Acoustic Source Localization Fusing Sparse Direction of ... - CiteSeerX

Acoustic Source Localization Fusing Sparse Direction of Arrival Estimates Ákos Lédeczi1, Gergely Kiss2, Béla Fehér2, Péter Völgyesi1 and György Balogh1 1

Institute for Software Integrated Systems, Vanderbilt University, Nashville, TN, USA {akos,volgy,bogyom}@isis.vanderbilt.edu 2

Department of Measurement and Information Systems, Budapest University of Technology and Economics, Budapest, Hungary [email protected], [email protected]

Abstract — This paper proposes a wireless sensor network based acoustics source localization and tracking system. Each individual node has a special purpose sensor board with four acoustic channels and a digital compass enabling Direction of Arrival (DOA) estimation of acoustic sources. Upon detecting a source of interest, the sparsely deployed sensor nodes report their DOA estimates to the base station that fuses the data for accurate localization. Due to the widely distributed sensing and the novel sensor fusion technique, the method can handle multiple measurement errors prevalent in reverberant environments. The paper presents the overall architecture of the system, as well as that of the advanced sensor board. Furthermore, it describes the DOA estimation algorithm and the applied middleware services for coordinated sensing and communication, introduces the sensor fusion algorithm and presents a detailed error analysis.

1 Introduction Acoustic source localization has many applications in the military and other areas. Typically, fixed microphone arrays are used for tracking vehicles at long distances [1]. Recently, the emergence of wireless sensor network (WSN) technology created a new research direction using ad hoc deployed cheap acoustic sensors for source localization. Estrin et al. presents a WSN-based system for locating birds in [2]. The system used IPAQ-class devices that are resource rich, but relatively expensive and power hungry. Ledeczi et al. describes a countersniper system that accurately locates multiple simultaneous shooters with unprecedented accuracy even in urban environments [3]. The system used a single acoustic channel per wireless mote and measured Time of Arrival (TOA) data for such transient events as muzzle blasts and ballistic shockwaves. On the other hand, our proposed system uses the same cheap, but severely resource constrained mote class devices but four acoustic channels per node for Direction of Arrival (DOA) estima-

LÉDECZI, KISS, FEHÉR ET AL. tion of periodic acoustic signals. The multiple DOA estimates are then fused at the central base station. The rest of the paper is organized as follows. First we present the overall architecture of the system. Then we describe the architecture and features of the sensor board. Next we summarize the middleware services that are running on the sensor network to provide space and time coordination. Then we present the sensor fusion algorithm. We conclude with an error analysis of the system.

2 System architecture and operation The system consists of a sparsely deployed network of sensor nodes and a central base station, typically a PC class laptop computer. Each node consists of a Crossbow (http://www.xbow.com) COTS MICA2 mote and the four channel sensor board described in the next section. The two main components of the MICA2 mote are the Atmel ATmega 128L low-power 8-bit microcontroller and the Chipcon CC1000 multi-channel transceiver with up to 100 meter range. The node has 128 kb of program memory, but only 4 kb of data memory. 512 kb of flash is also available for storing measurements data, for example. The different subtasks of the system are distributed on the three kinds of hardware components: the sensor boards, the motes and the base station. The sensor boards execute the detection, DOA estimation and self-orientation algorithms. The motes provide the space and time coordination and communication capabilities. Specifically, they are responsible for determining their own positions, carrying out time synchronization related tasks and running the message routing service. The base station is responsible for the sensor fusion as well as the user interface. The system operates as follows: After deployment, the motes carry out a sophisticated self localization algorithm to determine the precise location of all nodes. In parallel, the sensor nodes determine their orientation using the on-board digital compass. In case of a mobile system, these two tasks can be carried out continuously (or anytime a detection occurs). However, we leave mobility for future work. The node locations and orientation are shipped to the base station after the message routing system initializes itself. During normal operation the sensor board monitors a single acoustic channel for acoustic signals of interests. When one occurs, the sensor node interrupts the mote and schedules a coordinated DOA measurement sometime in the future, typically 1-2 seconds following the initial detection. The message routing system uses the integrated time synchronization service to notify every node in the network about the scheduled DOA measurement. It is then carried out in a coordinated fashion on all the nodes at the prearranged time with less than a millisecond error. The DOA estimates are shipped to the base station where they are fused and the result is displayed on its screen.

