using probabilistic methods for localization in wireless networks presented by adam kariv may, 2005

Using Probabilistic Methods for Localization in Wireless Networks

Presented by Adam KarivMay, 2005

Agenda

IntroductionTheoryOur AlgorithmPreliminary Results

Goal

Find the exact location of a wireless, mobile, network device.

Possible Applications

Smart BuildingsRoute incoming calls to the nearest phone-

extension.Print documents to the nearest printer.Download slides of the currently presented

lecture.Location-based Targeted Advertisement

Receive discount information of the store you're standing next to.

Our Solution Concept

A mobile station may use the received strengths of network signals in order to passively find it's own location.

Network Elements

Base Stations - Stationary network elements, usually used to connect the wireless network to external networks.

Mobile Stations - User agents, whose location is dynamic.

This is the location we aim to find!

Assumptions

Each mobile station is in the reception range of several base stations.

Mobile stations can easily list all base-stations in reception range.

Mobile stations know the strength of the received signal from each base-station in its reception range.

Examples for Wireless Networks

802.11 Wireless Local Area Networks.GSM Cellular Networks.

Drawbacks (1)

Our localization scheme is nearly network-independent - Better results may be obtained by utilizing data available from the network (e.g. cell id) designing a network to be "localization-aware" performing actual localization on the network side,

which has access to more data and better resources.

Obtaining location using a different technology.

Drawbacks (2)

Can't localize when too few base stations are in reception range.May not be a problem in 802.11 WLANCould be problematic in cellular networksProbably will be a problem in WiMax.

Agenda

IntroductionTheoryOur AlgorithmPreliminary Results

Reference Measurement (1)

Preparation:Measure in selected reference points the

exact received signal strength from each base station.

Store measurement for each location in the signal strength database.

Reference Measurement (2)

In order to localize:Measure exact signal strength from each

base station.Find the best match for the current

measurement in the signal-strength database.

Accuracy is proportional to reference points density.

Problems with Reference Measurement (1)

Tedious preparations phase, Low tolerance to changes in the amount

or location of base stations,In order to achieve better accuracy, we

must have more reference points

even longer preparation overhead.

Problems with Reference Measurement (2)

Noise in signal strength measurements during localization may cause jitter in resulting location.

Doesn't take into account prior knowledge we may have of the physical environment.

Using a physical model

In order to avoid the preparations phase, we could deduce the signal strength using a radio propagation model.

The model can predict the signal strength in each reference point.

Number of possible reference points is unlimited This method allows us to improve accuracy without

increasing overheads.

But - Is this feasible?

Problems with physical model

Achieving an accurate physical model is very difficult Many "real-world" phenomenon are hard to model:

Reflections, Signal decay when passing through obstacles,

We have many unknowns, such as: Floor plan of building, exact location and material of obstacles,

walls, windows, furniture… Exact location of base-stations, Transmission power of base-stations, Sensitivity and Amplification of receiving mobile-station

Achieving an accurate physical model is very difficult.

Simple physical model (1)

[as shown by Wallbaum & Wasch, 2004] Assumptions:

Disregards reflections. Floor plan of building is fairly known. Base-station locations are known Base-station and mobile-station properties are known

To compute received strength at point X of a signal transmitted from point Y - Count the number of obstacles of each kind on the straight

line from X to Y Use the following function:

Simple physical model (2)

Object classes and their parameters:

Hidden Markov Model

Hidden Markov Model - HMM Defines a set of random variables One “hidden” and one “observable” for each time

step. In our case:

The hidden variable has the actual location at each time step.

The observable has the sampled data at each time step – i.e. the reported signal strength from every base-station.

The HMM “tracks” the location of the mobile-station through time.

Using HMMs

This method assumes good knowledge of the following probability functions: A(l,l') = P( locationt+1 = l' | locationt = l )

B(l,s) = P( samplet = s | locationt = l )

Using these functions, we can easily compute the exact value of P( locationt = l | sample1 ... samplet ) The probability of being in any of the reference

locations at time t, given all the previous samples.

Previous Results

Castro, Chiu, Kremenek, Muntz (2001) Physical Model

Ladd, Bekris, Marceau, Rudys, Wallach Kavraki (IROS 2002) Physical Model + HMM

Haeberlen, Flannery, Ladd, Rudys, Wallach, Kavraki (MOBICOM 2004) Reference Measurement + HMM

Wallbaum, Wasch (WONS 2004) Physical Model + HMM

Agenda

IntroductionTheoryOur AlgorithmPreliminary Results

Tying it all together

Floor plan of Ross Building, Entrance Level:

Tying it all together

Use the physical model to fill initial values in the signal strength database.

Transition function: A(l,l') = P( locationt+1 = l' | locationt = l ) -

~1 - for staying in the same location <<1 - for moving to an adjacent reference

location 0 - otherwise

Emission function:B(l,s) = P( samplet = s | locationt = l ) Depends on the distance of s from the lth position in

the signal-strength database.

Tying it all together

To localize, for each sample, we calculate:

maxargl P( locationt = l | sample1 ... samplet )

Previous results already achieve good localization results – how can we do better?

The EM Algorithm

The EM algorithm is an iterative method used to find the most likely model for a given sample.

It has two steps:E - Estimate probabilities for each hidden

variable at each time.M - Find new model which maximizes the

likelihood of the samples.

Using EM to improve the model

Model may include the signal-strength database, the transition function, plus all the physical model's unknowns.

E step: Find P( locationt=l ) for each t, l Using signal-strength database and HMM

M step: Find new values for signal-strength database DB(l) = t [ P( loct=l )samplet ] / t P( loct=l )

Problems of EM

EM finds the model which maximizes the likelihood of the sampled data.This does not guarantee correctness…

EM has many local maximaBetter start close to the correct solution.

Agenda

IntroductionTheoryOur AlgorithmPreliminary Results

Performed Simulation (1)

Mobile-station performs a random-walk along the reference locations.

“Measured” signal strength is the sum of: Expected signal strength, according to the

Physical Model, Model Error, fixed for each location, modeling

inaccuracies in the physical model, Sensor Error, modeling measurement errors.

HMM is used to track the mobile-station’s location.

Inferred path is compared to actual path.

Performed Simulation (2)

The EM algorithm is used to learn a better model In our case - more accurate values for the

signal-strength database.

We will see results for two scenarios:Low model and sensor errors (~1dB)High model and sensor errors (~10dB)

Measures for Learning Quality

Location Accuracy Could be misleading – depends on reference-point

density.

Localization Error Inferred path vs. actual path 1-hop localization error

Signal-Strength Database Error Likelihood

Could be used as a measure for convergence.

Localization Error (1-hop)

Signal-Strength Database Error

Likelihood

Future Plans

Use better representations of Model Errors and Sensor Errors

Improve EM to Learn more of the physical model unknownsLearn the transition function (A matrix)Use multiple samples concurrently to

improve learning quality and speedPerform “field-test” with actual network

data.

Questions?