An Indoor Localization Strategy for a Mini-UAV in the Presence of Obstacles

Abstract

In this paper, we propose a novel approach to mini-UAV localization in a wireless sensor network. We firstly employ the environment adaptive RSS parameters' estimation method to estimate the parameters of range estimation model. However, the direct path from the target to a beacon is blocked by obstacles in a complicated indoor environment. So the proposed method, which employs a sequential probability ratio test to identify whether the measurement contains non-line of sight (NLOS) errors, is tolerant to parameter fluctuations. Finally, a particle swarm optimization-based method is proposed to solve the established objective function. Simulation results show that the proposed method achieved relatively higher localization accuracy. In addition, the performance analyses, carried out for a realistic indoor environment, shows that the proposed method still preserves the same localization accuracy.

Keywords

wireless sensor networks mini-UAV indoor localization non-line of sight (NLOS)particle swarm optimization

1. Introduction

The mini-UAV (Unmanned Aerial Vehicle) is an emerging technology which has the potential to be used in many applications like surveillance missions, building maintenance and precision farming. Mini-UAVs have special attractiveness to researchers due to their small size, outstanding manoeuvrability and low cost, in that, it is also suitable for indoor applications. Most UAVs obtain the location information from a GPS module. However, GPS does not work in an indoor environment. If the mini-UAV cannot obtain the location information, it will have difficulties flying autonomously. Image processing technology is based on optical measurements such as a digital charge-coupled device (CCD) camera [1]. Such processes are very slow and consume much power, and they also need appropriate pattern recognition algorithms. Due to the availability of low energy cost sensors, micro processors and radio frequency circuitry for information transmission, there is a wide and rapid diffusion of wireless sensor networks (WSN). We deploy the beacon nodes which know their locations in the building. The mini-UAV is capable of measuring the distance between it and the beacon node to estimate its location. The WSN-based localization strategy has the features of good flexibility, convenient maintenance and low cost updates. So WSNs are increasingly being used in indoor localization.

In WSN-based localization methods, the main approaches proposed to locate the unknown node are based on received signal strength (RSS), angle of arrival (AOA), time of arrival (TOA) or time difference of arrival (TDOA) [2]. One of the cheapest and less invasive ways to locate an unknown node with a WSN is based on radio signal strength measurements since it does not need additional hardware, however, it is not an accurate method. The TOA method measures travel times of signals between nodes, however, synchronization error can significantly affect ranging error. The angles between the unknown node and a number of anchor nodes are used in the AOA method to estimate the location, but these localization methods are not suitable for mini-UAVs. TDOA method locates by measuring the two signals' arrival time difference between anchor nodes and the unknown node, and it is able to achieve high ranging accuracy. The accuracy of the TDOA localization method depends on the propagation conditions. In this paper, we employ both RSS and TDOA methods to locate the position of the unknown node. The unknown node emits the acoustic and radio signals to the beacon nodes, and the beacon nodes measure the RSS and TDOA.

If line of sight (LOS) propagation exists between the target and all beacon nodes, high location accuracy can be achieved. However, in WSNs in which the direct path from the target to a beacon is blocked by obstacles, the signal measurements include an error due to the excess path travelled because of the reflection of acoustic signal, which is termed as the NLOS error. Previous works have demonstrated that the WSN can be effectively employed for mini-UAVs for locating applications. A time of flight-based localization framework [3] has been developed for a flying robot, however, no research has yet considered the NLOS propagation condition. The complicated indoor environment causes an NLOS environment and unstable communication, moreover, large location estimation error will occur in the above situation [4]. Therefore, the research on the localization in the NLOS environment remains a challenging topic and has highly practical applications.

In this paper, we firstly design a WSN-based mini-UAV localization module which is suitable for mini-UAV application. This module could provide the location information for a mini-UAV, so the mini-UAV could focus on its task. In addition, we then propose a NLOS identification method to detect the measurement condition. Finally a maximum joint probability localization method is proposed in an indoor environment.

The rest of the paper is organized as follows. Section 2 provides a brief overview of the localization methods in NLOS conditions. In Section 3 we describe the system and range measurement model. We will introduce our proposed strategy in Section 4. Some simulation and experiment results will presented in Section 5. The conclusions are given in Section 6.

2. Related Works

NLOS identification and mitigation methods have received significant attention in wireless sensor networks. There are two main approaches to solve NLOS errors: parametric methods and non-parametric methods. In this section, we give a brief overview of some key research in this area.

