NL2005603C2

NL2005603C2 - Method and system for localization in a wireless network.

Info

Publication number: NL2005603C2
Application number: NL2005603A
Authority: NL
Inventors: Bram Jeroen Dil; Paul Johannes Mattheus Havinga
Original assignee: Univ Twente; Ambient Holding B V
Priority date: 2010-10-29
Filing date: 2010-10-29
Publication date: 2012-05-02
Also published as: WO2012057627A1

Description

Method and system for localization in a wireless network

The present invention relates to a method and system for localization in wireless networks. More in particular, 5 the present invention is related to Received Signal Strength (RSS) based localization in wireless networks.

Localization in wireless networks describes the process of obtaining a physical location in an automated manner using wireless communication. Many wireless network 10 applications rely on location information to perform their tasks. Locations provide context to the measured data (e.g. like measuring temperature); localization can be a standalone application (e.g. inventory tracking in a distribution center) or provides support to the network service (e.g.

15 routing). Today, such applications have evolved into realtime location systems (RTLS) using a wide range of wireless technologies. Many of these localization applications are based on Received Signal Strength (RSS) measurements, as RSS information is obtained without additional hardware and 20 energy costs. Other localization systems use techniques like Time Difference Of Arrival (TDOA), Time Of Flight (TOF), Ultra Wide Band (UWB) and Angle Of Arrival (AOA). In general, these techniques are more accurate than RSS-based localization but require specialized hardware, more 25 processing, more communication and thus more energy (e.g.

[2]). Radio Interferometric Positioning holds the promise to break this paradigm.

Radio Interferometric Localization relies on pairs of nodes simultaneously transmitting unmodulated carriers at 30 slightly different frequencies that are highly correlated during the measurement time. Nodes that are within transmission range measure the energy of the envelope of the frequency beat signal. The relative phase offset of the 2 measured envelope of the frequency beat signal at two receivers is a function of the distances between the involved nodes and the carrier frequency. RIPS uses this information to estimate the position of the nodes ([3] ) .

5 The main disadvantage of the existing RIP

implementation is that it imposes a set of strict requirements on the radios: The existing RIP implementation requires the radio to tune its frequency in relatively fine-grain steps, such as the CC1000 (see [13], 65 Hertz 10 frequency resolution). Most Commercial-Off-The-Shelf (COTS) radios cannot comply with this strict requirement, like the CC2430 radio ([14]). Hence, most RIP implementations run on a CC1000 radio platform ([3], [4], ... [11]). [12] breaks with this implementation paradigm and shows that it is 15 possible to implement RIPS on a CC2430 radio platform ([14]). However, [12] also shows that the existing RIP algorithm cannot cope with the large and dynamic sources of error introduced by the CC2430 platform, as the current RIP algorithm provided a localization accuracy of « 3 meters in 20 a limited 12 x 9 mz set-up.

Using the Radio Interferometric Positioning System (RIPS) can be classified in four distinct phases: • Calibration phase • Measurement phase 25 · Estimate distance phase • Estimate position phase

Figure 1 shows an example of a typical RIPS set-up.

Here nodes A and B transmit an unmodulated carrier signal with frequencies fA and fB. The envelope of the composite 30 signal of A and B has a beat frequency of |ffBI , which is measured by nodes C and D. The relative phase offset of the measured frequency beat signal is a function of the distances between nodes A/B/C/D. RIPS assumes that the 3 location of three of the four nodes are known in order to solve the obtained system of equations. Moreover, the relative phase offset has to be measured over multiple frequencies in order to prevent distance estimate 5 ambiguities.

[12] shows that the phase measurement error and thus the positioning error increases with the frequency beat (|fA-fB|). The CC1000 RIPS implementation minimizes the frequency separation and thus the positioning error by 10 introducing a "Calibration phase" ([3]). The calibration phase ensures that the frequency beat is measurable given the user-defined measurement time and the hardware-defined RSSI sampling rate (9 KHz for the CC1000, [13]). The advantage of this approach is that it minimizes the 15 positioning error given the hardware specifications.

However, it imposes the requirement on the radio that it has the ability to tune its frequency in fine-grain steps smaller than the wanted frequency beat, like the CC1000 (see [13], 65 Hertz frequency resolution). Note that every 20 transmitter requires calibration, which further decreases the scalability of the target-as-transmitter implementation.

Our CC2430 RIPS implementation does not have a calibration phase as it searches for frequency beat signals "on the fly" ([12]). This means that not every transmitter 25 pair has to provide a measurable frequency beat. In the measurement phase, transmitters A and B send an unmodulated carrier signal and receivers C and D measure the envelope of the composite signal over multiple frequencies (see Figure 1). Figure 3 shows an example of one of these measured RSSI 30 signals over time. The existing RIPS implementations use a simple threshold crossing technique ([1]) in order to estimate the "phase" of the measured frequency beat signals of receivers A and B, while keeping the computational costs 4 low. Therefore, the CC1000 RIPS implementation filters frequency beat signals with an amplitude lower than a certain threshold, which increases the localization performance accordingly ([3] ) . This paper shows that similar 5 frequency beat signal filtering on the basis of the amplitude does not significantly increase the localization performance of the CC2430 RIPS implementation. Moreover, we show that setting the amplitude threshold too high even decreases the localization performance. The relative phase 10 offsets measured in the "Measurement phase" are a function of the distances between nodes A/B/C/D, assuming that fA > fe · Αφί = 2π ^AIICD ιηοά(2π) (1) κ

Here : 15 dabcd ~ dad — dBD + dBC — dAC (2)

Here Δφι represents the relative phase offset; dAD represents the distance between node A and D; λ± represents the wavelength of the intermediate frequency: c/fi=2c/(fA+fB) . Here c represents the speed of light; and fi represents 20 intermediate frequency i. We define dABcD as the q-range, as in [4] .

