Showing papers on "Kalman filter published in 2015"

Keyframe-based visual-inertial odometry using nonlinear optimization

Abstract: Combining visual and inertial measurements has become popular in mobile robotics, since the two sensing modalities offer complementary characteristics that make them the ideal choice for accurate visual-inertial odometry or simultaneous localization and mapping SLAM. While historically the problem has been addressed with filtering, advancements in visual estimation suggest that nonlinear optimization offers superior accuracy, while still tractable in complexity thanks to the sparsity of the underlying problem. Taking inspiration from these findings, we formulate a rigorously probabilistic cost function that combines reprojection errors of landmarks and inertial terms. The problem is kept tractable and thus ensuring real-time operation by limiting the optimization to a bounded window of keyframes through marginalization. Keyframes may be spaced in time by arbitrary intervals, while still related by linearized inertial terms. We present evaluation results on complementary datasets recorded with our custom-built stereo visual-inertial hardware that accurately synchronizes accelerometer and gyroscope measurements with imagery. A comparison of both a stereo and monocular version of our algorithm with and without online extrinsics estimation is shown with respect to ground truth. Furthermore, we compare the performance to an implementation of a state-of-the-art stochastic cloning sliding-window filter. This competitive reference implementation performs tightly coupled filtering-based visual-inertial odometry. While our approach declaredly demands more computation, we show its superior performance in terms of accuracy.

Fusion of WiFi, Smartphone Sensors and Landmarks Using the Kalman Filter for Indoor Localization

Abstract: Location-based services (LBS) have attracted a great deal of attention recently. Outdoor localization can be solved by the GPS technique, but how to accurately and efficiently localize pedestrians in indoor environments is still a challenging problem. Recent techniques based on WiFi or pedestrian dead reckoning (PDR) have several limiting problems, such as the variation of WiFi signals and the drift of PDR. An auxiliary tool for indoor localization is landmarks, which can be easily identified based on specific sensor patterns in the environment, and this will be exploited in our proposed approach. In this work, we propose a sensor fusion framework for combining WiFi, PDR and landmarks. Since the whole system is running on a smartphone, which is resource limited, we formulate the sensor fusion problem in a linear perspective, then a Kalman filter is applied instead of a particle filter, which is widely used in the literature. Furthermore, novel techniques to enhance the accuracy of individual approaches are adopted. In the experiments, an Android app is developed for real-time indoor localization and navigation. A comparison has been made between our proposed approach and individual approaches. The results show significant improvement using our proposed framework. Our proposed system can provide an average localization accuracy of 1 m.

Probabilistic forecasting and Bayesian data assimilation

Abstract: In this book the authors describe the principles and methods behind probabilistic forecasting and Bayesian data assimilation. Instead of focusing on particular application areas, the authors adopt a general dynamical systems approach, with a profusion of low-dimensional, discrete-time numerical examples designed to build intuition about the subject. Part I explains the mathematical framework of ensemble-based probabilistic forecasting and uncertainty quantification. Part II is devoted to Bayesian filtering algorithms, from classical data assimilation algorithms such as the Kalman filter, variational techniques, and sequential Monte Carlo methods, through to more recent developments such as the ensemble Kalman filter and ensemble transform filters. The McKean approach to sequential filtering in combination with coupling of measures serves as a unifying mathematical framework throughout Part II. Assuming only some basic familiarity with probability, this book is an ideal introduction for graduate students in applied mathematics, computer science, engineering, geoscience and other emerging application areas.

Consensus-Based Linear and Nonlinear Filtering

Abstract: This note addresses Distributed State Estimation (DSE) over sensor networks. Two existing consensus approaches for DSE, i.e., consensus on information (CI) and consensus on measurements (CM), are combined to provide a novel class of hybrid consensus filters (named Hybrid CMCI) which enjoy the complementary benefits of CM and CI. Novel theoretical results, limitedly to linear systems, on the guaranteed stability of the Hybrid CMCI filters under collective observability and network connectivity are proved. Finally, the effectiveness of the proposed class of consensus filters is evaluated on a target tracking case study with both linear and nonlinear sensors.

Deep Kalman Filters.

Abstract: Kalman Filters are one of the most influential models of time-varying phenomena. They admit an intuitive probabilistic interpretation, have a simple functional form, and enjoy widespread adoption in a variety of disciplines. Motivated by recent variational methods for learning deep generative models, we introduce a unified algorithm to efficiently learn a broad spectrum of Kalman filters. Of particular interest is the use of temporal generative models for counterfactual inference. We investigate the efficacy of such models for counterfactual inference, and to that end we introduce the "Healing MNIST" dataset where long-term structure, noise and actions are applied to sequences of digits. We show the efficacy of our method for modeling this dataset. We further show how our model can be used for counterfactual inference for patients, based on electronic health record data of 8,000 patients over 4.5 years.

