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# Drones as Sound Sensors for Energy-Based Acoustic Tracking on Wildfire Environments

Sérgio D. Correia, João Fé, Slavisa Tomic, Marko Beko

► To cite this version:

Sérgio D. Correia, João Fé, Slavisa Tomic, Marko Beko. Drones as Sound Sensors for Energy-Based Acoustic Tracking on Wildfire Environments. 4th IFIPIoT, Nov 2021, Virtual, Netherlands. pp.109-125, 10.1007/978-3-030-96466-5_8. hal-04471544

HAL Id: hal-04471544

https://inria.hal.science/hal-04471544v1

Submitted on 21 Feb 2024

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This document is the original author manuscript of a paper submitted to an IFIP
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# Drones as Sound Sensors for Energy-Based Acoustic Tracking on Wildfire Environments

Sérgio D. Correia¹,², João Fé¹,², Slavisa Tomic¹, and Marko Beko¹,³

¹COPELABS, Universidade Lusófona de Humanidades e Tecnologias, 1749-024 Lisbon, Portugal (scorreia@ipportalegre.pt)

²VALORIZA, Instituto Politécnico de Portalegre, Campus Politécnico n.10, 7300-555 Portalegre, Portugal

³Instituto de Telecominicações, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisbon, Portugal

**Abstract.** The present work proposes a method for continuous local- ization of a moving acoustic source based on energy measurements in the application of detecting/preventing wildfires. The main focus is on the case in which the acoustic sensors are located on a drone, i.e., when they are also in motion. This localization setting is more challenging than the classical one in which the sensors are typically static (anchors) or have slow dynamics compared with the source. The proposed solution consists of an extended Kalman filter (EKF) that deals with non-linearities and singularities in the acoustic observation model, as well as the dynamic trajectory of the sensors. Performed simulations corroborate its feasi- bility in different noisy environments and illustrate its superiority over techniques that do not consider process states’ prior knowledge.

**Keywords:** Acoustic Source Tracking, Energy-Based Localization, Kalman Filter, Wildfire Detection/Prevention

## 1 Introduction

The use of Unmanned Aerial Vehicles (UAVs) has gained considerable promi- nence given their success in simple domestic applications [13] or critical military operations [14]. They find several applications such as border control [2], coast patrol [23], fire perimeter monitoring [22], search and rescue [17], among sev- eral other examples that could be mentioned. More than automatizing labor or reducing operational costs in the referred contexts, UAVs can accomplish dan- gerous tasks for human operators or reach inaccessible regions. With regard to wildfire environments, UAVs can be used for monitoring [20], detection [18] or prediction [19], being increasingly present in a fire-fighting scenario.

From the point of view of communications, sharing, and data management, the *Internet of Things* (IoT) has emerged as an aggregating concept, both in terms of communication networks and in terms of data management and ma- nipulation [12, 1, 28]. The term IoT does not refer to technology but rather to a general concept that embraces different techniques and ideas, with profound im- plications for professional activities and life in society. It can be considered as: an
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arrangement of interconnected objects, consisting of electronics, software, sen-
sors, and actuators, which handle and transmit information to a wide network
infrastructure and between each other. Thus, IoT brings connectivity, portability,
and distributed processing, dramatically increasing the processing capacity and
its architectures, allowing the emergence of a whole set of new applications.

Bearing in mind the usage of drones in a fire-fighting scenario and the IoT
paradigm, the present work considers performing an energy-based acoustic local-
ization as an add-on to existing architectures that employ drones for fire-fighting
support. The new feature uses communication capabilities already in place to
send acoustic information to an edge or centralized data processing stage. The
sound location information may therefore be forwarded to rescue teams available
in the terrain. However, the present problem introduces certain complexity given
that both the acoustic source and the sensors (or microphones) are in motion.
Furthermore, it is considered that the trajectory of the drones, and therefore the
location of the acoustic sensors, are not controlled by the location platform, pre-
venting, for instance, the creation of an ideal path for the acquisition of location
data.