Equation 1 does not define a unique solution for dABcD due to mod (2π) -related ambiguity of dABcD· Therefore, existing RIPS implementations perform relative phase offset 25 measurements over several frequencies: fi...fN· Then the problem can be rewritten to the following optimization problem ( [4]): ERROR(dABCD) = J>,/iC£),-d,)2 (3) i=l

Here ( [4]) : f , _ \ 30 d- = round AHCD—— · λ· l k ) 5 represents the best fit given q-range cUbcd; Yi represents the phase offset relative to the wavelength y± =λιΔφί/ (2π) . Figure 4 shows the error (Equation 3) as a function of the q-range. The vertical line represents the real q-range. This figure 5 shows that the real q-range lies in a local optimum, which is a known problem of RIPS (e.g. [4]) as most RIP algorithms assume that the real q-range lies at the global optimum (cUbcd = min (ERROR (cUbcd) ) , e.g. [3]). [4] and [6] attempt to solve this problem: 10 · [4] iteratively constrains the search space of the q- range based on the estimated position. The problem is that this approach assumes that the q-ranges associated with the estimated positions are near the real q-range, especially in the first iterations. In other words, 15 this approach assumes that the global optimums are near the local optimums. This is for instance not the case in Figure 4. Therefore, iteratively constraining the q-range search space can decrease the localization accuracy dependent on the position estimates and 20 associated optimums. Moreover, the performance depends on the parameter values associated with constraining the search space. Determining the optimal values of these parameters are still an open field of research ([4] ) .

25 · [6] assumes that the error per phase measurement is below a certain threshold. We think this is a questionable assumption as the phase measurement error depends on the environment. The environmental influence is not known a priori. Therefore, it is difficult if 30 not impossible to determine the optimal value of this threshold.

The performance of the RIP algorithms described in [4] and [6] are dependent on parameter settings that can only be 6 determined empirically. Existing RIP implementations distinguish between two type of nodes, namely: • Reference nodes know their position in advance.

• Blind nodes do not know their location in advance and 5 are subject to localization.

This means that the values of dAc and dBc are known and that the values of dAD and dBD are unknown. Then, Equation 2 can be rewritten as follows: dabcd dAC — dBC — dA/) — dBD (4) 10 The value of the left hand side of Equation 4 is known: dmcD + dAC -dBc· We define dsscD + dAC - dBc as the t-range, as in [7] .

Equation 4 represents a hyperbolic curve over the localization surface as with TDOA measurements ([2]). The 15 intersection of two or more hyperbolic curves represents the position, assuming perfect q-range estimates. This means that RIP requires frequency beat measurements between two or more different pairs of senders in order to estimate the position. Figure 2 shows an example of two hyperbolic curves 20 (Hab and HAC) calculated by the following sender pairs: {A,B} and {A,C}. The circles represent the positions of the reference nodes A, B and C. The triangle represents the position of node D, the position of which is estimated by the intersection of the hyperbolic curves. Unfortunately, q-25 range measurements contain error, and the position can only be estimated.

The position estimate is defined by the following optimization function (e.g. [3] and [9]):

K

i, Σ (dABCD,j ~ dABCD ) ( 5 ) j=1 30 Here x and y represent the x- and y-coordinate of the position estimate; K represents the total number of q-ranges; dABCDj represents the j'th q-range calculated by 7 minimizing Equation 3; and dABCD represents the q-range to position estimate (x,y). For a detailed computational and sensitivity analysis of the described localization algorithm we refer to [5].

5 It is an object of the present invention to provide an alternative to the known localization method and system.

To that end, the present invention provides a method for localization of a receiving node in a wireless network, said wireless network comprising said receiving node and a 10 plurality of spatially separated nodes having a known position, each node of said plurality of nodes being capable of sending and/or receiving electromagnetic signals. These signals are received or sent wirelessly.

As a step a) of the method according to the invention, 15 a combination of a first and second node is selected from the plurality of nodes. This does not exclude that more than two nodes are selected. Moreover, as will be discussed later, both nodes need not be identical in behavior.

As a step b) of the method according to the invention, 20 a node from said plurality of nodes, different from said first and second node, is selected as a receiving node.

