Novel hybrid of strong tracking Kalman filter and wavelet neural network for GPS/INS during GPS outages

Aiming to improve positioning precision of the GPS/INS integrated navigation system during GPS outages, a novel model combined with strong tracking Kalman filter (STKF) and wavelet neural network (WNN) algorithms for INS errors compensation is proposed and tested. STKF is used to estimate INS errors as a replacement of Kalman filter (KF), and WNN is applied to establish a highly accurate model based on STKF when GPS works well and to predict INS errors during GPS outages. Performance of the proposed model has been experimentally verified using GPS and INS data collected in a land vehicle navigation test. The comparison results indicate that the proposed model combined with STKF/WNN algorithms can effectively provide high accurate corrections to the standalone INS during GPS outages.     

Robust cubature Kalman filter for GNSS/INS with missing observations and colored measurement noise

In order to improve the accuracy of GNSS/INS working in GNSS-denied environment, a robust cubature Kalman filter (RCKF) is developed by considering colored measurement noise and missing observations. First, an improved cubature Kalman filter (CKF) is derived by considering colored measurement noise, where the time-differencing approach is applied to yield new observations. Then, after analyzing the disadvantages of existing methods, the measurement augment in processing colored noise is translated into processing the uncertainties of CKF, and new sigma point update framework is utilized to account for the bounded model uncertainties. By reusing the diffused sigma points and approximation residual in the prediction stage of CKF, the RCKF is developed and its error performance is analyzed theoretically. Results of numerical experiment and field test reveal that RCKF is more robust than CKF and extended Kalman filter (EKF), and compared with EKF, the heading error of land vehicle is reduced by about 72.4%.     

A derivative UKF for tightly coupled INS/GPS integrated navigation

The tightly coupled INS/GPS integration introduces nonlinearity to the measurement equation of the Kalman filter due to the use of raw GPS pseudorange measurements. The extended Kalman filter (EKF) is a typical method to address the nonlinearity by linearizing the pseudorange measurements. However, the linearization may cause large modeling error or even degraded navigation solution. To solve this problem, this paper constructs a nonlinear measurement equation by including the second-order term in the Taylor series of the pseudorange measurements. Nevertheless, when using the unscented Kalman filter (UKF) to the INS/GPS integration for navigation estimation, it causes a great amount of redundant computation in the prediction process due to the linear feature of system state equation, especially for the case with system state vector in much higher dimension than measurement vector. To overcome this drawback in computational burden, this paper further develops a derivative UKF based on the constructed nonlinear measurement equation. The derivative UKF adopts the concise form of the original Kalman filter (KF) to the prediction process and employs the unscented transformation technique to the update process. Theoretical analysis and simulation results demonstrate that the derivative UKF can achieve higher accuracy with a much smaller computational cost in comparison with the traditional UKF.     

Vision coupled GPS/INS scheme for helicopter navigation

This paper presents a framework for a GPS/INS/vision-based helicopter navigation system. The conventional GPS/INS algorithm has weak points such as GPS blockage and jamming, while the helicopter is a speedy and highly dynamic vehicle that may easily lose a GPS signal. A vision sensor is not affected by signal jamming, and the navigation error of such a system does not accumulate. Hence, a GPS/INS/vision-aided navigation scheme was implemented to provide the robust localization suitable for helicopter operations in various environments. The core algorithm is the vision-based SLAM (simultaneous localization and mapping) technique. Flight tests were performed to verify the SLAM-aided vision navigation algorithm. During the tests, it was confirmed that the developed system is sufficiently robust under GPS blockage conditions. The system design, software algorithm, and flight test results are described in this paper.     

Outdoor position estimation based on a combination system of GPS-INS by using UPF

This paper proposes a technique that global positioning system(GPS)combines inertial navigation system(INS)by using unscented particle filter(UPF)to estimate the exact outdoor position.This system can make up for the weak point on position estimation by the merits of GPS and INS.In general,extended Kalman filter(EKF)has been widely used in order to combine GPS with INS.However,UPF can get the position more accurately and correctly than EKF when it is applied to real-system included non-linear,irregular distribution errors.In this paper,the accuracy of UPF is proved through the simulation experiment,using the virtual-data needed for the test.     