To address the motion problem and account for the highly non-linear decay
model of the acoustic energy, an Extended Kalman Filter (EKF) is envisioned
and implemented. The locations of the acoustic sensors (or anchors that are
usually assumed known) will consist of a provided discretized path along the
search-space. Several simulation conditions are created concerning the signal-
noise-ratio (SNR) of the measures and the number of available drones in the
range of the sound source. With those conditions, it is intended to demonstrate
that acoustic energy can be a reliable measure to accomplish sound localization,
retaining the advantages of being of a simple acquisition technique (it does not
require complex additional hardware).

It is worth mentioning that the proposed scenarios configure a problem that,
to the best of authors’ knowledge, has not been considered in the scientific lit-
erature, which is: besides the dynamics of the acoustic yet moving target and
the intrinsic simplicity of employing acoustic energy measures, the sensors are
also mobile. Thus, the proposed solution can be seen to support computer vision
systems at locations obstructed by smoke screens or dense vegetation, detection
of help requests, or tracking of physical means.

The remainder of this work is organized as follows. Section 2 summarizes
previous related work, and Section 3 formulates and characterizes the energy-
based acoustic localization problem on the wildfire scenario. Section 4 describes
the proposed methodology, while Section 5 presents and discusses simulation
results. Finally, Section 6 concludes the work.

2 Related Work

## 2.1 UAVs for Wildfire Detection, Prevention and Monitoring

Considering the past few years, several solutions based on data acquisition pro-
vided by UAVs have been proposed for wildfire prevention, prediction, and mon-
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itoring. Sensing capacity based on weather sensors data (temperature, humidity, CO, or CO2) are used to feed certain prediction model which in turn is processed, proving alerts for early detection or for analyzing the fire front evolution [21]. In such cases, the drones act as nodes in a wireless sensor network, and the IoT paradigm is applied to process the information on the edge of the network or in cloud environments [26]. The use of cameras for fire detection is one of the most used techniques. Nevertheless, the image sensor needs to have a visual line-of-sight towards the monitored zone. In an already started fire, both dense vegetation and smoke will prevent visibility to the actors in this scenario, such as firefighters, fire trucks, or even civilians that may need rescuing. In such situations, the possibility of acoustic sensing and consequent localization can be a significant advantage for rescue operations and ground support, for instance, locating people who yell for help. The work presented in [30] considers the problem of controlling the drone's path based on sound localization performed through an array of several microphones, monopolizing the drone's action and weighing the structure and energy consumption with multiple hardware. The use of microphone arrays is a well established technique to obtain directional data to triangulate the source position through sound, with the inconvenience being the requirement for multiple sensors distributed in the body of the drone [29].

The present work stands out with the methods proposed in the literature because it requires only one sound sensor in each drone, obtaining the necessary information for the positioning system by associating sources originating in multiple drones. This way, drones that are already assigned to patrol and rescue missions can easily be supplemented with an acoustic location functionality without significant changes in their structure.

## 2.2 Acoustic Localization

The localization of an acoustic source has been mainly addressed through range-based methods, where a measure translated into distance is acquired. While works considering time [25] or angle [15] have shown good performance results in terms of the localization error, those methods rely on high precision hardware for timing purposes, or they have to be equipped with an array of microphones, considerably increasing the complexity of the sensors. Considering the present application scenario, i.e., the fact that the necessary parts have to be applied in a moving drone with limited weight and electric power, these methodologies might not be the best solution. As an alternative, the acoustic energy measurement presents itself as an efficient solution, which allows for location of a sound source with light hardware resources and low computational complexity [5, 8, 9].

Since it was first proposed [11], the energy-based acoustic problem was solved through deterministic approaches [16]. From weighted least-squares, which the performance is degraded in noisy environments [?], to methods based on semidefinite programming [3], or second-order cone programming [4], that rely on approximating the original problem into a convex optimization one, has demonstrated robust results, even in noisy environments. More recently, solutions that depend on metaheuristic approaches, namely on swarm optimization [7, 6], showed that,
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through intelligent initialization of an initial candidate population, swarm optimization methods could present concurrent results but with low computational complexity. That is, those methodologies would be adequate to run on embedded processors, attaining a solution with low latency [8]. The fact that the mentioned algorithms were tested and evaluated on several different embedded processors [8] motivated us to use them here as a benchmark for comparison with the proposed methodology. To this end, Elephant Herding optimization and a weighted least squares approach (WLS) are used to determine individual solutions considering, at each time instant, the known position of the drone and its measures in those exact moments.

