1. Radio Interferometric Geolocation
By: Kate Hayes

2. Outline
Introduction
Theoretical background behind radio interferometry
Analyzing sources of error
Prototype implementation
Technique discussion for distance
Localization algorithm
Field Experiments
Conclusion

3. Introduction to State of the Art
Acoustic WSNs have limited range of high accuracy
Acoustic WSNs need special actuator/detector pairs which adds to the cost
A number of applications require privacy making the very limited Ultrasound signal the only option
Most WSNs are only available in 2D
There seems to be the ability to have adequate accuracy or acceptable range but not both simultaneously

4. Radio Interferometry
Radio interferometry is traditionally used in physics, geodesy, and astronomy
The method uses two or more directional antennae to measure the radio signal from a single source and performing cross-correlation
A radio interferometer is very expensive requires tunable, directional antennae; high sampling rates; and high precision time synchronization
This device is not directly applicable to WSNs

5. Radio Interferometric Positioning System (RIPS)
Radio Interferometric Positioning System (RIPS) is the novel idea to use the concepts behind interferometry and apply them to WSNs
The main idea is to use two nodes as transmitters that create the interference pattern which is measured by two receivers
The frequencies emitted by the transmitters are almost the same, which when combined create a low frequency envelope
The two receivers measure the wave packet’s phase difference and use this to determine the relative position of the four nodes
The key attribute is that the phase offset of a low frequency signal is measured and it corresponds to the wavelengths of a high-frequency carrier signal
The key attribute of this method is that the phase offset of a low frequency signal is measured, yet it corresponds to the wavelength of the high-frequency carrier signal.
Hence, we can use low precision techniques that are feasible on the highly resource constrained WSN nodes, yet we still achieve high accuracy

6. Phase offset
The composite (addition of the two transmitters signals) signal has a low beat frequency
Relative phase offset is measured rather than the phase offset so that timing synchronization can be avoided
Relative phase offset between two receivers depends on only on the four distances between the receivers and transmitters and the wavelength of the carrier frequency
By measuring different carrier frequencies it is possible to calculate linear combinations of the distances between nodes and infer position
How can the system figure out its position relevant to ground

7. Theorems of the RIPS methods Theorem 1
The RSSI signal is the power of the incoming radio signal measured in dBm after it is mixed down to an intermediate frequency fIF
It is then low pass filtered with filter cutoff frequency fcut, where fcut << fIF
Let r(t) denote this filtered signal
Theorem 1: Let f2 < f1 be two close carrier frequencies with δ = (f1 − f2)/2, δ << f2, and 2δ < fcut. Furthermore, assume that a node receives the radio signal s(t) = a1 cos(2πf1t + φ 1) + a2 cos(2 π f2t + φ 2) + n(t), where n(t) is Gaussian noise. Then the filtered RSSI signal r(t) is periodic with fundamental frequency f1 − f2 and absolute phase offset φ1 − φ 2

8. Theorems of the RIPS methods Theorem 2
Theorem 2: Assume that two nodes A and B transmit pure sine waves at two close frequencies fA > fB such that fA − fB < fcut, and two other nodes C and D measure the filtered RSSI signal. Then the relative phase offset of rC(t) and rD(t) is 2π[(2dAD − dAC ) / (c/fA) + (dBC − dBD) / (c/fB )] (mod 2π).
What does the mod 2pi mean

9. Theorems of the RIPS methods Theorem 3
Theorem 3: Assume that two nodes A and B transmit pure sine waves at two close frequencies fA > fB, and two other nodes C and D measure the filtered RSSI signal. If fA−fB < 2 kHz, and dAC, dAD, dBC, dBD 1 km, then the relative phase offset of rC(t) and rD(t) is 2π[(dAD − dBD + dBC − dAC)/(c/f)] (mod 2π) where f = (fA + fB)/2
dABCD = dAD − dBD + dBC − dAC