Quaternion kinematics for the error-state Kalman filter

Abstract: A tutorial of quaternion algebra, especially suited for the error-state Kalman filter, with the aim of building Visual-Inertial SLAM and odometry systems.

Maximum Correntropy Kalman Filter

Abstract: Traditional Kalman filter (KF) is derived under the well-known minimum mean square error (MMSE) criterion, which is optimal under Gaussian assumption. However, when the signals are non-Gaussian, especially when the system is disturbed by some heavy-tailed impulsive noises, the performance of KF will deteriorate seriously. To improve the robustness of KF against impulsive noises, we propose in this work a new Kalman filter, called the maximum correntropy Kalman filter (MCKF), which adopts the robust maximum correntropy criterion (MCC) as the optimality criterion, instead of using the MMSE. Similar to the traditional KF, the state mean and covariance matrix propagation equations are used to give prior estimations of the state and covariance matrix in MCKF. A novel fixed-point algorithm is then used to update the posterior estimations. A sufficient condition that guarantees the convergence of the fixed-point algorithm is given. Illustration examples are presented to demonstrate the effectiveness and robustness of the new algorithm.

Kalman Filter and Its Application

Abstract: Kalman filter is a minimum-variance estimation for dynamic systems and has attracted much attention with the increasing demands of target tracking. Various algorithms of Kalman filter was proposed for deriving optimal state estimation in the last thirty years. This paper briefly surveys the recent developments about Kalman filter (KF), Extended Kalman filter (EKF) and Unscented Kalman filter (UKF). The basic theories of Kalman filter are introduced, and the merits and demerits of them are analyzed and compared. Finally relevant conclusions and development trends are given.

An Adaptive Unscented Kalman Filtering Approach for Online Estimation of Model Parameters and State-of-Charge of Lithium-Ion Batteries for Autonomous Mobile Robots

Abstract: In this brief, to get a more accurate and robust state of charge (SoC) estimation, the lithium-ion battery model parameters are identified using an adaptive unscented Kalman filtering method, and based on the updated model, the battery SoC is estimated consequently. An adaptive adjustment of the noise covariances in the estimation process is implemented using a technique of covariance matching in the unscented Kalman filter (UKF) context. The effectiveness of the proposed method is evaluated through experiments under different power duties in the laboratory environment. The obtained results are compared with that of the adaptive extended Kalman filter, extended Kalman filter, and unscented Kalman filter-based algorithms. The comparison shows that the proposed method provides better accuracy both in battery model parameters estimation and the battery SoC estimation.

StructSLAM: Visual SLAM With Building Structure Lines

Abstract: We propose a novel 6-degree-of-freedom (DoF) visual simultaneous localization and mapping (SLAM) method based on the structural regularity of man-made building environments. The idea is that we use the building structure lines as features for localization and mapping. Unlike other line features, the building structure lines encode the global orientation information that constrains the heading of the camera over time, eliminating the accumulated orientation errors and reducing the position drift in consequence. We extend the standard extended Kalman filter visual SLAM method to adopt the building structure lines with a novel parameterization method that represents the structure lines in dominant directions. Experiments have been conducted in both synthetic and real-world scenes. The results show that our method performs remarkably better than the existing methods in terms of position error and orientation error. In the test of indoor scenes of the public RAWSEEDS data sets, with the aid of a wheel odometer, our method produces bounded position errors about 0.79 m along a 967-m path although no loop-closing algorithm is applied.

A Systematization of the Unscented Kalman Filter Theory

Abstract: 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.

Dynamic State Estimation of a Synchronous Machine Using PMU Data: A Comparative Study

Abstract: Accurate information about dynamic states is important for efficient control and operation of a power system. This paper compares the performance of four Bayesian-based filtering approaches in estimating dynamic states of a synchronous machine using phasor measurement unit data. The four methods are extended Kalman filter, unscented Kalman filter, ensemble Kalman filter, and particle filter. The statistical performance of each algorithm is compared using Monte Carlo methods and a two-area-four-machine test system. Under the statistical framework, robustness against measurement noise and process noise, sensitivity to sampling interval, and computation time are evaluated and compared for each approach. Based on the comparison, this paper makes some recommendations for the proper use of the methods.