## 3 Problem Formulation and Characterization

The problem envisioned implies to determine a set of positions $x_{t \in \{1,...,T\}} \in \mathbb{R}^2$ (the extrapolation to $\mathbb{R}^3$ is straightforward) of a sound source over some interval $T$. As to the acoustic sensors, $N$ drones with pre-determined paths fly over the search space acquiring the acoustic signals. Both the target and the drone's path are represented in Figure 1, where the red dashed line represents the acoustic source movement over the search-space (represented as a firetruck). The target's trajectory performs several changes in its direction to analyze response of the proposed algorithm.

<figure><img src="image_3.png" /><figcaption>Fig. 1: Drones and target trajectories over the search-space</figcaption></figure>
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The search-space is considered as a square with sides of 1km, that is, $x \in [0, 1000]m$ and $y \in [0, 1000]m$ in Cartesian space. Also, $N = 5$ drone trajectories (labelled as $D_1$ to $D_5$) are shown to create situations of crossing between the trajectories of the drones and the trajectory of the acoustic source. While position control of drones could be considered to improve error in the localization process as in [24], in this case, it would imply subverting the main function of drones. Thus, it is considered that the trajectory is determined as a function of the evolution of the fire front, control of the availability of means, avoidance of smoke columns, etc. The drone trajectories are here considered as parametric equations of time $t \in [50, 950]s$ as:

$$ \left\{ \begin{aligned} D_1(x, y) &= (t, -4 \cdot 10^{-4} \cdot t^2 + 0,2 \cdot t + 900) \\ D_2(x, y) &= (t, +9 \cdot 10^{-4} \cdot t^2 - 0,7 \cdot t + 300) \\ D_3(x, y) &= (t, +11 \cdot 10^{-4} \cdot t^2 - 0,4 \cdot t + 50) \\ D_4(x, y) &= (t, -4 \cdot 10^{-4} \cdot t^2 + 0,65 \cdot t + 665) \\ D_5(x, y) &= (t, -15 \cdot 10^{-4} \cdot t^2 + 1,0 \cdot t + 550) \end{aligned} \right. \quad (1) $$

<figure><img src="image_4.png" /><figcaption>Fig. 2: Drones to target distance over time</figcaption></figure>

To characterize the problem in more detail, namely in terms of the distance between the sensors and the target, Figure 2 shows the evolution of the distance between each sensor and the target (solid lines), and their mean value over
the considered time interval (dashed lines). As it can be seen, there are five intersections between trajectories ($d_i = 0$), several drones fly at distances greater than 500m (on the XY horizontal plane), and their mean value is around 350m.

The obtained energy measure at the $i^{th}$ sensor drone $D_i$ is modeled as follows, according to [11]

$$y_i^t = \frac{g_i P_d}{\|\mathbf{x}_t - \mathbf{D}_i\|^\beta} + \epsilon_i^t, \text{ for } i = 1, 2, \dots, N, \quad (2)$$

where $y_i^t$ is the energy acquired by sensor $i$ at time $t$, $g_i$ is the sensor gain, $P_d$ is the transmitted power at a reference distance $d$, $\beta$ is a decay propagation factor dependent on environment conditions (equal to 2 in free space [3]), $\mathbf{x}_t$ is the unknown acoustic source position at instant $t$, $\mathbf{D}_i$ is the position of the sensor $i$, and $\epsilon_i^t \sim \mathcal{N}(0, \sigma_e^2)$ is considered as a random zero-mean Gaussian noise, for each link $i$ and time $t$. For the sake of simplicity, $\sigma_e^2$ is considered constant over time and at each sensor link but will be adjusted regarding distance to touch upon the SNR considered at 1m.

