Optimizing neuro-fuzzy modules for data fusion of vehicular navigation systems using temporal cross-validation

The last two decades have shown an increasing trend in the use of positioning and navigation technologies in land vehicles. Most of the present navigation systems incorporate global positioning system (GPS) and inertial navigation system (INS), which are integrated using Kalman filtering (KF) to provide reliable positioning information. Due to several inadequacies related to KF-based INS/GPS integration, artificial intelligence (AI) methods have been recently suggested to replace KF. Various neural network and neuro-fuzzy methods for INS/GPS integration were introduced. However, these methods provided relatively poor positioning accuracy during long GPS outages. Moreover, the internal system parameters had to be tuned over time of the navigation mission to reach the desired positioning accuracy. In order to overcome these limitations, this study optimizes the AI-based INS/GPS integration schemes utilizing adaptive neuro-fuzzy inference system (ANFIS) by implementing, a temporal window-based cross-validation approach during the update procedure. The ANFIS-based system considers a non-overlap moving window instead of the commonly used sliding window approach. The proposed system is tested using differential GPS and navigational grade INS field test data obtained from a land vehicle experiment. The results showed that the proposed system is a reliable modeless system and platform independent module that requires no priori knowledge of the navigation equipment utilized. In addition, significant accuracy improvement was achieved during long GPS outages.     

Adaptive tuning of a Kalman filter via fuzzy logic for an intelligent AUV navigation system

This paper describes the implementation of an intelligent navigation system, based on the integrated use of the global positioning system (GPS) and several inertial navigation system (INS) sensors, for autonomous underwater vehicle (AUV) applications. A simple Kalman filter (SKF) and an extended Kalman filter (EKF) are proposed to be used subsequently to fuse the data from the INS sensors and to integrate them with the GPS data. The paper highlights the use of fuzzy logic techniques to the adaptation of the initial statistical assumption of both the SKF and EKF caused by possible changes in sensor noise characteristics. This adaptive mechanism is considered to be necessary as the SKF and EKF can only maintain their stability and performance when the algorithms contain the true sensor noise characteristics. In addition, fault detection and signal recovery algorithms during the fusion process to enhance the reliability of the navigation systems are also discussed herein. The proposed algorithms are implemented to real experimental data obtained from a series of AUV trials conducted by running the low-cost Hammerhead AUV, developed by the University of Plymouth and Cranfield University.     

Adaptive fuzzy neuro-observer applied to low cost INS/GPS

A combined MEMS Inertial Navigation System (INS) with GPS is used to provide position and velocity data of land vehicles. Data fusion of INS and GPS measurements are commonly achieved through a conventional Extended Kalman filter (EKF). Considering the required accurate model of system together with perfect knowledge of predefined error models, the performance of the EKF is decreased due to unmodeled nonlinearities and unknown bias uncertainties of MEMS inertial sensors. Universal knowledge based approximators comprising of neural networks and fuzzy logic methods are capable of approximating the nonlinearities and the uncertainties of practical systems. First, in this paper, a new fuzzy neural network (FNN) function approximator is used to model unknown nonlinear systems. Second, the process of design and real-time implementation of an adaptive fuzzy neuro-observer (AFNO) in integrated low-cost INS/GPS positioning systems is proposed. To assess the long time performance of the proposed AFNO method, wide range tests of a real INS/GPS with a car vehicle have been performed. The unbiased estimation results of the AFNO show the superiority of the proposed method compared with the classic EKF and the adaptive neuro-observer (ANO) including a pure artificial neural network (ANN) function approximator.     

Real-Time Implementation of GPS Aided Low-Cost Strapdown Inertial Navigation System

This work details the study, development, and experimental implementation of GPS aided strapdown inertial navigation system (INS) using commercial off-the-shelf low-cost inertial measurement unit (IMU). The data provided by the inertial navigation mechanization is fused with GPS measurements using loosely-coupled linear Kalman filter implemented with the aid of MPC555 microcontroller. The accuracy of the estimation when utilizing a low-cost inertial navigation system (INS) is limited by the accuracy of the sensors used and the mathematical modeling of INS and the aiding sensors’ errors. Therefore, the IMU data is fused with the GPS data to increase the accuracy of the integrated GPS/IMU system. The equations required for the local geographic frame mechanization are derived. The direction cosine matrix approach is selected to compute orientation angles and the unified mathematical framework is chosen for position/velocity algorithm computations. This selection resulted in significant reduction in mechanization errors. It is shown that the constructed GPS/IMU system is successfully implemented with an accurate and reliable performance.     