10. Theorems of the RIPS methods Theorem 4
Theorem 4: In a network of n nodes there are at most [(3/2)*(n−2)(n−3)] independent interference measurements that can be made
The solution to the system of equations is invariant under translation, rotation, and reflection
The number of unknowns is (2n - 3) in a 2D network and (3n – 6) in 3D
At least 8 nodes in 3D are needed to get more measurements (20) than the number of unknowns (18)

11. Sources of Error (1)
Carrier Frequency Inaccuracy – The difference between the nominal and actual carrier frequency of the transmitted signal.
Carrier Frequency Drift and Noise – The phase noise and drift of the actual carrier frequency of the transmitted signal during the measurement. Any noise of drift will be directly observable. This error can be minimized by shortening the length of a single phase measurement
Multipath Effects – Anytime the RF signal bounces off anything rather than traveling directly to the receiver. It is expected higher level algorithms can filter this error out

12. Sources of Error (2)
Antennae Orientation – Time of Flight can change if the antennae are not pointed directly at the receivers
RSSI Measurement Delay Jitter – The jitter of the delay between the antennae receiving the radio signal and the RF chip delivering the RSSI signal to the signal processing unit
RSSI Signal-to-Noise Ratio – The signal strength relative to the noise of the rC(t) signal. SNR mainly depends on the distance between transmitters and receivers as the amplitudes of the signal decrease exponentially in space
Signal Processing Error – Error introduced by the signal processing algorithm that calculates the phase offset
Time synchronization Error – Error of the time instance when the receivers measure their absolute phase offset of the received signal strength

13. Implementation
Selecting a pair of transmitters from a group of motes participating in the localization and scheduling their transmission time
Fine-grain calibration of the radios of senders to transmit at close frequencies
Transmission of a pure sine wave by the two senders at multiple frequencies
Analysis of the RSSI samples of the interference signal at each of the receivers to estimate the frequency and phase offset of the signal
Calculation of the actual dABCD range from the measured relative phase offsets for each pair of receivers
The Localization Algorithm
Selection and scheduling of transmitting pairs, distance calculations, freq. calibration, and localization are all done on the base station

14. Physical Attributes
Uses the MICA2 mote platform with TinyOS operating System
Chipcon CC1000 radio
Allows pure sine wave transmission at a specific frequency
Radio engine component that coordinates and synchs the particular nodes and handles the interference signal
A signal processing component estimates the phase and freq. of the sample signal
Transmits at different power levels and a wide freq. band
Time required to calibrate has a large 5 ms jitter

15. Time Synchronization
Measuring the relative phase offset of the interference signal at the receivers requires measuring the absolute phase offset relative to a common time instant
After getting the absolute phase offsets from each node the relative phase offset is achieved by subtracting them from each other
Only the 4 nodes participating are time synched and only for the duration of the synching
The master node sends out a packet with a precise timestamp to all participating nodes who then use that timestamp to calibrate to their local time
This message specifies when the calibration or tuning will take place in the future and at what powers to do them at
Microsecond precision is required to align the incoming RSSI signals
To compensate for the two receivers not receiving data at the same time. The time the RSSI sample first arrived is recorded and used to calibrate
Don’t super get this figure

16. Tuning
The CC1000 chip needs to perform internal calibration of the internal frequency synthesizer PLL (phase locked loop)
Calibration is required to compensate for supply voltage and temperature variations
Channel 0 is at 430 MHz and each channel is a MHz step up
PLL on C1000 chip can get up to 65 Hz freq. resolution
Due to time and sampling rate constraints the difference between the broadcast frequencies is from 200 – 100 Hz
Freq. tuning algorithm determines settings for transmitters of the same frequency
f = · channel + 65 · 10−6 · tuning.
the frequency error for two nodes does not stay constant for different channels.
as the frequency error is mainly caused by the imprecision of the crystal that drives the radio chip, it is approximately linear in frequency.
we can measure the correct tuning parameter for two different channels and interpolate these values to obtain the radio parameters for the other channels.
Different frequency channels were set so broadcasting on a different channel mandates recalibration