<figure><img src="image_5.png" /><figcaption>Fig. 3: Considered SNRs function of the distance</figcaption></figure>

With regard to the measurement noise, the energy observations $y_i^t$ are corrupted with an SNR of (105, 110, 115, 120)dB at a reference distance of 1m. It should be pointed out that, maintaining the SNR constant over the search space (and not the noise level), and highlighting that the energy decays at a rate of
$1/d^2$, the true SNR at a given distance is indeed much lower due to the high area of the search-space. Figure 3 shows the decay of the SNR considering its reference value at $1m$. For a distance measurement of 900m, as with $D_1$ (see Fig. 2), when considering an $SNR_{1m}$ of 105dB, its equivalent SNR at 900m will be approximately -13dB. This situation implies that, given the dimensions of the search-space, noise assumes very significant values for points far from the acoustic source. For the mean values of Fig. 2 ($\approx 350m$), the SNR assume values between 0dB and 20dB.

Lastly, a set of $M_c = 10.000$ measures are generated and corrupted for each instant $t$ through the parametric equation (3) (red dashed line on Fig. 1), being the simulations carried out over $M_c$ Monte Carlo runs.

$$x_{(x,y)} = (t, 10^{-5} \cdot (t - 520)^3 - (t - 300) + 800), \quad \text{for } t \in [50, 950] \quad (3)$$

## 4 The Proposed Methodology

The Bayesian theory, which integrates information given by observations with prior knowledge, extracted from some target motion model, is one of the major tools applied when considering target tracking [27, 10]. In the present situation, since the measurement model is non-linear, an EKF is employed. To this end, let $\theta_t = [\mathbf{x}_t^T, \mathbf{v}_t^T]^T$ denote the target state at some instant $t$, with $\mathbf{v}_t \in \mathbb{R}^2$ denoting the target velocity at time instant $t$ (as mentioned, the generalization to $\mathbb{R}^3$ is straightforward). When considering a constant velocity motion model, a state transition matrix $S$ can be defined through (4), in such a way that the state $\theta_{t+1}$ is obtained from $\theta_t$. The term $\mathbf{r}_t$ represents the noise perturbations and follows a Gaussian distribution with zero-mean and covariance $Q$, i.e., $\mathbf{r}_t \sim N(0, Q)$.

$$\theta_{t+1} = S\theta_t + \mathbf{r}_t \quad (4)$$

The matrices $S$ and $Q$ are defined as:

$$S = \begin{bmatrix} 1 & 0 & \Delta & 0 \\ 0 & 1 & 0 & \Delta \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix}, \quad Q = q \begin{bmatrix} \frac{\Delta^3}{3} & 0 & \frac{\Delta^2}{2} & 0 \\ 0 & \frac{\Delta^3}{3} & 0 & \frac{\Delta^2}{2} \\ \frac{\Delta^2}{2} & 0 & \Delta & 0 \\ 0 & \frac{\Delta^2}{2} & 0 & \Delta \end{bmatrix}, \quad (5)$$

where $q$ denotes the state process noise intensity [27].

A measurement $z_t$ of the state $\theta_t$ is made according to $z_t = h(\theta_t) + \epsilon_t$, where the $z_t$ corresponds to the measured energies $y^t$ and $\epsilon_t \sim N(0, R)$ the measurement noise, with $R$ being a covariance matrix composed by the energies variance $\sigma^2_\epsilon$:

$$R = \begin{bmatrix} \sigma^2_\epsilon & & & \\ & \ddots & & \\ & & \sigma^2_\epsilon & \\ & & & \sigma^2_\epsilon \end{bmatrix} \in \mathbb{R}^{N \times N}, \quad (6)$$
and the observation model $h(\theta_t)$ set as:

$$h_i(\theta_t) = \frac{g_i P_d}{\|\theta_{t_{1:2}} - D_i\|^2}, \quad \text{for } i = 1, 2, \dots, N. \qquad (7)$$

Since the EKF approximates the non-linear model by its first-order Taylor series expansion, the Jacobian matrix of (7) with respect to $\theta_t$ is defined as:

$$\mathbf{J}_h = \frac{\partial \mathbf{h}}{\partial \theta_t} = \begin{bmatrix} \frac{-2g_1 P_d(\theta_{t_1} - \mathbf{s}_{1,x})}{\|\theta_{t_{1:2}} - \mathbf{s}_1\|^4} & \frac{-2g_1 P_d(\theta_{t_2} - \mathbf{s}_{1,y})}{\|\theta_{t_{1:2}} - \mathbf{s}_1\|^4} & 0 & 0 \\ \vdots & \vdots & \vdots & \vdots \\ \frac{-2g_N P_d(\theta_{t_1} - \mathbf{s}_{N,x})}{\|\theta_{t_{1:2}} - \mathbf{s}_N\|^4} & \frac{-2g_N P_d(\theta_{t_2} - \mathbf{s}_{N,y})}{\|\theta_{t_{1:2}} - \mathbf{s}_N\|^4} & 0 & 0 \end{bmatrix}. \quad (8)$$