The advantage of the non-parametric method is that it does not need to know the parameters of the range estimation model, namely, it can be used with any of the ranging technologies and does not require prior information about the statistical properties of the NLOS measurements. In [5], the authors proposed a weighted least squares method which utilizes all NLOS and LOS measurements, but provides weighting to minimize the effects of the NLOS contributions in estimating the location of the unknown node. Nevertheless, the weighting strategy may provide unreliable results. In [6], a linear-programming approach to the problem of NLOS mitigation in wireless networks is proposed. This method uses the ranges' estimations in LOS to define the objective function and the range estimates in NLOS to restrict the feasible region for the linear program. Since the least squares algorithm estimates the location of the unknown node by minimizing the sum of squared residual, one large measurement error induces a relatively larger localization error. The robust multilateration method [7] can avoid this problem by minimizing the proposed objective function. The Min-Max algorithm is proposed in [8] to detect and compensate the large attenuation measurement error in obstructed environments. The basic approach is to divide the network area into small grids and perform the localization using the position probability grid. It uses Min-Max bound to determine the localization error and then corrects the estimated location. In [9], the authors proposed a residual weighting algorithm (Rwgh) which uses the sum of squared residuals of a least squares estimation as the indicator of the accuracy of the calculated node coordinates. They apply least squares multilateration on all possible combinations of the distance measurements and then the estimated location is computed as a weighted combination of these intermediate estimates.

The advantage of the parametric method is that it can determine the measurement condition and then correct the NLOS errors, however, it needs to know the parameters of the range measurement model. In [10], the authors present an algorithm to detect the NLOS error using the redundant information present in the TOA measurements. The NLOS identification problem is formulated as a binary hypothesis test [11] where the range measurements are modelled as being corrupted by additive noise. In [12], the authors investigate the NLOS error mitigation problem in TDOA and TDOA/AOA location schemes. Depending on how much a priori information is available, two approaches are proposed: a NLOS state estimation (NSE) algorithm can be used if some prior information on NLOS errors is available from the empirical database; and when the knowledge about NLOS is unknown, an improved residual algorithm can be applied to detect a small number of NLOS. A TOA-based localization method is investigated in [13]. A constant false alarm rate (CFAR) method, which is based on the CFAR detection theory in radar systems is proposed. The authors also proposed a maximum probability of detection (MPD) method, which determines the TOA estimation according to a comparison of the detection probabilities of a number of different possible TOA estimations.

3. System and Range Measurement Model Description

As shown in Figure 1, there are two modes for a TDOA localization system: passive mode and active mode. The beacon nodes with known locations are fixed on the ceiling. For the passive mode: the beacon nodes emit the radio and acoustic signals periodically. In order to avoid acoustic confliction, there is only one beacon node emitting the signals over a short time. In addition, an unknown node is fixed on the mini-UAV to communicate with the beacon nodes. The mini-UAV measures the time of difference arrival of these two signals to estimate the distance between the beacon node and mini-UAV. The advantage of this mode is that it can provide a positioning service for multiple targets. However, it is not suitable for mini-UAVs since it requires that the mini-UAV stops during collection of the distances from the beacon nodes. If the mini-UAV drifts in a random direction, it reduces the accuracy of localization results. In addition, it is an energy-consuming mode since the beacon nodes work continuously, regardless of whether or not the target.

Figure 1.

Two modes for TDOA localization system

For the active mode: the mini-UAV emits the radio and acoustic signals, the beacon nodes measure the time of difference arrival of these two signals to estimate the distance between the beacon node and mini-UAV. Then the beacon nodes send the estimated distances to the mini-UAV to calculate the location of the mini-UAV. The advantage of this mode is energy efficiency and time-saving. In this paper, we adopt the active mode for mini-UAV localization.

As illustrated in Figure 2, we have designed the sensor node. The size of the sensor node is 64mm (L) ×40mm (W). The size is suitable for mini-UAV application. It consists of four modules: the MCU and radio module, the battery module, the ultrasonic transmission or reception module and the display module. The MCU and radio module adopts a 2.4 GHz low power radio chip CC2430, and the antennas have an omnidirectional pattern. The beacon nodes are fixed on the ceiling and the mini-UAV carries an unknown sensor node to communicate with the beacon nodes.

Figure 2.