An Adaptive Prognostic Approach via Nonlinear Degradation Modeling: Application to Battery Data

Abstract: Remaining useful life (RUL) estimation via degradation modeling is considered as one of the most central components in prognostics and health management. Current RUL estimation studies mainly focus on linear stochastic models, and the results under nonlinear models are relatively limited in literature. Even in nonlinear degradation modeling, the estimated RUL is aimed at a population of systems of the same type or depend only on the current degradation observation. In this paper, an adaptive and nonlinear prognostic model is presented to estimate RUL using a system's history of the observed data to date. Specifically, a general nonlinear stochastic process with a time-dependent drift coefficient is first adopted to characterize the dynamics and nonlinearity of the degradation process. In order to render the RUL estimation depending on the degradation history to date, a state-space model is constructed, and Kalman filtering is applied to update one key parameter in the drifting function through treating this parameter as an unobserved state variable. To update the hidden state and other parameters in the state-space model simultaneously and recursively, the expectation maximization algorithm is used in conjunction with Kalman smoother to achieve this aim. The probability density function of the estimated RUL is derived with an explicit form, and some commonly used results under linear models turn out to be its special cases. Finally, the implementation of the presented approach is illustrated by numerical simulations, and an application for estimating the RUL of lithium-ion batteries is used to demonstrate the superiority of the method.

Real-Time RFID Indoor Positioning System Based on Kalman-Filter Drift Removal and Heron-Bilateration Location Estimation

Abstract: This paper proposes Kalman-filter drift removal (DR) and Heron-bilateration location estimation (LE) to significantly reduce the received signal strength index (RSSI) drift, localization error, computational complexity, and deployment cost of conventional radio frequency identification (RFID) indoor positioning systems without any sacrifice of localization granularity and accuracy. By means of only one portable RFID reader as the targeted device and only one pair of active RFID tags as the border-deployed landmarks, this paper develops a real-time portable RFID indoor positioning device and cost-effective scalable RFID indoor positioning infrastructure, based on Kalman-filter DR, Heron-bilateration LE, and four novel preprocessing/postprocessing techniques. Experimental results reveal that the proposed Kalman-filter DR method is faster and better to converge the distance measurement (DM) error than conventional probability/statistics in terms of various relative distances under certain RSSI drift effect condition, and the proposed Heron-bilateration LE method is also faster and better to converge the LE error than conventional proximity pattern matching and trilateration in terms of three or more landmarks under certain DM error condition. On the other hand, a portable RFID indoor positioning device is smoothly implemented on an Android smartphone platform attached with a portable Bluetooth-based RFID reader.

Optimal PMU Placement for Power System Dynamic State Estimation by Using Empirical Observability Gramian

Abstract: In this paper, the empirical observability Gramian calculated around the operating region of a power system is used to quantify the degree of observability of the system states under specific phasor measurement unit (PMU) placement. An optimal PMU placement method for power system dynamic state estimation is further formulated as an optimization problem which maximizes the determinant of the empirical observability Gramian and is efficiently solved by the NOMAD solver, which implements the Mesh Adaptive Direct Search algorithm. The implementation, validation, and the robustness to load fluctuations and contingencies of the proposed method are carefully discussed. The proposed method is tested on WSCC 3-machine 9-bus system and NPCC 48-machine 140-bus system by performing dynamic state estimation with square-root unscented Kalman filter. The simulation results show that the determined optimal PMU placements by the proposed method can guarantee good observability of the system states, which further leads to smaller estimation errors and larger number of convergent states for dynamic state estimation compared with random PMU placements. Under optimal PMU placements an obvious observability transition can be observed. The proposed method is also validated to be very robust to both load fluctuations and contingencies.

A Novel Kalman Filter for Human Motion Tracking With an Inertial-Based Dynamic Inclinometer

Abstract: Goal: Design and development of a linear Kalman filter to create an inertial-based inclinometer targeted to dynamic conditions of motion. Methods: The estimation of the body attitude (i.e., the inclination with respect to the vertical) was treated as a source separation problem to discriminate the gravity and the body acceleration from the specific force measured by a triaxial accelerometer. The sensor fusion between triaxial gyroscope and triaxial accelerometer data was performed using a linear Kalman filter. Wrist-worn inertial measurement unit data from ten participants were acquired while performing two dynamic tasks: 60-s sequence of seven manual activities and 90 s of walking at natural speed. Stereophotogrammetric data were used as a reference. A statistical analysis was performed to assess the significance of the accuracy improvement over state-of-the-art approaches. Results: The proposed method achieved, on an average, a root mean square attitude error of 3.6° and 1.8° in manual activities and locomotion tasks (respectively). The statistical analysis showed that, when compared to few competing methods, the proposed method improved the attitude estimation accuracy. Conclusion: A novel Kalman filter for inertial-based attitude estimation was presented in this study. A significant accuracy improvement was achieved over state-of-the-art approaches, due to a filter design that better matched the basic optimality assumptions of Kalman filtering. Significance: Human motion tracking is the main application field of the proposed method. Accurately discriminating the two components present in the triaxial accelerometer signal is well suited for studying both the rotational and the linear body kinematics.