3 The sensor board In order to provide a flexible and powerful platform for signal processing, the board is based on a Xilinx Spartan-3L FPGA. The sensor board has been separated into functional modules, consisting of multiple Microphone Modules (MMs), the Sensor Board (SB), the Digital Compass (DC) and other possible optional components. The MMs are connected to the SB with flexible ribbon cable. This allows the spatial separation of MMs to be

ACOUSTIC SOURCE LOCALIZATION FUSING SPARSE DOA ESTIMATES changeable according to the application requirements, as determined by the acoustic properties of the observed object. To provide cooperation and data fusion in sensor networks, the SB can be attached to the “industry standard” MICA motes, through their 51 pole expansion connector. The physical dimensions are also determined by the size of the mote, the final size is 72x34mm. The SB is powered by four AA rechargeable batteries, providing operation under different environmental conditions. The SB powers the mote as well. Different power save operation modes supports efficient energy utilization. 3.1 Microphone Modules The primary data acquisition units of the acoustic SB are the four Microphone Modules (MM). Each MM includes an electret microphone, a variable gain amplifier stage and an A/D converter. The microphone is a low cost Panasonic WM-60 having a bandwidth of 20-20kHz, sensitivity of -42dB, maximum power consumption of 0.5mA and a SNR higher than 58dB. This microphone shows excellent dynamic behaviour (very short recovery time) in case of extreme large transient sound pressure also. The variable gain is realized by a two stage linear amplifier using low-noise OPAs. The first stage has an amplification of 25; the second can be adjusted between 1 and 48, using a non-volatile programmable trimmer potentiometer, thus providing an overall amplification of +28 to +62 dB. The physical size of the MMs is 10x20mm, having components on one side only, which offers easy mounting to different surfaces using simple adhesives or velcro. The Analog Devices AD7476 ADC features throughput rates up to 1MSPS. It is a 12bit, low power, successive-approximation ADC without internal pipe-line delay, which makes it ideal for time delay measurements. Having a digital serial interface, it needs a 20MHz clock for the highest sampling rate. The MMs can be attached to the SB with ribbon cables of different lengths, thus enabling application dependent physical sensor arrangements, supporting near field or far field measurement operations. 3.2 Sensor Board The SB includes all functional units necessary to realize local data acquisition, preprocessing, DOA calculation, interfaces for communications and an efficient power module. The main components are the high performance FPGA with configuration flash, pseudo static RAM, FLASH, IO interfaces, LEDS, Bluetooth module, MICA interface and switching power supply. The Xilinx Spartan-3L FPGA (XC3S1000L-FT256-4) has an equivalent 1 million system gates complexity and contains 432Kbits Block RAM, 24 dedicated multipliers and 4 digital clock manager (DCM) modules. As the physical size constraints are of primary importance, the smallest BGA package has been selected. It provides maximum 173 IO pins when routed on six layers, but in order to reduce cost, we use only four layers, which means that not all of the pins can be routed. The loss of 4 user I/O pins is a good trade off against the 2 extra layer of the PCB. The available 169 pins are still sufficient for the design. Most of the FPGA pins are used on board by the two memory modules; others provide interfaces for the 6 external interfaces with 10 pins each. These are for the 4 sensor microphones, the digital compass, and an auxiliary unit, for example, for external GPS. The configuration of the FPGA can be done either from the onboard XCF04S Xilinx Platform Flash or via a dedicated JTAG cable during algorithm development. To provide a standard 3.3V compatible JTAG programming interface, some voltage level converters

LÉDECZI, KISS, FEHÉR ET AL. are needed, as the Xilinx FPGA configuration pins are powered by 2,5V. The development connector contains 4 pins for a high speed 3.3V level UART like communication interface also for debugging and communication. During system development the USB based LOGSYS Development Cable can be used, which provides operating power, enables FPGA configuration update through JTAG SVF download, and opens a simple terminal interface on a desktop computer.