Application of unscented R–T–S smoothing on INS/GPS integration system post processing for airborne earth observation

The Kalman Rauch–Tung–Striebel (R–T–S) smoother has been applied to fuse data from the inertial navigation system (INS) and global positioning system (GPS) for post processing, but its optimality heavily depends on linearity. For the case of in-flight startup, the INS/GPS integration is a nonlinear system with large initial attitude errors, the linear estimation approaches become inapplicable. In this paper, the Unscented R–T–S Smoother (URTSS) is utilized to deal with the nonlinear problem in the INS/GPS integration post processing, and the performance of this algorithm is compared with a similar smoother based on Extended Kalman Filter (ERTSS) through the Monto Carlo simulations. Furthermore, an INS/GPS integration system is implemented using URTSS and applied to airborne digital camera imaging. Through numerical simulation and flight test, it is shown that URTSS has obvious accuracy advantage over ERTSS in attitude estimation.     

Maximum correntropy square-root cubature Kalman filter with application to SINS/GPS integrated systems

For a nonlinear system, the cubature Kalman filter (CKF) and its square-root version are useful methods to solve the state estimation problems, and both can obtain good performance in Gaussian noises. However, their performances often degrade significantly in the face of non-Gaussian noises, particularly when the measurements are contaminated by some heavy-tailed impulsive noises. By utilizing the maximum correntropy criterion (MCC) to improve the robust performance instead of traditional minimum mean square error (MMSE) criterion, a new square-root nonlinear filter is proposed in this study, named as the maximum correntropy square-root cubature Kalman filter (MCSCKF). The new filter not only retains the advantage of square-root cubature Kalman filter (SCKF), but also exhibits robust performance against heavy-tailed non-Gaussian noises. A judgment condition that avoids numerical problem is also given. The results of two illustrative examples, especially the SINS/GPS integrated systems, demonstrate the desirable performance of the proposed filter.     

Robust proportional-integral Kalman filter design using a convex optimization method

This paper proposes a design approach to the robust proportional-integral Kalman filter for stochastic linear systems under convex bounded parametric uncertainty, in which the filter has a proportional loop and an integral loop of the estimation error, providing a guaranteed minimum bound on the estimation error variance for all admissible uncertainties. The integral action is believed to increase steady-state estimation accuracy, improving robustness against uncertainties such as disturbances and modeling errors. In this study, the minimization problem of the upper bound of estimation error variance is converted into a convex optimization problem subject to linear matrix inequalities, and the proportional and the integral Kalman gains are optimally chosen by solving the problem. The estimation performance of the proposed filter is demonstrated through numerical examples and shows robustness against uncertainties, addressing the guaranteed performance in the mean square error sense.     

GPS/INS组合导航系统的研究

讨论了飞机惯性导航系统(INS)与全球卫星导航系统(GPS)的利与弊以及卡尔曼滤波方法在组合定位中的应用情况,进一步提出了基于神经网络数据融合方法的GPS/INS组合导航系统.系统神经网络结构采用单隐层的三层神经网络,输入输出神经元数目是4个,基于256个训练样本由经验公式求得隐层神经元数目为8个,同时还建立了惯导系统的数学模型和数据融合的数学模型.给出了利用MATLAB编制的神经网络训练程序并对这一神经网络进行了训练和仿真.实验表明,组合导航系统经度误差可达9m,纬度误差可达8m,与单独GPS定位和INS定位相比精度得到了提高.     

GPS/SINS组合导航系统中卡尔曼滤波器的应用

在现代生活中,GPS/SINS组合导航系统得到了越来越多的应用.文中介绍了卡尔曼滤波器在处理多个导航系统传来的数据中的应用,并且能够自动校正系统,以达到更高精度的要求.     

Comparison of Linearized Kalman Filter and Extended Kalman Filter for Satellite Motion States Estimation

The performance of the conventional Kalman filter depends on process and measurement noise statistics given by the system model and measurements.The conventional Kalman filter is usually used for a linear system,but it should not be used for estimating the state of a nonlinear system such as a satellite motion because it is difficult to obtain the desired estimation results.The linearized Kalman filtering approach and the extended Kalman filtering approach have been proposed for a general nonlinear system.The equations of satellite motion are described.The satellite motion states are estimated,and the relevant estimation errors are calculated through the estimation algorithms of the both above mentioned approaches implemented in Matlab are estimated.The performances of the extended Kalman filter and the linearized Kalman filter are compared.The simulation results show that the extended Kalman filter is much better than the linearized Kalman filter at the aspect of estimation effect.     

