Radio Frequency TOF DistanceMeasurement for Low-CostWireless Sensor Localization

Steven Lanzisera, David Zats and Kristofer S. J. Pister

Introduction 1.• Paper was published in 2010• Localization is a hot topic

– Creating location-aware sensor networks– Enabling mobile phones to host a lot of new

applications• Requirements

– Low-cost / low energy consumption is crucial– If we require a certain accuracy – we have to deal

with measurement errors

Introduction 2.• Methods of localization

– Acustic (BeepBeep, we have seen it)– RF techniques (no GPS)– GPS

• The paper proposes an RF solution– Low cost / narrowband– No time-syncronization required– No base-station required– Approaches the Cramér-Rao bound in noisy environment– Accuracy – only in the order of a few meters (!)

Abbreviations• RSS – Received Signal Strength• TOF – Time-of-flight• TWR – Two-way ranging• TWTT – Two-way Time Transfer• UWB – Ultra wide band• CMS – Code modulus synchronization• CRB – Cramér-Rao Bound• SNR – Signal-Noise Ratio• RMS – Root Mean Square• MSE – Minimum Squared Error• CDF – Cumulative Distribution• MSK – Minimum Shift Keying (FSK = Frequency ~)

Localization problem• Localization consists of two parts

– Measure relationships between nodes– Using this information to determine position of

nodes• Received Signal Strength

– Well-studied method– Determines range based on signal strength– Very inaccurate

Alternatives• Using Ultra Wide Band ranging

– UWB receivers are very complex and expensive• Narrowband solutions

– They usually require time synchronization, that adds complexity again

• A low cost – simple technology is needed with meter-level accuracy

The presented system• Two-way ranging system• CMS (Code modulus synchronization)

– No time-sync required– Online measurement – Offline range extraction

• Works well in noise-limited environment• Mitigates the effects of multipath propagation

– Idea: take measurements on multiple frequencies• Approaches the Cramér-Rao bound• Room-level accuracy satisfied (~1-3m)

Cramér-Rao bound• Statistics – estimation theory• Expresses a theoretical lower bound on variance of

estimators of a deterministic parameter• – unknown deterministic parameter

– number of measurements – probability density function of – expected value• Cramér-Rao bound

where

Test-implementation• Commercially available accessories• 2.4GHz radio – Frequency Shift Keying• IEEE 802.15.4

– Standard which specifies physical layer and media access control for low-rate wireless PANs

– Zigbee, MiWi ... etc. • FPGA• Overall accuracy: 1m outdoor / 1-3m indoor

Localization method 1.• Multilateration

– Determining the a 2D position with 3 reference nodes (reference nodes: fixed, known position)

• More nodes – better accuracy

Localization method 2.• More reference nodes should be used than

strictly necessary• The geometry of the ref. nodes is important

– Collinear references do not work• This area is highly understood, the more

important part is determining the position from erroneous measurements

Range estimation methods• RSS – constructive and destructive interference

make it unsuitably inaccurate• Time-of-Flight methods

– Speed of light = 299,792,458 m/s– 1 meter range accuracy = 3ns time resolution– Low-cost devices provide the same sampling

resolution as their clock frequency ~50ns– Cost, complexity and terrestrial environment (in

comparison with GPS) make TOF ranging unsuitable

Types of errors to consider• Clock synchronization• Noise• Errors of samping artifacts• Multipath channel effects

Clock synchronization• Usually a common time reference is required

in TOF systems• TWTT – Two-way time transfer

– mitigates the time offset, but not the frequency error (clock drift) – we have to deal with it!

A

BTs,A Tr,A

Tr,B Ts,B

Noise 1.• We consider white noise• The accuracy depends on two components:

– Bandwidth (B)– Energy-to-noise ratio (Es/N0)

• CRB:

for most signals:ts – signal duration; SNR – Signal/noise ratio

Noise 2.• Increasing the bandwidth increases tsB• Larger bandwidth – improved noise perform.• CRB can be closely approached if:

• Increasing the number of measurements improve the results in quadratic order

• Conclusion: noise alone does not prevent 1m accuracy if bandwidth is over a few MHz

Noise 3.• Cramér-Rao bound as function of bandwidth• Basically, we increase power to increase Es/N0

Sampling error 1.• Range binning

– Sampling rate: fs = 2B– Estimating the time of arrival– The space is divided into bins with c / fs width

• Sampling adds uniform uncertainity in each bin of :

• This will be (43m)2 if B = 2Mhz and fs = 1/B, BUT can be decreased to (1m)2 by making 1000 measurements

Sampling error 2.• Tracking, filtering, averaging can eliminate this

error, but that is very unefficient• OR: Signal can be oversampled

– Usually the sampling error dominates the overall error, and not the CRB (the noise) – unless the sampling is very fast

Sampling error 3.• (continued)

– In real systems usually 15dB < Es/N0 < 30dB, and noise is not a problem

– If we sample the signal above the Nyquist limit(fs > 2B) the entire information is captured and smaller sampling error is achieveable

– Interpolation can be done, but its complexity and power consumption is usually way out of the capabilities

Multipath effects 1.• The signal reaches the receiver via different

paths – a path is called a channel• Impulse response of the channel:

• i=0 represents the direct path• Received signal:

(m(t) – transmitted signal)

