Transcript Map-Matching for Outdoor Tracking Guobin (Jacky) Shen [email protected] Microsoft Research Asia Mobile Location Sensing Tutorial, Mobisys’13.

Map-Matching
for Outdoor Tracking
Guobin (Jacky) Shen
[email protected]
Microsoft Research Asia
Mobile Location Sensing Tutorial, Mobisys’13.
Applications
• Navigation
• Personal location diary:
– Keep track of trips and location-based notes
• Traffic estimation from crowd/fleet sources
• Package, trash tracking
– Low power embedded chip
• Etc, etc, …
What is map matching?
• Map-matching is the process of aligning a
sequence of observed user positions with the
road network on a digital map.
• Essentially, a map-constrained filtering
process
Map Data
Raw sensor
Data
Location
Samples
Matching
Engine
Trajectory
Typical sensors and techniques
• Sensors:
– GPS
– WiFi
– Cellular
– IMU (accelerometer,
compass, gyroscope)
GPS
• Techniques:
Relative
Energy
Consumption
WiFi
IMU
– Hidden Markov Model
Cellular
5-10m 75m
150m
300m
A trivial task when using GPS?
• Seemingly trivial
– GPS’s accuracy: < 10m
– “nearest road” alg.
• But it’s not always true.
– Sampling frequency:
• Unaffordable continuous
location acquisition
• GPS is energy hungry
– Canyon effect
More challenging using other sensors
The Case of WiFi
The Case of Cellular
BRIEF INTRODUCTION TO HMM
Markov Models
• Set of states: {s1 , s2 ,, sN }
• Process moves from one state to another generating a
sequence of states : si1 , si 2 ,, sik ,
• Markov chain property:
– Probability of each subsequent state depends only on
what was the previous state:
P(sik | si1 , si 2 ,, sik 1 )  P(sik | sik 1 )
• To define Markov model needs these probabilities:
– Transition probabilities, aij  P(si | s j )
– Initial probabilities  i  P(si )
Example of Markov Model
0.3
0.7
Rain
Dry
0.2
0.8
• Two states : ‘Rain’ and ‘Dry’.
• Transition probabilities. E.g., P(‘Dry’|‘Rain’)=0.7
• Initial probabilities:
– P(‘Rain’)=0.4 , P(‘Dry’)=0.6 .
Calculation of sequence probability
• By Markov chain property, prob of state sequence:
P(si1 , si 2 ,, sik )  P(sik | si1 , si 2 ,, sik 1 ) P(si1 , si 2 ,, sik 1 )
 P(sik | sik 1 ) P(si1 , si 2 ,, sik 1 )  
 P(sik | sik 1 ) P(sik 1 | sik 2 ) P(si 2 | si1 ) P(si1 )
• Prob of the state sequence {‘Dry’,’Dry’,’Rain’,’Rain’}
P({‘Dry’,’Dry’,’Rain’,Rain’} )
= P(‘Rain’|’Rain’) P(‘Rain’|’Dry’) P(‘Dry’|’Dry’) P(‘Dry’)
= 0.3*0.2*0.8*0.6
Hidden Markov models.
• Markov Model:
– Set of states, sequence of states,
– Markov chain property,
– Transition prob A, Initial prob .
• Hidden Markov Model:
– States are not visible, but each state generates one random
observable/visible states {v1 , v2 ,, vM }
• To define an HMM, needs additional probabilities:
– Emission/Observation probabilities B: bmi = P(vm | si )
• HMM: M=(A, B, )
Example of Hidden Markov Model
• Two states : ‘
0.3
– Low’ and ‘High’
atmospheric pressure.
0.7
Low
• Two observations :
High
– ‘Rain’ and ‘Dry’.
