Multiplicative Kalman filtering

We study a non-linear Hidden Markov Model, where the process of interest is the absolute value of a discretely observed Ornstein–Uhlenbeck diffusion, which is observed after a multiplicative perturbation. We obtain explicit formulae for the recursive relations which link the relevant conditional distributions. As a consequence the predicted, filtered, and smoothed distributions for the hidden process can easily be computed. We illustrate the behaviour of these distributions on simulations.     

A control chart based approach to monitoring supply network dynamics using Kalman filtering

In today's global market, a critical issue for companies to survive the increasing competition is how to handle uncertainty in their supply network. In this paper, we explore the application of Kalman filtering to estimate the dynamic states in a supply network. Two state-space models are developed. The first one focuses on processing each individual order which includes both waiting time and value-added processing time. Considering the correlation of consecutive orders, the second one enhances the state-space model by employing autoregressive model of waiting time. To signal potential abnormal events, the estimates from the models are further used in control charts with control limits being updated at each monitoring stage according to the related estimation error. A supply network case example is studied and we conclude in the benchmark model (without using Kalman filtering) and the first state-space model, the data collected from the bottleneck stage turns out to be most valuable for increased accuracy in detecting tardy orders. The second state-space model consistently outperforms both the benchmark model and the first state-space model for robustly early detection of abnormalities at all stages, especially the stages before the bottleneck stage, of the system.     

小波变换与卡尔曼滤波结合的RLG降噪方法

针对激光陀螺随机游走噪声其非平稳和非正态分布的特性,提出了基于小波变换的卡尔曼滤波的RLG降噪方法,该方法既具有小波变换对自相似过程的去相关作用和多分辨分析的功能,同时又保持了卡尔曼滤波器对未知信号的线性无偏最小方差估计的特点,实现了激光陀螺随机游走噪声的实时多尺度分解和最优估计。实测激光陀螺零偏信号去噪的结果表明,基于小波变换的卡尔曼滤波器使随机游走噪声的标准差降低了10.3%,降噪效果优于传统的卡尔曼滤波器。     

Multimodel Kalman filtering for adaptive nonuniformity correction in infrared sensors

We present an adaptive technique for the estimation of nonuniformity parameters of infrared focal-plane arrays that is robust with respect to changes and uncertainties in scene and sensor characteristics. The proposed algorithm is based on using a bank of Kalman filters in parallel. Each filter independently estimates state variables comprising the gain and the bias matrices of the sensor, according to its own dynamic-model parameters. The supervising component of the algorithm then generates the final estimates of the state variables by forming a weighted superposition of all the estimates rendered by each Kalman filter. The weights are computed and updated iteratively, according to the a posteriori-likelihood principle. The performance of the estimator and its ability to compensate for fixed-pattern noise is tested using both simulated and real data obtained from two cameras operating in the mid- and long-wave infrared regime.     

非线性系统的小波分频的扩展Kalman滤波

基于噪声的小波变换特点,结合量测的多尺度分解和扩展Kalman滤波(EKF),提出了一种小波“最佳”尺度分解的分频EKF滤波算法。该算法依据小波变换模功率谱选择最佳小波分解尺度,并将小波多尺度分解去噪和分频EKF滤波结合起来。对实际中含强噪声的非线性动态系统进行状态估计效果较好。Monte-Carlo仿真表明,与普通EKF滤波相比,本文算法的滤波精度平均提高约10%。     

Kalman filtering for adaptive nonuniformity correction in infrared focal-plane arrays

A novel statistical approach is undertaken for the adaptive estimation of the gain and bias nonuniformity in infrared focal-plane array sensors from scene data. The gain and the bias of each detector are regarded as random state variables modeled by a discrete-time Gauss-Markov process. The proposed Gauss-Markov framework provides a mechanism for capturing the slow and random drift in the fixed-pattern noise as the operational conditions of the sensor vary in time. With a temporal stochastic model for each detector's gain and bias at hand, a Kalman filter is derived that uses scene data, comprising the detector's readout values sampled over a short period of time, to optimally update the detector's gain and bias estimates as these parameters drift. The proposed technique relies on a certain spatiotemporal diversity condition in the data, which is satisfied when all detectors see approximately the same range of temperatures within the periods between successive estimation epochs. The performance of the proposed technique is thoroughly studied, and its utility in mitigating fixed-pattern noise is demonstrated with both real infrared and simulated imagery.     