As a step c) of the method according to the invention, a beat signal is generated at the node to be localized and at the receiving node using said combination, the beat 25 signal corresponding to interference of a first and second electromagnetic signal emanating from the first and second node, respectively, said first and second electromagnetic signal having a frequency component at closely adjacent frequencies. Here, closely adjacent frequencies should 30 preferably be interpreted as frequencies separated by a frequency offset that is negligible small compared to either of two (or more) frequencies. As mentioned above, electromagnetic signals emanate from the first and second 8 node. The term emanate is chosen to illustrate that a node does not necessarily need to transmit the electromagnetic signal actively. It could be reflecting an electromagnetic signal coming from elsewhere. However, from the viewpoint of 5 the receiving node and the node to be localized, electromagnetic signals having a different frequency behavior, e.g. such as a frequency spectrum, appear to be coming from distinctive places.

As a step d) of the method according to the invention, 10 a first and second beat signal are measured using received signal strength indicator (RSSI) measurements corresponding to the electromagnetic signals received at the node to be localized and at the receiving node, respectively.

As a step e) of the method according to the invention, 15 a relative phase offset is determined between the beat signals of the receiving node and the node to be localized.

As a step f) of the method according to the invention, steps a) to e) are repeated for a plurality of said closely adjacent frequencies and a plurality of combinations having 20 a different node composition. Hence, relative phase offsets are determined as a function of the frequencies of the first and second electromagnetic signals and combination composition.

As a step g) of the method according to the invention, 25 the position of the node to be localized is estimated. The estimating process is usually the starting point of an optimization process. Still, a priori knowledge about the position of the node to be localized could speed up the process .

30 As a step h) of the method according to the invention, an error for each relative phase offset is calculated. Subsequently, in step i) of the method according to the 9 invention, the errors calculated under h) are accumulated to give an accumulated error.

As a step j) of the method according to the invention, the accumulated error is minimized by repeating steps g)-i) 5 by varying the estimate.

Contrary to the known implementation of RIPS, an error is not determined for each relative phase offset for a particular combination. For instance, as indicated by equation 3), a q-range is determined for a particular 10 combination albeit using a plurality of frequencies. The determined q-range is in that case used as a given during the subsequent calculation of the position according to equation 5). In the method according to the present invention however, this distinction is not made. A single 15 position estimate is used to determine an error for all relative phase offsets. The applicant has found that this approach reduces the sensitivity of the localization method to factors such as multipath influences, and hardware and environmental inaccuracies.

20 Typically, one of the first and second electromagnetic signal has a frequency component at (fi+d/2) Hz and another of said first and second electromagnetic signal has a frequency component at (fi-d/2) Hz, wherein fi represents an intermediate frequency and d a frequency offset. Using this 25 notation, the influence of the frequency offset becomes negligible for the calculations of the position of the node to be localized. Hence, step f) can be reduced to repeating steps a) to e) for a plurality of intermediate frequencies and a plurality of combinations having a different node 30 composition.

Typically, a node emits or transmits only a single tone comprising an unmodulated carrier signal. This produces a simple beat signal. However, with the advent of low cost 10 high precision and high frequency sampling devices it is possible to have the first and/or second node emit or transmit electromagnetic signals having a more complex frequency spectrum, for instance comprising more tones. In 5 this way, a combination of multiple beat signals may be identified at the receiving node and/or the node to be localized. This allows some of the measurements, for instance the frequency sweep, to be done by a single emission or transmission.

10 Additionally or alternatively, step b) could comprise selecting a plurality of receiving nodes. In such a case, steps c) to e) are adapted to measure a separate relative phase offset between the beat signal of the node to be localized and of each of the receiving nodes. Compared to 15 the known implementation of RIPS, this provides redundant information, because only two receiving nodes, including the node to be localized, need to be used to determine the position. However, as will be shown later, the redundancy might be helpful in obtaining a better position estimate.

20 The method according to the invention may comprise constructing a q-range error distribution using a plurality of relative offset measurements pertaining to a plurality of frequencies for a particular combination. In this aspect, the same definition of q-range is used as in the 25 abovementioned prior art. Similar to the known implementation, a q-range is determined for a given combination of transmitters/receivers. The q-range error distribution provides an accumulated error for the plurality of relative offset measurements as a function of the q-30 range. Using the q-range error distribution, the minimizing under step j) may comprise as a first step calculating a q-range corresponding to the position estimate for a particular combination. According to equation 4), given a 11 position estimate, the corresponding q-range can be calculated. Using this value, and given the corresponding q-range error distribution for the particular combination of transmitters and receivers, a q-range error can be computed.

5 This calculation should be repeated for all combinations. In this way, redundant information may be used. By adding the q-range errors calculated for each of the combinations an overall error can be determined.

The sensitivity of the method to variations caused 10 inter alia by multipath effects can be reduced by smoothening the q-range error distribution for each combination prior to calculating a q-range error for that calculation. For instance, if two combinations are used for determining the position of the node to be localized, and 15 each q-range error distribution corresponding to one of the two combinations shows a high error value and low error value close to each other, such as indicated in figure 4, it might occur that a high error for one of the combinations is added to a low error for the other combination during the 20 adding up of the errors for each combination, even though that particular position (estimate position) is very close to the true position. Hence, due to the high-frequency nature of the q-range error distribution, errors in positioning may occur. Smoothening solves this problem.

25 A first example of smoothening comprises determining a lower envelope of the q-range error distribution. This reduces the unwanted influence of closely separated local minima and maxima.