• Transition probabilities
0.2
0.6
Rain
0.4
0.8
0.6
0.4
Dry
– Same as before
• Observation probabilities :
P(‘Rain’|‘Low’)=0.6 ,
P(‘Dry’|‘Low’)=0.4 ,
P(‘Rain’|‘High’)=0.4 ,
P(‘Dry’|‘High’)=0.3
• Initial probabilities:
P(‘Low’)=0.4,
P(‘High’)=0.6
Main problems using HMMs
• Given the HMM M=(A, B, ) and the observation
sequence O=o1 o2 ... oK ,
– Evaluation problem: calculate the probability that the
model M has generated sequence O.
– Decoding problem: calculate the most likely sequence of
hidden states Si that produced this observation sequence O.
• Learning problem. Given some training observation
sequences O, and general structure of HMM
(numbers of hidden and visible states), determine
HMM parameters A, B,  that best fit training data.
Decoding problem
• Given the HMM M=(A, B, ) and the observation sequence
O=o1 o2 ... oK, find the state sequence Q= q1,…, qK which
maximizes P(Q | O ), or equivalently P(Q, O).
o
Trellis
representation
1
o
o
k
s1
s1
s2
s2
a1j
k+1
o
(
K
= Observations)
s1
s1
s2
s2
sj
si
a2j
si
si
aij
aNj
Time=
sN
sN
sN
sN
1
k
k+1
K
Viterbi algorithm (1)
• General idea:
– if best path ending in qk= Sj goes through qk-1= Si, then it
should coincide with best path ending in qk-1= Si.
qk-1
s
1
s
i
s
qk
a1j
aij
s
j
aNj
N
– To backtrack best path, keep the predecessors of Sj was Si.
Viterbi algorithm (2)
• Define: k(i) as the maximum probability of producing
observation sequence o1 o2 ... ok when moving along any
hidden state sequence q1… qk-1 and getting into qk= Si .
k(i) = max P(q1… qk-1 , qk= Si, o1 o2 ... ok)
where max is taken over all possible paths q1… qk-1 .
• Recursion formula:
k(i) = max P(q1… qk-1 , qk= Si, o1 o2 ... ok)
= maxi [aijbj(ok)k-1(j)]
Viterbi algorithm (3)
• Initialization:
1(i) = max P(q1= Si, o1) = i bi (o1) , 1<=i<=N.
• Forward recursion:
k(i) = maxi [aijbj(ok)k-1(j)] (1<=j<=N, 2<=k<=K)
• Termination:
Choose best path ending at time K (i.e., maxi [ K(i) ])
• Backtrack best path.
THE CASE OF GPS
Paul Newson and John Krumm, "Hidden Markov Map Matching Through Noise and Sparseness", ACM
SIGSPATIAL GIS 2009, pp. 336-343.
A trivial task when using GPS?
• Seemingly trivial
– GPS’s accuracy: < 10m
– “nearest road” alg.
• But it’s not always true.
– Sampling frequency:
• Unaffordable continuous
location acquisition
• GPS is energy hungry
– Canyon effect
Many people encountered loops in navigation when using GPS.
Three Insights
1. Correct matches tend to
be nearby
2. Successive correct
matches tend to be
linked by simple routes
3. Some points are junk,
and the best thing to do
is ignore them
Mapping to a HMM
Three Insights, Three Choices
1. Match Candidate
Probabilities
2. Route Transition
Probabilities
3. “Junk” Points
Obtaining probabilities
GPS Difference Probability
Distance Difference Probability
0.12
7
Data Histogram
0.1
Data Histogram
6
Gaussian Distribution
Exponential Distribution
5
0.08
4
0.06
3
0.04
2
0.02
1
0
0
0
5
10
15
Distance Between GPS and Matched Point (meters)
Emission Probability Model
20
0
0.5
1
1.5
abs(great circle distance - route distance) (meters)
Transition Probability Model
2
Match Candidate Limitation
• Don’t consider roads
“unreasonably” far
from GPS point
• “Junk Points”
Route Candidate Limitation
• Route Distance Limit
• Absolute Speed Limit
• Relative Speed Limit
Robustness to Sparse Data
Error vs. Sampling Period
1
0.9
• HMM Map Matcher works “perfectly”
up to 30 second sample period
• HMM Map Matcher is reasonably
good up to 90 second sample period
0.8
Route Mismatch Fraction
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Data: http://research.microsoft.com/en-us/um/people/jckrumm/MapMatchingData/data.htm
600
540
480
420
360
300
240
180
120
90
60
45
30
20
10
5
2
1
Sampling Period (seconds)
THE CASE OF WIFI
Thiagarajan, Arvind et al. “Vtrack: Accurate, Energy-Aware Road Traffic Delay Estimation using Mobile
Phones, In Sensys’09, pages 85-98.