Figure 1: Sensor board (SB) The clock signal is provided by a 20MHz Geyer KXO-V99 clock oscillator having a maximum consumption of 8mA. With the help of the digital frequency synthesizer function of the built in DCMs of the FPGA, it is possible to generate a wide range of operating frequencies, either higher or lower. The multiplication and division factors range from 2 to 32, providing a great variety of applicable clock frequencies. Energy efficiency is one of the most important requirements for wireless sensor networking devices. The available operating power is provided by rechargeable batteries, with limited capacity and changing source voltage. All DC-DC power conversion should be done with minimal loss, and special dynamic power management technique should be applied. The SB is equipped with a 2 two level energy distribution system. An independent low dropout regulator (LDO) generates 3,3V for the MICA and the Bluetooth unit (BlueGiga WT12), enabling remote activation/deactivation of the main system components of the boards. This technique can be exploited when a single board monitors the environment, wakes up the others and schedules a coordinated DOA measurement in the next 1-2 seconds interval through the message routing service. The standby power consumption is limited to the radio interfaces only, as only they have to stay awake continuously (or utilize a coordinated wakeup scheduling technique). The main power supply must provide different voltage levels for the FPGA and the other onboard components. The Texas TPS75003 triple-supply power management IC generates all three necessary voltages (1.2V, 2.5V, and 3.3V). It has two high current buck controllers with about 95% efficiency and a lower power LDO for the 2.5V auxiliary supply. The buck controllers need external p-channel MOSFETs and inductors. The input level can range from +2.2 to +6V, so that operation is guaranteed even with deeply discharged batteries. The module guarantees the monotonic voltage ramp specified in the

ACOUSTIC SOURCE LOCALIZATION FUSING SPARSE DOA ESTIMATES FPGA datasheet and start-up order of the outputs is programmable, thus eliminating inrush current spikes, typical for SRAM based FPGAs. The pre-processing of sensor signals and the calculation of DOA needs different types of algorithms and computational performance. The Spartan 3L FPGA supports both HW based data-flow type digital signal processing and implementation of internal soft microcontrollers, such as the 32-bit MicroBlaze or 8-bit PicoBlaze. Both versions can be instantiated in more than one copy to increase parallelism and reduce the clock rate, which is a usual technique for achieving better energy efficiency. The 64-Mbit onboard pseudo SRAM extends the FPGA internal 432Kbit BlockRAM. It can be used as a large external sensor data buffer or temporary storage for intermediate variables. In case of CPU controlled SOPC design, the pSRAM and the 32Mbit FLASH modules are the primary memory components of the system. Both devices are characterized by minimal power requirements and auto standby operation. The SB has multiple interfaces. The primary indicator is an emulated Compass Rose using 8 LEDs. This simple display is very useful during testing and development, and it provides orientation data during field experiments also. With the onboard Bluetooth module, the SB can communicate with any device supporting Bluetooth connections, such as PDAs, notebooks or cell phones, implementing a personal area network for data exchange. This short range communication capability is extremely useful for the redistribution of the results of the sensor network data fusion to the graphical user interface of the local user. The main wireless sensor network interface is the MICA mote implementing the system management, communication and synchronization tasks. Sophisticated localization, time synchronization and data communication middleware services are implemented on the MICA mote presented in chapter 5. The sensor board contains the standard 51 pin extension connector, so it can interface with both the MICA2 or MICAZ type motes. The 4 AA batteries are able to provide 10 hours of continuous operation of the mote/SB assembly. Aggressive power management, both at the node and the network level, should increase the lifetime significantly, but we do not have any hard data on that. 3.3 Optional components Measurements and DOA estimation done by the SB are always relative to node positioning and orientation. In order to provide self orientation, a Digital Compass (DC) module can be attached to each SB. For appropriate accuracy, a precision 3D tilt compensated compass is used, with a dedicated interface. The Honeywell HM3300 DC solution features 1 degree level heading accuracy and an 8Hz update rate. In case of a static deployment, after the orientation phase, it can be switched off to reduce power consumption. An auxiliary header is also implemented on the SB. Its main purpose is to make possible future expansions, such as interfacing with a GPS unit, provide control signal output, or just offer easy connections for debugging.