A second example of smoothening comprises interpolating 30 local minima of the q-range error distribution. In this example, the local minima are determined, for instance within a predetermined range, and are subsequently connected using known curve fitting algorithms.

12 A third example of smoothening comprises determining an error value for a given q-range by determining one of a global minimum and a local minimum average within a predetermined area around said given q-range, and 5 interpolating the determined error values. In this approach, an average is determined for the minima within a predetermined area around a given q-range. Subsequently, for the given q-range, being a discrete point in the error function, a corresponding error can be identified. This 10 error can be interpolated as described above.

Alternatively or additionally, the impact of the high frequency nature of the q-range error distribution can be mitigated by weighing the different q-ranges computed for the various combinations. For instance, if a particular q-15 range error distribution has a very low (global) minimum, this distribution can be identified as reliable, and a high weighing factor can be assigned accordingly. However, if the distribution function shows a series of local minima and maxima not differing significantly with a predetermined 20 region, a low weighing factor can be assigned.

As mentioned before, in order to obtain a beat signal there need to be at least two signals with different frequencies. This could be achieved according to the invention if step c) comprises the first node emitting the 25 first electromagnetic signal and the second node receiving at least a part of the first electromagnetic signal from the first node. In this case, the second node is not functioning as a stand-alone receiver. Instead it frequency converts the received at least part of the first electromagnetic signal 30 and emits the converted signal as the second electromagnetic signal.

13

Another option is to use the first node and the second node to concurrently emit the first and second electromagnetic signal, respectively.

According to a second aspect, the invention provides a 5 network for localization of a receiving node in a wireless network. The wireless network comprises the receiving node, and a plurality of spatially separated nodes having a known position. Each node of said plurality of nodes and said receiving node are capable of sending and/or receiving 10 electromagnetic signals, and are provided with a detector for measuring a received signal strength indicator (RSSI) of incoming electromagnetic signals. The network further comprises a memory for storing the RSSI measurements and a controller for setting each node of said plurality of 15 spatially separated nodes node in a receive, transmit, or inactive mode and for controlling the transmitting or receiving of said node. A processing unit is communicatively connected to the memory and is configured for calculating a position of the node to be localized. The controller is 20 configured for conducting steps a)-f) of appended claim 1, and the processor is configured to determine said position using the steps g)-j) of claim 1. However, the controller and/or processor may be configured to conduct the further steps as described above.

25 In an embodiment, the memory comprises local memory in each node for storing RSSI measurements done by said each node, and wherein the processor is connected, preferably wirelessly, for accessing the measurements stored in said each node. Hence, each node is able to store its 30 measurements results. The processor may be configured to read out all the measurement results once the measurements are finished.

14

Next, the invention will be described in more detail with reference to the accompanying drawings, wherein:

Figure 1 illustrates a prior art RIPS configuration;

Figure 2 illustrates the process of localization using 5 hyperbolic curves as used in the prior art RIPS system;

Figure 3 shows a typical freguency beat signal measurement;

Figure 4 depicts a typical g-range error distribution;

Figures 5 and 6 show a Fourier transformation of two 10 freguency beat signals;

Figures 7 and 8 illustrate the g-range error distribution for a good or bad combination composition, respectively;

Figure 9 illustrates a smoothed g-range error 15 distribution;

Figure 10 illustrates a smoothed q-range error distribution over the localization surface;

Figures 11 and 12 illustrate separate and accumulated t-ranges, respectively; 20 Figure 13 shows a typical radio for carrying out the invention;

Figure 14 shows a measurement environment; and

Figures 15-18 show a quantitative comparison between the prior art RIPS system and the system/method according to 25 the invention.

Before we describe the present invention and analyze its performance in a practical localization set-up, we perform several frequency beat measurements in a limited set-up used throughout this section in order to prove that 30 the CC2430 hardware is suitable for radio interferometric positioning. The limited set-up consists of four nodes placed in the corners of a 1 x 1 m2 rectangle. The short range and line-of-sight measurements minimize the influence 15 of the environment on the received signal strength so that we measure the performance of the CC2430 hardware. We placed all radios on tripods at the same height of 1.5 meter and we did not place objects in the vicinity of the radios in order 5 to further decrease the influence of disturbing reflections ([4]). Moreover, the conditions during the measurements were static (temperature, humidity, no moving objects). Not transmitting nodes measured the RSS with a sample rate of 62.5 KHz over multiple frequencies in a bandwidth of 2.406 10 ...2.480 GHz. The frequency beat signals are measured with all possible transmitter and receiver pair tuples: 4x3/(2x1)=6 possible transmitter and receiver pair tuples. The nodes all had a widely used "omnidirectional" dipole antenna with a vertical orientation. All individual RSS 15 measurements were sent to a computer and logged for post processing. The CC2430 RIP implementation does not require a calibration phase as it searches for frequency beat signals "on the fly".

In this section we measure how many of 16 different 20 crystal oscillators and thus CC2430 radios produce a measurable frequency beat. In this measurement set-up, the receiving nodes measured 500 consecutive RSS measurements for 8 milliseconds over the following two frequencies: 2.478 and 2.480 GHz. We measured the frequency beat of 48 25 transmitter pairs. This means that every CC2430 radio was paired with 6 different CC2430 radios. These measurements show that: • One CC2430 transmitter could not produce a measurable frequency beat with all 6 other radios. This means that 30 15/16 x 100% * 94% of the CC2430 radios produce measurable frequency beats.

