# Differential Bearing Estimation for RF Tags

- Ákos Lédeczi
^{1}Email author, - János Sallai
^{1}, - Péter Völgyesi
^{1}and - Ryan Thibodeaux
^{1}

**2009**:682183

**DOI: **10.1155/2009/682183

© Ákos Lédeczi et al. 2009

**Received: **25 August 2008

**Accepted: **5 February 2009

**Published: **10 May 2009

## Abstract

Fusing spatially distributed observations in wireless sensor networks or asset tracking in a shipyard are just two-example applications where the location of radio nodes needs to be known. Localization and tracking of wireless nodes have been an active research area, yet a universal solution has not emerged so far. This paper introduces a novel method for bearing estimation based on a rotating antenna generating a Doppler shifted RF signal. The small frequency change can be measured even on low-cost resource constrained nodes using a radio interferometric technique introduced previously. Bearing information between anchors nodes at known locations and RF tags at unknown positions can be derived. A few such measurements provide enough information to enable accurate node localization.

## 1. Introduction

While there are many practical localization systems for mobile ad hoc networks, wireless sensor networks (WSN) and unattended air or ground vehicles (UAV, UGV), there are still applications with such requirements that none of the existing solutions is satisfactory. GPS, for example, typically does not work indoors and it is also not well suited when low cost and/or very long lifetime are the main design drivers. Techniques based on ultrasonic and infrared signal modalities have short range and require line-of-sight. Clearly, RF-based approaches have many advantages for most applications. A radio is already available on any wireless node, so it comes at no added cost and it is already included in the power budget. RF range is superior to most other signals. Line-of-sight may not be necessary, since radio signals may propagate through walls; however, radio propagation, especially indoors, presents significant problems of its own.

Radio signal strength (RSS)-based approaches are the most straightforward for estimating distance from an RF signal; however, such methodologies are relatively imprecise due to fading. The accuracy of numerous RSS techniques is typically meter-scale [1–3]. A few commercial systems, such as PinPoint [4], based on time of arrival (TOA) and RSS measurements have also been developed with similar accuracy. The Location Engine [5] developed at Motorola Research depends on RSS measurements and anchor nodes at known positions. Chipcon (now Texas Instruments) licensed and integrated the technology into the CC2431 transceiver chip and claims 3 m accuracy.

Active RFID systems use self-powered tags to identify and locate objects. LANDMARC relies on multiple-fixed RFID readers and reference tags. It estimates the proximity of a given tag to reference tags by correlating their respective signals by multiple readers [6]. The accuracy achieved is meter-scale with high enough reference tag density. PanGo is a commercial asset tracking system using 802.11 active RFID tags [7] providing room-level resolution relying on dense access point infrastructure.

Ultra-Wideband (UWB) systems are resistant to multipath effects in both communication and ranging. UWB-based range measurements have accuracy of 1.5 m or better [8, 9]. Ubisense has recently developed a UWB-based fine-grained localization system with an accuracy of about 20 cm [10]. The disadvantage of UWB is that it relies on the time-of-flight of radio signals; hence, it requires high sampling rates and/or nanosecond-scale time synchronization thus increasing cost. Also, the Federal Communications Commission (FCC) has limited the maximum power of UWB radio transmissions restricting the maximum range of UWB methods typically to 20 m [11, 12].

Recently, a radio interferometric solution was proposed for the localization and tracking of resource-constrained wireless nodes [12–15]. By measuring the phase difference of a signal generated by two transmitters with close frequencies at two receivers, information on the relative distances of the four nodes involved can be deduced. In addition to the node transmitting a sinusoid of frequency , an auxiliary node is transmitting a sinusoid of frequency . The superposition of the two signals generates an interference field with beat frequency . Tuning the transmitters, so that the interference frequency is a few hundred Hz, makes it possible to measure the phase of the signal with resource-constrained wireless nodes. The receiver can observe the low-frequency beating using the the received signal strength indicator (RSSI) signal provided by the RF transceiver chip. The RSSI signal is the power of the incoming signal mixed down to an intermediate frequency and low-pass filtered. It was shown in [12] that a phase change in the high-frequency sinusoid results in an equivalent phase change in the RSSI signal. Taking the difference of the phases observed at two receivers eliminates the unknown initial phases of the transmitters. However, it complicates the ranging because one measurement provides information on the pairwise distances of four nodes, but making multiple measurements in a network of at least six nodes provides enough information to compute the relative location of all nodes.

