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In this paper, we propose a learning technique to solve parameter adjustment problems of Unscented Kalman Filter (UKF) for accurate localization. The parameter adjustment process of Kalman filters is very cumbersome for mobile robot developers and needs significant engineering cost and time. The parameters of UKF consist of three kinds of parameters as follows: I) the covariance matrix of input noise, II) the covariance matrix of measurement noise, III) Hyper-parameter of UKF. From a simulation result, it is shown that UKF localization performance critically depends on these Hyper-parameters. One of discriminative training methods is adopted to obtain the optimal parameters. The learning technique needs a highly accurate instrument for evaluating the filtering performance. A coordinate ascent algorithm is used as a training algorithm to optimize these parameters included in complicated functions. The technique promises to relieve mobile robot developers of the tedious task of adjusting several parameters by hand. Simulation and experimental results are presented. We demonstrate the effectiveness of the proposed learning method for localization, and the localization result using the proposed method outperforms the result of hand-tuning and the result of covariance learning.

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... For nonlinear systems an Unscented Kalman Filter (UKF) is proposed where unscented transformation (UT) is used to estimate uncertainties (Hartikainen et al. 2011). In Sakai and Kuroda (2010) a learning technique to help developers to adjust the UKF parameters (input-and measurement-noise covariance matrices and unscented transformation parameters) for an accurate localisation is used. In this work a statistical analysis of a lineralisation approach and UT is made to estimate covariances of the line segment nonlinear transformation. ...

... The appropriate operation of EKF depends on the correct assumption of uncertainties that influence state estimation process (Borges and Aldon 2003;Sakai and Kuroda 2010). In the following some directions and the validation of the proposed method for the estimation of observation uncertainty are given. ...

... where √ Z is obtained using Cholesky factorisation and c = α 2 (n + κ) is scaling parameter. The positive constants α, β and κ in the comparison are α = 0.01, β = 2 and κ = 1 (for more details see Sakai and Kuroda 2010;Hartikainen et al. 2011). ...

In this paper an extended Kalman filter (EKF) is used in the simultaneous localisation and mapping (SLAM) of a four-wheeled mobile robot in an indoor environment. The robot’s pose and environment map are estimated from incremental encoders and from laser-range-finder (LRF) sensor readings. The map of the environment consists of line segments, which are estimated from the LRF’s scans. A good state convergence of the EKF is obtained using the proposed methods for the input- and output-noise covariance matrices’ estimation. The output-noise covariance matrix, consisting of the observed-line-features’ covariances, is estimated from the LRF’s measurements using the least-squares method. The experimental results from the localisation and SLAM experiments in the indoor environment show the applicability of the proposed approach. The main paper contribution is the improvement of the SLAM algorithm convergence due to the noise covariance matrices’ estimation.

... 24 Deploying a UKF or related nonlinear Kalman filter (KF) in an embedded system 25 provides numerous advantages over traditional computational platforms in the context 26 of biological systems. The use of embedded hardware dedicated to the specific 27 application allows for tight control over task scheduling, minimizes feedback latency in 28 closed-loop applications, and avoids interruptions in communication that can occur with 29 more complex operating systems. Embedded systems can often be converted into a 30 wearable form. ...

... The sigma point weights W i can be adjusted not only to 386 include or excludex from among the sigma points but also to incorporate prior 387 knowledge of the higher-order moments of the state distribution [17,19]. Methods for 388 tuning the weights are described in [28][29][30][31][32]. We weighted the sigma points by the 389 reciprocal of their total number. ...

... We weighted the sigma points by the 389 reciprocal of their total number. Finally, the noise covariance matrices Q and R may 390 also undergo tuning, as addressed in [28,31,33]. We held Q and R constant and inflated 391 the element in Q corresponding to the uncertainty of the unknown input δ. ...

