Journal of Robotics

Volume 2018, Article ID 7806854, 9 pages

https://doi.org/10.1155/2018/7806854

## Particle Filter and Finite Impulse Response Filter Fusion and Hector SLAM to Improve the Performance of Robot Positioning

^{1}Qazvin Islamic Azad University, Iran^{2}Allameh Tabataba’i University, Iran^{3}University College London, UK

Correspondence should be addressed to Amin Bassiri; moc.liamg@irissab.nima

Received 13 April 2018; Revised 30 July 2018; Accepted 6 September 2018; Published 11 November 2018

Guest Editor: Ling-Ling Li

Copyright © 2018 Amin Bassiri et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Indoor position estimation is essential for navigation; however, it is a challenging task mainly due to the indoor environments’ (a) high noise to signal ratio and (b) low sampling rate and (c) sudden changes to the environments. This paper uses a hybrid filter algorithm for the indoor positioning system for robot navigation integrating Particle Filter (PF) algorithm and Finite Impulse Response (FIR) filter algorithm to assure the continuity of the positioning solution. Additionally, the Hector Simultaneous Localisation and Mapping (Hector SLAM) algorithm is used to map the environment and improve the accuracy of the navigation. The paper implements the hybrid algorithm that uses the integrated PF, FIR, and Hector SLAM, using an embedded laser scanner sensor. The hybrid algorithm coupled with Hector SLAM is tested in several scenarios to evaluate the performance of the system, in terms of continuity and accuracy of the position estimation, and compares it with similar systems. The scenarios where the system is tested include reducing the laser sensor readings (low sampling rate), dynamic environments (change in the location of the obstacles), and the kidnapped robot situation. The results show that the system provides a significantly better accuracy and continuity of the position estimation in all scenarios, even in comparison with similar hybrid systems, except where there is a high and constant noise, where the performance of the hybrid filter and the simple PF seems almost the same.

#### 1. Introduction

The positioning technologies have faced several challenges for indoor applications. Reference [1] studied several most widely used positioning technologies, including Wireless Local Area Network (e.g., Wi-Fi) based systems, Bluetooth Low Energy (BLE), Ultra-Wide Band (UWB), Inertial Navigation Systems (INS), Radio Frequency Identification (RFID), and Tactile based systems, from fitness-for-purpose point of view, and concluded that, for almost all of the indoor Location Based Services (LBS) applications, including indoor navigation, none of these stand-alone positioning technologies could yet provide the required level of positional accuracy and continuity.

One of the biggest challenges of indoor localisation is the existence of a relatively high ratio of noise to signal. Also, Non-Line-Of-Sight (NLOS), where the received signal does not traverse the direct path between the receiver and the transmitter, introduces a big challenge for the ranging-based positioning systems. This is a common situation where the positioning technology is being used for indoor applications. To handle some of these issues, up to some degrees, many of the positioning systems use a state estimator for an estimated but accurate position solution in a cluttered and noisy environment [2], such as inside the buildings. The state estimator, which is also called the stochastic filter, is a mathematical algorithm that estimates the state variables of a system from noisy and biased measurements [3].

One of the most widely used state estimators is Kalman filter (KF), which functions particularly well for the linear systems with a Gaussian noise [4]. For indoor localisation, the state-space model is typically nonlinear; therefore, the nonlinear filters such as the Extended (or Enhanced) Kalman filter (EKF) and the Particle Filter (PF) could respond better [2, 3]. The PF, e.g., Monte Carlo Localization (MCL), can provide with a better performance, in comparison with the EKF, in the highly nonlinear environments [5]. While the EKF requires the initial position and can only solve the relative positioning solutions [2], e.g., for tracking purposes [6], the ability of the PF to function and provide the positioning solutions with no initial (a priori) data allows many applications to apply and use it. In addition, the PF is relatively easier to implement, particularly in comparison with the EKF [7]. However, the PF performance is highly associated with the sample distribution and diversity, which can be an issue in systems that are based on the low rate sampling. The loss of diversity among the samples may result in failing to estimate the state or potentially the large estimation errors [8]. This is referred as the sample impoverishment problem and can happen when the measurement noises are small and/or the number of particles is not enough. To handle this, several attempts have been made and some solutions are provided. They include the Regularized Particle Filter (RPF) [9], Markov Chain Monte Carlo (MCMC) move step [10], and combined/integrated Particle and Kalman filters [11]. Despite these, the enhanced versions of the PF may still not be able to prevent and/or cop with the sample impoverishment completely. In addition, there may a compromised performance for the PF, and in the extreme cases, the filter can fail to function completely [8]. Such extreme cases can include the situations that have got a very small measurement noise or a very low number of particles [12]. There are various preventive methods against sample impoverishment and PF failures. However, they concluded that an effective and general remedy to cure a completely failed (or diverging) PF has yet to be proposed [13].

