Time-varying Noise Statistics Research Articles

Localization of underground pipe jacking machinery: A reliable, real-time and robust INS/OD solution

Accurate positioning is important for guidance control in pipeline construction, but traditional approaches fail in GPS-denied environments. This paper addresses the underground localization problem for the pipe jacking machine by presenting an Inertial Navigation System (INS)/ODometry (OD) scheme. It is a loosely coupled navigation system that combines an INS and an OD to provide reliable, real-time, and robust location estimation in an enclosed and restricted space. The combination is achieved by a multi-sensor fusion algorithm to avoid the divergence of standalone INS. Compared with the traditional localization technologies, the advantage of the INS/OD scheme is that there is no performance degradation or service failure despite severe blockage of the thick soil layer due to the selection of dead reckoning-based sensors. Moreover, an Unbiased Finite Impulse Response (UFIR) filter serves as the fusion mechanism to improve the robustness against a prior knowledge of noise, considering unknown and time-varying noise statistics in practice. The INS/OD scheme is verified through a numerical simulation and employed on-site in a real underground sewage pipeline construction project. Despite the construction site being more than 10 meters deep underground, the INS/OD scheme continues to perform reliably and robustly in real-time, significantly benefiting the engineering guidance enterprise.

Modified Strong Tracking Slide Window Variational Adaptive Kalman Filter With Unknown Noise Statistics

The filter performance will be degraded in the measurements with time-varying and unknown noise statistics. To combat the above challenges, a modified strong tracking slide window variational adaptive Kalman filter algorithm is proposed in this article. Firstly, the multiple fading factors are integrated into the proposed algorithm to adjust the error covariance. Next, an improved adaptive slide window method is designed for variational Bayesian Kalman filtering by adaptively adjusting the slide window size and correcting the previous state according to the later state, which improves the estimation accuracy and computational efficiency. Finally, the inverse Wishart distribution is considered for modeling process and measurement noise, and the state vector, as well as noise statistics, are inferred via the variational Bayesian technique without prior noise covariance information. Simulation results demonstrate that the proposed filter algorithm is more robust than existing filters in counteracting measurement and process noise uncertainties.

The MAPWE-Boosted AEKF with Recursive-Against-Iteration Noise Statistic for Feature-Based SLAM Algorithm

The unknown noise statistic might degrade the Filter performance or even lead to filter divergence. Accordingly, to enhance the classical EKF to approximate the recursive process and measurement noise statistic, based on Maximum A Posteriori creation and Weighted Exponent (WE) as the divergence suppression method, abbreviated as MAPWE, an adaptive EKF is proposed through this paper. Moreover, the existence of simplification during estimating noise statistics under MAP creation might also degrade its quality. Thus, the suboptimal MAP solution was also estimated based on Weighted Exponent. Indeed, the time-varying noise statistic under this process seems strongly accurate. But the complexity of the measurement covariance might also diverge from its positive definite characteristic. Thus, aiming to prevent this condition, the additional divergence suppression method was also involved in correcting the error state covariance in the smoothing step. This improvement is then used as SLAM algorithm for a mobile robot. Comparing to the conventional methods, it is better in term of RMSE for the estimated path and estimated map.

A Scheme of MEMS-SINS Initial Alignment Aided by Laser Spot Perception System for the Boom-Type Roadheader

The initial alignment is one of the difficult problems of the strapdown inertial navigation system based on the microelectromechanical systems (MEMS-SINS) applied to the navigation of boom-type roadheader under a coalmine. To overcome the complex environment of the underground coalmine and the large noise of the MEMS gyroscope, the laser spot perception system (LSPS) was developed to provide the heading information of the roadheader to aid the initial alignment of the MEMS-SINS. During the process of initial alignment, the differential equation of heading error is derived, the heading error is extended as a state variable, and a nonlinear initial alignment model aided by heading error is built up. To cope with the time-varying noise statistics of MEMS-SINS in the working face of the coal mine roadway, a simplified strong tracking Unscented Kalman Filter (SST-UKF) algorithm is proposed by combining covariance matching technology with UKF. In the calculation of the measurement prediction covariance and the cross covariance, the fading factor is introduced, respectively, to avoid the contradiction between the residuals before and after the introduction; according to the characteristics of the observation equation being a linear equation, it proves that the state prediction covariance matrix change does not affect the observation measurement and uses unscented transform (UT) only once in the state estimation and variance prediction; thus, the computational burden of the algorithm is reduced and the real-time performance is improved. The simulation and onboard experiment results show that the proposed scheme can achieve horizontal alignment within 40 s and convergence azimuth misalignment angle to 0.9° within 450 s, which fully meets the requirements of MEMS-SINS initial alignment for underground coalmine roadheader.