While both the range and the accuracy of the method proved superior to many other approaches [3, 16, 17] in open areas, multipath propagation impacts the accuracy of the technique. A variation of the method replaces the phase measurements with that of frequency. The technique assumes a moving transmitter at an unknown location (and with an unknown velocity vector). As such, it generates a Doppler shift. The reference implementation works on Crossbow Mica2 nodes operating at 430 MHz [18]. A person walking with the transmitter at 0.3 m/s induces a 0.4 Hz shift, a ratio, which is impossible to measure on the cc1000 radio chip or on much more expensive instrumentation either. However, the radio interferometric approach works here as well; the same amount of Doppler shift appears in the beat signal as in the carrier [15] and it can be measured accurately enough using simple, inexpensive hardware. If this shift is measured at multiple receivers, the location and velocity of the tag can be accurately estimated [19].

The obvious disadvantage of this method is the requirement for movement, since without it, there would be no Doppler shift. This observation led us to the idea of rotating the antenna of the transmitter (or even the entire node) at a constant speed and radius. To a stationery observer, the signal will have a continuously changing frequency due to the Doppler effect. Again, radio interferometry is required to be able to measure this accurately. How the frequency changes over time depends on the angular velocity of the transmitter, the radius of the circle, and the distance between the rotating transmitter and the receiver. While it is trivial to compute the distance given the radius and the angular velocity, the result is very sensitive to measurement errors if the distance is large. To tackle this issue, we leverage the fact that the correlation of the observed frequency change across multiple receivers provides valuable information on the location of the nodes involved. In this paper, we analyze the case of localizing a rotating transmitter using fixed receivers at known locations.

The remainder of the paper is structured as follows. In Section 2, we develop a differential bearing estimation approach which is based on Doppler frequency measurements. The signal processing technique to estimate the Doppler-shifted frequency is described in Section 3. Then, in Section 4, we propose a localization algorithm based on differential bearing estimates. We present experimental and simulation results in Section 5 and conclude the paper assessing the practical applicability of our technique and highlighting future research directions.

## 2. Ranging Approaches

where is the baseline frequency emitted by the transmitter and is the speed of light.

When using radio-interferometry as described in Section 1, that is, a stationary auxiliary transmitter is emitting a sine wave of frequency (where ), it was shown in [15] that the same amount of Doppler shift appears in the low-frequency envelope signal.

where is the distance between receivers and . While we obtain an angle, the result is still similar to traditional pairwise ranging in that one "range" estimate constrains the location of the node to a circle. Except the center of the circle in our case is not another node, but a location that can be computed from the locations of the two receivers and the measured angle.

While attractive, this method relies on measuring the Doppler shift at any one receiver accurately. However, in most computers and wireless devices, uncompensated crystal oscillators are used to generate the clock signals. The short-term stability of these oscillators are typically between and for one second. In our case, this corresponds to possibly more than 1 Hz error that cannot be compensated for, because we cannot measure the baseline frequency directly (i.e., when the transmitter is stationary). We need to rely on measuring the difference between the maximum and the minimum frequencies and take their mean. Since the time between these events may not be much less than one second, short term stability can cause a larger error than the phenomenon we are trying to measure. Temperature-compensated crystal oscillators have somewhat better stability, while oven-controlled crystal oscillators are at least an order of magnitude more precise. Unfortunately, their price and power requirements are both significantly higher, and they are not used in everyday devices. The question is then how can we eliminate this significant source of error?

*T*and its components pointing toward receivers and , respectively. From Figure 4 we see that (5) can be rewritten as and .

*far field*assumption, the angle , denoted as , is fixed. Without the loss of generality, let us assume that . Therefore, and . Substituting these relationships into (9) yields

Therefore, by measuring the maximum difference of the Doppler shifts measured at receivers and , we can estimate . In the presence of noise, however, the maximum of the signal cannot be measured precisely. Obviously, measurement noise can be mitigated by iteratively measuring and averaging the observed values, though such a technique is time consuming.

Therefore, it is sufficient for the two receivers to measure the frequency of the received signal for the duration of merely one rotation in order to compute .

## 3. Frequency Estimation

We selected the GNU Radio [20] software platform and the USRP [21] hardware frontend to verify the proposed ranging ideas. The Software Defined Radio (SDR) is an ideal tool for experimentation, since it allows for rapid prototyping of experimental algorithms. Using an SDR is a promising approach not only for increasing the computational budget, but also for making detailed observations on the signals. While SDR is a more powerful and more flexible platform than those used previously in radio interferometric localization [12–14], our primary goal was to test and fine-tune the proposed algorithms using an SDR, then to port the final solution to low-power wireless nodes, such as the Berkeley Mica2 or the XSM mote [22].

