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Dynamic Model-Based Filtering forMobile Terminal Location Estimation

Michael McGuire

Edward S. Rogers Department of Electrical & Computer Engineering

University of Toronto,

10 King’s College Road, Toronto, Ontario, Canada M5S 3G4

mmcguire@dsp.toronto.edu

Dynamic Model-Based Filtering for Mobile Terminal Location Estimation – p.1/51

Outline

1. Signal Processing for Future Wireless CommunicationsSystems.

2. Introduction to Mobile Terminal Location.

3. Zero Memory Estimation

4. Dynamic Estimation

5. Conclusions.

6. Future Work.

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Evolution of Wireless Services

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Mobility & Multimedia

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Mobility & Multimedia

3G Systems

{

UMTS (ETSI)IMT-2000 (ITU)

Support user bit rates up to 2 MbpsHigh mobility environment: 144 kbps

Ad Hoc Systems

{

IEEE 802.11Bluetooth

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Signal Processing for Wireless

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Signal Processing for Wireless

Key problems:CapacityResource allocationConnection managementChannel management

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Signal Processing for Wireless

Present: Reactive control methods

Future: Proactive control methodsRequires future system state estimation.

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State Estimation

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State Estimation

Adaptive estimationLearning model.Adapting to changing model.

Estimation techniquesParametricNon-parametric

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Mobility Management

Need to know resources that terminals require in futurePrediction of future locations.

ChannelsHandoff algorithmRouting

Power/Bandwidth allocationPower controlCode selection (CDMA)

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Mobility Management

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Mobile Terminal Location

Locating mobile terminal from radio signal

ApplicationsResource allocationLocation sensitive informationEmergency communications

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Terminal Location Methods

Handset basedPerception of user privacy.Currently greater accuracy.

Network basedCheaper terminals.Greater potential accuracy

FCC RequirementsConfiguration Accuracy Requirement

> 67% > 95%

Handset 50 m 150 mNetwork 100 m 300 m

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Terminal Location Measurements

Received Signal Strength(RSS),Time of Arrival (ToA),Time Difference of Arrival (TDoA).

Angle of Arrival (AoA).

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Terminal Location Measurements

Measurement Type Advantages Disadvantages

Received Signal Strength(RSS)

• low cost measurements• simple computations

• low accuracy in large cells

Angle of Arrival (AoA) • simple computations • specialized antennae• low accuracy in large cells

Time of Arrival (ToA) • time measurement re-quired for TDMA/CDMAnetwork operation

• simple computations

• synchronized network re-quired

• receiver must know timeof transmission

• expensive measurement

Time Difference of Arrival(TDoA)

• time measurement re-quired for TDMA/CDMAnetwork operation

• receiver does not needtime of transmission

• synchronized network re-quired

• expensive measurement• complex calculations

TDMA - Time Division Multiple Access, CDMA - Code Division Multiple Access

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Radio Signal Measurements

Non-linear effects make problem more complex

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Radio Signal Measurements

τ (k) is the vector of propagation time measurements forsample time k

τ (k) = d(k) + ε(k)

d(k) is the vector of propagation distances.ε(k) is the vector of measurement noise.

z(k) is ToA/TDoA measurement vector:

z(k) = Fτ (k)

F is the measurement difference matrix.

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Geometric Dilution of Precision (GDOP)

High Precision Geometry

Low Precision Geometry

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My Contribution

1. Improved Zero Memory Estimation

2. Bounds on Zero Memory Estimation Error

3. Model-based Dynamic EstimationNew Filter Algorithm Developed

4. Bound on Dynamic Estimation Error

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Zero Memory Estimation

Previously proposed techniques are MaximumLikelihood Estimators(MLE).

Problems with MLE:Prior knowledge is ignored.Assumed Line of Sight (LOS) propagation model.

NLOS is common in urban areas of interest.

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Zero Memory Estimation

Observations:Statistical knowledge of terminal position availablefrom hand off algorithm.Propagation survey made during networkconfiguration.

=⇒ Network has knowledge that can be used forlocation.

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Zero Memory Estimation

k is sample interval.

θ(k) is location of mobile terminal at k.

θ̂(k) is estimated location of mobile terminal at k.

Survey data: j survey point, j ∈ {1, 2, ..., n}.θj , location of survey point j.zj, measurement taken at survey point j.

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Zero Memory Estimation

Estimated location is weighted average of survey pointlocations:

θ̂(k) =

∑nj=1

θjh(z(k), zj)∑n

j=1h(z(k), zj)

h(·) is kernel function.Estimated location is weighted average of surveypoint locations.Weights determined by kernel functions.

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Zero Memory Bounds

NLOS propagation creates discontinuities inpropagation equations.