Background
• Road Traffic Problem:
– Causes inefficiency, Fuel Waste, Frustration
• Trends:
– More cars on road, more time wasted in traffic
• Smartphone Capabilities
– Massive Deployment
– GPS , WiFi, and Cellular localization capabilities
• The ask:
– Accurate, energy-aware road traffic delay estimation using
mobile phones?
VTrack
• VTrack is a system for travel time estimation using
smart phones sensors (GPS, WiFi).
• Key Challenges
– Sensor unreliability
• GPS outages
• WiFi is only applicable when APs are available
– Energy consumption
• WiFi is more energy efficient (2x) but less accurate
• Need to find optimal sample rate
Key idea: HMM map matching to produce the actual
trajectories using WiFi location estimation
System Architecture
• Users with smartphones (crowdsourcing)
– Run VTrack reporting application
– Report position data periodically to the server
VTrack algorithm
• Preprocess the position samples to remove outliers
– Speed constraint (<200mph)
• HMM map matching
• Bad zone removal
– Viterbi decoding confidences
Raw trace
Outlier removal
& interpolation
Viterbi matching
Bad zone removal
HMM Map Matching
• Hidden states: road segments
• Observables: position samples
• Emission probability:
– Assumed to be uniform, 1/N
• Transition probabilities p = P(Sj,t|Si,t-1):
– If i=j, p= (constant set to <= 1/(dmax+1), where dmax is
maximum out-degree of any intersection).
– If j does not start where i ends, p=0.
– If j does start where i ends, p=  or 0.
Results
• HMM-based map matching
– Robust to noise
– Error < 10%
• When only WiFi
• With 40m Gaussian noise
• GPS available and accurate, periodic sampling helps
with both
THE CASE OF CELLULAR
Thiagarajan, Arvind et al. "Accurate, Low-Energy Trajectory Mapping for Mobile Devices.” NSDI 2011.
Problem statement
• Can we process cellular signal information to
produce accurate trajectories? How accurate?
Motivation
• Push down the energy consumption
– GPS signals are energy-intensive
• Frequent GPS sampling drains battery fast
– Cellular consumes almost no additional energy
• But, existing cellular location
systems aren’t good enough
to find tracks
• Existing map-matching algs.
perform poorly w/ cellular
signals.
Key insights
• Proper preprocessing is crucial!
– Translating raw sensor data to location stamps is a
kind of preprocessing, but not necessarily good.
• Cellular has very localization accuracy, introduce too
much noises.