• One CC2430 transmitter pair could not produce a measurable frequency beat within the 8 milliseconds ι6 measurement time, as the frequency separation was « 100

Hz. We deduced this information from frequency beat measurements with other radios.

The measurements show that 41/48 x 100% « 85% of the 5 frequency beat measurements produced measurable frequency beats within 8 milliseconds measurement time. We expect that this is sufficient for practical applications. Moreover, the mean frequency beat was « 5 KHz and the standard deviation of the measured frequency beats was « 3.5 KHz. This means 10 that we measured a large variety of frequency beats with a minimum of « 210 Hz and a maximum of « 14 KHz. The coherence time is the time in which the phase of an electromagnetic wave autocorrelates with its source. In other words, it defines the maximum measurement time for our beat signals to 15 exist. Therefore, increasing the measurement time beyond the coherence time does not provide reliable phase measurements as expressed by Equation 1.

The coherence time does not include the influence of the environment, it represents the capabilities of the 20 hardware. Note that the coherence time also include the hardware depended errors mentioned in [3].

In this section, we experimentally prove that the coherence time is sufficient for the CC2430 RIPS implementation. To this purpose, we use the 1 x 1 m2 25 measurement set-up in an open space. We compute the lower bound for the coherence time by accumulating the 500 channel multichannel analyzer. The receiving nodes measured 5000 consecutive RSS measurements for 80 milliseconds over 38 frequencies in a bandwidth of 2.406 ...2.480 GHz. We 30 calculated the bandwidth of the first 500 measurements and over all 5000 measurements.

Figures 5 and 6 show the Fourier transformation of the two frequency beat signals. The graph indicated with the 17 crosses represents the Fourier transformation of the first 500 measurements and the graph indicated with the triangles represents the Fourier transformation of the 5000 measurements. These figures clearly show that the bandwidth 5 of the graph with triangles (« 20 Hz) is a factor 10 smaller than the graph with crosses (« 200 Hz). The other measurements show similar results. This means that the coherence time is at least 80 milliseconds, long enough to generate a bandwidth on the carrier frequency of « 20 Hz, 10 yielding a measurement accuracy of roughly 1% in the KHz range where our beat frequencies are.

Next, a description of our new RIP algorithm will be given, which hereinafter will be referred to as Probabilistic Radio Interferometric Positioning (PRIP). The 15 first subsection describes and analyzes different types of errors. In the second subsection, we describe PRIP. In the third subsection, we show that PRIP evaluates information that is considered redundant by existing work on RIPS. In the last subsection, we compare how PRIP and the original 20 RIP algorithm handles the q-range errors described in the first subsection. For simplicity, we distinguish between three types of q-range distributions: • A "good" q-range distribution with one global optimum at the real q-range. Moreover, the global optimum tends 25 to have a relatively low error compared to the local optimums. Figure 7 shows an example of such a q-range distribution .

• A q-range distribution with ambiguities with its global optimum not at the real q-range and with some local 30 optimums. Moreover, the q-range distribution with ambiguities tends to have larger phase measurement errors than the "good" q-range distribution, which flattens the q-range distribution. For instance the ι8 difference between the minimum and maximum of the "good" q-range and the q-range distribution with ambiguities represented by Figures 7 and 4 is: 3.2 in comparison with 2.2.

5 · A bad q-range distribution with many local optimums, as illustrated by Figure 8. A "bad" q-range distribution tends to have larger phase measurement errors than the q-range distribution with ambiguities, which flattens the q-range distribution. For instance the difference 10 between the minimum and maximum of the q-range distribution with ambiguities and the "bad" q-range distribution represented by Figures 7 and 4 is: 2.2 in comparison with 1.6.

In general, we categorize the q-range measurements as 15 the three types of errors as given above. This means that the q-range error differs per sender/receiver pair tuple. Moreover, the q-range error depends on the environment. Therefore, we do not make any assumption about the maximum phase measurement error, as is done in [4] and [6].

20 This subsection describes our new algorithm called PRIP. The main difference between the existing RIP algorithms and PRIP is that PRIP evaluates the q-range distribution as it is. This idea is represented by the following equation:

K

2 5 POS _ ERROR(x, y) = £ ERROR(dABCD j) (6) j=i

Here ERROR (dABCD, j) represents the error calculated by Equation 3; POS_ERROR(x,y) represents the function that calculates the error for a given x- and y-coordinate: (x,y).