A derivative UKF for tightly coupled INS/GPS integrated navigation.

Abstract: 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.

Distributed Kalman Filtering With Dynamic Observations Consensus

Abstract: This paper studies distributed estimation of unstable dynamic random fields observed by a sparsely connected network of sensors. The field dynamics are globally detectable, but not necessarily locally detectable. We propose a consensus+innovations distributed estimator, termed Distributed Information Kalman Filter. We prove under what conditions this estimator is asymptotically unbiased with bounded mean-squared error, smaller than for other alternative distributed estimators. Monte Carlo simulations confirm our theoretical error asymptotic results.

Human Joint Angle Estimation with Inertial Sensors and Validation with A Robot Arm

Abstract: Traditionally, human movement has been captured primarily by motion capture systems. These systems are costly, require fixed cameras in a controlled environment, and suffer from occlusion. Recently, the availability of low-cost wearable inertial sensors containing accelerometers, gyroscopes, and magnetometers have provided an alternative means to overcome the limitations of motion capture systems. Wearable inertial sensors can be used anywhere, cannot be occluded, and are low cost. Several groups have described algorithms for tracking human joint angles. We previously described a novel approach based on a kinematic arm model and the Unscented Kalman Filter (UKF). Our proposed method used a minimal sensor configuration with one sensor on each segment. This paper reports significant improvements in both the algorithm and the assessment. The new model incorporates gyroscope and accelerometer random drift models, imposes physical constraints on the range of motion for each joint, and uses zero-velocity updates to mitigate the effect of sensor drift. A high-precision industrial robot arm precisely quantifies the performance of the tracker during slow, normal, and fast movements over continuous 15-min recording durations. The agreement between the estimated angles from our algorithm and the high-precision robot arm reference was excellent. On average, the tracker attained an RMS angle error of about $3^\circ$ for all six angles. The UKF performed slightly better than the more common Extended Kalman Filter

Robust Multirate Control Scheme With Predictive Virtual Lanes for Lane-Keeping System of Autonomous Highway Driving

Abstract: In this paper, we propose a new approach for a robust multirate lane-keeping control scheme with predictive virtual lanes. First, the multirate lane-keeping control scheme is proposed to improve the lane-keeping performance and to reduce the ripple in the yaw rate. To improve the lane-keeping performance on a curved road, the integral of the lateral offset error is added to the state feedback controller. A multirate Kalman filter (KF) has been developed to resolve the problems caused by slow lane detection due to the vision processing system. This multirate KF estimates vehicle states at a fast rate using a microprocessor. Utilizing the estimated states, the linear quadratic state feedback control operates at the same fast update rate of the microprocessor. Thus, a multirate control scheme can reduce the ripple in the yaw rate. Second, we propose a virtual lane prediction method that compensates for the momentary failure of lane detection from unexpected problems. If the camera sensor momentarily fails while obtaining lane information, the predicted virtual lane can be substituted for the lane detection using the camera sensor in the proposed control scheme. Thus, the proposed control scheme can normally operate when the lane information is momentarily unavailable. The performance of the proposed method was evaluated via experiments.

Security in stochastic control systems: Fundamental limitations and performance bounds

Abstract: This work proposes a novel metric to characterize the resilience of stochastic cyber-physical systems to attacks and faults. We consider a single-input single-output plant regulated by a control law based on the estimate of a Kalman filter. We allow for the presence of an attacker able to hijack and replace the control signal. The objective of the attacker is to maximize the estimation error of the Kalman filter - which in turn quantifies the degradation of the control performance - by tampering with the control input, while remaining undetected. We introduce a notion of e-stealthiness to quantify the difficulty to detect an attack when an arbitrary detection algorithm is implemented by the controller. For a desired value of e-stealthiness, we quantify the largest estimation error that an attacker can induce, and we analytically characterize an optimal attack strategy. Because our bounds are independent of the detection mechanism implemented by the controller, our information-theoretic analysis characterizes fundamental security limitations of stochastic cyber-physical systems.