Enhancing positioning accuracy of GPS/INS system during GPS outages utilizing artificial neural network

Integrated global positioning system and inertial navigation system (GPS/INS) have been extensively employed for navigation purposes. However, low-grade GPS/INS systems generate erroneous navigation solutions in the absence of GPS signals and drift very fast. We propose in this paper a novel method to integrate a low-grade GPS/INS with an artificial neural network (ANN) structure. Our method is based on updating the INS in a Kalman filter structure using ANN during GPS outages. This study focuses on the design, implementation and integration of such an ANN employing an optimum multilayer perceptron (MLP) structure with relevant number of layers/perceptrons and an appropriate learning. As a result, a land test is conducted with the proposed ANN + GPS/INS system and we here provide the system performance with the land trials.     

Inertially Aided Visual Odometry for Miniature Air Vehicles in GPS-denied Environments

Unmanned miniature air vehicles (MAVs) have recently become a focus of much research, due to their potential utility in a number of information gathering applications. MAVs currently carry inertial sensor packages that allow them to perform basic flight maneuvers reliably in a completely autonomous manner. However, MAV navigation requires knowledge of location that is currently available only through GPS sensors, which depend on an external infrastructure and are thus prone to reliability issues. Vision-based methods such as Visual Odometry (VO) have been developed that are capable of estimating MAV pose purely from vision, and thus have the potential to provide an autonomous alternative to GPS for MAV navigation. Because VO estimates pose by combining relative pose estimates, constraining relative pose error is the key element of any Visual Odometry system. In this paper, we present a system that fuses measurements from an MAV inertial navigation system (INS) with a novel VO framework based on direct image registration. We use the inertial sensors in the measurement step of the Extended Kalman Filter to determine the direction of gravity, and hence provide error-bounded measurements of certain portions of the aircraft pose. Because of the relative nature of VO measurements, we use VO in the EKF prediction step. To allow VO to be used as a prediction, we develop a novel linear approximation to the direct image registration procedure that allows us to propagate the covariance matrix at each time step. We present offline results obtained from our pose estimation system using actual MAV flight data. We show that fusion of VO and INS measurements greatly improves the accuracy of pose estimation and reduces the drift compared to unaided VO during medium-length (tens of seconds) periods of GPS dropout.     

An intelligent navigator for seamless INS/GPS integrated land vehicle navigation applications

The Kalman filter (KF) has been implemented as the primary integration scheme of the global positioning system (GPS) and inertial navigation systems (INS) for many land vehicle navigation and positioning applications. However, it has been reported that KF-based techniques have certain limitations, which reflect on the position error accumulation during GPS signal outages. Therefore, this article exploits the idea of incorporating artificial neural networks to develop an alternative INS/GPS integration scheme, the intelligent navigator, for next generation land vehicle navigation and positioning applications. Real land vehicle test results demonstrated the capability of using stored navigation knowledge to provide real-time reliable positioning information for stand-alone INS-based navigation for up to 20 min with errors less than 16 m (as compared to 2.6 km in the case of the KF). For relatively short GPS outages, the KF was superior to the intelligent navigator for up to 30 s outages. In contrast, the intelligent navigator was superior to the KF when the length of GPS outages was extended to 90 s. The average improvement of the intelligent navigator reached 60% in the latter scenario. The results presented in this article strongly indicate the potential of including the intelligent navigator as the core algorithm for INS/GPS integrated land vehicle navigation systems.     

基于MLP神经网络改进组合导航算法

为解决GPS信号失锁条件下,GPS/INS(inertial navigation system)组合导航系统解算精度降低甚至发散的问题,提出采用多层感知机神经网络(multilayer perceptron neural networks,MLPNN)来辅助组合导航系统.在GPS信号有效时对神经网络进行训练,在GPS...     

无人飞行器的北斗卫星组合导航算法研究

北斗卫星导航系统是中国自行研制的全球卫星定位与通信系统,为促进北斗卫星系统在导航方面的运用,降低我国导航方面对GPS的依靠,从而进一步降低成本,提高无人飞行器的导航精度,本文对捷联式惯性导航系统（INS）和北斗定位导航系统的组合导航算法进行了研究,通过惯性导航系统的原理和导航解算的过程,选择惯导系统和北斗系统的速度、位置差值作为观测量,建立组合导航系统的状态方程和观测方程,利用无迹卡尔曼滤波得到惯导系统状态量和惯性敏感器的误差,对惯导系统进行误差补偿,从而实现无人飞行器的高精度导航控制.并使用Matlab进行仿真,得出高精度的模拟输出轨迹.     