Unscented卡尔曼滤波在捷联惯导系统初始对准中的应用

在四元数方法的基础上建立了一种非线性捷联惯导系统(SINS)误差模型.该误差模型无需对姿态误差角进行小角度假设.在该SINS误差模型中,采用四元数表示姿态矩阵,速度误差模型为非线性方程.为了对静基座大失准角SINS进行初始对准,通过对SINS误差模型进行简化,得到了适用于SINS静基座初始对准的误差模型.由于SINS误差模型中含有非线性方程,通过采用unscented卡尔曼滤波解决SINS的初始对准问题.对SINS静基座初始对准的仿真结果表明,unscented卡尔曼滤波能有效估计SINS失准角.     

A measurement method based on Kalman filtering for ultrasonic time-of-flight estimation

A new digital signal-processing method for ultrasonic time-of-flight (TOF) estimation is presented. The method applies the discrete extended Kalman filter (DEKF) to the acquired ultrasonic signal in order to accurately estimate the shape factors of the echo envelope as well as locate its onset. It is also possible to assure reduced bias and uncertainty in critical TOF measurements, such as those involving low signal-to-noise ratio (SNR) as well as severe distortion of echo shape. A number of numerical tests are conducted on simulated signals with the aim of highlighting the good performance of the method when operating in critical conditions. Results attained in TOF-based distance measurements finally assess the reliability and efficacy of the method in the presence of actual ultrasonic signals.     

基于改进的Kalman滤波的语音增强算法

传统的kalman滤波方法在推导过程中假定观测噪声为白噪声。通常对于有色噪声需要用白噪声激励的方法予以模拟,并且需要以牺牲运算量作为代价。本文提出了一种改进的基于kalman滤波的语音增强算法,可以处理白噪声和有色噪声情况,不需要增加计算量,仿真结果表明了该算法对有色噪声的语音增强性能要优于基于传统kalman滤波方法。     

Kalman filtering of tunable diode laser spectrometer absorbance measurements

A recursive Kalman time-series filter was applied to absorbance measurements obtained with a tunable diode laser spectrometer. The spectrometer uses frequency modulation spectroscopy and a nearinfrared diode laser operating at 1.604 μm to monitor the CO(2)-vapor concentration in a 30-cm absorption cell. The Kalman filter enhanced the signal-to-noise ratio of the spectrometer by an order of magnitude when an absorbance of 6 × 10(-5) was monitored.     

Cooperative SLAM using fuzzy Kalman filtering for a collaborative air-ground robotic system

ABSTRACT

This paper presents a three-dimensional (3D) cooperative simultaneous location and mapping (SLAM) method for a collaborative air-ground robotic system, designed to manage an indoor quadrotor flying done together with a Mecanum-wheeled omnidirectional robot (MWOR) in indoor unknown and no GPS environments. An ORB (Oriented Fast and Rotated BRIEF)-SLAM 2.0 (ORB- SLAM 2.0) approach is used to produce a 3D map and discover the position of the indoor quadrotor simultaneously, and a particle-filter SLAM (FastSLAM 2.0) approach is employed to build the 2D map of the global environment for the MWOR. A more accurate 3D quadrotor position estimation (QPE) method for the quadrotor is proposed with the assistance of the MWOR. A cooperative SLAM using fuzzy Kalman filtering is proposed to fuse the outputs of the ORB-SLAM 2.0, FastSLAM 2.0, and QPE approaches, in order to localize the quadrotor more accurately. Both SLAM approaches, quadrotor position estimation method and cooperative SLAM have been implemented in the robotic operation system (ROS) environment. Moreover, the cooperative SLAM method is exploited to achieve landing of the quadrotor atop the MWOR. Five experiments are conducted to show the effectiveness and superiority of the proposed cooperative SLAM method.     

基于Kalman滤波的多分辨率图像融合新算法

以尺度类似于时间,对具有不同分辨率的多幅图像建立起状态方程和观测方程;以标准Kalman滤波为工具,将具有不同性能与特点的图像进行融合,并给出了分块快速算法.利用估计误差绝对值均值对融合的性能进行了评估.多组实验与分析表明:所提出的图像融合算法不仅能有效的去除噪声和提高图像分辨率,而且通过图像融合,能够大大改善存在部分遮挡和恶劣天气等影响下获取的存在灰度、对比度变化的图像的性能.     