Then, the EKF can be implemented as shown in Alg. 1, where two issues are beyond the standard EKF, that is the calculation of the initial state $\hat{\theta}_{1|1}$, and the treatment of trajectory intersections.

### Algorithm 1 The proposed extended Kalman filter

**Require:** $Q, S, R$

1. Starting State ($t = 1$):

2. $\hat{x}_t \leftarrow \text{solve (9) for } y^t \text{ via } i\text{EHO [6]}$

3. $\hat{\theta}_{t|t} = [\hat{x}_t^T, 0, 0]^T \quad \triangleright \text{Set unknown velocity to } 0$

4. $\hat{P}_{t|t} = I_4$

5. **for** $t = 2, 3, \dots, T$ **do**

6. $i = \arg \max_{i \in \{1, \dots, N\}} y_i^t$

7. **if** $y_i^t > \xi$ **then**

8. $\hat{\theta}_{t|t} = [D_i, [\hat{\theta}_{t|t}]_{3:4}^T]^T \quad \triangleright \text{A high energy measure means the source is most probably close to the drone that acquired this measurement}$

9. **else**

10. **Prediction:**

11. $\hat{\theta}_{t|t-1} = S\hat{\theta}_{t-1|t-1}$

12. $\hat{P}_{t|t-1} = S\hat{P}_{t-1|t-1}S^T + Q$

13. **Update:**

14. $H_t = \mathbf{J}_h(\hat{\theta}_{t|t-1})$

15. $K = \hat{P}_{t|t-1}H_t^T(H_t\hat{P}_{t|t-1}H_t^T + R)^{-1}$

16. $\hat{\theta}_{t|t} = \hat{\theta}_{t|t-1} + K(y^t - h(\hat{\theta}_{t|t-1}))$

17. $\hat{P}_{t|t} = (I_4 - KH_t)\hat{P}_{t|t-1}$

18. **end if**

19. **end for**

With regard to the filter implementation details the filter's initialization is performed by solving a WLS problem, considering the initial point measurements only and a metaheuristic approach (further explanations in Eq. 9). Also,
the problem is treated when the drone trajectory crosses the target trajectory, which may imply singularities in the decay of the acoustic model. Due to its linear approximations, the EKF becomes unstable when the order of energy measures increases abruptly (which happens when a drone gets close to the acoustic target). To prevent the EKF from diverging, a special condition is evaluated before each iteration of the filter. This condition tests if any of the measured energies at the current time instant is greater than a threshold $\xi$. If it evaluates to true that EKF iteration is passed over, and instead the estimated position of the source is updated to the position of the drone that measured the high energy, while the estimated velocity and the process covariance matrix remain unchanged. Considering the energy decay model, one can see that, for a high threshold $\xi$, estimating the source current position as the current position of the drone will not be too erroneous. In particular, considering a threshold $\xi = 300$, $g_i = 100$ and $P = 20$, the estimated position of the acoustic source is assumed as the position of the drone $D_i$ whenever the drone is at an estimated distance $\tilde{d} = \sqrt{\frac{g_i P}{y_i}} \approx 2.58\text{m}$ or less from the target source (meaning that the expected tracking error during that time is equal or less to 2.58m).

With the purpose of evaluating and comparing the performance of the proposed methodology, a WLS approach is defined as (and summarized in Alg. 2):

$$ \hat{x}_t = \arg \min_{\mathbf{x}_t} \sum_{i=1}^{N} w_i^t \left( y_i^t - \frac{g_i P_d}{\|\mathbf{x}_t - \mathbf{D}_i\|^2} \right)^2, \quad (9) $$

where weight, $w_i^t = \frac{\tilde{d}_i^{-1}}{\sum_{i=1}^{N} (\tilde{d}_i^{-1})}$ (with $\tilde{d}_i^t = \sqrt{\frac{g_i P_d}{y_i^t}}$), imputes more importance to energies measured by closer sensors (based on the distance estimate). The estimator (9) is highly non-convex, non-linear, and non-continuous with singularities at $D_i$, making gradient-based optimizers likely to converge to local optima. However, when employing metaheuristics to solve the Alg. 2, in particular the Improved Elephant Herding Optimizer (iEHO), it is possible to obtain good results for acoustic source localization problem [8, 6].