Map Data
Raw sensor
Data
Sequencing
Location &
Smoothing
Samples
Matching
Engine
Trajectory
Overall workflow
Sensor
Hints
Cell Tower
Fingerprints
Grid Sequencing
Training
Database
Sequence
of Grids
Smoothing and
Interpolation
• Instead, first sequence GSM
FPs on a spatial grid
Sequence of
Coordinates
Segment Matching
Sequence of
Road Segments
• Not convert radio FP to
(lat,lon) coords and then
match to a map
Road Map
Three key steps
HMM fingerprints
to grid sequence
HMM smooth grid
to road segments
HMM for grid sequencing
• Given a sequence of GSM fingerprints,
find most likely sequence of grid cells
– Hidden state: Grid Cell
– Observables: <CellTowerID, RSSI>
• Emission score:
– P(Signature | Grid Cell)
• Transition score:
– P(GCi|GCi-1)
• Decoding:
– max(Emission Score * Transition Score)
Smoothing and interpolation
• Smoothing:
– Step1: centroid(training points in a grid)
– Step2: centroid(Cg in a sliding window)
• Interpolation: to increase the sample rate s.t.,
minimum road segment (~30m) has one sample
HMM for road segment matching
• Hidden state: road segment
• Observables: <lat, lon>
• Emission score:
Score = e
-d 2
• Transition score:
– P(RSi|RSi-1)
Add motion state and turn hints
• Binary motion states: still or moving (from Acc)
• Binary turn hints: turn or not turn (from Compass)
• Consider hints in transition score
– P(RSi|RSi-1)*P(Move|Move Hint)*P(Turn|Turn Hint)
Evaluation results
• 75% precision, 2.4x better than existing approaches
• Sequence first before converting
to <lat, lon> is critical
• Sensor hints lead to small
improvement in system metrics,
but can correct some systematic
errors (e.g., kinks, looping)
THE CASE OF IMU
Santanu Guha, et al., AutoWitness: Locating and Tracking Stolen Property While Tolerating GPS and Radio
Outages, Sensys’10.
AutoWitness
• Objectives
– Detection of theft
– Tracking of the stolen tag
– Pinpointing of the location
• Challenges - Cost & Energy
– Hardware selection
– Theft classifier
– Tracking method
System Overview
Emded tag
Dormant
Motion
Vehicular movement
Motion detection
(vibration dosimeter)
Classification
(Accelerometer)
Distance / turn estimate
(Accelerometer / Gyro)
Transfer to server
(GSM / GPRS)
Path reconstruction
Sufficient time &
RF power available
Turns Angle Estimate
• Gyro  single integration  change in the attitude
• Heading angle detection:
– Absolute value of
1st difference
• Thresholds, Dh & Dl
• Activation time
– From Dh to Dl
Distance Estimate
• 2nd order Butterworth Filter to
remove noise
• Median of 20 samples
 mean of 10 such medians
• Accelerometer
 Double integration
– Leverage still states to reset
accelerometer drift
– Handling curved roads –
angular rotation info
HMM Map Matching
• Hidden states: (compound) road segments
• Observables: as unique to hidden state as possible
– Distance between successive stops
– Total length of the segment (btwn successive turns)
• Initial state:
– Assumed to be uniform, 1/N, all intersections within radius r of
the tag deployed position.
• Transition probabilities p = 𝑃(𝑆𝑗,𝑡|𝑆𝑖,𝑡−1):
– Obtained using Bayesian inferencing
– Jointly determined by distance, d, traveled on segment j and
the angle of turn, , from segment i to j.
• Emission probabilities
Transition probability inference
• Associate estimation margins d for distance, and  for turn
• For travel distance d, road
segments intersecting within
dd and turn within 
form candidate set Ci.
• Set uniform prior prob
Pi(j) = 1/|Ci|.
• Assume Gaussian distribution
for Pi(d|j)~N(u, 2), trained
from experimental data.
• Transition prob: 𝑃𝑖(𝑗|𝑑) = 𝑃𝑖(𝑑|𝑗)𝑃(𝑗)
𝑃(𝑑)
Emission probability
• Cause: distance estimation error
• Let 𝑃(𝑦|𝑥) denote the probability of obtaining x from
distance estimation when the true distance is y.
– 𝑃(𝑦|𝑥) = 0, if |y−x|> d,
– 𝑃 𝑦 𝑥 = 1 − |𝑦−𝑥|
, else.
𝑦
• Pinning to the traffic light
Evaluation
THE CASE OF CELLULAR + IMU
He Wang, et al., WheelLoc: Enabling Continuous Location Service on Mobile Phone for Outdoor Scenarios,
Infocom’13.