Standard bounds (e.g. Cramer-Rao no longer apply).

Use other boundsBarankin boundsWeinstein-Weiss bounds.

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Simulated Environment

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Zero Memory Results

0

50

100

150

200

15 20 25 30 35 40 45 50

RM

SE (

m)

Standard Deviation of Range Error

Parametric MLE (TDoA)Parametric MLE (ToA)

Non-parametric MAP (TDoA)Non-parametric MAP (ToA)

Parzen Gaussian (TDoA)Parzen Gaussian (ToA)

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Zero Memory Results

10 15 20 25 30 35 40 45 505

10

15

20

25

30

35

40

σd (standard deviation of range error)

RM

SE (

m)

WWB ToASimulated ToAWWB TDoASimulated TDoA

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Dynamic Estimation

Combine measurements from different samplingperiods.

Use dynamic model of mobile terminal motion.

Dynamic model consists of:Kinematic model.Human Decision model.

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Mobile Terminal Motion Model

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Kinematic Model

x(k) is terminal state.

u(k) is control input.

w(k) is process noise.Dynamic Model-Based Filtering for Mobile Terminal Location Estimation – p.31/51

Human Decision Model

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Zero Memory Estimator Preprocessor

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Dynamic Estimation

Prediction phase

Correction phase

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Dynamic Estimation

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Bounds on Dynamic Estimation

Combine following information sources:Zero Memory Estimator.Dynamic model for mobile terminal motion.Prior distribution for mobile terminal location.

Bound calculated on squared error.

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Dynamic Estimation Results

Fixed Control Input

0 20 40 60 802

4

6

8

10

12

14

16

Samples

RM

SE (

m)

Evaluation BoundDynamic FilterZero Memory Estimator

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Dynamic Estimation Results

Changing Control Input

0 20 40 60 80

4

6

8

10

12

14

16

Samples

RM

SE (

m)

Evaluation BoundDynamic FilterZero Memory Estimator

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Dynamic Filter Comparison

6

7

8

9

10

11

12

13

14

0 20 40 60 80 100

RM

SE (

m)

Samples

Zero memory estimatorSimple Kalman filter (Hellebrandt et al.)

Simple Kalman filterMulti-model filter

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Dynamic Filter Comparison

Changing Control Input

2

3

4

5

6

7

8

9

10

0 20 40 60 80 100

RM

SE (

m/s

)

Time (s)

Multi-model filterSimple Kalman Filter

Simple Kalman Filter (Hellebrandt et al.)

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Dynamic Filter Robustness

6

8

10

12

14

16

0 0.2 0.4 0.6 0.8 1

RM

SE (

m)

Pr(TURN)

multi-model filter, optimized for Pr(TURN)=0zero memory estimator

multi-model filter, optimized for Pr(TURN)=2/3best multi-model filter for Pr(TURN)

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Dynamic Filter Robustness

7

8

9

10

11

12

13

0 5 10 15 20

RM

SE (

m)

Maximum Mean Velocity

multi-model filter, optimized for C=2.5 m/s2

zero memory estimator

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Dynamic Filter Robustness

7.5

7.6

7.7

7.8

7.9

8

8.1

8.2

8.3

0.1 0.15 0.20.1

0.15

0.2

α

α (F

ilter

)

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Results

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 5 10 15 20 25 30 35 40 45

Prob

abili

ty

Distance Error (m)

Dynamic Filter EstimatorZero Memory Estimator

Configuration Accuracy (ToA σd = 15 m)

67% 95%

Zero Memory Estimator 12.17 m 21.16 m

Dynamic Estimator 7.12 m 14.28 m

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Conclusions

Use all information sources.

Model-based estimation gives accurate locationestimates.

Efficiently combines information from different timeperiods.

Estimation methods are robust.Zero memory estimator robust to changes innoise/propagation model.Dynamic estimator robust to changes in dynamicmodel.

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Future Work

1. Applications of mobile terminal location.

2. Long term motion models.

3. Data fusion.

4. Location of terminals in ad hoc networks.Location of terminals in hybrid networks.

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Applications

Resource allocation

Hand off algorithms

Many possibilities for collaboration.

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Long Term Motion Models

Current dynamic filter based on short term motionmodels.

Long term motion models will improve estimation.

Improve motion prediction.

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Data Fusion

Use data from multiple information sources.RSS is cheap with wealth of propagation data buthas large uncertainty.ToA/TDoA are expensive with low uncertainties.AoA requires special antennae and provides varyingaccuracy.

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Ad Hoc Networks

Examples: Bluetooth, IEEE 802.11

Terminal must be low cost.

Limited connectivity between terminals.

Hybrid networks

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Final words

Large amount of work to be done.

Many applications of results.

Potential to develop new estimation and filteringalgorithms.

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