<caption>**Algorithm 2** Series of T localizations by WLS</caption>

1: **for** t = 1, 2, ..., T **do**
2:     $\hat{x}_t \leftarrow \text{solve (9) for } y^t \text{ via iEHO [6]}$
3:     **end for**

It's worth remembering that the drone trajectories ($D_{(x_i, y_i)}$) are predetermined based on features related to the wildfire dynamics. Those would have the purpose of collecting information for the fire front prediction, providing communications links for ground teams, etc. Bottom line, the trajectories are not controlled by the acoustic localization system; instead, they are distributed among
the space, to cover the wildfire environment, independent of the current location of the acoustic source, and with no information about its maneuvers.

## 5 Results and Discussion

To validate the proposed method and evaluate its performances, several simulations were carried on both the EKF algorithm and the WLS counterpart. The results shown in this section include the performances of the methods considering three typologies for the sensors drone, that is $N \in \{3, 4, 5\}$, four different SNRs (120, 115, 110, 105)dB, $q = 0, 6m^2/s^3$, $\Delta = 1s$, each evaluated for $Mc = 10.000$ runs. The model parameters were $P = 20, g_i = 100$ (for $i = 1, \dots, N$), and $\beta = 2$. The simulations were performed using MATLAB® R2020b, on a machine with an AMD Ryzen™ 3 3100 quad-core processor at 3.6GHz, with 16GB of RAM, and Ubuntu 18.04.4 LTS (Linux kernel 5.4.0) operating system.

The results are made up of two sets of metrics. Figures 5, 7, and 9 plot the mean error (distance between the real and estimated target position) over the $Mc$ runs for $N = 3, N = 4$, and $N = 5$ respectively. The dashed constant line and the value overlapping the graph correspond to the plot's mean over the all trajectory. Additionally, Figs. 4, 6, and 8 represents the mean trajectory obtained over the $Mc$ runs. The shaded areas in Figs. 4, 6, and 8 illustrate the standard deviation of the trajectory for the $Mc$ runs. This area is the union of $T$ ellipses, where half the width of the $t^{th}$ ellipse is equal to the standard deviation (of $Mc$ runs) in $x$ axis of the $t^{th}$ point of the trajectory. Also, half the height of the ellipse is equal to the standard deviation in $y$ axis of the $t^{th}$ point of the trajectory, and the center of the ellipse is at the $t^{th}$ point of the mean trajectory. These figures also present the drones' trajectories (dashed lines) to seek correlations with the shape of the graph. Finally, Table 1 resumes the overall mean error for the considered scenarios.