Design of H(infinity) robust fault detection filter for linear uncertain time-delay systems

In this paper, the robust fault detection filter design problem for linear time-delay systems with both unknown inputs and parameter uncertainties is studied. Using a multiobjective optimization technique, a new performance index is introduced, which takes into account the robustness of the fault detection filter against disturbances and sensitivity to faults simultaneously. The reference residual model is then designed based on this performance index to formulate the robust fault detection filter design problem as an H(infinity) model-matching problem. By applying robust H(infinity) optimization control technique, the existence condition of the robust fault detection filter for linear time-delay systems with both unknown inputs and parameter uncertainties is presented in terms of linear matrix inequality formulation, independently of time delay. In order to detect the fault, an adaptive threshold which depends on the inputs is finally determined. An illustrative design example is used to demonstrate the validity of the proposed approach.     

动基座传递对准信息延时的分析与仿真

讨论了动基座弹载传递对准过程中的信息延时问题。参考信息从主惯导到子惯导传递过程中的延时会影响卡尔曼滤波器的收敛速度和精度,从而影响对准性能。为了改善由信息延时引起的对准性能下降的问题,提出了一种简单有效的方法,通过拉格朗日插值运算对滞后数据进行外推得到当前时刻的参考信息,从而基本消除信息延时,改善滤波性能。通过设计传递对准仿真环境进行了仿真,结果表明所设计的信息延时补偿算法是有效的。     

Improving ultrasonic-based seamless navigation for indoor mobile robots utilizing EKF and LS-SVM

The ultrasonic positioning system is able to provide centimeter-level location information. However, the signal of the system is easy to be disturbed and the outages of the positioning system appear. Inertial measuring units (IMUs) is a self-contained device and can provide long-term navigation information independently, but it has the drawback of error drift. In order to obtain accurate and continuous location information indoors for indoor mobile robots, this work proposed a seamless integrated navigation utilizing extended Kalman filter (EKF) and Least Squares Support Vector Machine (LS-SVM). In this mode, the EKF estimates the position and the velocity of the robot while the signals of ultrasonic positioning system are available. Meanwhile, the compensation model is trained by LS-SVM with corresponding filter states. Once the signals of ultrasonic positioning system are outages, the model is able to correct inertial navigation system (INS) solution as filter does. A prototype of the system has been worked in a real scenario. The results show that the performance of EKF is robust, and the prediction of LS-SVM is able to work as EKF does during the outages.     

An adaptive three-stage extended Kalman filter for nonlinear discrete-time system in presence of unknown inputs

Considering the performances of conventional Kalman filter may seriously degrade when it suffers stochastic faults and unknown input, which is very common in engineering problems, a new type of adaptive three-stage extended Kalman filter (AThSEKF) is proposed to solve state and fault estimation in nonlinear discrete-time system under these conditions. The three-stage UV transformation and adaptive forgetting factor are introduced for derivation, and by comparing with the adaptive augmented state extended Kalman filter, it is proven to be uniformly asymptotically stable. Furthermore, the adaptive three-stage extended Kalman filter is applied to a two-dimensional radar tracking scenario to illustrate the effect, and the performance is compared with that of conventional three stage extended Kalman filter (ThSEKF) and the adaptive two-stage extended Kalman filter (ATEKF). The results show that the adaptive three-stage extended Kalman filter is more effective than these two filters when facing the nonlinear discrete-time systems with information of unknown inputs not perfectly known.     

Robust cubature Kalman filter based on variational Bayesian and transformed posterior sigma points error

An improved robust cubature Kalman filter (RCKF) based on variational Bayesian (VB) and transformed posterior sigma points error is proposed in this paper, which not only retains the robustness of RCKF, but also exhibits adaptivity in the presence of time-varying noise. First, a novel sigma-point update framework with uncertainties reduction is developed by employing the transformed posterior sigma points error. Then the VB is used to estimate the time-varying measurement noise, where the state-dependent noise is addressed in the iteratively parameter estimation. The new filter not only reduces the uncertainty on sigma points generation but also accelerates the convergence of VB-based noise estimation. The effectiveness of the proposed filter is verified on integrated navigation, and numerical simulations demonstrate that VB-RCKF outperforms VB-CKF and RCKF.     