Motion State Estimation of Target Vehicle under Unknown Time-Varying Noises Based on Improved Square-Root Cubature Kalman Filter.

In the advanced driver assistance system (ADAS), millimeter-wave radar is an important sensor to estimate the motion state of the target-vehicle. In this paper, the estimation of target-vehicle motion state includes two parts: the tracking of the target-vehicle and the identification of the target-vehicle motion state. In the unknown time-varying noise, non-linear target-vehicle tracking faces the problem of low precision. Based on the square-root cubature Kalman filter (SRCKF), the Sage–Husa noise statistic estimator and the fading memory exponential weighting method are combined to derive a time-varying noise statistic estimator for non-linear systems. A method of classifying the motion state of the target vehicle based on the time window is proposed by analyzing the transfer mechanism of the motion state of the target vehicle. The results of the vehicle test show that: (1) Compared with the Sage–Husa extended Kalman filtering (SH-EKF) and SRCKF algorithms, the maximum increase in filtering accuracy of longitudinal distance using the improved square-root cubature Kalman filter (ISRCKF) algorithm is 45.53% and 59.15%, respectively, and the maximum increase in filtering the accuracy of longitudinal speed using the ISRCKF algorithm is 23.53% and 29.09%, respectively. (2) The classification and recognition results of the target-vehicle motion state are consistent with the target-vehicle motion state.

Adaptive Unscented Kalman Filter Based Estimation and Filtering for Dynamic Positioning with Model Uncertainties

A novel adaptive unscented Kalman filter (AUKF) is presented and applied to ship dynamic positioning (DP) system with model uncertainties of time-varying noise statistics, model mismatch and slow varying drift forces. The adaptive algorithm is proposed to simultaneously online adapt the process and measurement noise covariance by adopting the main principle of covariance matching. The measurement noise covariance is adapted based on residual covariance matching method, and then the process noise covariance is adjusted by using adaptive scaling factor. Simulation comparisons among the proposed RQAUKF, the strong tracking UKF (RSTAUKF) and the standard UKF show that the proposed RQAUKF can effectively improve the estimation accuracy and stability, and can assist the controller to obtain better control performance.

Application of improved fifth-degree cubature Kalman filter in the nonlinear initial alignment of strapdown inertial navigation system.

This paper addresses the state estimation of the nonlinear initial alignment of the strapdown inertial navigation system (SINS), which mainly focuses on the initial alignment on the swaying base and under the in-motion condition with the measurement uncertainties. In order to achieve a higher alignment precision, stronger numerical stability, and lower computational cost for the initial alignment of SINS on the swaying base, a new discrete large azimuth misalignment error model of SINS is established, and an improved fifth-degree cubature Kalman filter (5th-CKF) algorithm is proposed, which combines the 5th-CKF and a simplified dimensionality reduction filtering algorithm. The 5th-CKF is introduced to solve the nonlinear filtering problem, a simplified dimensionality reduction algorithm is derived to reduce the large calculation values of 5th-CKF. Furthermore, under the Bayesian framework, a novel filtering approach named the fifth-degree variational Bayesian (VB) adaptive cubature Kalman filter is deduced for the in-motion alignment with a large azimuth misalignment angle and unknown and time-varying measurement noise statistics, which combines the iterative VB approach and 5th-CKF. The 5th-CKF is exploited to handle the nonlinear initial alignment model, and the VB approach is utilized to iteratively estimate the sufficient statistics of the measurement noise. Mathematical simulation, turntable, and vehicle experiments are performed to demonstrate the effectiveness and the superiority of the proposed approaches.

