1

Cognitive Personal Positioning Based

on Activity Map and Adaptive Particle

Filter

Presented by: Hui Fang (NTU)

Co-authors:Wen-Jing Hsu (NTU)

Larry Rudolph (MIT)

MSWiM 2009

Outline

Background and Motivation• Personal Positioning

My Research Focus• Mining User Positional Log• Map-guided Filter Positioning

My Conclusion

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Background and Motivation

Personal Positioning refers to the inference of a mobile user’s position and movement with sensors and historical data for wearable devices.

Challenges Human behavior difficult to characterize Sensor functions are limited ( power,

accuracy)

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GPSCell Tower

Smart Phone

Personal Historical Data

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2008-01-23 19:51:46CellID=(525, 5, 12, 51153)GPS=(1.34690833333333,

103.678925)

2008-01-23 19:53:06CellID=(525, 5, 12, 13901)GPS=(1.34690833333333,

103.678925)

2008-01-23 19:55:46CellID=(525, 5, 12, 51683)GPS=None

2008-01-23 19:55:51CellID=(525, 5, 12, 51683)GPS=(1.34690833333333,

103.678925)

2008-01-23 19:55:56CellID=(525, 5, 12, 51683)GPS=(1.34690833333333,

103.678925)

History repeats itself!Can we learn from these accumulating logs?

Disjoint traces are formed Some traces get connected

Motivation and Application Scenarios

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Smart device learns its owner’s movement from both logs and new measurement, and applies the knowledge to provide personalized location services to user.

Map learning, the process of transforming raw data into a suitable representation

Localization, the process of deriving the current position of the mobile user

Path planning, the process of predicting a future path given the current position

My Research Focus

Mining Personal Historical Data• Identifying significant places• Identifying representative paths• Identifying user activity map

Map-guided Filter Positioning

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Identifying Significant Places

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Dwelling time: average time staying at the place

Density: number of samples within the place

The number of significant places remains relatively invariant

SPs are identified as office, gym, residence, and playground etc.

Identifying Representative Paths

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segmentation

raw data

traces paths

consolidation

PCM: Pair-wise Curve Merging AlgorithmCompare every two traces, and merge similar

segments in terms of their Hausdorff distanceRepeat this until there is no more

substitutions

PCM: Pair-wise Curve Merging Algorithm

PCM algorithm runs in O(n2mlogm) time, where n is the number of traces and m the maximum length of traces

P΄ ,Q΄ are the new curves obtained from P and Q respectively after executing subroutine merge(P,Q,ε). If the distance between P and Q is less than ε, then the distance between any two curves among {P,Q, P΄ ,Q΄} is less than ε

M = { Pi } is a set of traces, and V is the set of the trace vertices of M. If a path expansion U(Q, ε /2) covers all traces in M, then a polygonal curve P* can be constructed by a subset of V such that:

U(P*, ε ) covers all traces in M, and | P* | ≤ |Q|

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User Activity Map

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User activity map includes rich information rather than a 2D graph

Each vertex saves coordinates, radius, dwelling time, and density

Each edge saves average speed, number of traversals, and path width

User activity map provides an efficient basis for personal positioning

My Research Focus

Mining User Positional Log

Map-guided Filter Positioning• Modeling on User Habit• Adaptive Sampling

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Positioning via Particle Filter

Motivation Dealing with User Non-Linear Movements Sampling on Map Branches to Improve Accuracy

System Formalization User Habit Dynamics Particle Weight Update

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Modeling User Dynamics Observation

User tends to follow the same paths of activity map as before. Position knowledge can be adjusted by new measurement.

Predict directions When nearing an edge of the map, follow this edge When nearing a vertex of the map, follow outgoing edges

E(x) defines a set of edges which indicate likely directions for a point x

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Modelling User Dynamics-II Habit-guided prediction. When nearing an edge e, user follows

the edge direction with a tendency to return to the edge

G(x): x’s nearest point in the graph A(x): distance vector from x to the graph dot(x): speed

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samplings

Modelling User Dynamics-III When nearing a branching

point v, sampling user positions on outgoing edges according to pdf(v)

xk-1 : position at time step k-1

v: xk-1 nearest point in graph

e1, e2: v’s outgoing edges, with transition probability 0.3,0.7 respectively

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Stability of Map-Guided Dynamics System

System ConvergenceMap-guided filter positioning system converges to the user activity map for long run when b is negative. (Lemma 4.1)

Certainty Estimate The confidence covariance can be obtained by Lemma 4.2

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Optimal Particle Weight Updating

xk: actual position at step k

fk(xk-1i): prediction

zk: observation

qk, rk: radii of confidence ellipse

d: distance between observation and prediction

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wki = exp{ –d2/2(qk

2+rk2)} wk-1

i

Optimal solution chooses the proper importance density to minimize the variance of different weights.

Optimal importance density can be obtained by Lemma 4.3

Outline: Map-guided Filter Positioning Algorithm

1. User’s position is estimated by particles with weights { (xi, w i): i = 1,..., Ns}, where i the index of particle

2. Generate particles from user dynamcis (prediction)

importance density p(xk |x

k-1i), where k the time step

3. Update particles’ weight by observation zk (smoothing)

wki = p(z

k|x

ki) w

k-1i

4. Output the particle with maximum weight.

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Adaptive Map-Guided Filter Positioning

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Variable number of particles is sampled around branching points

Let N1 be a minimum number of particles in use

For each time step:• If nearing an edge, set the

number of particles to be N1 ; • Otherwise (i.e., nearing a

branching point), set it to be N1 * #(outgoing edges).

Experiment of Personal Positioning

User historical records

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Particles sampled along a journey, within user activity map

My Conclusion

I present

construction algorithm of user activity map that offers

provable consistency guarantee

adaptive positioning model that guarantees optimal

sampling and efficiency

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Thank You

Q&A

Hui Fang

Nanyang Technological University

hfang@ntu.edu.sg

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