The unscented Kalman filter (UKF) is finding increased application in biological fields. While realizing a complex UKF system in a low-power embedded platform offers many potential benefits including wearability, it also poses significant design challenges. Here we present a method for optimizing a UKF system for realization in an embedded platform. The method seeks to minimize both computation time and error in UKF state reconstruction and forecasting. As a case study, we applied the method to a model for the rat sleep-wake regulatory system in which 432 variants of the UKF over six different variables are considered. The optimization method is divided into three stages that assess computation time, state forecast error, and state reconstruction error. We apply a cost function to variants that pass all three stages to identify a variant that computes 27 times faster than the reference variant and maintains required levels of state estimation and forecasting accuracy. We draw the following insights: 1) process noise provides leeway for simplifying the model and its integration in ways that speed computation time while maintaining state forecasting accuracy, 2) the assimilation of observed data during the UKF correction step provides leeway for simplifying the UKF structure in ways that speed computation time while maintaining state reconstruction accuracy, and 3) the optimization process can be accelerated by decoupling variables that directly impact the underlying model from variables that impact the UKF structure.
Author summary
Powerful statistical tools can be used to estimate unmeasured information in biological systems and predict the system’s future state. Translating these tools from a desktop computer to small, wearable or implantable platforms can unlock many benefits, but presents many design challenges, because tradeoffs between computational simplicity and system accuracy must be balanced. We present an approach to translating one such widely used statistical tool, the unscented Kalman filter, from a desktop computer to a miniature device. We demonstrate the approach with a case study centering on the neural circuits governing the mammalian sleep-wake cycle. By exploiting uncertainty in the biology being estimated and the corrective influence of biological measurements, we arrive at a design that is easily computable on the miniature device and maintains a high level of accuracy. We anticipate that our approach will aid others in designing such miniaturized systems for a broad range of applications.

... In [15], a new version of the UKF has also been proposed that involves tuning of three parameters (α, β, and k) instead of one; while, there are few theoretical guidelines available as how to tune up such parameters. Although numerous heuristics including model-based optimisation, gradient-free optimisation, and learning techniques have been proposed to find near optimal values for such scaling parameters [16][17][18][19]. ...

... Due to symmetry of the sigma points, i.e. δx (i) = − δx (i + n) , all oddordered terms in (17) sum to zero (see (18)) Then ...

This work, based on the standard unscented Kalman filter (UKF), proposes a modified UKF for highly non-linear stochastic systems, assuming that the associated probability distributions are normal. In the standard UKF with 2n + 1 sample points, the estimated mean and covariance match the true mean and covariance up to the third order, besides, there exists a scaling parameter that plays a crucial role in minimising the fourth-order errors. The proposed method consists of a computationally efficient formulation of the unscented transform that incorporates N - 1, N ≥ 2, constant parameters to scale 2n(N - 1) + 1 sample points such that the 2Nth order errors are minimised. The scaling parameters are obtained by solving a set of algebraic equations. Through rigorous analytical processes and numerical simulations, it is demonstrated that the new filter provides consistent estimates and the estimation error of the modified UKF is smaller than that of the standard UKF. With the help of a well-studied case, univariate non-stationary growth model, the authors evaluate the estimation performance of the new technique using 4n + 1 sample points over 100 independent runs.

... Several studies have investigated the selection of the proper scaling parameter of the UKF, taking both an online approach [25][26][27][28] and an offline approach [23,24]. However, the offline approach for the selection of the scaling parameter causes performance degradation when it is applied to the dynamic system. ...

In this paper, an adaptation method for adjusting the scaling parameters of an unscented Kalman filter (UKF) is proposed to improve the estimation performance of the filter in dynamic conditions. The proposed adaptation method is based on a sequential algorithm that selects the scaling parameter using the user-defined distribution of discrete sets to more effectively deal with the changing measurement distribution over time and avoid the additional process for training a filter model. The adaptation method employs regularized optimal transport (ROT), which compensates for the error of the predicted measurement with the current measurement values to select the proper scaling parameter. In addition, the Sinkhorn–Knopp algorithm is used to minimize the cost function of ROT due to its fast convergence rate, and the convergence of the proposed ROT-based adaptive adjustment method is also analyzed. According to the analysis results of Monte Carlo simulations, it is confirmed that the proposed algorithm shows better performance than the conventional algorithms in terms of the scaling parameter selection in the UKF.

... Here, we use the likelihood function as the criterion, which can be approximated by Gaussian distribution, expressed asp τ (z k |z k−1 ) N {ẑ k|k−1 , P z,k|k−1 } (36)where τ is designed to achieve the maximum likelihood [17]. ...