Multipath effects 2.• Noise does not effect multipath performance• We consider the two-path case

• For small periods, the , and are random variables, but they are freqency-independent over a given RF communication band

• We consider them constant for small periods

Multipath effects 3.• A few MHz change in frequency dramatically

effects the multipath environment– Because of interference (constructive/destructive)

• Measured RSS (fixed transmitter/receiver)

Multipath effects 4.• Delay spread: time between

first and last paths• Most of the signal

bandwidth is observable if

• Typical interpath delay, is more important• Indoors is usually between 5 and 10 ns• The estimate is blurred by the multipath effect• To resolve this problem we need B>100MHz, or at

least B>1/

T R

Delay spread

t

Multipath effects 5.• Possible solutions to mitigate multipath effects:

– Increase bandwidth– Estimating channel impulse response– Multipath bias reduction

• The first two are well-studied• Using devices with larger bandwidth (UWB) is

expensive and they consume to much power• The achieveable accuracy appears to be around

30m with the second method – not sufficient

The solution

Ranging error mitigation• The paper presents two new methods to

mitigate all the errors– Code modulus synchonrization

• Combats sampling effects and poor time syncronization– Frequency diverse range estimation

• Improves range estimation accuracy

Code modulus synchronization 1.• CMS uses a periodic signal, to modulate an RF

carrier, so large B*ts is possible (therefore noise is not a problem)

• First shaded region: C transmits the code to D• The phases are offset, but D knows the length

Code modulus synchronization 2.• D samples and demodulates the signal, and

stores it• At this point D has a local copy of the code, but

it is shifted due to the clock phase offset• Now D sends back (two copies of) the code

Code modulus synchronization 3.• C receives the transmission of D, and records it,

synchronized to its own local reference• The circular phase shift will be exactly undone this

way because of the round-trip nature of the system• C computes the cross-correlation and the measured

code-offset is the TOF

Code modulus synchronization 4.• The received code can be interpolated to

improve resolution up to the noise limit• The system approaches the CRB even with a

single measurement• Multiple measurements can be averaged – this

helps achieving good noise-performance• Correlation and code-offset estimation can be

done offline after the RT part has ended

CMS vs. TWTT 1.• CMS vs. TWTT

– Only one node performs the calculation → better sampling performance

BUT– The full processing gain of the system is not realized

at second node → Noise penalty– This means, that the second transmission (D→C)

contains noise from the first part (C→D)

CMS vs. TWTT 2.• Only one node performs the calculation →

better sampling performanceBUT

• The full processing gain of the system is not realized at second node > Noise penalty

• This means, that the second transmission (D>C) contains noise from the first part (C>D)

CMS vs. TWTT 3.

• - number of code copies averaged• The last factor represents the noise penalty of CMS

– For very low SNR, it is approximately ½ if no averageing is used ( = 1)

– For moderate to large values of , there is almost zero penalty

• Single measurement variance is also better• CMS is better to approach the CRB

Frequency diverse range estimation 1.• Mitigates the multipath effect• Takes measurements on several carrier

frequences• The problem:

– Signal comes via two paths: one direct, more reflected– There is a delay and phase difference between them– Only the phase depends on the actual value– IEEE 802.15.4 uses MSK, a version of FSK– When changes to , the signal from the second

path have not arrived yet

Frequency diverse range estimation 2.• Simulation shows, that this can result in either

positive or negative biases in range estimation

• According to the figure, we should make measurements over the same channel, with different phase relationships – averaging the value will reduce the overall bias

Frequency diverse range estimation 3.

• Because the phase differencedepends on the , they usedifferent carrier frequencies

• The median of 16 estimateshad the best error performance,(compared to averaging): 80% below 3m error

• The demonstration environment implements this method

Prototype 1.• Waldo device

– 2.4GHz radio– DA interfaces– FPGA (Verilog)– Microcontroller (C)

• Implementation– Bandwidth = 2MHz– Binary frequency shift keying: +/- 0.75MHz– Sampling: 5MHz digital demodulation– Demodulated data bandwidth limit: 2MHz with 16MHz

sampling – randge bins of 19m

Prototype details• Ranging between node pairs

– Coordination / acknowledgement– 16 measurements – median is used– Maintaining CMS (2-period-length code 32 times)– Non-RT processing offline (linear regression to

estimate TOF)

Tests 1.

• Better than 3m overall accuracy• Noise performance

– Verification with cable and simulated noise– Work within a factor of 2 of the CRB

Because of the limited dynamic range of the digital baseband processor

Tests 2.• Ranging demonstrations (compared to RSS)

outdoor indoor

Received SignalStrength

CBS + Freq. Diverse Range Estimation

Error ratio (outdoor) 20% <1m 80% <1m

Error ratio (indoor) 50% <8m 50% <1m; 80% <3m

Tests 3.

• Open area – 40×50m– Max distance: 70m– 4 static nodes– Simple MSE estimation– 80% of errors < 2m

Conclusion

• CMS is a TWR method that approaches the CRB• Freq. diverse ranging estimation is a strategy

that improves ranging in multipath environments

• Overall accuracy: 1m outdoors, 1-3m indoors• Where Es/N0 is large, sampling error dominates

the noise-induced error, but CMS avoids this• Easy implementation, low costs, no UWB device

required

Thank you for you attention!