Localization of chemical sources in urban scenarios (large cities) is a major challenge for intelligence and police authorities. In the clandestine production phase of illicit substances like explosives, but also drugs, significant levels of precursors are spread in the atmosphere. Such suspicious compounds could be reported by a system of mobile sensors and could be located using localization algorithms, providing complementary information to the authorities for intervening at an early stage.
Several strategies for source localization have been proposed in the literature [1
]. These strategies have been integrated into robot systems with tracking abilities. Many of these tracking strategies have been inspired by bacteria or animal behavior using olfaction for foraging or mating: lobster, blue crabs, ants and moths provide behavioral models for odor tracking [2
]. One of the simplest strategies consists in seeking changes in local concentration within an odor plume assuming a smooth chemical gradient in a diffusion dominated flow. However, this approach, called chemotaxis [4
], is not useful in a realistic environment where fluid flow is dominated by turbulence, which can be caused by forced ventilation, temperature gradients or the presence of obstacles. Under these conditions, on the order of ten min are required to determine the time-averaged concentration with sufficient accuracy to perceive the gradient concentration [5
]. In consequence, the exploration of the area of interest becomes too slow. Some other strategies additionally exploit both fluid velocity information and chemical concentration (anemotaxis [6
]). More recent proposals based on information theory, like infotaxis [8
] are based in binary detections and, information plays a role similar to that of concentration in chemotaxis. Odor patches are expected to be found only intermittently in the medium, and then information is sparse. In some cases, methods aim to estimate the gas distribution through analytical Gaussian models [9
], others are focused on to create a plume mapping via hidden Markov methods [12
], whereas in Farrell et al. [13
] a strategy for chemical plume tracing and source location declaration is presented.
Navigation experiments aiming to find chemical sources are strongly limited by the limit of detection and selectivity of the low cost chemical sensors and even medium-priced detectors (e.g., ion mobility spectrometers). Thus, the rapid decay in the chemical concentration with increasing distance from the source can be a critical issue. Poor limits of detection result in a reduced area where the plume can effectively be detected. This is especially important in applications where the search zone has an area of several square kilometers. In such situations, it becomes very important to set the detection thresholds very close to the noise level, but this would results in a high number of false alarms and most localization algorithms would fail catastrophically. To the best of our knowledge, none of the published methods have addressed this problem.
Additionally, in any real scenario, there could be background levels of a multitude of chemicals caused by environmental pollution. Because of limited selectivity, there will be substances which will produce interference in the detector reading, hindering the detection and localization tasks. The presence of combination of detector electronic noise and mainly interfering chemical agents result in variable background readings that may change with time and with the position of the detector. These shifts in background levels hamper the selection of an optimum threshold that is usually considered to be constant all along the area under exploration. As far as we know, this problem has not been previously tackled in the literature.
To address these two issues (threshold close to the limit of detection and presence of background levels) probabilistic approaches like plume mapping Bayesian methods appear to be a good choice. Pang and Farrell published a source-likelihood mapping approach based on Bayesian inference in 2006 [14
]. The main idea behind the algorithm consists in implementing a stochastic approach for plume modeling and in estimating the most likely source position considering the sequence of detection/non-detection events and fluid flow measurements along the robot‘s trajectory. Pang’s algorithm has been tested successfully with data previously collected using an autonomous underwater vehicle [13
However, this algorithm uses binary detection events, and no chemical concentration information is used to build the probability map, since it only considers the concentrations above a certain threshold as detection or non-detection events. Moreover, after setting the threshold level, the approach assumes that the rate of false alarms is very low. In a real scenario where background signals are present, this is only achieved when the threshold is set at a high level. However, this option seriously reduces the maximum plume detection distance. Therefore, there is a trade-off; on the one hand, the threshold needs to be set low enough (close to the sensor detection limit) if chemicals from the source are to be detected at large distances; on the other hand, the threshold needs to be high enough to prevent false alarms. So, how to set the threshold level becomes a critical issue in real environments using existing approaches, especially when the background intensity is non-uniform in the explored area.