The stability analysis of the adaptive fading extended Kalman filter using the innovation covariance

The well-known conventional Kalman filter gives the optimal solution but to do so, it requires an accurate system model and exact stochastic information. However, in a number of practical situations, the system model and the stochastic information are incomplete. The Kalman filter with incomplete information may be degraded or even diverged. To solve this problem, a new adaptive fading filter using a forgetting factor has recently been proposed by Kim and co-authors. This paper analyzes the stability of the adaptive fading extended Kalman filter (AFEKF), which is a nonlinear filter form of the adaptive fading filter. The stability analysis of the AFEKF is based on the analysis result of Reif and co-authors for the EKF. From the analysis results, this paper shows the upper bounded condition of the error covariance for the filter stability and the bounded value of the estimation error. Keywords: Adaptive Kalman filter, forgetting factor, nonlinear filter, stability analysis. Recommended by Editorial Board member Huanshui Zhang under the direction of Editor Young Il Lee. Kwang-Hoon Kim received the Ph.D. degree in the School of Electrical Engineering and Computer Science at Seoul National University in 2006. His research interests include Kalman Filtering, GNSS/INS integration system, and GNSS signal processing algorithm. Gyu-In Jee received the Ph.D. degree in Systems Engineering from Case Western Reserve University in 1989. His research interests include Indoor GPS positioning, Software GPS receiver, GPS/Galileo baseband FPGA design, and IEEE 802.16e based wireless location system. Chan-Gook Park received the Ph.D. degree in Control and Instrumenta-tion Engineering from Seoul National University in 1993. His research interests include INS/GPS integration system, inertial sensor calibration, navigation and control for micro aerial vehicles, and estimation theory. Jang-Gyu Lee received the Ph.D. degree from the University of Pittsburgh in 1977. He is currently a Professor at the School of Electrical Engineering and Computer Science at Seoul National University. His research interests include micro inertial sensors, inertial navigation systems, GPS, and filtering theory.     

Constant-round zero-knowledge proofs of knowledge with strict polynomial-time extractors for NP

Barak and Lindell showed that there exist constant-round zero-knowledge arguments of knowledge with strict polynomial-time extractors.This leaves the open problem of whether it is possible to obtain an analogous result regarding constant-round zero-knowledge proofs of knowledge for NP.This paper focuses on this problem and gives a positive answer by presenting a construction of constant-round zero-knowledge proofs of knowledge with strict polynomial-time extractors for NP.     

GPS/INS组合导航数据同步时标的计算方法研究

以GPS/INS组合导航系统为应用背景,针对GPS数据和惯性数据中时间同步的问题,提出了基于横摆角速度匹配、实时计算GPS延迟的方法,用于修正惯性数据与GPS的同步时标,提高了组合导航和车辆状态检测的精度。实验结果表明,计算得到的GPS延迟能够起到较好的修正效果。该方法仅利用导航系统数据,无需汽车内部参数和采集信号,具有自主性,有利于应用于外置检测和导航系统。     

路网辅助的车载INS/GPS组合导航方法

针对车载INS/GPS组合导航系统在GPS无效时精度迅速下降的问题,提出了将车辆行驶的路网约束作为虚拟传感器,采用多传感器数据融合的方式,与INS和GPS组成INS/GPS/路网组合导航系统.当GPS失效时,使用路网辅助INS.仿真结果表明,在GPS无效时间段,该方法能有效减小系统定位误差.     

基于cubature Kalman filter的INS/GPS组合导航滤波算法

INS/GPS组合导航系统的本质是非线性的,为改善非线性下INS/GPS组合导航精度,提出将一种新的非线性滤波cubature Kalman filter（CKF）应用于INS/GPS组合导航中.为此,建立了基于平台失准角的非线性状态模型和以速度误差及位置误差描述的观测模型,分析了CKF滤波原理,设计了INS/GPS组合滤波器,对组合导航非线性模型进行了仿真.仿真结果显示,相对于扩展卡尔曼滤波（EKF）,CKF降低了姿态、位置和速度估计误差,CKF更适合于处理组合导航的状态估计问题.     

Intelligently tuned wavelet parameters for GPS/INS error estimation

This paper presents a new algorithm for de-noising global positioning system (GPS) and inertial navigation system (INS) data and estimates the INS error using wavelet multi-resolution analysis algorithm (WMRA)-based genetic algorithm (GA) with a well-designed structure appropriate for practical and real time implementations because of its very short training time and elevated accuracy. Different techniques have been implemented to de-noise and estimate the INS and GPS errors. Wavelet de-noising is one of th...     

Principles of Fusion of Inertial Navigation and Dynamic Vision

The possibility of fusion of navigation data obtained by two separate navigation systems (strap‐down inertial one and dynamic vision based one) is considered in this paper. The attention is primarily focused on principles of validation of separate estimates before their use in a combined algorithm. The inertial navigation system (INS) based on sensors of medium level quality has been analyzed on one side, while a visual navigation method is based on the analysis of a sequence of images of ground landmarks produced by an on‐board TV camera. The accuracy of INS estimations is being improved continuously by optimal estimation of a flying object's angular orientation while the visual navigation system offers discrete corrections during the intervals of presence of landmarks inside the camera's field of view. The concept is illustrated by dynamic simulation of a realistic flight scenario. © 2004 Wiley Periodicals, Inc.     