The position estimate is then defined by: 30 min~ ~ POS _ERROR(x,y) (7)

Equation 7 defines the position estimate as the position that minimizes the error given by Equation 6. The problem 19 with this approach is that the q-range error distribution (see Equation 3) is periodic with a high frequency, as shown in figures 4, 7 and 8. As a direct result, the calculated error for a given position (Equation 6) becomes 5 unpredictable. We solve this problem by smoothing the q-range error distribution by using the following equation: ERRORprip(dABCD) = min(ERROR([dABCD - W,dABCD + IV])) (8)

Here W is a constant dependent on the used frequency band of the radio, which is 2.4 GHz in the CC2430 implementation; 10 [dABCD-W, dABCD+W] represents an interval; min (ERROR ( [dABcD -W, dABCD +W] ) ) represents the minimum value of Equation 3 over the specified interval. In our implementation we set W to 12.5 centimeter. We rewrite Equation 6 to: POS_ERROR(x,y) = ^ ERRORpr1p (dABCDj) (9) i=i 15 Figure 9 shows an illustrative example of the smoothed q-range error distribution of Figure 4 using Equation 8. We use Equation 8 for calculating the probability distribution over the localization surface. Figure 10 shows the smoothed q-range error distribution over the localization surface 20 using Equation 8, shown in Figure 4 before smoothing. Here the cross represents the true location of the blind node; the regions with a triangle represent a large error and the regions with a dot represent a small error. Note that the two minimums shown in Figures 4 and 9 are represented by the 25 two lines with a diamond in Figure 10.

In this paper, we use a grid-based Monte Carlo approach to minimize Equation 9 and estimate the position of the blind node. Note that the computational costs of PRIP is similar to the algorithms described in [3], [4] and [6].

30 This means that this implementation of PRIP increases the computational costs quadratically with the number of heard transmitter pairs. In comparison with the existing RIP

20 algorithms, PRIP further increases the localization performance by evaluating the q-range distributions of all possible receiver pairs containing the blind node. Existing RIP implementations consider this information as redundant, 5 while PRIP uses these measurements to increase its robustness against erroneous q-range distributions.

PRIP accumulates the calculated smoothed t-range distributions from the possible receiver pairs. The t-range distribution can simply be calculated from the q-range 10 distribution (see Equation 4 for details). This minimizes the influence of phase measurement errors created by the reference nodes.

Figures 11 and 12 show an example of how a "good" t-range distribution minimizes the influence of a "bad" t-15 range distribution. The graph indicated with a triangle and an asterix in Figure 11 represent the smoothed "good" and "bad" t-range measurements (see Figure 7 and 8), respectively. The vertical lines represent the true t-range, the optimum of the "good" and "bad" t-range distributions.

20 Figure 11 shows that the "good" t-range distribution has its global optimum near the real t-range and that the "bad" t-range distribution does not provide a clue about the real q-range.

Figure 12 shows the mean of the two t-range 25 distributions. This figure shows that the optimum of the accumulated t-range is near the real t-range value. This is because the influence of "good" t-range distributions is larger, as "bad" t-range distributions are in general flatter. Moreover, Figure 12 shows the estimated t-range of 30 the original RIP algorithm, which is the mean of the optimums of both t-range distributions. Figure 12 clearly shows an illustrative example when PRIP outperforms the original algorithm. Note that this works in a similar 21 fashion when the accumulated t-ranges are summed over the localization surface (see Equation 7).

This section describes how PRIP deals with the different q-range errors and distributions in comparison 5 with the original RIPS algorithm. It was shown that an increasing phase measurement error increases the q-range error and flattens the q-range distribution and thus the t-range distribution. Therefore, it is logical that t-range measurements are weighted according to their accuracy: 10 · The original RIPS algorithm weights every t-range equally.

• PRIP weights the t-ranges according to the error calculated by the smoothed t-range distribution (Equation 8).

15 Figures 11 and 12 show how equally weighted and weighted t-range distributions increase the performance. For details we refer to the previous subsection. It was shown that the global optimum does not always represent the true t-range value. Therefore, it is logical to evaluate all 20 optimums: • The original RIPS algorithm assumes that the global optimum represents the true t-range value.

• PRIP evaluates all minimums and maximums of the smoothed t-range distribution.

25 Figure 10 shows how PRIP evaluates the t-range distribution with two optimums shown in Figure 9. Note that the blind node is positioned in the lighter grey line, which is a local optimum in Figure 10. This means that PRIP assumes that there is a relatively high probability that the 30 blind node is positioned on the lighter grey line, however PRIP assumes that there is a higher probability that the blind node is positioned on the darker grey line. The other q-range measurements will likely exclude one of the two 22 lines. Hence, PRIPS selects the global optimum and RIPS the erroneous local one.

This section first provides a description of the measurement and localization set-up. After that, this 5 section evaluates the performance of the existing RIP

algorithm and PRIP with different parameter settings. The measurements were conducted in a 20 x 20 m outdoor environment shown in Figure 14 with six CC2430 radios (Figure 13, [14] ) . We used four CC2430 radios as reference 10 nodes which were located at the corners of the localization surface; these reference nodes were static during and between the measurement rounds. We used two CC2430 radios as blind nodes; these blind nodes measured the RSS at 12 different locations in a 4 x 4 grid. We determined the 15 locations of the reference and blind nodes with a tape measure. The blind node measured 500 consecutive RSS measurements over 8 ms per frequency over a total of 38 frequencies in a bandwidth of 2406...2480 MHz. The radios were all placed at the same height at 1.5 meter in order to 20 minimize noise (e.g. [4]). All individual RSS measurements were sent to a computer and logged for post processing.

These measurements were performed over a period of two days with changing weather conditions. We used this measurement set-up as it is a similar environment and set-up as 25 described in [3].