INS/SFGPS PPP紧组合系统动态补偿滤波算法

惯性/卫星组合导航系统结合精密单点定位技术可有效提高导航定位精度。但精密单点定位技术一般需采用双频接收机,成本较高;同时该系统中采用载波相位作为部分或全部观测量,极容易受到周跳的影响而导致精度下降和系统不稳定。针对上述问题,设计了一种惯性/卫星精密定位紧组合导航系统以及基于动态周跳补偿的鲁棒滤波算法。该系统采用低成本的单频接收机(SFGPS),以精密单点定位技术(PPP)处理过的伪距和载波相位作为观测信息,与惯性导航系统(INS)等效观测量进行紧组合,建立了相应紧组合观测模型并引入周跳作为信息融合滤波状态模型中的状态量,以滤波器信息构建周跳检测统计量并对周跳幅值进行识别和估计,实时补偿观测量以提高观测信息精度,同时以前述周跳估计的结果对状态模型中周跳状态量部分滤波参数进行实时调节。上述方法通过动态补偿周跳误差提高导航精度,通过滤波器参数自适应调节提高滤波稳定性。仿真结果验证了该系统模型及算法的有效性。     

A robust H∞ learning approach to blind separation of slowly time-varying mixture of acoustic electromechanical signals

Although many techniques have been developed for solving the blind source separation (BSS) problem, some issues related to robustness of BSS algorithms are yet to be addressed. Most of the BSS algorithms developed assume the mixing system to be stationary. In this paper, we present a robust approach based on H_∞ learning to address the instantaneous BSS problem in a non-stationary mixing environment. The motivation behind applying H_∞ filter is that these are robust to errors arising out of model uncertainties, parameter variations and additive noise. Acoustic electromechanical signals have been considered for simulation purpose. Simulation results demonstrate that the H_∞ filter performs superior to Kalman filter and VS-NGA algorithm. To ensure practicability of the proposed approach, the H_∞ learning algorithm has been implemented and tested on Texas Instrument's TMS320C6713 floating point DSP platform successfully.     

交互多模型在车辆组合定位系统中的应用（英文）

为解决扩展卡尔曼滤波器(extended Kalman filter,EKF)在车辆组合定位系统中因车辆加减速、转弯(以下简称机动)而存在的精度低、稳定性差等问题,设计了一种将交互多模型(interacting multiple model,IMM)算法与非线性卡尔曼滤波器相融合的自适应滤波算法。该算法使用三种状态空间模型来描述车辆的运动模式,采用多个非线性滤波器对每个模型并行滤波,通过模型匹配似然函数对滤波结果进行加权融合,最终得到系统的定位信息。该方法具备非线性系统滤波器优点,克服了单一模型滤波算法对机动目标定位效果差的缺点。利用该方法和EKF算法分别对GPS/INS/DR车辆组合定位系统中进行了仿真实验,结果表明,该算法的滤波定位精度明显优于目前组合定位系统中所用的EKF滤波器,大幅提高了组合定位系统的稳定性和定位精度。     

Identifying Bearing Rotor-Dynamic Coefficients Using an Extended Kalman Filter

An extended Kalman filter is developed to estimate the linearized direct and indirect stiffness and damping force coefficients for bearings in rotor-dynamic applications from noisy measurements of the shaft displacement in response to imbalance and impact excitation. The bearing properties are modeled as stochastic random variables using a Gauss-Markov model. Noise terms are introduced into the system model to account for all of the estimation error, including modeling errors and uncertainties and the propagation of measurement errors into the parameter estimates. The system model contains two user-defined parameters that can be tuned to improve the filter's performance; these parameters correspond to the covariance of the system and measurement noise variables. The filter is also strongly influenced by the initial values of the states and the error covariance matrix. The filter is demonstrated using numerically simulated data for a rotor-bearing system with two identical bearings, which reduces the number of unknown linear dynamic coefficients to eight. The filter estimates the direct damping coefficients and all four stiffness coefficients correlated well with actual values, whereas the estimates the cross-coupled damping coefficients were the least accurate.