<table><caption>Table 1: Summary of the mean error (ME) obtained for the overall trajectories.</caption><thead><tr><th>$N$ (number of drones)</th><th>SNR<sub>1m</sub> (dB)</th><th>$ME_{WLS}$ (m)</th><th>$ME_{EKF}$ (m)</th></tr></thead><tbody><tr><td rowspan="4">3</td><td>105</td><td>91,499</td><td>53,170</td></tr><tr><td>110</td><td>65,215</td><td>30,893</td></tr><tr><td>115</td><td>45,752</td><td>29,053</td></tr><tr><td>120</td><td>34,272</td><td>26,900</td></tr><tr><td rowspan="4">4</td><td>105</td><td>42,473</td><td>27,938</td></tr><tr><td>110</td><td>34,491</td><td>24,758</td></tr><tr><td>115</td><td>30,483</td><td>24,737</td></tr><tr><td>120</td><td>25,097</td><td>20,298</td></tr><tr><td rowspan="4">5</td><td>105</td><td>20,215</td><td>20,254</td></tr><tr><td>110</td><td>15,605</td><td>15,733</td></tr><tr><td>115</td><td>12,518</td><td>11,638</td></tr><tr><td>120</td><td>9,744</td><td>8,532</td></tr></tbody></table>
<figure><img src="image_6.png" /><figcaption>Fig. 4: Mean trajectory of $M_c$ runs for $N = 3$.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>Fig. 5: Mean error of $M_c$ runs for $N = 3$.</figcaption></figure>
<figure><img src="image_8.png" /><figcaption>Fig. 6: Mean trajectory of $M_c$ runs for $N = 4$.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Fig. 7: Mean error of $M_c$ runs for $N = 4$.</figcaption></figure>
<figure><img src="image_10.png" /><figcaption>Fig. 8: Mean trajectory of $M_c$ runs for $N = 5$.</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>Fig. 9: Mean error of $M_c$ runs for $N = 5$.</figcaption></figure>
When considering the overall results presented in Table 1 one can see that when performing the acoustic measurements with $N = 3$ drones, the EKF implies a reduction of about 40% when compared with the WLS implementation. When considering the error over the trajectory path (Fig. 5), besides the first instants of the path until the EKF does not establishes useful prior information, the obtained error is always lower. Nevertheless, when considering the error deviation (see Fig. 4), it is pretty highlighted that the EKF has a much stable and reliable overall path. Another evidence that can be extracted from Fig. 4 is the behavior of the proposed scheme for the trajectories intersections, that is when the drones intersect the target trajectory, the error is minimal, a situation that is also valid when trajectories approach each other ($750s < t < 850s$). The same analysis can be performed when considering $N = 4$ sensor drones (Figs. 6 and 7), although the reduction is somewhat less significant, reaching values in the order of 25%. Finally, when considering $N = 5$ sensor drones, the overall decline is marginal; meanwhile, Fig. 8 demonstrates that the deviation is much higher for the WLS implementation. When considering Fig. 9, one can see that the moment when EKF has a higher error that EKF is in the first moments of the path. It should be pointed out that although the position is initialized with the WLS method, the velocity is initialized with $[0, 0]^T$, that is, without considering any previous information of the system dynamics (line 3 of Alg. 1). As a concluding remark, in the worst-case scenario, when $N = 3$ and the SNR is $105dB$, a mean error over the trajectory of about $50m$ is obtained when considering a search-space of $1000 \times 1000m^2$. Not forgetting that, for these conditions, the mean distance of the sensors reaches $350m$, which would imply a local SNR of about $3dB$. Moreover, by simply enlarging the drone's fleet, the mean overall error is reduced to about $28m$ in the same conditions ($SNR = 105dB$), resulting in a reduction of almost 50%.

# 6 Conclusions and Future Work

In this work, the problem of tracking a moving acoustic source was addressed based on energy measurements, which are considered to be acquired by microphones positioned on drones, and thus, also with some moving dynamics. The proposed methodology is based on implementing an Extended Kalman Filter that, besides dealing with the measurement model non-linearity, also deals with the trajectories intersections, avoiding the filter divergence. Simulations performed over different sets of number of drone sensors and different SNR corrupting the energy measures show the effectiveness, stability, and repeatability of the method. These results were also compared with a WLS implementation that does not consider the prior knowledge given by the motion model as a well-known and accepted benchmark that validates the credibility of the solutions presented. The present work establishes the energy-based acoustic source localization strategy, which brings simplicity to physical implementation and processing level when placed alongside with its counterparts. Ultimately, the present work proposed an EKF methodology for acoustic localization validated
with results that demonstrates its effectiveness and reliability. It can be concluded that using energy-based measurements to perform the localization of a moving target can be considered as an add-on to current wildfire platforms.

As future work, the analysis of fusion techniques that make use of the estimated location to govern the movement of the sensor drones, contributing to reduction of the estimation error without jeopardizing its primary function on the wildfire scenario will be considered. Also, to enhance the credibility of the present work, it is important to extend the developed experiments to real-world scenarios.

**Acknowledgments.** This research was funded by Fundação para a Ciência e a Tecnologia under Projects UIDB/04111/2020 and foRESTER PCIF/SSI/0102/2017; and Instituto Lusófono de Investigação e Desenvolvimento (ILIND) under Project COFAC/ILIND/COPELABS/1/2020.

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