4 DOA estimation Accurate local measurements and DOA estimation on the individual sensor nodes are essential for reliable source localization. A wide range of techniques can be used either in the time or frequency domains, each having its own advantages and disadvantages. For a traditional far field (planar wavefront model), narrow band DOA estimation, a simple

LÉDECZI, KISS, FEHÉR ET AL. linearly arranged sensor array can form a spatial filter and traditional beamforming algorithms can be employed. Although the far field and/or narrow band assumptions do not hold in all acoustic source localization problems, these approximations can be applied with acceptable errors in many cases. 4.1 Methods Acoustic source localization is usually performed in air, where the propagation speed of the signal is about 340 m/s (the underwater speed is around 1500m/s). Assuming general audio signals, most energy is delivered in the low and middle frequency range, from 20Hz – 2kHz. The corresponding wavelengths are 17m – 17 cm. These parameters determine the necessary spacing and arrangements of the acoustic sensors. In case of narrowband beamforming, regularly spaced sensors could lead to grating lobes in the beam pattern and cause ambiguity in DOA estimations, if the spacing is lower, than λ/2 (spatial aliasing). In wideband beamforming this effect is averaged out, independently of the spacing of the sensor array [10]. The most important algorithms for this approach are Capon and MUSIC [1]. For characteristic wideband and/or transient signals, time of arrival (ToA) measurements and direct time delay calculations are more appropriate. From the measured time delays, using linear, spherical or hyperbolic intersection techniques, the location of the source can be estimated even in the acoustic near field. However, these methods might need to be trained for the characteristic event (smart trigger). Another class of time delay measurement methods is the cross-correlation type DOA estimation. The peaks of the cross-correlation function show possible delays between the signals. Simply using these peaks has the risk that the largest peak may be a false delay caused by multipath effects, reverberation and echoes because of the early classification. An advanced version of this method is accumulated correlation [9]. It keeps pairwise cross-correlation, but instead of determining the peak in each cross correlation vector, it accumulates them by mapping the vectors onto a hemisphere and looks for a unified peak in this coordinate system. Beamforming methods generally provide greater accuracy than time delay estimation methods, but require higher computation capability. It is showed in [9] that accumulated correlation has almost the same accuracy as beamforming, while needing only a fraction of time. Another possibility is using frequency domain transformation of the incoming wideband signal, where each part of the spectrum can be treated as narrowband components. Short incoming sample series of each sensor are transformed and used as phase shifted version of the narrowband component. The Steered Covariance Matrix (STCM) algorithm presented in [1] also uses this approach. 4.2 Sample Measurement The following experimental measurement was made using three MMs sampled at 781.25kHz. The MMs are positioned in a symmetrical triangle, having a separation of 60cm from each other (see Figure 2). The experimental signal source has been applied from M0 direction as shown. The peaks of the cross-correlation functions (right) allow delay estimations, but it is hard to decide which peaks are the main ones. (Note that we did not employ accumulated correlation).

ACOUSTIC SOURCE LOCALIZATION FUSING SPARSE DOA ESTIMATES

The cross-correlation gives the following delays: M0 to M1 M0 to M2 M1 to M2

Sample -843 -738 111

Time -1.079ms -0.945ms 0.142ms

Distance 36.7cm 32.1cm 4.83cm

The sum of last two distances is 36.9cm rather than 36.7cm, because the signal source was very close to the sensor array (near field effect). Based on this measurement, the estimated local DOA is 212 degrees (M1 points to 0 degrees in the local coordinate system), which will be the basis for the sensor data fusion. This simple measurement demonstrates the feasibility of local DOA estimation.

