algorithm

• Works in RTK mode (static or kinematic)

• No (re-)initialization times lost in favour of precise positioning

from the start

• No ambiguity estimation is needed, because they are

mathematically eliminated

• Good results even under the influence of cylce slips (trees, loss

of signal etc.)

Further modifications and improvements

• Approximate position of have wavelenght no problem by

introducing parallel WL linear combination as observation

• New GNSS chips will include multiple frequencies. So ambiguity

and cycle slip robust ionosphere estimation is enabled by QIF-L3

(or full QIF) RAF

• Sensor fusion of all smartphone sensors, especially

• MEMS IMU sensors (www.navka.de)

• Optical sensor fusion



References

• Zebauser. B. (1999): Zur Entwicklung eines GPS-Programmsystems für Lehre und

Tests unter besonderer Berücksichtigung der Ambiguity Function Methode.

Dissertation. Institut für Astronomische und Physikalische Geodäsie. TU München.

• Takasu (2009): “RTKLIB: Open Source Program Package for RTK-GPS”,

www.rtklib.com

• Bastian (2019): “Redesign der klassischen Ambiguity und Cycleslip freien

Ambiguity-Funktions-Methode (AFM) als echtzeitfähige L2-/L1-Normschätzung im

Gauß-Markov-Modell (RAF) und Implementierung sowie Evaluierung unter

MATLAB und RTKLIB/C++”, Bachelorthesis at University of Applied Sciences,

Karlsruhe

• PREcise GNSS ON Smartphones (PREGON-X) ZIM-Project: www.navka.de


navka smartphone rtk - cycle slip and ambiguity robust ... · georeferencing on smartphones and...

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