Prior-Information-Based Finite-Frequency $\text{H}_{\infty}$ Control for Active Double Pantograph in High-Speed Railway

The fluctuation in contact force between the pantograph and the catenary severely affects the current collection quality of electric multiple units in high-speed railway. In particular, when double pantographs operate simultaneously, the contact force on trailing pantograph (TP) fluctuates violently due to the passage of leading pantograph (LP). To address this problem, a prior-information-based finite-frequency $\text{H}_{\infty}$ controller, incorporating an adaptive estimator, is proposed for the active control of double pantographs in this paper. As the prior information is of great importance, the frequency characteristics of contact force are analyzed based on power spectrum density and utilized in calculating the control gain matrix. The finite-frequency control is employed to decrease the contact force fluctuation within the concerned frequency range with limited control force. Considering the unknown and time-varying noise statistic, an adaptive cubature Kalman filter is presented to estimate the states of pantographs. The effectiveness and robustness of the proposed control strategy are evaluated with implementations in a nonlinear double-pantograph-catenary system model under different operational conditions. The results show that, for both LP and TP, the control strategy can adequately decrease the contact force fluctuation. Particularly, it has a good capability to reject parameter perturbations and external disturbance.

Time-Varying Noise Statistic Estimator Based Adaptive Simplex Cubature Kalman Filter

To address the problem that filtering accuracy is reduced with the inaccurate time-varying noise statistic in conventional cubature Kalman filter, a noise statistic estimator based adaptive simplex cubature Kalman filter is put forward in this paper. First, the simplex cubature rule is adopted to approximate the intractable nonlinear Gaussian weighted integral in the filter. Secondly, a suboptimal unbiased constant noise statistic estimator is derived based on the maximum a posteriori estimation criterion. For the time-varying noise, the above estimator is modified using an exponential weighted attenuation method to realize the oblivion of stale data which results in a fading memory estimator, which has the ability to estimate the time-varying noise statistic to revise the filter online. The simulation results indicate that the proposed filter can achieve higher accuracy than conventional filters with inaccurate noise statistic.

Improved adaptive unscented Kalman filter algorithm for target tracking

An adaptive unscented Kalman filter (AUKF) algorithm is proposed to solve the problem that the statistical characteristics of the process noise are unknown in the target tracking, which leads to filter divergence or low filtering precision. The improved Sage-Husa estimator is used to estimate the statistical characteristics of the unknown process noise in the filtering process, and to judge and suppress the filtering divergence, which effectively improves the numerical stability of the filtering and reduces the error of the state estimation. The simulation results show that the improved AUKF algorithm not only keeps convergence but also improves the accuracy and stability of the target tracking under the condition of unknown time-varying process noise statistic, compared with the standard UKF algorithm.

Noise-aware localization algorithms for wireless sensor networks based on multidimensional scaling and adaptive Kalman filtering

The range-based MDS-MAP (multidimensional scaling-MAP) localization algorithm has been widely applied to the estimation of node position in wireless sensor networks (WSNs). However, the range for the MDS-MAP is often influenced by measurement noise so that there is an error, which will greatly reduce the positioning precision of MDS-MAP. Although the current improved MDS-MAP algorithms, such as MDS-MAP(P) and MDS-MAP(P,R), and the algorithms based on the theory of the rigid graph can obtain higher accuracy compared to the MDS-MAP, they are not suitable for the occasion where there are large errors in distance measurements between most nodes, namely the non-rigid graph. Therefore, Kalman filter (KF) is employed to refine the node coordinates from the MDS-MAP on this occasion, but it requires obtaining accurate noise statistics in advance and cannot adapt to the change of noise statistics. In the real WSN localization scenario with unknown or time-varying noise statistics, the inaccurate statistical parameter of noise will seriously weaken the refinement effect of KF on the MDS-MAP, especially under large noise-statistic bias. In this work, we propose two types of two-stage noise-aware localization algorithms for WSNs based on MDS-MAP and adaptive KF (AKF), i.e. an existing adaptive extended KF and an innovative adaptive unscented KF. The positioning accuracy and the time complexity of the AKF for the proposed algorithms are better than those of the spring relaxation for the rigid-graph based localization and the least square optimization for the improved MDS-MAP in the noisy environment. The results of extensive simulations show that compared with the present algorithms for refining the MDS-MAP, our proposed algorithms can always achieve higher positioning accuracy and lower time complexity regardless of the placement way of node, the shape of network topology, the communication radius of node, the node degree of network, and the deviation of noise statistics.