M1

M0

M2

v

Figure 2: Sample recording

5 Middleware services The coordinated sensing and communication in the wireless network are provided by distributed middleware services. Of particular importance are sensor node self localization, multi-hop message routing and time synchronization. For this system, we were able to reuse technology we originally developed in the context of our countersniper system [3]. Below is a summary of these services.

LÉDECZI, KISS, FEHÉR ET AL. 5.1 Self localization Many applications of wireless sensor networks (WSN) require the knowledge of where the individual nodes are located. While there are many approaches in existence, they all have significant weaknesses that limit their applicability to real world problems. Techniques based on accurate—typically acoustic—ranging have limited range. They need an actuator/detector pair that adds to the cost and size of the platform. Furthermore, a considerable number of applications require stealthy operation making ultrasound the only acoustic option. However, ultrasonic methods have even more limited range and directionality constraints. Methods utilizing the radio usually rely on the received signal strength that is relatively accurate in short ranges with extensive calibration, but imprecise beyond a few meters. The simplest of methods deduce rough location information from the message hop count. In effect, they also use the radio signal strength, but they quantize it to a single bit. Finally, many of the proposed methods work in 2D only. The novel idea behind our radio interferometric ranging is to utilize two transmitters to create an interference signal [6]. If the frequencies of the two emitters are almost the same then the composite signal will have a low frequency envelope that can be measured by cheap and simple hardware readily available on a wireless node. Trying to use this signal to deduce information on the positions of the two transmitters and the receiver directly would require tight synchronization of the nodes involved mandating hardware support. Instead, we use the relative phase offset of the signal at two receivers which is a function of the relative positions of the four nodes involved and the carrier frequency. Therefore, the method is not pairwise ranging. It provides an estimate of the quantity dABCD which is defined as dABCD = dAD − dBD + dBC − dAC, for any four nodes A,B,C and D. In order to have enough equations to solve for all unknowns, it is necessary to make multiple measurements in an at least 8-node network to reconstruct the relative location of the nodes in 3D. Similarly, it is possible to calculate the absolute position of a node in the presence of 4 anchors. 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 wireless nodes, yet we still achieve high accuracy. Our prototype RIPS implementation on MICA2 nodes consists of the following steps: (1) selecting a pair of transmitters from a group of motes participating in the localization and scheduling their transmission times, (2) fine-grain calibration of the radios of senders to transmit at close frequencies, (3) transmission of a pure sine wave by the two senders at multiple frequencies, (4) analysis of the RSSI samples of the interference signal at each of the receivers to estimate the frequency and phase offset of the signal, (5) calculation of the actual dABCD range from the measured relative phase offsets for each pair of receivers, and (6) a localization algorithm. These steps are described in detail in [6]. The accuracy of RIPS is as high as a few centimetres at ranges up to 170m [4]. 5.2 Message routing The Directed Flood-Routing Framework (DFRF) [8] is built around an engine that manages the routing of messages on all nodes in the network. Application components using the flood-routing engine can send and receive regular sized data packets according to an