To perform surveillance of a hypersonic cruise vehicle (HCV), space-based infrared system is a reliable and feasible means, which has been putting on the schedule for providing positioning and tracking information of the high-altitude unmanned vehicles. In this paper, a space-based HCV tracking method based on infrared satellite constellation is proposed. The method contains three main parts: constellation coverage analysis, a bearing-only positioning algorithm, and a tracking algorithm. For target tracking, an adaptive scaling unscented Kalman filter (ASUKF) is applied for high estimation performance. Simulation results are presented to show the effectiveness of the method.

... Next, parameter α i is adjusted in the PUKF in order to ensure fulfilment of Eq. (14) for the same data set. Such an off-line approach has also been proposed in [26] in a different context. Algorithm 1 states the proposed PUKF. ...

... Next, parameter α is adjusted in the PUKF in order to ensure fulfilment of Eq. (14) for the same data set. Such an offline approach has been also proposed in [33] in a different context. ...

Accurate state estimation of large-scale lithium-ion battery packs is necessary for the advanced control of batteries, which could potentially increase their lifetime through e.g. reconfiguration. To tackle this problem, an enhanced reduced-order electrochemical model is used here. This model allows considering a wider operating range and thermal coupling between cells, the latter turning out to be significant. The resulting nonlinear model is exploited for state estimation through unscented Kalman filters (UKF). A sensor network composed of one sensor node per battery cell is deployed. Each sensor node is equipped with a local UKF, which uses available local measurements together with additional information coming from neighboring sensor nodes. Such state estimation scheme gives rise to a partition-based unscented Kalman filter (PUKF). The method is validated on data from a detailed simulator for a battery pack comprised of six cells, with reconfiguration capabilities. The results show that the distributed approach outperforms the centralized one in terms of computation time at the expense of a very low increase of mean-square estimation error.

... In this case, the scaling parameter is a function of the state-space dimension only. In [Sakai and Kuroda, 2010], a technique for the off-line scaling parameter selection using a training procedure was proposed. Contrary to the previous procedure, adaptive techniques for the parameter selection has been of interest in past few years [Duník et al., 2010, Turner and Rasmussen, 2012. ...

The paper deals with analysis and illustration of the impact of the σ-point set rotation on the approximation quality of the unscented transformation and the estimation performance of the unscented Kalman filter. It is shown that the covariance matrix factor, used in σ-point computation, can be multiplied by an arbitrary rotation matrix which moves the σ-points along the surface of a hyper-ellipsoid related to the covariance matrix. The rotation matrix can be thus considered as another user-defined parameter (in addition to the scaling parameter) and the unscented Kalman filter with adaptive selection of both user-defined parameters is proposed. The impact of fixed or adaptively selected parameters on the performance of the unscented Kalman filter is illustrated by a numerical study.

... Regarding the choice of the tuning parameter, a couple of results have already been proposed in the literature. The authors in [64] provide an off-line way of computing it by maximizing the likelihood function with a training set of data. In [22], an on-line method of computing the tuning parameter by means of maximizing a Gaussian approximation of the likelihood function is proposed. ...

In this paper, we propose a systematization of the (discrete-time) Unscented Kalman Filter (UKF) theory. We gather all available UKF variants in the literature, present corrections to theoretical inconsistencies, and provide a tool for the construction of new UKF's in a consistent way. This systematization is done, mainly, by revisiting the concepts of Sigma-Representation, Unscented Transformation (UT), Scaled Unscented Transformation (SUT), UKF, and Square-Root Unscented Kalman Filter (SRUKF). Inconsistencies are related to 1) matching the order of the transformed covariance and cross-covariance matrices of both the UT and the SUT; 2) multiple UKF definitions; 3) issue with some reduced sets of sigma points described in the literature; 4) the conservativeness of the SUT; 5) the scaling effect of the SUT on both its transformed covariance and cross-covariance matrices; and 6) possibly ill-conditioned results in SRUKF's. With the proposed systematization, the symmetric sets of sigma points in the literature are formally justified, and we are able to provide new consistent variations for UKF's, such as the Scaled SRUKF's and the UKF's composed by the minimum number of sigma points. Furthermore, our proposed SRUKF has improved computational properties when compared to state-of-the-art methods.

... Regarding the choice of the tuning parameter, a couple of results have already been proposed in the literature. The authors in [60] provide an off-line way of computing it by maximizing the likelihood function with a training set of data. In [19], an on-line method of computing the tuning parameter by means of maximizing a Gaussian approximation of the likelihood function is proposed. ...

