Design and Evaluation of Integrity Algorithms for PPP in

Kinematic ApplicationsKazuma Gunning, Juan Blanch, Todd Walter, Stanford University;

Lance de Groot, Laura Norman, Hexagon Positioning Intelligence, Canada

Bottom line up front:

We use solution separation techniques developed for aviation combined with a PPP engine to produce meter-level protection levels for static, driving, and flight scenarios.

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Solution Separation

Position Solution

Covariance

Nominal model-no faults are present

Protection Level?

PRN 1

PRN 2

PRN 3

PRN 4

PRN 5

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Solution Separation

Faulted MeasurementClock and/or ephemeris

Large multipath

PRN 1

PRN 2

PRN 3

PRN 4

PRN 5

Producing fault-tolerant subsets

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Solution Separation

PRN 1

PRN 2

PRN 3

PRN 4

PRN 5

Protection Level 5

Precise Point Positioning (PPP)• External precise orbit and clock corrections

• Kalman filter to estimate float carrier phase ambiguities, tropospheric delay

• Able to achieve sub-decimeter accuracy after convergence

• Globally available

6User Receiver

𝚽𝒊𝒇(𝒊)

= 𝒙𝒔(𝒊)− ෝ𝒙𝒓𝒙 + 𝒄 𝒃𝒓𝒙,𝒄 − 𝒃𝒔

(𝒊)+ 𝑻(𝒊) + 𝒄𝜹𝒕𝒓𝒆𝒍 + 𝒃𝒑𝒘𝒖

𝒊 − 𝑨𝒊 + 𝚫𝐫𝐫𝐜𝐯𝐫𝒊

+ ො𝝐 𝒊 + 𝝐 +⋯

IGS sat position

Rx position

IGS sat clock

Rx clock tropodelay

relativistic effects

phase wind-up

carrier phase

ambiguity

site displacement

effects

PPP Algorithm

Estimated errors

Measurement noise

• General strategy: • Use precise external inputs and model as many effects as possible,

and estimate the rest

Estimated error could include multipath, orbit and clock error, etc.

PPP Algorithm

Kalman filter state vector (real-time sequential estimator)

𝑠𝑡𝑎𝑡𝑒 = 𝑥𝑟𝑥 , 𝑦𝑟𝑥 , 𝑧𝑟𝑥 , 𝑏𝑢,1,… , 𝑏𝑢,𝑛, Δ𝑇, 𝐴1, … , 𝐴𝑚, 𝜖1, … , 𝜖𝑚′

Measurements:

𝚽𝒊𝒇(𝒊)

= 𝒙𝒔(𝒊)− ෝ𝒙𝒓𝒙 + 𝒄𝒃𝒓𝒙,𝒄 +𝒎(𝒊)𝚫𝑻 − 𝑨𝒊 + 𝒐𝒕𝒉𝒆𝒓 𝒎𝒐𝒅𝒆𝒍𝒔

…

𝝆𝒊𝒇(𝒊)

= 𝒙𝒔(𝒊)− ෝ𝒙𝒓𝒙 + 𝒄𝒃𝒓𝒙,𝒄 +𝒎(𝒊)𝚫𝑻 + 𝒐𝒕𝒉𝒆𝒓 𝒎𝒐𝒅𝒆𝒍𝒔

…

Given measurement noise characteristics, process noise, etc., estimate!

Subsets and Parallel Filters

12345

PRN

12345

PRN

12345

PRN

…

All-in-View

Subset 1

Subset 5

Solution separation requires multiple Kalman filters running in parallel

Steps have been taken to reduce computational complexity

Simplified error modeling to reduce statesSharing computations across subsets

t = 1 2 3 4 5 6 7 9

Ingest available measurements

Subset management

New subset based on new measurements

State management

Time update

Range Modeling(non-estimated)

f(x(0),t)

Measurement update and

residual checks (measurement

exclusion)

Subset with faulted PRN

Protection level computation and potential signal

exclusion

1 computation per subset

1 computation total-significant time savings

SS PPP Implementation

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Protection Level Algorithms

PL Algorithm Speed Fault Detector

Separation Based- Basic Fast No

Cov. Based Exact Search Too Slow Yes

Cov. Based Approx. Fast Yes

Cov. Based Approx. Coarse Fast Yes

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Dataset overview

Stanford, California, USA

1. Static rooftopNominal conditions

Injected step error

Injected ramp error

Calgary, Alberta, CA

2. Open sky drivingNominal ConditionsInjected ramp error

3. Suburban drivingAtlantic City, New Jersey, USA

4. Flight

All runs post-processed

MGEX precise clock and ephemeris

PHMI = 10-7

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• Stanford Aero/Astro department rooftop receiver STFU (IGS MGEX Network)

• Trimble NetR9

• 1 hour of static data on November 7, 2017

• 1 Hz GPS (L1C-L2P semi-codeless), GLONASS (L1C-L2P)

• Truth position from IGS station solution

• Processed in dynamic mode

Dataset 1- Stanford rooftop

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Step fault injection• Step error of 20 meters added to precise clock of GPS PRN 8 five

minutes into the run

• Bad measurements are caught in the residual check

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Ramp fault injection• Ramp error injected into PRN 8 precise clock- 9 meters per hour

• Slow enough that much of the ramp is pulled into the error states associated with PRN 8.

• Once the PL threshold is tripped, all PRN 8 measurements are excluded henceforth, and the filter is reset

Subset with PRN 8 excluded becomes new all-in-view solution

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• Just outside Calgary International Airport

• Benign, open sky environment

• 1 Hour Driving on March 1, 2018• Seven laps

• Receiver: NovAtel OEM 7500

• 1 Hz GPS (L1C-L2P semi-codeless), GLONASS (L1C-L2P)

• Truth: Novatel OEM729 with tactical-grade IMU

Dataset 2 - Open Sky Driving

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Open sky driving bounding and solution error

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Dataset 3- suburban driving• Suburban Calgary

• Largely benign environment with occasional full measurement outages

• 1 Hour Driving on March 1, 2018

• 1 Hz GPS (L1C-L2P semi-codeless), GLONASS (L1C-L2P)

• Truth: Novatel OEM729 with tactical-grade IMU

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Suburban driving bounding and solution error

Overpass

Heavy foliage

Tall buildings

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Dataset 4- flight• FAA Global 5000 Aircraft

• 1 Hz GPS (L1C-L2P semi-codeless), GLONASS (L1C-L2P)

• Trimble BD935

• 2 Hours of Flight Data on 6-30-2017

• Truth: NRCan PPP

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Flight bounding and solution error

Normalized Position Error Statistics

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Thank you to Hexagon Positioning Intelligence for partneringThank you to FAA for flight dataThank you to IGS for Precise Products

Solution separation techniques have been used to produce meter-level protection levels for automobile and aviation scenarios

Min. Hor. PL Median PL

Static 1.70 m 2.13 m

Car 1 2.05 m 2.76 m

Car 2 2.86 m 3.84 m

Flight 1.08 m 1.54 m

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