A Blind Adaptive SOR/JGS Iterative Kalman MUD Algorithm for Multiple Access Communication System

Based on the fast stable convergence characteristics of successive over relaxation (SOR) iterative and Jacobi Gauss- Seidel (JGS) iterative, a blind adaptive SOR/JGS iterative Kalman multi-user detection (MUD) algorithm (SJK) is proposed for multiple access communication system as direct sequence spread spectrum code division multiple access (DS- CDMA) system with multi-path fading channel. The proposed combination of blind adaptive Kalman filtering theory, SOR and JGS iterative method can adaptively control the selection of relaxation parameters and damping parameter, and then effectively deal the problem as time-varying noise statistics estimation. Compared with traditional standard Kalman filter (SKF), fading Kalman filter (FKF) and robust adaptive Kalman filter (RAKF) algorithm, the proposed algorithm can effectively estimate unknown noise statistics characteristics on-line while conducting state filtering, totally track the time-varying channel, minimize the detection error diffusion, and thus effectively reduce multiple access interference (MAI). Simulation results show that the SJK algorithm is of better detection accuracy, convergence ability, dynamic tracking capability, and lower bit error rate (BER) performance.  Index Terms communication system is asynchronous or synchronous. When the distance between interference user and base station is closer than expected user, the received power of interference user would be much larger than expected user, then the correlation between spreading sequence and interference user would surely be much larger than that between spreading sequence and expected user. This would always cause a significant increase of MAI component in the traditional Multi-User Detection (MUD) receiver, and it may easily cause that the expected user signal is submerged by interference user signal. Namely, the Bit Error Rate (BER) of MUD receiver is very sensitive to the difference between expected user and interference user. Based on the above situation, the traditional MUD algorithm for DS-CDMA system such as Matched Filter (MF) and decorrelation detection receiver cannot effectively eliminate the impact of MAI and FNP. This makes SKF, Fading Kalman Filter (FKF) and Robust Adaptive Kalman Filter (RAKF) the focus of research.

Adaptive UKF Filtering Algorithm Based on Maximum a Posterior Estimation and Exponential Weighting

摘要: 针对传统Unscented卡尔曼滤波器(Unscented Kalman filter, UKF)在噪声先验统计未知时变情况下非线性滤波精度下降甚至发散的问题, 设计了一种带噪声统计估计器的自适应UKF滤波算法. 首先根据极大后验(Maximum a posterior, MAP)估计原理, 推导出一种次优无偏MAP常值噪声统计估计器; 接着在此基础之上, 采用指数加权的方法, 给出了时变噪声统计估计器的递推公式; 最后对自适应UKF算法进行了性能分析. 相比于传统UKF, 该自适应UKF算法在噪声统计未知时变情况下不仅滤波依然收敛, 滤波精度及稳定性显著提高, 而且其具有应对噪声变化的自适应能力. 仿真实例验证了其有效性. 关键词: 非线性 / 自适应UKF滤波算法 / 常值噪声统计估计器 / 时变噪声统计估计器 / 极大后验估计 / 指数加权

Simulation of the Newly Designed Adaptive Controller

In the first part of the paper, a new design adaptive controller with generalized cost-function is derived for timevarying systems with unknown timevarying noise statistics. The controller consists of two part. The first part, using the modified adaptive Kalman filtering, is to identify timevarying systems with unknown timevarying noise statistics, the second part is to compute multistep adaptive predictor on-line based on the estimated parameters and noise statistics, then, to compute adaptive controller with generalized cost-function. In the second part of the paper, two simulated examples are given to show the performance of the presented controller.

A parallel filtering algorithm for linear systems with unknown time varying noise statistics

The problem of estimating the state of a linear dynamic system driven by additive Gaussian noise with unknown time varying statistics is considered. Estimates of the state of the system are obtained which are based on all past observations of the system. These observations are linear functions of the state contaminated by additive white Gaussian noise. A previously developed algorithm designed for use in the case of stationary noise is modified to allow estimation of an unknown Kalman gain and thus the system state in the presence of unknown time varying noise statistics. The algorithm is inherently parallel in nature and if implemented in a computer with parallel processing capability should only be slightly slower than the stationary Kalman filtering algorithm with known noise statistics.