The unscented Kalman filter (UKF) is finding increased application in biological fields. While realizing a complex UKF system in a low-power embedded platform offers many potential benefits including wearability, it also poses significant design challenges. Here we present a method for optimizing a UKF system for realization in an embedded platform. The method seeks to minimize both computation time and error in UKF state reconstruction and forecasting. As a case study, we applied the method to a model for the rat sleep-wake regulatory system in which 432 variants of the UKF over six different variables are considered. The optimization method is divided into three stages that assess computation time, state forecast error, and state reconstruction error. We apply a cost function to variants that pass all three stages to identify a variant that computes 27 times faster than the reference variant and maintains required levels of state estimation and forecasting accuracy. We draw the following insights: 1) process noise provides leeway for simplifying the model and its integration in ways that speed computation time while maintaining state forecasting accuracy, 2) the assimilation of observed data during the UKF correction step provides leeway for simplifying the UKF structure in ways that speed computation time while maintaining state reconstruction accuracy, and 3) the optimization process can be accelerated by decoupling variables that directly impact the underlying model from variables that impact the UKF structure.

A Dongfanghong-X804 tractor was used as a platform and an automatic steering controller based on double closed-loop control was developed to realize autonomous navigation of agricultural machinery. The make-up of the whole steering system and the working principle are presented: using an angle sensor KMA199 to measure steering angle and a gyroscope integrated in ADIS16300 to measure angular rate. In order to realize servo control of steering system, electro-hydraulic valves, shift solenoid valve and relief valve were used as actuators for automatic steering. Then the mathematical model of steering system was derived and the hardware circuit realization was described with CAN network design. According to characteristic of the system nonlinear, the transfer function between the proportional valve input current and steering angular can be seen as a second-order inertial part and a latency part, and a double closed-loop control algorithm for steering system was designed, using Matlab System Identification Toolbox to estimate transfer function parameters. Finally, tests were conducted to examine the steering system, including a calibration test for ADIS 16300, which indicated the high accuracy of ADIS16300 angular velocity integral values, with the average error of 0.53#x000b0;; and a test of the steering control system was carried out to verify the performance of double closed-loop control algorithm, which showed that the steering control system solved the control overshoot well and the average error is 0.4°, with 1.3 s tracking time; the average angular rate tracking error is 1.25#x000b0;/s, with 0.2 s tracking time. © 2015, Chinese Society of Agricultural Engineering. All right reserved.

This paper discusses choice for scaling parameter of the unscented transformation. By analyzing and comparing some scaling parameter selection methods, the scaling parameter is selected as an optimization objective. Differential Evolution (DE) algorithm is applied to the Unscented Kalman Filter (UKF), the optimized scaling parameter leads to the minimum error at each time interval. An adaptive UKF based on DE is proposed. The experiments show that the accuracy of UKF is significantly improved by the adaptive strategy which not only to avoid random divergence with the constant parameter but also suitable for any form of UKF without the constraints of the number of parameters.

The paper deals with state estimation of nonlinear discrete time stochastic dynamic systems with a focus on derivative-free filters. Design parameters of the filters are treated and an efficient way for their adaptation is proposed. The efficiency is based on observing a degree of nonlinearity of the nonlinear state and measurement functions at the working point by means of a non-Gaussianity measure. The adaptation is executed only if the nonlinearity is severe and the design parameter adaptation may bring a significant improvement of the estimate quality. Otherwise the adaptation is switched off to keep computational complexity of the filter low. The developed algorithm is illustrated using a numerical example of bearings-only target tracking.

The unscented Kalman filter (UKF) is one of the most used approximate solutions to the problem of nonlinear filtering. It is relatively easy to implement, and it produces better state estimates than the extended Kalman filter, especially when the nonlinearities of the dynamic system are significant. The quality of the estimates yielded by the UKF is dependent on the tuning of the parameters that govern the unscented transform (UT). To the user, manually tuning the UT means picking proper values for three scalar variables with almost no theoretical guidance. To help relieve the user from this burden, we approach the tuning of the UT parameters as an optimization problem and propose a tuning algorithm based on ideas of the bootstrap particle filter. The proposed algorithm is analyzed and numerically tested against both a set of popular nonlinear filters and a recently published model-based tuning algorithm.