This paper applies a hybrid filter that integrates PF and Finite Impulse Response filtering (FIR), which has been proposed by [13], and couples it with a Hector SLAM algorithm to improve the performance, i.e., accuracy, reliability, and continuity of the localisation under harsh conditions. This system is tested using a laser scanner sensor embedded in a robot to measure the performance of the system in different challenging scenarios and compare the results with the systems that use (a) PF/FIR only [13], and (b) Particle Filter only. While laser scanner can be considered as a stand-alone positioning technology, the hybrid filter uses a PF as the core main filter, integrated and enhanced by another robust FIR filter, based on the proposed scheme by [13]. The PF estimates the state of the robot in the ‘normal’ condition, i.e., where there is no sample impoverishment or positioning solution failure. Once an enormous estimation error is detected, the FIR filter starts functioning and helps the PF to recover. Note the hybrid system does not enhance the PF and so it can be integrated into currently developed and deployed PF-based systems. The novelty of the paper is to use this integrated PF-FIR system [13] with a Hector SLAM for simultaneously localisation and mapping purposes. Also, this paper uses Manhattan distance for PF failure detection as it seems more compatible with the grid-based environment where the experiments are conducted. So, the system uses a hybrid filter to integrate PF and FIR, which prevent the PF failure, while a laser scanner embedded on a robot is used to apply Hector SLAM and improve the continuity, usability of the system at different scenarios. This will be examined through some experiments where the system is tested with different sampling rates and noises levels imposed to the system and/or the environments.

The used hybrid filter coupled with Hector SLAM is implemented and several experiments and tests are conducted in both simulation and real-world environments in different scenarios, including environments with dynamic/changing obstacles and at different levels of noise. The proposed system also compared against (a) PF only and (b) the hybrid only systems. The results of the experiments show that the hybrid system coupled with Hector SLAM improves the continuity and reliability of the positioning solutions, particularly in harsh scenarios where the number of particles and/or level of measurement noise may be low. Also, it seems to function with better robustness in the case of extreme noise in comparison with FP/FIR, where usually PF fails to function. Also, the tests show that the used hybrid filters (both with and without Hector SLAM) continue functioning and so are able to solve the kidnapped robot situations.

This paper is organised as follows: the next section is about the mathematical background of the hybrid filter, explaining the principles of the PF and FIR separately. Then the hybrid filter is explained in detail. Then the implementations of the used hybrid filter and the experiments at different scenarios are discussed. And finally, there is a conclusion and a forward-looking discussion on future work.

#### 2. System Design

In order to estimate the state of a system, one of the most widely used approaches is Bayesian filter framework, which uses the observed values and the corresponding confidence coefficients, i.e., the covariance matrix, to estimate the state of the system [14]. For many linear variables, the Kalman filter can accurately estimate the state using a Gaussian distribution [2]. However, for nonlinear variables, the KF may not be able to provide an accurate estimation and so an enhancement is needed. The EKF algorithm is used for the linear approximation of a nonlinear system using the Gaussian distribution [2]. In contrast, the Particle Filter estimates the state of the nonlinear (non-Gaussian) systems using a set of the particles distributed in the state space [14, 15]. So, the Particle Filter provides a numerical approximation for the nonlinear problem [16].

While the Particle Filter can approximate the nonlinear systems numerically, PF may fail due to a wide range of reasons [3, 8] and so resetting the failed PF is important to have a continuous state estimation. Resetting the failed PF also means generating new particles. To generate new particles, this paper uses Finite Impulse Response.

FIR has been applied by several positioning systems, particularly as an alternative to the filters with Infinite Impulse Response structures such as Kalman filter [13, 17–21]. FIR can improve the overall performance of such systems [18–20] as it provides with a robust response despite the availability of noise and/or model parameter uncertainty [18]. While the PF is basically an Infinite Impulse Response (IIR) filter, which can potentially provide a more accurate position estimation than FIR filters generally, it may fail to estimate the state if there is the case of sample impoverishment. To keep the balance hybrid filter (PF and FIR) may provide a good solution. The hybrid filter allows overcoming the issues and limitations of either the stand-alone versions of the PF and the FIR filters [13]. This paper uses the hybrid filter, combining the PF and the FIR, to provide a reliable, continuous, and robust position estimation. The hybrid filter acts like a PF as long as it can estimate the state. As soon as an extreme noise or any other circumstances that could fail the functionality of the PF, the FIR filter takes over and assures the continuity of the position estimation. However, this paper couples the hybrid filter with a Hector SLAM for even more continuity and autonomy of the whole system.

The hybrid filter uses the PF as its main filter in normal conditions, and as soon as any abnormality occurs it uses FIR to recover the whole system. The hybrid filter, integrating PF and FIR, was initially proposed by [13] and its general process is represented in Figure 1. As the flowchart (Figure 1) illustrates, having been initialised and calibrated, the PF starts functioning. As long as there is no failure diagnosed in the PF, the system relies solely on the PF. This means the relative position of the robot, which can be used for calculation of heading and absolute position, is estimated by the PF. This is mainly because the PF can provide the system, as a whole, with a better performance in comparison with the hybrid filter [13]. However, in the case of PF failure, the FIR takes over and estimates the state and error. FIR is practically an auxiliary or a backup filter that only acts as a plan B, i.e., when the PF fails to estimate the state. The estimation of the state and error from the FIR are fed into the ‘initialisation’ phase and based on these a secondary initial sample set is generated.