ACOUSTIC SOURCE LOCALIZATION FUSING SPARSE DOA ESTIMATES interchangeable flooding policy. The flooding policy specifies the “direction” of flooding and how intermediate nodes rebroadcast messages. The DFRF engine keeps the recently received data packets in a table together with their priority (which is managed by the policy), periodically selects the packets with the highest priority, packs them into a single radio message and broadcasts it to the neighboring nodes. When the DFRF engine (re)broadcasts a radio message, it does not include the current node ID in the message, but a policy dependent value, called the rank of the node. The rank describes the progress of a data packet in a policy-dependent way, and is used to determine what to do with incoming data packets. For the DFRF engine the rank is simply an array of bytes passed to the flooding policy when a data packet arrives. It is important to note that the rank does not depend on the data packet, thus the single rank value is used for multiple aggregated data packets. For the converge-cast policy used in the system, the node rank is the hop-count distance from the root. Apart from defining the rank of nodes, the flooding policy has the primary role of governing the data packet life-cycle at each node. The life-cycle of a particular data packet is a finite state machine. There are states in which the data packet is eligible for retransmission, and there are states in which the data packet must be remembered but should not be retransmitted. For example, if an intermediate node retransmits a data packet and then receives the same packet from a node that is closer to the target than itself, then the packet should not be retransmitted. However, the node must remember the packet to prevent retransmitting the same data packet in case it receives it later from a node further from the target than itself. The DFRF engine maintains a table of data packets and their current state. Each state is associated with a unique priority. The engine has three basic activities: broadcasting and receiving radio messages, and “aging” data packets in the table. When a message has been sent, the engine calculates the new state based on the policy for each data packet contained in the message. Then it packs the highest priority transmittable messages into a radio message buffer. The engine stops sending messages if there are no more transmittable data packets in the table. When a new radio message is received, the engine unpacks each contained data packet. For each packet it looks for a match in the table. If there is none, it places it in an available slot. If the table is full then the packet with the lowest priority is evicted. This evicted packet is overwritten by the newly arrived data packet with maximum priority. Finally, the DFRF engine periodically ages all valid data packets in the table by executing the next step in the packet life-cycle state machine defined by the flooding policy. For the source localization system, the convergecast policy is utilized. Similar to gradient based routing schemes, the algorithm utilizes its estimated distance from the base. The base initializes the gradient estimation by sending flooding broadcast messages to the network. Each sensor records the hop-count from the base to itself when a message is received for the first time, and then rebroadcasts the message. Using multiple flooding broadcasts, the average of these hop-count measurements provides a good estimate of the distance from the base. 5.3 Time synchronization Post facto synchronization is suitable for many application domains, thus no continuous synchronization is required. Systems collecting data or reacting to rare events, but requiring exact time measurements belong to this class of applications. The Routing Integrated

LÉDECZI, KISS, FEHÉR ET AL. Time Synchronization (RITS) embeds the synchronization into the message routing protocol [5]. This solution does not require any additional message exchange apart from the routing messages, but does require precise message time-stamping on both the transmitter and receiver sides. When a sensor in the network detects an event, it is time-stamped using the sensor’s local, unsynchronized clock. The target node, i.e. the base station, possibly several hops away from the sensor, needs to know the time of the event in its own local time. Without explicit synchronization in the network, the routing process can be used to perform implicit time synchronization. Along with the sensor reading, a radio message includes an age field, which contains the elapsed time since the occurrence of the acoustic event. This additional information adds only a very small overhead to the message. Each intermediate mote measures the offset, which is the elapsed time from the reception of the packet with the sensor reading till its retransmission. The age field is updated upon transmission using a precise lowlayer time stamping method [7]. When the sensor reading arrives at the destination, the age field contains the sum of the offsets measured by each of the motes along the path. The destination node can determine the time of the event by subtracting age from the time of arrival of the message. For the source localization system, RITS is used in “reverse.” Instead of using the time translation to determine detection times in the past, we can schedule coordinated sensing in the future. When one node decides to carry out a DOA estimation in exactly T milliseconds, RITS is used to notify all other nodes to do the same. When the message arrives at a particular node, it contains the remaining time before the measurements needs to be carried out. That is, instead of the original T, it contains (T-D) milliseconds where D is the time it took for the message to travel from the source to the destination.