The paper deals with an analysis and illustration of the impact of the δ-point set rotation on the accuracy of the derivative-free approximation techniques and on the performance of filters utilizing these approximations. Namely, approximations based on the unscented transform and the Stirling interpolation are considered. It is shown that the covariance matrix factor used in the δ-point set computation can be multiplied by an arbitrary rotation matrix which rotates the δ-points along the surface of a hyper-ellipsoid defined by the covariance matrix. The rotation matrix can be thus considered as another user-defined parameter (in addition to the scaling parameter) greatly affecting the filter performance and therefore it needs to be carefully chosen. Choice of the appropriate δ-point set rotation is discussed and its impact on the filter performance is illustrated using a bearing-only tracking example.

The paper deals with analysis and illustration of the impact of the cr-point set rotation on the approximation quality of the unscented transformation and the estimation performance of the unscented Kalman filter. It is shown that the covariance matrix factor, used in cr-point computation, can be multiplied by an arbitrary rotation matrix which moves the σ-points along the surface of a hyper-ellipsoid related to the covariance matrix. The rotation matrix can be thus considered as another user-defined parameter (in addition to the scaling parameter) and the unscented Kalman filter with adaptive selection of both user-defined parameters is proposed. The impact of fixed or adaptively selected parameters on the performance of the unscented Kalman filter is illustrated by a numerical study.

In order to study the application of polynomial Kalman filter(PKF) in the vehicle location, and to analyze state estimation accuracy of PKF affected by the order of polynomial and evaluate the performance of the PKF, in this paper, by adopting polynomial fitting method in system model of kalman filter to model nonlinear system, three PKFs were established and applied for vehicle localizaiton experiment with mulitiple sensors fusion. Firstly, previous researches on PKF in tracking accuracy affected by the order of polynomial and in performance evaluation were introduced. Then, zero-order, first-order and second-order PKF were establish using corresponding order of polynomial to fit the longitudinal velocity and heading of encoder dead-reckon model. Experiment was conducted on Pioneer3-AT moble robot platform with Encoder and AHRS used as sensor data input, measurement of RTK-GPS was as reference trajectory. Also, the theorectical error and actual error of the PKF were compared to evaluate the performance of the three PKFs. The experiment result showed that the actual error of the three PKFs were within the theorectical error bounds in more than 68% filtering time which indicated normal status of the filters. The localization accuracy of zero-order PKF were increased by 63% and 73% in X, Y axis respectively compared with encoder dead-reckon method. Localization accuracy of first-order PKF was better than zero-order, and second-order was better than zero-order but worse than first-order, which showed that polynomial fitting the longitudinal velocity and heading of encoder dead-reckon model using higher order could not contribute to even better localization accuracy. This paper provides references for the construction and performance evaluation of PKF, as well as its practical implementation on vehicle localization.

The unscented Kalman filter (UKF) is a widely used nonlinear Gaussian filter. It has the potential to deal with highly nonlinear dynamic systems, while displaying computational cost of the same order of magnitude as that of the extended Kalman filter (EKF). The quality of the estimates produced by the UKF is dependent on the tuning of both the parameters that govern the unscented transform (UT) and the two noise covariance matrices of the system model. In this paper, the tuning of the UKF is framed as an optimization problem. The tuning problem is solved by a new stochastic search algorithm and by a standard model-based optimizer. The filters tuned with the proposed algorithm and with the standard model-based optimizer are numerically tested against other nonlinear Gaussian filters, including two UKF tuned with state-of-the-art tuning strategies. One of these strategies relies on online tuning and the other on offline tuning.

This technical note deals with the unscented Kalman filter for state estimation of nonlinear stochastic dynamic systems with a special focus on the scaling parameter of the filter. Its standard choice is analyzed
and its impact on the estimation quality is discussed. On the basis of the analysis, a novel method for adaptive setting of the parameter in the unscented Kalman filter is proposed. The results are illustrated in a numerical example.

A new spacecraft attitude estimation approach based on the unscented filter is derived. For nonlinear systems the unscented filter uses a carefully selected set of sample points to map the probability distribution more accurately than the linearization of the standard extended Kalman filter, leading to faster convergence from inaccurate initial conditions in attitude estimation problems. The filter formulation is based on standard attitude-vector measurements using a gyro-based model for attitude propagation. The global attitude parameterization is given by a quaternion, whereas a generalized three-dimensional attitude representation is used to define the local attitude error. A multiplicative quaternion-error approach is derived from the local attitude error, which guarantees that quaternion normalization is maintained in the filter. Simulation results indicate that the unscented filter is more robust than the extended Kalman filter under realistic initial attitude-error conditions.