Motivation
• Many applications call for location service as a first
class citizen of modern mobile OS
– Always available, good accuracy
personal diary
geo-fencing
location based reminder
– GPS: energy hungry, long time cold start, canyon effect
– WiFi: energy hungry, coverage problem, low accuracy
– Cellular: energy efficient, very low accuracy
WheelLoc
• Seeks to leverage energy-efficient IMU
sensors, cellular and road-map for continuous
location service
cell tower
distance and direction
More advanced
pre-processing
Raw sensor
Data
road map
Map Data
Distance &
Direction
Matching
Engine
Trajectory
Overview
Sensor Readings
Motion State Detection
Cell ID
Distance and Direction
Cell Tower Location
DB
Map Matching
Interpolation and Extrapolation
Road Map
Motion State Detection
• Framework
{F1, F2, F3, …}
sensor readings
feature extraction
• Driving v.s. Still
slight vibration
decision tree
Mobility Trace Estimation – Driving
• Distance and Distance Estimation
a2
a
a1
time
large horizontal acceleration difference
heading vector =
a1 – a2
Mobility Trace Estimation – Driving
• Speed and Distance Estimation
Mobility Trace Estimation – Driving
• Direction Estimation
x
compass
y
z
heading direction
calculate direction from magnetic field directly
Mobility Trace Estimation – Driving
• Direction Estimation
x
y
z
heading vector
projection of magnetic field
magnetic field
Mobility Trace Estimation – Cycling
• Speed and Distance Estimation
Slow (1 Hz)
Fast (2 Hz)
Mobility Trace Estimation – Cycling
• Direction Estimation
Take right chances!
Mobility Trace Estimation – Evaluation
Distance error is within 10% most of time.
Direction error is within 25 degree most of time.
Map Matching – HMM
O
1
observations:
O
2
O
3
...
S
2
S
3
...
emission
S
1
states:
transition
states in WheelLoc:
road segments on the track
cell tower
emission
distance
direction
transition
69
The probabilities
• Initial states: determined by cell tower coverage
• Emission probability
– A road segment has large intersection with coverage
of multiple cell towers
– 𝑃 = 𝑁(𝑑𝑖𝑠𝑡 𝑙𝑡, 𝑐𝑡 , 𝑅)
• Transition probability: also Bayesian inferencing
– Similar to AutoWitness
• Prune candidates with estimated distances and turn angles
• Error distribution of estimated distances (as the prior prob.)
– Apply cell tower coverage constraint
System Evaluation – Location Accuracy
376
30
71
APPLICATION-AWARE ENERGY
SMARTNESS
Kaisen Lin, et al., Energy-Accuracy Trade-off for Continuous Mobile Device Location, Mobisys’10.
Location is important
• Social Networking
– Show the closest friends
• Mobile Search/Ads
– Nearby restaurants
– Offers for nearby products/tasks from
your calendar or shopping lists
– Nearest movie show times, events
• Track based apps
• Context aware apps
• But continuous accurate location is
energy intensive
Observations
• Not all apps need high accuracy all the time
• Sensor accuracy varies across sensors, changes with
time/space
Accuracy needed for restaurant
search in Portland, OR
A-Loc Location Service
Input
Dynamic
Accuracy
Requirement
Sensor Energy
Model
Dynamic Sensor
Accuracy Model
Output
Sensor Selection
Algorithm
Sensor Data
Location
Sensor Accuracy Model
• Error, x, learned as a function of 2D location
– Used in conditional distribution p(z|x) for algorithm
• Characterizes expected accuracy of each sensor in
different regions
– Only load city around current location to save memory
Error ()
6
4
2
3
0
1
1
2
3
X1
4
X2
Sensor Energy Models
• Energy to obtain sensor reading
– Switching energy included if the radio not already on for
other usage (Eg. WiFi power on: 115mJ and off: 65mJ)
– Cold and warm start differ for GPS
100000
Energy (mJ)
10000
1000
100
10
1
Min
Max
Dynamic Accuracy Requirements
• Accuracy required depends on density of
interesting entities
– Search: density of vendors
– Ads: density of advertisers for products/tasks mined
from user’s calendar or shopping lists
• Eg. Density of movie theatres, density of
competitor franchises
– Social networks: density of nearby friends
– Context based device optimizations: geographical
separation between home, office, malls etc
Accuracy Requirement
• Can be determined using
known Yellow Pages/POI
data for most cases
• Easy to determine if
accurate location known
– Need to determine
accuracy requirement
using only estimated
location
• Guaranteed to yield
correct list of nearest
entities
Eg. Accuracy needed for pizza restaurant search
in Portland, OR. Darker shades represent higher
accuracy needed.