Finally, in order to speed up the area exploration it is important that the algorithm can be extended to work with multiple robots. Recently, Kang and Li [15
] have presented a novel plume tracking algorithm via multiple autonomous robots by using a leader-follower strategy, demonstrating its superiority versus a single robot algorithm, in terms of both the computational cost and the accuracy in source location. Meng et al. [3
] have also studied the multi-robot problem for plume tracking in fluctuating airflow environments, showing the efficiency and robustness of the adapted ant colony optimization (ACO) algorithm over the traditional ACO algorithm. Meng remarks the importance of a proper number of robots and a well-defined cooperation mechanism, although it is not strictly necessary to track the plume to obtain a good estimation of the source location. The most likely source position is estimated during the robot's mission for arbitrary trajectories by recursively building a probability map using Bayesian inference. The problem of background estimation over the exploration area can be considered as the problem of scalar field mapping. Algorithmic approaches using mobile sensor networks have been already proposed, however they assume that the agents have communication capabilities so that their exploration paths are optimized after data fusion [16
]. However, in our scenario we expect that the sensors can be mounted on vehicles that serve other tasks beyond chemical source localization. In this sense, we consider cases where there is no feedback between the chemical sensing and the agent’s trajectories.
Our main motivation for the present work is to extend the Bayesian plume source localization algorithm, previously described by Pang and Farrell [14
], using the chemical concentration (instead of binary detections) and assessing its performance in simulated and real environments, where background signals may arise. Thus, Pang’s algorithm is reformulated for use with continuous analog concentration readings instead of binary detections. Moreover, the algorithm is extended to work with multiple mobile sensors. This new approach requires a probabilistic model for the background and for the plume which are described in the following sections.
The present algorithm was initially developed [19
] for applications to Home Security (European project LOTUS: Localization of Threat Substances in Urban Society FP7-SEC-217925). In the considered scenario, police cars equipped with GPS and gas chemical sensors (eventually other fast analyzers like ion mobility spectrometers can be used) carry out their routine patrols while sending the sensors’ readings to a central station. Instead of moving towards the chemical source, the patrol vehicles would maintain their normal patrol routes while a centralized system is continuously analyzing the acquired signals seeking suspicious activity.
The paper is organized as follows: Section 2.1
and Section 2.2
and shows the basics of the algorithm and the plume and background model. Section 2.3
and Section 2.4
describes the synthetic and real scenarios for the test and Section 3
reports the results and the analysis.
In the present paper, modifications of a previously described (binary-based) algorithm have been introduced. The original algorithm can be easily extended to work with multiple mobile sensors. All the information from the mobile sensors can be integrated in the algorithm, whatever their positions are. The algorithm only needs to know in which cell the concentration readings were obtained, then a probability map will be recursively updated. Moreover, the mobile sensors do not need to solely perform plume tracking and might be used for other tasks.
Additionally, in a real scenario, pollution and some interfering substances may appear in the background, increasing the number of false alarms. Unlike the binary-based algorithm, which uses a threshold to assess whether a concentration is considered as a detection or non-detection event; our algorithm, based on continuous concentrations, builds a background model to assess whether a concentration comes from the background or from a source located further away. Simulation results show that our algorithm behaves much more robustly in the presence of false alarms and better estimates the real source location.
All concentration readings are considered in our algorithm, incorporating them in a continuous manner instead of just using them as binary detections above a certain threshold. This fact removes the need for a threshold level, thereby reducing the number of false alarms (a background model is estimated) and the number of missed detections thus improving the performance of the algorithm proposed by Pang and Farrell. A sensitivity study regarding robustness of the algorithm against deviations from the true value has been presented. It has been shown, the results improve significantly using the concentration-based algorithm if the source strength can be estimated.
Finally, experiments with real data have shown that the concentration-based algorithm seems to perform slightly better than the binary-based one, confirming our results obtained for the simulation experiments. A critical point in our proposal is that the algorithm assumes that the source strength is known. Thus, estimating the source strength would be a promising direction for future research. Results from real experiments show that when the plume dispersion model hypothesis do not hold, both algorithm are still able to perform the estimation tasks although the differences diminish.
The described algorithm is available in MATLAB code from the authors under request.