A new spacecraft attitude estimation approach based on the Unscented Filter is derived. For nonlin-ear systems the Unscented Filter uses a carefully se-lected set of sample points to more accurately map the probability distribution than the linearization of the standard Extended Kalman Filter, leading to faster convergence from inaccurate initial conditions in at-titude estimation problems. The filter formulation is based on standard attitude-vector measurements us-ing a gyro-based model for attitude propagation. The global attitude parameterization is given by a quater-nion, while a generalized three-dimensional attitude representation is used to define the local attitude error. A multiplicative quaternion-error approach is derived from the local attitude error, which guarantees that quaternion normalization is maintained in the filter. Simulation results indicate that the Unscented Filter is more robust than the Extended Kalman Filter under realistic initial attitude-error conditions.

Localizing a vehicle consists in estimat-ing its state by merging data from proprioceptive sen-sors (inertial measurement unit, gyrometer, odome-ter, etc.) and exteroceptive sensors (GPS sensor). A well known solution in state estimation is provided by the Kalman filter. But, due to the presence of non-linearities, the Kalman estimator is applicable only through some alternatives among which the Extended Kalman filter (EKF), the Unscented Kalman Filter (UKF) and the Divided Differences of 1 st and 2 nd order (DD1 and DD2). We have compared these filters using the same experimental data. The results obtained aim to rank these approaches by their performances in terms of accuracy, confidence and consistency.

This paper considers the use of non-parametric system models for sequential state estimation. In particular, motion and observation models are learned from training examples using Gaussian process (GP) regression. The state estimator is an unscented Kalman filter (UKF). The resulting GP-UKF algorithm has a number of advantages over standard (parametric) UKFs. These include the ability to estimate the state of arbitrary nonlinear systems, improved tracking quality compared to a parametric UKF, and graceful degradation with increased model uncertainty. These advantages stem from the fact that GPs consider both the noise in the system and the uncertainty in the model. If an approximate parametric model is available, it can be incorporated into the GP; resulting in further performance improvements. In experiments, we show how the GP-UKF algorithm can be applied to the problem of tracking an autonomous micro-blimp.

Particle filters have been applied with great success to various state estimation problems in robotics. However, particle filters often require extensive parameter tweaking in order to work well in practice. This is based on two observations. First, particle filters typically rely on independence assumptions such as "the beams in a laser scan are independent given the robot's location in a map". Second, even when the noise parameters of the dynamical system are perfectly known, the sample-based approximation can result in poor filter performance. In this paper we introduce CRF-filters, a novel variant of particle filtering for sequential state estimation. CRF-filters are based on conditional random fields, which are discriminative models that can handle arbitrary dependencies between observations. We show how to learn the parameters of CRF-filters based on labeled training data. Experiments using a robot equipped with a laser range-finder demonstrate that our technique is able to learn parameters of the robot's motion and sensor models that result in good localization performance, without the need of additional parameter tweaking.

This paper describes an implementation of a mobile robot system for autonomous navigation in outdoor concurred walkways. The task was to navigate through nonmodified pedestrian paths with people and bicycles passing by. The robot has multiple redundant sensors, which include wheel encoders, an inertial measurement unit, a differential global positioning system, and four laser scanner sensors. All the computation was done on a single laptop computer. A previously constructed map containing waypoints and landmarks for position correction is given to the robot. The robot system's perception, road extraction, and motion planning are detailed. The system was used and tested in a 1-km autonomous robot navigation challenge held in the City of Tsukuba, Japan, named “Tsukuba Challenge 2007.” The proposed approach proved to be robust for outdoor navigation in cluttered and crowded walkways, first on campus paths and then running the challenge course multiple times between trials and the challenge final. The paper reports experimental results and overall performance of the system. Finally the lessons learned are discussed. The main contribution of this work is the report of a system integration approach for autonomous outdoor navigation and its evaluation. © 2009 Wiley Periodicals, Inc.