This subsection evaluates the performance of the original RIP algorithm and PRIP as a function of the number of evaluated measurements. Figures 15 and 16 show the performance of the original RIP algorithm and PRIP as a 30 function of the number of evaluated measurements. The x-axis represents the number of consecutive RSS measurements. The four graphs represent the performance of the RIP algorithms using a different number of measurements per sender pair, 23 using the full frequency bandwidth of the available frequency band (2.406...2.480 GHz). This means that we increase the frequency hop length to: {2, 4, 6, 8} MHz; instead of decreasing the frequency bandwidth to: 5 {2.406...2.480, 2.406...2.444, 2.406...2.432, 2.406...2.426}. We use the frequency hop strategy as measurements show that it provides significantly better results than the frequency bandwidth strategy.

Figures 15 and 16 show that PRIP outperforms the 10 original RIP algorithm in all cases. PRIP increases the localization accuracy by an order of magnitude from 4.1 to 0.3 meter when we evaluate the maximum number of measurements described before. The difference in performance further increases from 15.2 to 0.4 meter, when we decrease 15 the number of evaluated measurements by a factor, see "19 measurements" at "Number of measurements per phase measurement: 50" in Figures 15 and 16. This means that the measurement time can be decreased from 2 to 0.1 seconds, without a significant performance loss. Note that decreasing 20 the number of phase measurements decreases the accuracy of the q-range distribution. Figures 15 and 16 verify that PRIP can cope with this uncertainty in the q-range distribution, in contradiction with the original RIP algorithm.

Figure 17 shows the number of measurable phase 25 measurements as a function of the number of consecutive RSS measurements. Not every phase measurement provides a measurable or useable relative offset measurement ( [3]) . Figure 17 shows that the number of measurable relative phase offsets decreases with the number of consecutive RSS 30 measurements. This means for instance that the number of used measurements are decreased by a factor 33 instead of a factor 20 at "19 measurements" at "Number of measurements per phase measurement: 50" in Figures 15 and 16. Note that 24 not every frequency beat associated with a transmitter pair can be measured within the specified measurement time of 0:8 milliseconds (50 consecutive RSS measurements). Therefore, we expect that the measurement time can be further reduced 5 to 70 milliseconds, without any performance loss.

In this subsection we analyze whether the amplitude filter implemented on the CC1000 RIPS provides similar results on the CC2430 implementation. The amplitude filter filters frequency beat signals with an amplitude smaller 10 than a certain threshold ( [3]) .

Figure 18 shows the performance of the original RIP and PRIP algorithms as a function of this threshold. This figure shows that the amplitude filter does not significantly increase the performance and that it can decrease the 15 performance when it is set too high. We expect that this is because increasing the threshold decreases the amount of evaluated phase measurements, which in turn decreases the localization performance.

The present invention has been described using 20 exemplary embodiments thereof. It should be obvious to the skilled person that various modifications can be made without departing from the scope of protection which is defined by the appended claims.

For instance, the invention has been described making 25 use of electromagnetic signals. However, the method and system are equally applicable for other signals such as acoustic signals.

Furthermore, the invention minimizes an accumulated error by varying the position estimate. In a further 30 embodiment, multiple positions can be found in such a manner, for instance by restricting the range in which the position estimate may vary. A single position estimate can 25 then be found by weighing the multiple positions, preferably in dependence of the associated accumulated error.

26

Bibliography

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5 Transactions on Information Theory, Volume 20, Issue 5, pp. 591598, September 1974.

[2] N.Patwari: Location estimation in sensor networks. Thesis of Neal Patwariat University of Michigan, 2005.

10 [3] M.Marti, P.Vlgyesi, S.Dra, B.Kusy, A.Ndas, A.Ldeczi, G.Balogh, K.Molnr: Radio interferometric geolocation. SenSys 2005: pp. 1-12.

15 [4] B.Kusy, .Ldeczi, M.Maroti, L.G.L.T.Meertens: Node density independent localization. IPSN 2006: 441-448.

[5] B.Kusy, J.Sallai: Analytical solution for radio-interferometric localization of mobile sensors. ISIS

20 technical report, ISIS-06-710. May 2006.

[6] B.Kusy, G.Balogh, J.Sallai, .Ldeczi, M.Marti: InTrack: High Precision Tracking of Mobile Sensor Nodes. EWSN 2007: 51-66.

25 [7] B.Kusy, J.Sallai, G.Balogh, .Ldeczi, V.Protopopescu, J.Tolliver, F.DeNap, M.Parang: Radio interferometric tracking of mobile wireless nodes. MobiSys 2007: 139-151.

30 [8] B.Kusy, .Ldeczi, X.D.Koutsoukos: Tracking mobile nodes using RF Doppler shifts. SenSys 2007: 29-42.

27 [9] H.Wu, H.Chang, C.You, H.Chu, P.Huang: Modeling and optimizing positional accuracy based on hyperbolic geometry for the adaptive radio interferometric positioning system. International Symposium on Location- and Context-Awareness 5 (LOCA 2007), Oberpfaenhofen, Germany, September 2007, pp 228-244.