TDOA ranging hardware

3.1 TDOA Measurement Model

In LOS propagation conditions, the estimation of TDOA is modelled as follows:

\hat{t} = t + n_{i}

(1)

Where t is the true TDOA of two signals, n_i is the measurement noise modelled as zero mean white Gaussian with variance σ². The range estimation, using TDOA, is modelled as follows[14]:

{\hat{d}}_{L O S} = c \cdot t + n_{i L} = d + n_{i L}

(2)

Where d is the true Euclidean distance between mobile and beacon nodes. Since c_radio » c_acoustic, so c denotes the velocity of acoustic propagation c_acoustic, ni is the measurement noise modelled as zero mean white Gaussian with variance σ_Ti².

In NLOS propagation conditions, the range estimation is as follows:

{\hat{d}}_{N L O S} = d + n_{i} + n_{N L O S}

(3)

where n_i is the measurement noise with zero mean and σ_Ti² variance. n_NLOS is the NLOS errors and is assumed to be independent of the measurement noise n_i. The positive bias error (n_NLOS) is uniformly distributed: n_NLOS ~ U (0,B_max). Where B_max is the maximum bias.

3.2 RSS Measurement Model

We applied the signal propagation model as the log-normal shadowing model. Empirical studies have shown that the log-normal model provides more accurate multipath channel models than the well-known Nakagami and Rayleigh models for indoor environments with obstructions [15]. The received signal strength (RSS) of i-th node can be expressed as:

P_{i} = P_{0} - 10 n \log_{10} (d) + S

(5)

where P₀ is the path loss at 1 metre and n is the path loss exponent. d is the true Euclidean distance between mobile and beacon nodes. S ~ N(0, σ²) is the RSS measurement noise modelled as zero mean white Gaussian with variance σ², S ~ N(0, σ_SL²) under LOS condition and S ~ N(0, σ_SN²), σ_SL² < σ_SN² under NLOS condition.

In order to be tolerant of the parameter variations caused by environmental variations, we employ an environment adaptive RSS parameters' estimation method [16]. We can obtain the parameters of the RSS model. The estimation method is as follows: the beacon node takes turns transmitting the message, the other beacon nodes measure the RSS. Since the distances between the transmitter and receivers are known, the receivers compute the parameters through the least squares method.

4. Proposed Algorithm

4.1 NLOS Identification Algorithm

In this subsection, we propose a sequential probability ratio test-based NLOS identification algorithm. This algorithm only needs the parameters of an RSS ranging model to determine the condition of measurement.

The probability density function of RSS is as follows:

\begin{array}{l} f_{L O S} (P_{i} | H_{0}) = \frac{1}{\sqrt{2 π σ_{S L}^{2}}} \exp (\frac{{(P_{i} - P_{0, LOS} - 10 n_{0} \log_{10} (d))}^{2}}{- 2 σ_{SL}^{2}}) \end{array}

(6a)

\begin{array}{l} f_{N L O S} (P_{i} | H_{1}) = \frac{1}{\sqrt{2 π σ_{S N}^{2}}} \exp (\frac{{(P_{i} - P_{0, NLOS} - 10 n_{1} \log_{10} (d))}^{2}}{- 2 σ_{SN}^{2}}) \end{array}

(6b)

where H₀ represents that the environment is LOS and H₁ represents that the environment is NLOS. σ_SL² and σ_SL² is the variance of the noise in LOS and NLOS environments respectively. P_0,LOS and P_0,NLOS is the path loss at 1 metre in LOS and NLOS conditions respectively.

The probability density function of TDOA can be expressed as:

\begin{array}{l} f_{L O S} (\hat{d} | H_{0}) = \frac{1}{\sqrt{2 π σ_{τ}^{2}}} \exp (\frac{{(\hat{d} - d)}^{2}}{- 2 σ_{i}^{2}}) \end{array}

(7a)

\begin{array}{l} f_{N L O S} (\hat{d} | H_{1}) = \frac{1}{\sqrt{2 π {(b - a)}^{2}}} \exp (φ (\frac{b - \hat{d} + d}{σ_{i}}) - φ (\frac{a - \hat{d} + d}{σ_{i}})) \end{array}

(7b)

where,

φ (x) = \frac{1}{\sqrt{2 π}} \int_{- \infty}^{x} e^{- \frac{t^{2}}{2}} d t .