The challenge in the DARPA Learning Applied to Ground Robots (LAGR) project is to autonomously navigate a small robot using stereo vision as the main sensor. During this project, we demonstrated a complete autonomous system for off-road navigation in unstructured environments, using stereo vision as the main sensor. The system is very robust—we can typically give it a goal position several hundred meters away and expect it to get there. In this paper we describe the main components that comprise the system, including stereo processing, obstacle and free space interpretation, long-range perception, online terrain traversability learning, visual odometry, map registration, planning, and control. At the end of 3 years, the system we developed outperformed all nine other teams in final blind tests over previously unseen terrain. © 2008 Wiley Periodicals, Inc.

Localizing a vehicle consists in estimating its state by merging data from proprioceptive sensors (inertial measurement unit, gyrometer, odometer, etc.) and exteroceptive sensors (GPS sensor). A well known solution in state estimation is provided by the Kalman filter. But, due to the presence of nonlinearities, the Kalman estimator is applicable only through some alternatives among which the Extended Kalman filter (EKF), the Unscented Kalman Filter (UKF) and the Divided Differences of 1(st) and 2(nd) order (DD1 and DD2). We have compared these filters using the same experimental data. The results obtained are aimed at ranking these approaches by their performances in terms of accuracy and consistency.

Rigid body orientation can be estimated in a "sourceless manner" through the use of small three degree of freedom sensor modules containing orthogonally mounted triads of micromachined angular rate sensors, accelerometers, and magnetometers. With proper filter design, drift errors can be eliminated. However, variations in the direction of the local magnetic field reference vector can cause errors in the estimated orientation. The experimental work described in this paper attempts to quantify these errors with an eye toward the development of corrective algorithms. To determine the types and magnitudes of errors that can be expected, three different types of inertial/magnetic sensor modules were subjected to controlled changes in the direction and magnitude of the local magnetic field. The amount of magnetic variation caused by several common objects was also measured in order to gain insight into the magnitude of errors that can be expected during operation in a typical environment. The experiments indicate that variations in the direction of the local magnetic field lead to errors only in azimuth estimation when using inertial/magnetic sensor modules. In a common room environment, errors due to local variations caused by objects such as electrical heaters, CRT monitors, and metal furniture can be expected to be no more than 16 degrees. In most cases these errors can be avoided by maintaining a separation of approximately two feet from the source of interference.

The Rao-Blackwellized particle filter (RBPF) and FastSLAM have two important limitations, which are the derivation of the Jacobian matrices and the linear approximations of nonlinear functions. These can make the filter inconsistent. Another challenge is to reduce the number of particles while maintaining the estimation accuracy. This paper provides a robust new algorithm based on the scaled unscented transformation called unscented FastSLAM (UFastSLAM). It overcomes the important drawbacks of the previous frameworks by directly using nonlinear relations. This approach improves the filter consistency and state estimation accuracy, and requires smaller number of particles than the FastSLAM approach. Simulation results in large-scale environments and experimental results with a benchmark dataset are presented, demonstrating the superiority of the UFastSLAM algorithm.

Probabilistic inference is the problem of estimating the hidden states of a system in an optimal and consistent fashion given a set of noisy or incomplete observations. The optimal solution to this problem is given by the recursive Bayesian estimation algorithm which recursively updates the posterior density of the system state as new observations arrive online.

In this paper, we propose a new particle lter based on sequential importance sampling. The algorithm uses a bank of unscented lters to obtain the importance proposal distribution. This proposal has two very ice" properties. Firstly, it makes ecient use of the latest available information and, secondly, it can have heavy tails. As a result, we nd that the algorithm outperforms standard particle ltering and other nonlinear ltering methods very substantially. This experimental nding is in agreement with the theoretical convergence proof for the algorithm. The algorithm also includes resampling and (possibly) Markov chain Monte Carlo (MCMC) steps. 1 Introduction Filtering is the problem of estimating the states (parameters or hidden variables) of a system as a set of observations becomes available on-line. This problem is of paramount importance in many elds of science, engineering and nance. To solve it, one begins by modelling the evolution of the system and the noi...