结合Hough变换与Kalman滤波的车道线检测方法

车道线检测是智能驾驶系统的重要组成部分,它提供了车辆与车道位置关系的信息.针对智能车辆驾驶系统在视觉导航过程中车道线检测的精确性和鲁棒性的问题,提出一种有效的车道线检测方法.首先对原始RGB图像分别进行感兴趣区域设定、逆透视变换、灰度化和阈值处理;然后进行霍夫变换处理,利用斜率和中心点位置筛选检测结果;最后利用卡尔曼滤波对检测到的线段进行跟踪,预测当前车道线位置.实验结果表明,该算法能够有效解决图像中车道线不清晰以及一些干扰遮挡的问题,车道线检测准确率可达94%,具有较好的准确性、鲁棒性和较低的计算复杂度,有利于实时性检测系统的构建.     

基于扩展卡尔曼滤波的轮式移动机器人定位技术

针对单一传感器或现有多传感系统在信息传递提取上的不足,应用一种信息融合方法,对机器人进行相对定位与绝对定位的融合分析,得出机器人的最优位置信息,最终实现了移动机器人的精确定位。首先,采用码盘、陀螺仪进行机器人相对定位,采用激光雷达进行机器人绝对定位;其次,建立环境地图、传感器及机器人运动模型;最后,以扩展卡尔曼滤波作为多传感器融合技术,建立多传感器信息融合模型,实现精确定位。     

Analysis of low-coherence interference fringes by the Kalman filtering method

Interferometers with low-coherence illumination allow noncontact measurement of rough-surface relief with a wide range of measurement definition by locating the visibility maxima of interference fringes. The problem is light scattering by the surface to be measured, which can cause distortion of low-coherence interferometric signals. We propose to use a stochastic fringe model and a Kalman filtering method for processing noisy low-coherence fringes dynamically. Prediction of the fringe's signal value at each discretization step is based on all the information available before this step; the prediction error is used for dynamic correction of the estimates of the fringe envelope and phase. The advantages of the Kalman filtering method consist in its immunity to noise, optimal fringe evaluation, and data-processing speed.     

Neural filtering of colored noise based on Kalman filter structure

In this paper, adaptive filtering approaches of colored noise based on the Kalman filter structure using neural networks are proposed, which need not extend the dimensions of the filter. The colored measurement noise is first modeled from a Gaussian white noise through a shaping filter. The Kalman filtering model of colored noise is then built by adopting an equivalent observation equation, which can avoid the dimension extension and complicated computations. An observation correlation-based algorithm is suggested to estimate the variance of the measurement noise by use of a single layer neural network. The Kalman gain can be obtained when a perfect knowledge of the plant model and noise variances is given. However, in some cases, the difficulties of the correlative method and the Kalman filter equations are the amount of computations and memory requirements. A neural estimator based on the Kalman filter structure is also analyzed as an alternative in this paper. The Kalman gain is replaced by a feedforward neural network whose weight adjustment permits minimization of the estimation error. The estimator has the capability of estimating the states of the plant in a stochastic environment without knowledge of noise statistics. If the noise of the plant is white and Gaussian and its statistics are well known, the neural estimator and the Kalman filter produce equally good results. The neural filtering approaches of colored noise based on the Kalman filter structure are applied to restore the cephalometric images of stomatology. Several experimental results demonstrate the feasibility and good performances of the approaches.     

Kalman filtering to suppress spurious signals in adaptive optics control

In many scenarios, an adaptive optics (AO) control system operates in the presence of temporally non-white noise. We use a Kalman filter with a state space formulation that allows suppression of this colored noise, hence improving residual error over the case where the noise is assumed to be white. We demonstrate the effectiveness of this new filter in the case of the estimated Gemini Planet Imager tip-tilt environment, where there are both common-path and non-common-path vibrations. We discuss how this same framework can also be used to suppress spatial aliasing during predictive wavefront control assuming frozen flow in a low-order AO system without a spatially filtered wavefront sensor, and present experimental measurements from Altair that clearly reveal these aliased components.     

Infrared species tomography of a transient flow field using Kalman filtering

In infrared species tomography, the unknown concentration distribution of a species is inferred from the attenuation of multiple collimated light beams shone through the measurement field. The resulting set of linear equations is rank-deficient, so prior assumptions about the smoothness and nonnegativity of the distribution must be imposed to recover a solution. This paper describes how the Kalman filter can be used to incorporate additional information about the time evolution of the distribution into the reconstruction. Results show that, although performing a series of static reconstructions is more accurate at low levels of measurement noise, the Kalman filter becomes advantageous when the measurements are corrupted with high levels of noise. The Kalman filter also enables signal multiplexing, which can help achieve the high sampling rates needed to resolve turbulent flow phenomena.