The baseline configuration consists of a fixed position SDR transmitter and a rotating transmitter. The rotating node emits a pure sine wave continuously, thus it can be implemented using a simple, low-cost device, such as a WSN. The fixed position transmitter transmits a pure sine wave at a close frequency. Since multiple receivers need to make synchronized measurements, a time synchronization approach is necessary. Instead of implementing a time synchronization protocol on the SDR platform, we embed timing information in the transmitted signal itself. The SDR transmitter periodically emits a windowed chirp signal before a pure sine wave segment. That chirp can be accurately decoded on the receiver side and it makes a common time reference point for all receivers. The range of this short frequency sweep does not overlap with the frequencies of the pure sinusoids.

The lower part of Figure 5 describes the signal processing steps on the software side. On the GNU Radio platform, the signal processing blocks are implemented in C++, but the blocks are configured and wired by Python scripts, which provides a very flexible environment without compromising on performance. Although many of the signal processing steps of the proposed approach (envelope decoding, time synchronization, and filtering) are implemented on the GNU Radio platform, the published results are based on recorded data and offline processing in MATLAB [23]. However, the final signal processing chain contains no steps which are infeasible to implement in a real-time GNU Radio application.

The time synchronization decoder processes the received samples independently from the rest of the signal processing path and produces time reference points at the end of the chain. It uses a matched filter and a peak detector to find the exact position of the chirp signal in the data stream. The current implementation provides 1 microsecond accuracy which is far better than required.

## 4. Localization

Performing the angle estimation for each pair of receivers from the set of , , and , three distinct angles will be obtained ( , , ). Each angle and the known positions of its corresponding receivers define a circle. Calculating the center of this circle and its radius for each estimate is straightforward and necessary for the localization estimate; however, this task is complicated by the symmetrical properties of the geometry. Each angle and its receivers define not one but two circles that are symmetrical about the chord between the positions of the receivers, that is, the centers of the circles are reflections about a line connecting the locations of the two receivers. Resolving this dual solution would be impossible without knowing the direction of rotation of the transmitter . While omitting details, we indicate here that assuming a known direction of rotation, the proper circle can be selected from the angular separation in time of the observed Doppler shifted frequencies between two receivers and their spatial relationship with the calculated centers of the symmetrical circles of interest. More plainly, each solution (circle), provided the assumed direction of rotation, will influence the order in which the two receivers observe their maximum/minimum Doppler shifted frequencies (e.g., either before or vice versa).

Accordingly, three unique circles are obtained (one for each ), and the desired localization estimate is calculated from their intersection points. Note that we obtain not one intersection point but up to three, because the circle of rotation is not zero and there is measurement error. Therefore, the localization estimate is formulated as the geometric mean (centroid) of these points.

## 5. Results

In this section, we present experimental results and characterize the corresponding measurement noise. Then, we provide a simulator that, for a given experiment configuration (coordinates of transmitters and receivers, transmit and sampling frequencies, etc.), generates ideal measurement values, that is, a time series of frequency measurements at each receiver. The location solver's sensitivity to measurement errors is evaluated by feeding in this data perturbed by noise with empirically derived characteristics.

### 5.1. Experimental Results

In a slightly modified configuration, we used two fixed position SDR transmitters and two SDR receivers indoors and executed 300 experiments—one every 10 seconds—as previously described. A single experiment resulted in 100 frequency estimates. During the full set of experiments (50 minutes, 300 000 estimates), the largest difference of the measured envelope frequency was 63.8 Hz, again due to the instability of the transmit frequency. However, the two receivers never differed by more than 0.5 Hz (maximum error) and the standard deviation of their difference was 0.045 Hz.

The central component of the signal processing chain is the frequency estimator for which many different methods have been developed and published [12, 24, 25]. We selected, implemented, and evaluated some of these, but one of the potential future directions is a more exhaustive study and analysis of the applicability of existing methods.

### 5.2. Simulator

Currently, the localization estimates are calculated in MATLAB [23] for a given experimental configuration and input data set of frequency measurements. The experimental configuration minimally requires that the positions of at least three static receivers be specified along with the center of rotation of the rotating transmitter . The known position of the static transmitter is provided but does not influence the results. During initialization, the various experimental parameters (e.g., 2D locations of transmit/receive nodes, transmission frequencies, sampling rate, radius of rotation of transmitter , etc.) are specified. Localization estimates are formulated from either experimental measurements obtained from hardware or generated data. Either form of data consists of the measured Doppler shifted envelope frequencies at each receiver over a time interval. Generated data is calculated from the known geometry of the nodes and the configuration parameters, and the simulator further allows the experimenter to include noise in the generated signals (zero-mean Gaussian noise with adjustable standard deviation).