A-Loc Location Service
Input
Dynamic
Accuracy
Requirement
Sensor Energy
Model
Dynamic Sensor
Accuracy Model
Output
Sensor Selection
Algorithm
Sensor Data
Location
Sensor Selection Algorithm
• Predict error for each modality
– Suppose x = location (estimate) and z =
observation (2D vectors)
• If modality i were to be selected:
p(x|zi) = p(zi|x) p(x|z(t-1))
Distribution of Sensor
predicted model at x
location
Belief of location
based on past
observation
ei
Predicted error: spread of
distribution p(x|zi)
Take weighted mean over
predicted zi since
computed before sensing
Algorithm (contd.)
• p(x|z(t-1)): Location belief based on prior
observation
– Obtained via any existing prediction method
• 2nd order HMM (considers direction of motion)
• linear extrapolation in new locations (HMM not yet learned)
– Can incorporate shared knowledge on where mobile users
more likely to be (land use data, prior locations)
• Using error expected from each modality, select one
that meets the required error for lowest energy
Bayesian Estimation Algorithm
User
Data
Global
Data
User Query
p(x|z(t-1))
Energy
Model
Location model
(prior)
accuracy
constraint
posterior
Selection
Algorithm
Sensor model
p(zi|x)
Sensor
Observation
Location
Past
Observations
p(x|zi) = p(zi|x) p(x|z(t-1))
Summary
• Covered several representative work
• HMM is an effective map-matching method
• Proper pre-processing (and post-processing) is
crucial towards improved system performance
• Multi-source sensor fusion and map matching is
one promising direction towards continuous and
accurate location provisioning.
Major References
•
•
•
•
•
•
•
Paul Newson and John Krumm, “ Hidden Markov Map Matching Through Noise and Sparseness,”
ACM SIGSPATIAL GIS 2009, pp. 336-343.
Arvind Thiagarajan, Lenin Ravindranath, Katrina LaCurts, Samuel Madden, Hari Balakrishnan, Sivan
Toledo, and Jakob Eriksson, “Vtrack: Accurate, Energy-Aware Road Traffic Delay Estimation using
Mobile Phones,” In Sensys’09, pages 85-98.
Arvind Thiagarajan, Lenin Ravindranath, Hari Balakrishnan, Samuel Madden, and Lewis Girod,
“Accurate, Low-Energy Trajectory Mapping for Mobile Devices,” in NSDI 2011.
Santanu Guha, Kurt Plarre, Daniel Lissner, Somnath Mitra, Bhagavathy Krishna, Prabal Dutta and
Santosh Kumar, AutoWitness: Locating and Tracking Stolen Property While Tolerating GPS and Radio
Outages, in Sensys’10.
Arvind Thiagarajan, James Biagioni, Tomas Gerlich and Jakob Eriksson, “Cooperative Transit Tracking
using Smart-phones,” in Sensys’10.
He Wang, Zhiyang Wang, Guobin Shen, Fan Li, and Feng Zhao, “WheelLoc: Enabling Continuous
Location Service on Mobile Phone for Outdoor Scenarios,” in Infocom’13.
Kaisen Lin, Aman Kansal, Dimitrios Lymberopoulos and Feng Zhao, “Energy-Accuracy Trade-off for
Continuous Mobile Device Location,” in Mobisys’10.