6 Sensor fusion The straightforward technique for fusing the multiple DOA estimates is to apply least square (LS) optimization [2]. However, measurements errors, especially ones caused by non-line-of-sight sensors, can greatly degrade the overall accuracy, since they contribute to the overall solution. Instead, we developed a technique where these outliers are identified and only the accurate line-of-sight sensor readings are used to determine the source location. The novel method is similar to the one we developed for muzzle blast localization previously [3]. We define a consistency function over the 3D space of the area of interest and find the global maximum corresponding to the source. A DOA estimate defines a line in space starting from the sensor location. Ideally, all such lines intersect in a single point, the source of the sound. Measurement errors, such as time synchronization inaccuracy, imprecise sensor locations and orientation, detection errors etc., prevent this intersection. Nevertheless, most of these lines will pass near each other and hence, the ideal point. (Again, there will typically be outliers due to echoes that won’t come near the true source location.) As the sources of these relatively small errors are known, their worst-case effect can be accurately estimated. Let’s define the maximum cumulative source location error within the specified maximum range due to time synchronization, node localization and orienta-

ACOUSTIC SOURCE LOCALIZATION FUSING SPARSE DOA ESTIMATES tion, and detection uncertainties to be d centimetres. Then all line-of-sight DOA estimates will cross a cube of 2d size centred at the source location. The consistency function, hence, is defined for cubes in space as the maximum number of DOA bearing estimates that intersect the given cube. The same multiresolution search algorithm based on interval arithmetic that was utilized in [3] can then be used to locate the acoustic source. The procedure starts with a small set of overlapping cubes covering the entire search space, selects the one with highest consistency value and then subdivides it into n overlapping cubes and continues. When it zooms in on smaller and smaller cubes, the consistency value typically decreases. The procedure sometimes needs to backtrack and evaluate alternative paths. Nevertheless, it quickly finds the maximum value corresponding to the minimal size cubes as defined by the estimate maximum errors. The above search algorithm was modified due to the fact that the localization error caused by the error sources listed above depends on the range from the sensor. Hence, there is no fixed cube size where the procedure should stop. Instead, the minimum value of the consistency value N is defined. This has many advantages including more accurate localization because only the best N detections are used to determine the location. The final cube size corresponding to N also provides an error estimate, i.e. a confidence value of how accurate the result is. The only disadvantage is that it requires at least N line-ofsight detections. However, for accurate localization, this is required in any case. In our experience, N=6 gives very accurate locations as shown in the next section.

7 Error analysis We carried out a set of simulations to evaluate the overall accuracy of the system. 20 sensor nodes were distributed randomly within a 200m radius. Sensor locations were known with 0.2m accuracy. The cumulative sensor self orientation and DOA detection errors were simulated with a Gaussian distribution with zero mean and 2-degree variance. The detection probability for each event and each sensor was 80%. Finally, each detection was an echo with 20% probability. An echo means a random DOA value between 0 and 360 degrees. The simulation was run at ranges between 100m and 1500m from the centre in 100m increments. Each data point represents the average error of 250 runs with randomly generated source locations at the given range. If the cube size was larger than 25m when the consistency functions reached the minimum value (6), the results was declared invalid. The lowest detection rate at any distance was 99%. The overall results are shown in the figure below.

Figure 3: Localization accuracy

LÉDECZI, KISS, FEHÉR ET AL. The results are very encouraging. Within the sensor field, that is within 200m of the centre, the error was less than 30cm and the localization rate was 100%. Outside the sensor field with increasing range, the overall error increased as expected, but even at 1500m it was still less than 13m, while the lowest localization rate was 99%. To evaluate the effects of DOA detection errors and such reverberant environment as cluttered urban terrain, we varied the angle error and the echo probabilities. The results are summarized below. Within the sensor field, that is, near the centre, the overall accuracy remains within half a meter even with 40% echo probability and 4-degree cumulative DOA and self orientation variance. Similarly, the average error outside the network, in this case for ranges around 1000m, is 12m using the worst combination of error sources. Note that the lowest successful localization rate was 89%.

Figure 4: The effects of DOA error and echoes within and outside of the sensor field

8 Conclusion We presented an acoustic source localization system that promises very high accuracy and robustness. While we have not tested the full system yet, most of the individual parts, including the time synchronization, message routing, sensor node localization, and sensor fusion have been field tested and have demonstrated excellent performance. Furthermore, the simulation results of the sensor fusion technique highlight the great potential of this system. We plan to finish the implementation of the DOA estimation on the sensor board and test the whole system under a realistic deployment scenario in the near future.

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