17. Peak Detection and filtering
Samples are processed on nodes
Signal Processing Algorithm estimates the frequency and phase of RSSI signal
Some of the data is processed online, but it is limited and more extensive data is processed later post-processing
820 CPU cycles realy limit the amount of post-processing allowed on the nodes. FFTs and autocorrelation are not feasible

18. Frequency and phase estimation
Raw samples are filtered in a way to enhance SNR
Max and Min peaks are acquired from the leading 24 samples for the adaptive peak detection algorithm
The acquired amplitude serves as quality indicator
Peaks are discarded if they do not cross the low threshold in order to get rid of false positives
Post-processing works on peak indexes and determines the period and freq. is the reciprocal of the period
Phase is estimated by the average phase of the filtered peaks
Leading 24 contains at least one full period

19. Scheduling High-Level Low-Level
Responsible for selecting the pair of transmitters
Minimizes the number of interference measurements while still allowing enough to acquire a 3D localization
Base selects all possible pairs of transmitters while all nodes within range act as receivers
Coordinates the activities of the two transmitters and multiple receivers
Frequency tuning algorithm and phase offset estimation require proper freq. calibration and timing
Has different transmitters use different powers to account for differing distance from the receivers
different radio power settings to compensate for the effect of one transmitter being much closer to a receiver than the other.
Currently, three combinations are used: full power/full power or the two combinations of full power/half power.

20. Range Calculation dABCD = λini + γi = λjnj + γj ,
A set of wavelengths is needed so that their least common multiple is larger than the domain of the distance
The equations become invalid due to noise and are reduced to similar inequalities
Solving for the inequalities gives the average di value
The answer with minimum value to its error function becomes the final estimate
λi = c/fi is the wave length, γi = λi *(vi/2*pi) is the phase offset relative to the wave length, vi is the measured phase
offset, and ni is an integer
This figure?? It lines up black green red at solution but what is the key??
May be multiple solutions to inequalities differing by wavelength
Use 10 frequencies instead of 3 for better accuracy

21. Localization
RIPS does NOT provide ranging between nodes but rather a combination of distances between the 4 nodes
Remember dABCD = dAD − dBD + dBC − dAC
A Genetic Algorithm (GA) is used to determine the relative position of the nodes
The algorithm uses all the given ranges and tries to minimize the difference between the input range and the range in the solution
The solution with the least amount of error is selected
GA uses permutation and mutation to seek the best solution
We extended the genetic representation of the solution to include the set of used measurements and let the GA optimize this set as well.

22. Effective Range
Determining range is not straightforward because it is not direct pairwise
The maximum distance between a transmitter and receiver is the related to the radio range
The interference signal can be “heard” almost twice as far away as the radio range this is called the Interferometric Radio Range (IRR) (r)
No constraint on distance between two transmitters or receivers, however they need to be in twice the IRR
Signals need to be tuned so one signal is not much stronger than the other transmitter’s
Possible values of the distance : − 2r < dABCD < 2r.
How is the 3D determined above ground? How is the cluster of nodes related to actual space or ground. They could be anywhere.

23. Experimental setup 16 nodes in a 4x4 grid
3 anchor points randomly chosen
18x18 meters
This is only testing 2D
Testing on flat grassy field

24. Frequency accuracy
Results comparable to high resolution discrete Fourier transforms were achieved
One of the senders changed its carrier freq. in small increments
Ideal V-shaped curve appears matching tuning parameters
Phase difference (bottom) have more noise as expected
Top is frequency bottom is phase offset

25. Phase Accuracy One pair of motes were fixed as transmitters
Frequency tuning around 0 Hz interference
Repeated 30 times
Median phase and average deviation at each frequency
Calculated average of the deviations
Used amplitude as a quality of measurement indicator
Don’t understand V-curves

26. Ranging Accuracy
The error distribution of the calculated dABCD ranges can be approximated by the superposition of a set of Gaussian distributions
Filtering is used to improve the number of 0 error peaks while keeping enough information to use
Amplitude of the signal shows strong correlation with error in ranging
Interference signal is measured by all modes in range
Bad frequency measurements lead to bad range measurements and are filtered out
Note number of measurements from fig 8 to 9