In this paper, we propose a set of techniques for accurate and practical Simultaneous Localization And Mapping (SLAM) in dynamic outdoor environments. The techniques are categorized into Landmark estimation and Unscented particle sampling. Landmark estimation features stable feature detection and data management for estimating landmarks accurately, robustly, and at a low-calculation cost. The stable feature detection removes dynamic objects and sensor noise with scan subtraction, detects feature points sparsely and evenly, and sets data association parameters with landmark density. The data management calculates landmark existence probability and spurious landmarks are removed, utilizes landmark exclusivity for data association, and predicts importance weights using the observation range. Unscented particle sampling is based on Unscented Transformation for accurate SLAM. Simulation results of SLAM using our landmark estimation and experimental results of our SLAM in dynamic outdoor environments are presented and discussed. The results show that our landmark estimation decrease SLAM calculation time and maximum position error by 80% compared to conventional landmark estimation, and position estimation of SLAM with Unscented particle sampling ismore accurate than FastSLAM2.0 in dynamic outdoor environments.

Abstract-This paper introduces a kinematic model of a deep-sea mining vehicle in presence of sliding parameters. The model describes both the noises features of sliding parameters and the deep-sea condition features. To handle sliding parameters noises, a recursive algorithm to minimize difference between the filter-computed and the actual innovation covariance is adopted, which is a novel integrated navigation method based on unscented Kalman filters (UKF). Taking into account the influence of measurement data delay, UKF fuses the localization information of long base line (LBL) sonar localization system and dead-reckoning (DR) to perform the state estimation. Simulation results show that the adaptive UKF has better localization estimation than a normal UKF for a deep-sea tracked vehicle (DTV).

In this paper, we propose an efficient solution to 6 degrees of freedom (6DOF) localization using unscented Kalman filter for planetary rovers. The solution is a technique augmented the unscented Kalman filter for accurate 6DOF localization, named augmented unscented Kalman filter (AUKF). The AUKF is designed to deal with problems which occur on other planets: wheel slip, visual odometry error, and gyro drift. To solve the problems, the AUKF estimates the slippage ratio in an augmented state vector, the accuracy of the visual odometry with the number of inliers among feature points, and sensor usefulness with gyrodometry model. Experimental results of rover runs over rough terrain are presented, the effectiveness of the AUKF and its each component is shown.

In this paper, we propose stereo vision based visual odometry with an effective feature sampling technique for untextured outdoor environment. In order to extract feature points in untextured condition, we divide an image into some sections and affect suitable processes for each section. This approach can also prevent concentration of feature points, and the influence with a moving object can be reduced. Robust motion estimation is attained using the framework of 3-point algorithm and RANdom SAmple Consensus (RANSAC). Moreover, the accumulation error is reduced by keyframe adjustment. We present and evaluate experimental results for our system in outdoor environment. Proposed visual odometry system can localize the robot's position within 4% error in untextured outdoor environment.

Kalman filters are a workhorse of robotics and are routinely used in state-estimation problems. However, their performance critically depends on a large number of modeling parameters which can be very difficult to obtain, and are often set via significant manual tweaking and at a great cost of engineering time. In this paper, we propose a method for automatically learning the noise parameters of a Kalman filter. We also demonstrate on a commercial wheeled rover that our Kalman filter's learned noise covariance parameters—obtained quickly and fully automatically—significantly outperform an earlier, carefully and laboriously hand-designed one.

In this paper, we propose an efficient solution to 6-d.o.f. localization using an unscented Kalman filter (UKF) for planetary rovers. The solution is a technique using a modified UKF for accurate planetary rover localization. The technique is able to cope with problems that occur frequently on other planetary surfaces: wheel slip, pulsive noise of visual odometry (VO) and gyro drift. To solve these problems, the technique estimates a slippage ratio with the UKF, the accuracy of the VO with the number of inliers of feature points and sensor usefulness with a gyrodometry model. Experimental results of rover runs over rough terrain are presented and discussed; the effectiveness of proposed method and its components is shown.

In this paper we propose a novel method for nonlinear, non-Gaussian, on-line estimation. The algorithm consists of a particle filter that uses an unscented Kalman filter (UKF) to generate the importance proposal distribution. The UKF allows the particle filter to incorporate the latest observations into a prior updating routine. In addition, the UKF generates proposal distributions that match the true posterior more closely and also has the capability of generating heavier tailed distributions than the well known extended Kalman filter. As a result, the convergence results predict that the new filter should outperform standard particle filters, extended Kalman filters and unscented Kalman filters. A few experiments confirm this prediction.

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- E Van Niekerk
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- G Alessandrini
- B Bradski
- S Davies
- A Ettinger
- A Kaehler
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