Each localization estimate from the simulator is formulated according to the steps detailed in Section 2. From an input data set of Doppler shifted frequency measurements, the velocity differences between each pairwise combination of receivers are used to calculate the angles according to the relationship in (15) and (16). From each calculated , the corresponding circles are calculated (see Figure 4), and the centroid of their pairwise intersection points forms the localization estimate. The following section will detail preliminary results obtained using our approach and the simulator for estimating the 2D location of a rotating transmitter.

### 5.3. Simulation Results

For our initial experimental evaluation, we assume three static receivers
,
, and
positioned on the Cartesian *xy*-coordinate plane (with axial units in meters) at locations (6, 16), (14, 13), and (7.5, 6), respectively. The input sampling rate of each receiver is 500 Hz. The fixed transmission frequencies of the two transmitters
and
are 430 MHz and 431 MHz (
kHz), respectively. Regarding the rotating transmitter
, the radius of rotation is 0.12 m, the rate of rotation is 45 RPM (
rad/s), and the direction of rotation is given to be counterclockwise. Assuming the speed of light is
m/s, using (3) and the relationship
yields an expected Doppler shift ranging between
Hz at any receiver.

With this configuration, we would like to evaluate how accurately we can estimate the center of rotation of
from the calculated
angles using our proposed method. Since the geometry of where
is with respect to the receivers will influence the magnitudes of the
angles, our experimental evaluation needs to generate localization estimates over a range of positions for
that adequately characterizes the field of the receivers. Accordingly, the experimental simulations were conducted by sweeping the location of
from 1 to 21 meters along the *x*-axis and from 21 to 1 meters along the *y*-axis in 0.2 m increments (a total of 10,201 unique locations). Simulation results for locations where any receiver is coincident or within the circle of rotation of the rotating transmitter
are ignored. For such a large number of experiments, generated input data was used for the simulations instead of physically-gathered data.

Figure 9(b) shows the same type of error plot for the calculated angle ( angle between receivers and ). The colorbar (in units of radians) indicates calculated 's with errors below 0.01 radians are white and above 0.2 radians are black. From the plot we see that the only significant errors occur when is positioned on the line connecting receivers and . The presence of the errors can be attributed to two sources: the finite resolution of the calculations for generating the simulation input data and determining the 's and the assumption that the 's are constant while the transmitter is rotating. For the former, as the sampling rate of the receivers is increased, some of the errors decrease to near zero. The latter source of error follows from our approximation that the radius of rotation is negligible compared to the distance between the transmitter and the receivers, and it cannot be generally compensated for or disregarded.

Figure 10(b) shows the error plot for the calculated angle with the noisy input data. The colorbar distribution is the same as the previous experiment ( 's with errors below 0.01 radians are white and above 0.2 radians are black). We observe the errors along the line connecting the receivers are accentuated. Note the interesting error pattern along the line in between the receivers; the largest errors along the line occur at a distance of about one radius ( of ) off the line. This phenomenon can most likely be attributed to the influence of the noise on the calculations in conjunction with the zero-radius approximation inherent in our method.

## 6. Conclusion

We presented a novel idea for ranging and localization of wireless radio nodes and our preliminary work validating it. While we have not carried out measurements with an actual rotating transmitter, the stationery experiments and simulation results indicate that the method is not only feasible, but has the potential for achieving high-accuracy localization. In fact, we have barely scratched the surface of what's possible. We have not explored different cases, for example, where the rotating transmitter is at a known position and the tracked node is a receiver. We have not assumed that the rotating node can be synchronized to the receivers, which could provide bearing information. If the transmit frequency is stabile in the short term (using, e.g., an oven-controlled oscillator), then measuring the maximum of the Doppler shift provides 3D bearing since the maximum observable speed in the plane of the rotation is given by the known radius and angular rate. However, our next logical step needs to be the construction of a stabile rotating platform and a large-scale experiment to validate the method under real-world conditions.

One might question the practical applicability of a rotating node (or antenna). Obviously, in most tracking applications the tags need to be small and inexpensive, so rotation is not really an option. However, in many applications the coverage area is fixed and can be equipped with more expensive, so-called infrastructure nodes. For example, one can imagine a large stadium being equipped with a few rotating nodes at known locations forming the anchor nodes of the system. In a mobile application, a few vehicles can have both GPS for tracking their own positions and the rotating nodes for tracking possibly many other nodes that do not have GPS. Finally, a smart antenna array may be able to mimic the rotation of the transmitter, thus making the system cheaper, more robust and energy efficient.

## Declarations

### Acknowledgment

This work was supported in part by NSF Grant CNS-0721604 and ARO MURI Grant W911NF-06-1-0076.

## Authors’ Affiliations

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