27. Localization accuracy
Localization was run using the filtered data
Genetic optimization was run for 2 minutes with the results in the above right figure
Average accuracy was 5 cm
Largest error was under 10 cm
RIPS is pretty accurate in 2D

28. Latency
Because so many measurements are required to take place between different arrangements, different algorithms, freq. tuning, and actual measurements the process takes about 80 minutes
The tuning algorithm, range calculations, and localization are done on the base station
Using less combinations would drastically reduce the time to get results without sacrificing accuracy
If the tuning algorithm is implemented on the motes the time can also be cut down by shortening message routes
Its possible to decrease the number of tuning steps required as well
The network is easily scalable since each section can be divided up by radio range

29. Conclusion RIPS achieves high accuracy and long range simultaneously
Supports 3D localization
Does not require extra hardware or calibration
Two transmitters create an interference signal whose phase offset is measured by receivers
This phase offset can be used to determine the range related to all 4 nodes involved in the measurement
From all the relative measurements the map of the 3D network can be determined

30. RF angle of arrival-based node location

31. Outline Introduction Technique Analysis of Technique Implementation
Experimental Results
Conclusion

32. Introduction
In comparison to other localization methods which use large infrastructure, extensive processing, and/or long latencies TRIPLOC is a rapid localization distribution method that uses radio interferometry like RIPS but improves upon it
TRIPLOC gathers it’s four nodes into a group of three orthogonal nodes and one or more receiver farther away
On the anchor antennae array two of the nodes are transmitters and one is a receiver
The measured phase difference between the receiver on the TRIPLOC array and the other receiver constrains the location of the latter to the hyperbola
Orthoganal to get rid of parasitic affects
Since all the antennas are within half the wavelength, the modulo ambiguity is also eliminated
The name TripLoc comes from the fact that a triplet of nodes constitutes an anchor node array in our localisation scheme

33. Some terminology
Node position is usually determined by ranging or bearing
Ranging- node estimates its difference to different reference points
Bearing- the angle between forward facing direction and direction to object
Triangulation is the process of determining the position of an object from the bearings of known reference points
TRIPLOC employs Bearing from multiple nodes to determine location

34. Radio interferometry (RI)
Bearing estimates are useful when anchor positions are known
Several acoustic beamforming techniques have been proposed to find the angle of incidence if a signal at an array of sensors
There have been several improvements on the RIPS system to track mobile devices and improve latency
Mobile nodes have their RF signals undergo a Doppler shift
From the Doppler shift the motion and position can be determined
TRIPLOC cannot do localization for mobile nodes, but it performs the calculations so fast that it can do it for slowly moving nodes

35. RI Measurements
TRIPLOC array midpoint is assumed known as well as distance between antennae
At predetermined time P and A_1 transmit a pure sinusoidal signal at slightly different frequencies
A_2 and the receiver node (R) measure the low-frequency beat interference pattern created by P and A_1
This is termed a Radio Interferometric Measurement (RIM)
The maximum distance difference will occur when the receiver node is collinear with the transmitters this removes the 2pi modulo ambiguity
dA_1PR =ДΦλ/2π
TRIPLOC has multiple antennae array anchors at known positions and cooperating sensor nodes at unknown locations
The array contains three nodes a primary (P) and two assistants (A_1, A_2)

36. Bearing approximation 1
dA_1PR defines the arm of the hyperbola that intersects the position of node R and whose asymptote passes through the midpoint of the line A_1 and P
The distance between the hyperbola center and the intersection point H is defined as a
The length of the line segment perpendicular to the axis containing the foci that extends from the H to the asymptote is called b
In order to solve for β the values of a and b must be determined
β= 𝑐𝑜𝑠 −1 ( 𝑑 𝐴_1𝑃𝑅 𝑑 𝐴_1𝑃 )
H is a vertice
R must be farther away from the node because the error in beta will be larger if it is close due to the hyperbolic shape
If the phase difference is negative (i.e. R A2 ϕ <ϕ ) then the position of R will lie on the left arm of the hyperbola.
When this is the case, β is taken clockwise, and we must adjust it by subtracting it from π.