[10] J.Tian, H.Chang, T.Lai, H.Chu: SpinTrack: Spinning Infrastructure Nodes for Precise Indoor Localization. In the 10 poster session of UBICOMP, September 2008.

[11] H.Chang, J.Tian, T.Lai, H.Chu, P.Huang: Spinning Beacons for Precise Indoor Localization. ACM SENSYS 2008, November 2008.

15 [12] B.J.Dil, P.J.M.Havinga: A Feasibility Study of RIP Using 2.4 GHz 802.15.4 Radios. MELT 2010, November 2010.

[13] http://focus.ti.com/lit/ds/symlink/cclOOO.pdf, 20 2010.

[14] http://focus.ti.com/lit/ds/symlink/cc2430.pdf, 2010.

Claims

A method of locating a receive node in a wireless network, said wireless network comprising said receiving node and a plurality of spaced-apart nodes having a known position, each node of said plurality of nodes in is capable of transmitting and / or receiving electromagnetic signals, the method comprising the steps of: a) selecting a combination of a first and second node from said plurality of nodes; b) selecting a node from said plurality of nodes, different from said first and second node, as a receive node; c) generating a beat signal at the node to be located and at the receiving node using said combination, the beat signal corresponding to interference from a first and second electromagnetic signal coming from the first and second node, respectively, the first and second node electromagnetic signal having a frequency component at nearby frequencies; D) measuring a first and second beat signal using received signal strength indicator (RSSI) measurements corresponding to the electromagnetic signals received at the locating node and at the receiving node, respectively; E) determining a relative phase shift between the beat signals of the receive node and the node to be located; f) repeating steps a) - e) for a plurality of said nearby frequencies and a plurality of combinations provided with a different node composition; G) estimating the position of the node to be located; h) calculating an error for each relative phase shift; i) accumulating the errors calculated under h) 10 to provide an accumulated error; j) minimizing said accumulated error by repeating steps g) -i) by varying the estimate.

The method of claim 1, wherein one of the first and second electromagnetic signals has a frequency component on (fi + d / 2) Hz and another of said first and second electromagnetic signals has a frequency component on (fi-d / 2) 2) Hz, where fi represents an intermediate frequency and d a frequency shift, and wherein step f) comprises repeating steps a) -e) for a plurality of intermediate frequencies and a plurality of combinations with a different node composition. 25

The method of claim 1 or 2, wherein the first and second electromagnetic signals are substantially single-tone signals.

Method according to one of the preceding claims, wherein a plurality of receiving nodes is selected in step b) and steps c) -e) are adapted to measure a separate relative phase shift between the beat signal of the node to be located and each of the receiving nodes.

The method of any one of the preceding claims, further comprising constructing a q-range error distribution using a plurality of relative shift measurements regarding a plurality of frequencies for a given combination, said q-range error distribution providing an accumulated error for said plurality of relative shift measurements as a function of the q range, and wherein said minimizing in step j) comprises: calculating a q range corresponding to the position estimate for a given combination; calculating the q-range error using the error distribution for the given combination; repeating these steps for all combinations; and adding the q range errors calculated for each of the combinations to determine the accumulated error.

6. The method of claim 5, further comprising smoothing the q-range error distribution for each combination prior to calculating a q-range error.

The method of claim 6, wherein said flattening comprises determining a lower envelope of the q-range error distribution.

The method of claim 6, wherein said smoothing comprises interpolating local minima of said q-range error distribution.

The method of claim 6, wherein said smoothing comprises: determining an error value for a given q-5 range by determining one of a global minimum and a local minimum average within a predetermined area around the given q range ; and interpolating the determined error values.

The method of any one of claims 6-9, wherein said adding the q range errors comprises weighting each q range error.

11. Method according to claim 10, wherein said weighing is performed in dependence on a depth of a global minimum of the corresponding q-range distribution.

12. Method as claimed in any of the foregoing claims, wherein step c) comprises: the first node transmitting the first electromagnetic signal; receiving at least a portion of the first electromagnetic signal from the first node by the second node; frequency converting the receiving at least a portion of the first electromagnetic signal; and transmitting said converted signal as the second electromagnetic signal by said second node.

The method of any one of claims 1-12, wherein step c) simultaneously transmitting the first and second electromagnetic signal by the first node and second node, respectively.

14. Network for locating a receiving node in a wireless network, said wireless network comprising: said receiving node; a plurality of spaced-apart nodes having a known position, wherein each node of said plurality of nodes is capable of transmitting and / or receiving electromagnetic signals, and being provided with a detector for measuring a receive signal strength indicator (RSSI) of incoming electromagnetic signals; 15 a memory for storing the RSSI measurements; a controller for setting each node of said plurality of spaced-apart nodes in a receive, send, or inactive mode and for controlling the sending or receiving of said node; and a processing unit which is communicatively coupled to said memory and adapted to calculate a position of the node to be located; wherein the controller is adapted to perform steps a) -f) according to claim 1, and wherein the processing unit is adapted to determine said position using the steps g) -j) of claim 1.

The system of claim 14, wherein the memory comprises local memory in each node for storing RSSI measurements made by said each node, and wherein the processing unit is coupled, preferably wireless, for accessing the measurements stored in the said each node.