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

Radio Frequency TOF Distance Measurement for Low-Cost Wireless Sensor Localization Steven Lanzisera, David Zats and Kristofer S. J. Pister

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**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

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**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 (!)

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**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 ~)

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**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

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**Alternatives Using Ultra Wide Band ranging Narrowband solutions**

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

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**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)

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**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 I(teta) = Fisher information

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**Test-implementation Commercially available accessories**

2.4GHz radio – Frequency Shift Keying IEEE 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

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**Localization method 1. Multilateration More nodes – better accuracy**

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

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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

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**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

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**Types of errors to consider**

Clock synchronization Noise Errors of samping artifacts Multipath channel effects

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**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! Tr,B Ts,B A B Ts,A Tr,A

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**ts – signal duration; SNR – Signal/noise ratio**

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

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**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

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**Noise 3. Cramér-Rao bound as function of bandwidth**

Basically, we increase power to increase Es/N0

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**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

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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

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**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

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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)

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**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

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Multipath effects 3. A few MHz change in frequency dramatically effects the multipath environment Because of interference (constructive/destructive) Measured RSS (fixed transmitter/receiver)

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**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

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**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

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The solution

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**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

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**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

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**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

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**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

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**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

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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)

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CMS vs. TWTT 2. 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)

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**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

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**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 uses MSK, a version of FSK When changes to , the signal from the second path have not arrived yet

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**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

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**Frequency diverse range estimation 3.**

Because the phase difference depends on the , they use different carrier frequencies The median of 16 estimates had the best error performance, (compared to averaging): 80% below 3m error The demonstration environment implements this method

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**Prototype 1. Waldo device Implementation 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

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**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)

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**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

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**Received Signal Strength CBS + Freq. Diverse Range Estimation**

Tests 2. Ranging demonstrations (compared to RSS) outdoor indoor Received Signal Strength CBS + Freq. Diverse Range Estimation Error ratio (outdoor) 20% <1m 80% <1m Error ratio (indoor) 50% <8m 50% <1m; 80% <3m

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**Tests 3. Open area – 40×50m Max distance: 70m 4 static nodes**

Simple MSE estimation 80% of errors < 2m

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**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

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**Thank you for you attention!**

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