Merits and limitations of using fuzzy inference system for temporal integration of INS/GPS in vehicular navigation

Most of the present vehicular navigation systems rely on global positioning system (GPS) combined with inertial navigation system (INS) for reliable determination of the vehicle position and heading. Integrating both systems provide several advantages and eliminate their individual shortcomings. Kalman filter (KF) has been widely used to fuse data from both systems. However, KF-based integration techniques suffer from several limitations related to its immunity to noise, observability and the necessity of accurate stochastic models of sensor random errors. This article investigates the potential use of adaptive neuro-fuzzy inference system (ANFIS) for temporal integration of INS/GPS in vehicular navigation. An ANFIS-based module named “P–δP” is designed, developed, implemented and tested for fusing INS and GPS position information. The fusion process aims at providing continuous correction of INS position to prevent its long-term growth using GPS position updates. In addition, it provides reliable prediction of the vehicle position during GPS outages. The P–δP module was examined using real navigation system data compromising an Ashtech Z12 GPS receiver and a Honeywell LRF-III INS. The proposed module proved to be successful as a modeless and platform independent module that does not require a priori knowledge of the navigation equipment utilized. Limitations of the ANFIS module are also discussed.     

Bearing-only visual SLAM for small unmanned aerial vehicles in GPS-denied environments

This paper presents a hierarchical simultaneous localization and mapping(SLAM) system for a small unmanned aerial vehicle(UAV) using the output of an inertial measurement unit(IMU) and the bearing-only observations from an onboard monocular camera.A homography based approach is used to calculate the motion of the vehicle in 6 degrees of freedom by image feature match.This visual measurement is fused with the inertial outputs by an indirect extended Kalman filter(EKF) for attitude and velocity estimation.Then,another EKF is employed to estimate the position of the vehicle and the locations of the features in the map.Both simulations and experiments are carried out to test the performance of the proposed system.The result of the comparison with the referential global positioning system/inertial navigation system(GPS/INS) navigation indicates that the proposed SLAM can provide reliable and stable state estimation for small UAVs in GPS-denied environments.     

Adaptive Fuzzy Prediction of Low-Cost Inertial-Based Positioning Errors

Kalman filter (KF) is the most commonly used estimation technique for integrating signals from short-term high performance systems, like inertial navigation systems (INSs), with reference systems exhibiting long-term stability, like the global positioning system (GPS). However, KF only works well under appropriately predefined linear dynamic error models and input data that fit this model. The latter condition is rather difficult to be fulfilled by a low-cost inertial measurement unit (IMU) utilizing microelectromechanical system (MEMS) sensors due to the significance of their long- and short-term errors that are mixed with the motion dynamics. As a result, if the reference GPS signals are absent or the Kalman filter is working for a long time in prediction mode, the corresponding state estimate will quickly drift with time causing a dramatic degradation in the overall accuracy of the integrated system. An auxiliary fuzzy-based model for predicting the KF positioning error states during GPS signal outages is presented in this paper. The initial parameters of this model is developed through an offline fuzzy orthogonal-least-squares (OLS) training while the adaptive neuro-fuzzy inference system (ANFIS) is implemented for online adaptation of these initial parameters. Performance of the proposed model has been experimentally verified using low-cost inertial data collected in a land vehicle navigation test and by simulating a number of GPS signal outages. The test results indicate that the proposed fuzzy-based model can efficiently provide corrections to the standalone IMU predicted navigation states particularly position.     

Optimization of Intelligent Approach for Low-Cost INS/GPS Navigation System

Due to the inherent highly nonlinear vehicle state error dynamics obtained from low-cost inertial navigation system (INS) and Global Positioning System (GPS) along with the unknown statistical properties of these sensors, the optimality/accuracy of the classical Kalman filter for sensor fusion is not guaranteed. Therefore, in this paper, low-cost INS/GPS measurement integration is optimized based on different artificial intelligence (AI) techniques: Neural Networks (NN) and Adaptive Neuro-Fuzzy Inference System (ANFIS) architectures. The proposed approaches are aimed at achieving high-accuracy vehicle state estimates. The architectures utilize overlapping windows for delayed input signals. Both the NN approaches and the ANFIS approaches are used once with overlapping position windows as the input and once with overlapping position and velocity windows as the input. Experimental tests are conducted to evaluate the performance of the proposed AI approaches. The achieved accuracy is presented and discussed. The study finds that using ANFIS, with both position and velocity as input, provides the best estimates of position and velocity in the navigation system. Therefore, the dynamic input delayed ANFIS approach is further analyzed at the end of the paper. The effect of the input window size on the accuracy of state estimation is also discussed.