37. Bearing approximation 2
β could be +/- because if the symmetry of the hyperbola
In essence each RIM gives two possible β measurements
To solve for this the assistant nodes switch roles and perform a second RIM
Due to the fact that the center of the hyperbolas are not the same for each RIM there is an allowed error threshold
The average of the two βs that have error under the error threshold is the bearing estimate βhat
R must be farther away from the node because the error in beta will be larger if it is close due to the hyperbolic shape

38. Triangulation
When the approximate bearing of R is determined (β) its position can be determine using triangulation
Using two known angles and a known side the distance to R from either anchor node can be determined
If R is ambiguous then three have to be used, but if a β is slightly off then there will be error
The triangulation technique used was Least Squares Orthogonal Error Vector Solutions which basically uses linear algebra to come up with Rhat the position estimate with noising bearing measurements
REMEMBER Triangulation is the process of determining the position of an object from the bearings of known reference points
for the case B R is in-between and its ambiguous so three anchors have to be used

39. Bearing estimation error
Because computing distance differences can be computationally intensive several assumptions are made by the TRIPLOC system
Measurements noise
Asymptotic approximation
Translation of bearing candidates
The analysis of array position and orientation errors are purposefully omitted
These assumptions are made instead
The antenna configurations are known
Transmitter location is known
Relative bearings are known
Relative bearings means that the computed bearings are given in local coordinates and location and orientation errors are not considered

40. Measurement Noise Error
Distance Differences can contain error in the form of measurement error
This error can come from non-ideal signal propagation, noise from circuitry, sampling error, or other sources
Estimating the amount of error in βhat is done by taking the partial derivative with respect to distance
To see what amplification effect an error in a given distance difference d produces on the bearing estimate, evaluate the partial derivative at d
When the absolute value of the measured distance difference is close to the antenna separation, the computed bearing candidates are very sensitive to measurement noise
A distance difference from a pair of transmitters in the array constrains the location of the receiver to one arm of a hyperbola, the foci of which are the positions of the two transmitters.
I don’t super understand these figures. WHAT is distance difference
For instance, if the distance difference is 80% of the antenna separation, an infinitesimally small error in the measurement will be amplified tenfold in the bearing estimate.

41. Asymptote Approximation
For a pair of transmitters the bearing of the receiver is approximated with angles of the asymptote of the receiver
It is assumed that the receiver lies on the hyperbolic asymptote, rather than on the hyperbola itself
For close receivers errors of this type are not negligible
This error is βhat minus β and is given the symbol ε
The error of the approximation decreases as the distance of the receiver from the transmitter array increases
Its okay to assume this for far away because the asymptote basically converges
What's counting out on the circle of the graph

42. Translation of bearing candidates
At least two transmitter anchors are needed because for each transmitter pair there are two possible βs
Bearing candidates are treated as vectors from the center of the hyperbola
These vectors need their coordinates translated from the hyperbolic to the system coordinates
A vector translated this way will not point directly at the bearing anymore but slightly off
If the receiver is far enough away it won’t be off enough to matter
Because a hyperbola has two asymptotes the angle of either one could be correct
We assume that the transmitter is a uniform circular array of three antennas, with a pairwise antenna distance of less than λ/2.
The coordinate system of the array is set up such that the midpoint of the array is at the origin, and antenna P lies on the positive side of the x-axis

43. Compound bearing estimation error
Two transmitter pairs each report two bearing candidates for a total of four bearing estimates
Its likely only two should be close to each other (The correct ones)
In order to figure out which ones they are all possible pairs of one from each transmitter are taken
The pair with the least pairwise angular distance is selected and the average is taken to give βhat
In the diagram over 500 simulations are run with an added Gaussian noise
Errors peak where expected where the individual transmitter pairs exhibit high error sensitivity