Fig.3 (a) and Fig.3 (b) are the probability distributions using the RSS and TDOA estimation models respectively. As shown in Fig.3 (a), the probability distribution of RSS can provide good information regarding whether or not the received signal is LOS or NLOS. The probabilities of LOS and NLOS are also distinct even with the biased distance estimation. However, since the probability distribution of TDOA is not distinct, the TDOA cannot be used to detect the propagation condition. We firstly assume the current propagation is H₀ (LOS condition), then we compute the estimated distance d̂ between the mini-UAV and the beacon node using the TDOA method. Then we plug the estimated distance d̂ into Equation (6) So we can obtain the generalized likelihood ratio as follows:

Figure 3.

The probability distributions of RSS and TDOA

Λ ({\hat{P}}_{i}) = \frac{f_{L O S} ({\hat{P}}_{i} | H_{1})}{f_{N L O S} ({\hat{P}}_{i} | H_{0})}

(8)

In practice, due to inaccurate prior knowledge and noisy observations, it is possible that the parameters cannot be obtained accurately. In a binary hypothesis test, a threshold is selected to determine the propagation condition. However, the success rate of this method will reduce when the parameters fluctuate. So we employ a sequential probability ratio test which is relatively more tolerant to parameter fluctuations in detecting the propagation condition. The stop rule is as follows:

If Λ(P̂_i) ≤ a, accept H₀.

If Λ(P̂_i) ≤ b, reject H₀ and accept H₁.

If a < Λ(P̂_i) ≤ b, continue to measure.

Where, $a = \frac{β}{1 - α}$ and $b = \frac{1 - β}{α}$ . α is the probability of eventually rejecting H₀ when it is true, i.e., Type I error. β is the Type II error.

4.2 Localization Algorithm

After identifying the measurement's condition, we attempt to estimate the location of the mini-UAV. In this section, a maximum joint probability (MJP) in LOS is proposed. This method utilizes the probability density function of d̂ from the TOA estimation model in LOS conditions to estimate the location of the mini-UAV. The objective function is established as follows:

(\hat{x}, \hat{y}) = \arg \max {\prod_{i = 1}^{L} f_{L O S}^{i} ({\hat{d}}_{i} | H_{0}^{​})}

(9)

where L is the number of LOS measurements. $f^{i} _{L O S} (\hat{d} | H_{0}) = \frac{1}{\sqrt{2 π σ_{τ}^{2}}} \exp (\frac{{({\hat{d}}_{i} - d_{i})}^{2}}{- 2 σ_{i}^{2}})$ and d_i = √(x_i + ◯)² + (y_i + ŷ)², (x_i, y_i) is the position of i-th beacon node and (◯, ŷ) is the estimated location of the mini-UAV.

A straightforward method to find a solution that maximizes (9) is the exhaustive search algorithm. However, the computation cost is extremely high. We use particle swarm optimization (PSO) to find a solution [17–18]. Particle swarm optimization is a swarm intelligence algorithm that id used mainly for numerical optimization tasks. It mimics the behaviour of flying birds and their communication mechanism to solve optimization problems. Simulating this scenario, PSO was developed and used as a useful computation technique to tackle the optimization problem.

We assume that a swarm consists of 20 particles S={X₁,…X₂₀}. The search space is a 2 dimensional vector and then the particle i of the swarm can be represented by a 2 dimensional vector X_i=(x_i,y_i). At step k, the velocity of particle i and its new position will be assigned according to the following two equations:

v_{i}^{k} = ω v_{i}^{k - 1} + c_{1} ξ (p b e s t_{i}^{k - 1} - X_{i}^{k - 1}) + c_{2} η (g b e s t_{​}^{k - 1} - X_{i}^{k - 1})

(10)

X_{i}^{k} = X_{i}^{k - 1} + v_{i}^{k}

(11)

The inertia weight for t iteration is given by:

ω = ω_{\max} - \frac{t (ω_{\max} - ω_{\min})}{t_{\max}}

(12)

where, v_i^k stands for the velocity of particle i at step k. X_i^k is the position of the i-th particle. ω is the inertia weight to balance exploitation and exploration, where ω_max = 0.9, ω_min = 0.4. pbest_i^k-1 represents the best location in the search space ever visited by particle i and gbest^k–1 is the best location discovered so far. c₁ and c₂ are two acceleration constants, where c₁=c₂=2. ξ and η are two uniform random numbers in [0,1]. The maximum number of iterations t_max=80 and the pseudocode of the proposed strategy is shown as follows:

1. Initialize the necessary parameters of PSO 2. Randomly generate an initial population with positions S={X₁,…X₂₀} and velocities {V₁,…V₂₀} 3. Evaluate the fitness values F={f₁,…f₂₀}of S 4. Set S to be the pbest={pb₁,…pb₂₀} for each particle 5. Set the particle with best fitness to be gbest 6. For t=1 to t_max do 7. For i=1 to 20 do 8. Update the velocity of particle X_i using Equation (10) 9. Update the location of particle X_i using Equation (11) 10. Evaluate the fitness values of the new particle X_i 11. If the fitness value of X_i is better than the fitness values of pb_i 12. Then set X_i to be pb_i 13. End if 14. If the fitness value of X_i is better than the fitness values of gbest 15. Then set X_i to be gbest 16. End if 17. End for 18. End for

5. Simulation and Experiments

In this section we present some simulation and experiment results to show the performance of our proposed algorithms. In the simulation, the beacon nodes are randomly deployed in a region sized 10m×10m. The values of the parameters are shown in Table 1. In each simulation case, 2000 Monte Carlo runs are performed with the same parameters. The performance of the proposed algorithm is measured by average localization error (ALE):

Table 1.

Parameters of system model

Parameters	Values	Parameters	Values
σ_Ti	0.25	P _0,NLOS	−37.3
B_max	2	n₀	1.79
σ_SL	2.22	n₁	3
σ_SN	5	α	0.2
P₀,_LOS	−41.5	β	0.5

error = \frac{1}{N_{t}} \sum_{i = 1}^{N_{t}} \sqrt{{({\hat{x}}_{i} - x)}^{2} + {({\hat{y}}_{i} - y)}^{2}}

(13)

where N_t = 2000, (x, y) is the true location of mini-UAV. (◯_i, ŷ_i) is the estimated location of mini-UAV.

We firstly evaluate the success rate of the proposed NLOS detection method. Figure 4 shows the success rate against the standard variance of the measurement noise σ_Ti in the TDOA estimation model for different B_masx. The results show that the success rate of the proposed method decreases as the value of σ_Ti increases. In addition, the success rate is less affected by B_max. The proposed method achieves a relatively higher success rate.

Figure 4.

The success rate versus σ_Ti

The impact of standard variance of measurement noise σ₀ on success rate is investigated in Figure 5. In this simulation, the standard variance of measurement noise in LOS condition σ₀ is varied from 1 to 4.6 and the standard variance of measurement noise in NLOS condition σ₁ is varied from 3 to 6. The results show that that the probability of LOS and NLOS is not distinct when σ₀ > σ₁.

Figure 5.

The success rate versus σ₀

Figure 6 shows the relationship between the average localization error and the standard variance of the measurement noise σ_Ti in the TDOA estimation model. The results show that the Rwgh outperforms other methods when σ_Ti is relatively smaller. However, the proposed method has the highest localization accuracy when the value of σ_Ti increases.

Figure 6.

The average localization error versus σ_Ti

In Figure 7 we evaluate the impact of B_max on average localization error. The results show that B_max has a higher impact on the localization error. In addition, the MJP and Rwgh methods are robust to the B_max. The proposed method has the best performance when B_max was varied from 2 to 5 in comparison with other methods.

Figure 7.

The average localization error versus B_max

Table 2 shows the experiment results. In this experiment, we deployed 6 beacon nodes in the ceiling and 3 obstacles were deployed between the beacon nodes and mini-UAV. The obstacle leads to the deflection of acoustic signal. 50 indoor positions are measured in this experiment. The average localization error shows that the proposed method has the highest localization accuracy in comparison with other methods.

Table 2.

Experiment results

	MJP	ML	Rwgh
ALE/m	0.85	1.3	0.98

6. Conclusion

In this paper we present a NLOS identification and a maximum joint probability algorithm to solve the problem of localization in NLOS environments. The proposed method only needs the parameters of the RSS estimation model to identify the propagation condition and in addition a PSO-based maximum joint probability algorithm to estimate the location of the mini-UAV. Simulation results show that the NLOS detection algorithm achieves a relatively higher success rate. In addition, the PSO-based maximum joint probability algorithm outperforms other methods. The experiment results also show a similar performance.

Footnotes

7. Acknowledgments

This work has been supported in part by the National Natural Science Foundation of China under grant no. 60874103, Station Key Laboratory of Robotics under grant no. RLO200913, the Fundamental Research Fund for the Central Universities of China (N110404030, N110804004, N110404004, N090304003).

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