44. Position Estimation Error analysis
Triangulation is used to compute the distance to the receiver from the bearing measurement
Simulation results are presented to demonstrate the effect of error from different sources and reference real experiments
Position error comes from three different sources:
Position of the arrays
Orientation of the arrays
Bearing estimation error

45. Position Error of the arrays
T_2 is varied along the x axis and error is calculated for whether the measurement of T_2 was off by .1, .2, or .3 m

46. Orientation error of the arrays
To simulate orientation error a constant was added to the bearing reported from T_2
As expected R between the two Ts gives a large error estimate

47. Bearing estimation error
Assume location and orientation of the two antenna arrays are known
Assume that the bearing estimates have added white noise in form of a Gaussian random variable with σ being changed for each run
Results suggest that as standard deviation of the bearing error is increased the standard deviation of the location area increases as well
100 simulation rounds
Darker is more error

48. TRIPLOC System Specs Crossbow ExScal motes TI CC1000 radio chip
Mutually orthogonal antennae to reduce parasitic effects (35.35 cm apart) and with a wavelength greater than 70.7 cm to avoid 2pi modulo
TinyOS operating system
All operations run locally
Initialization of localization process is required first
Create and broadcast a schedule of when array anchors perform the RIMs
All anchors keep track of when each anchor is performing the RIM so they know when it is their turn
Tuning is required. Two broadcast in increments and one monitors until it finds the matching beat frequency lets the others know
Calibration of the bearing system is requires. To calibrate place receivers at known locations and run the estimation algorithm, the difference is the true orientation of the arrays

49. Making Radio Interferometric Measurements
Because phase difference is used to calculate the bearing the signal must be measured at the same instant
TRIPLOC uses the same method as RIPS to synchronize clocks with a primary node sending out a message with the time of its system in the message, a receiver measures the time it received this message and calibrates the two times
After synchronization the radio needs to be acquired from the MAC layer
Next the radio is calibrated
Transmit and sample enough RSSI periods (about 6) to get a phase difference
Restore the radio to its original state so information can be shared by the nodes

50. Latency analysis
Latency is the amount of time it takes from making the measurement to getting the result, in this case the position of the receivers
Since TRIPLOC is intended for mobile arrays it must perform very fast RIMs so the sensor hasn’t had time to move far
Each array performs two RIMs, one for each P,A pair
The bottom line is TRIPLOC allows its receivers to calculate their position in less than 1 s
Therefore, localization using two arrays will take no longer than 0.93 s, three arrays will take no longer than 1.34 s and no longer than 1.74 s when using four arrays.

51. Experiment 1
Experiment 1 measures the bearing accuracy of six receiver nodes
The nodes are placed 60 degrees apart 10 m from the center anchor node A
Performed 50 bearing estimates
This experiment is consistent with the error predictions for bearing estimations
Every 60 deg 10 m from the center A

52. Experiment 2
Experiment 2 was measuring the accuracy of 14 receiver nodes from three arrays
Outdoor, low-multipath environment
More real world than other experiments
35 bearing estimates from each anchor to all nodes so 1470 estimates total
This experiment is also consistent with expected results from the bearing error estimate analysis

53. Experiment 3
20x20 m with 4 anchors in the corners and 16 nodes in a slightly randomized grid
Each target node (one in grid) periodically estimates its position using the bearing estimation and triangulation techniques presented in the paper
100 estimations for each target
Average overall position error was found to be .78 m
The anchor nodes are set back from the target nodes in order to minimise the position error that results at sensitive bearings

54. Conclusion
TRIPLOC is a method for rapidly distributed bearing estimation and localization
The array anchor consists of three nodes arranged orthogonally to each other
Two transmit slightly different frequencies and one measures the phase difference of the beat frequency with another receiver a distance away
The phase distance defines a hyperbola from which bearings can be estimated
From these bearing estimations localization can be calculated
Average bearing accuracy is 3.2 deg. and avg. position accuracy is .78 m
All processing is done on nodes and avoids the 2pi modulo ambiguity
TRIPLOC has a very fast localization time of about 1 second