Kalman Filter Structure Research Articles

3D Indoor Position Estimation Based on a UDU Factorization Extended Kalman Filter Structure Using Beacon Distance and Inertial Measurement Unit Data.

The development of the GPS (Global Positioning System) and related advances have made it possible to conceive of an outdoor positioning system with great accuracy; however, for indoor positioning, more efficient, reliable, and cost-effective technology is required. There are a variety of techniques utilized for indoor positioning, such as those that are Wi-Fi, Bluetooth, infrared, ultrasound, magnetic, and visual-marker-based. This work aims to design an accurate position estimation algorithm by combining raw distance data from ultrasonic sensors (Marvelmind Beacon) and acceleration data from an inertial measurement unit (IMU), utilizing the extended Kalman filter (EKF) with UDU factorization (expressed as the product of a triangular, a diagonal, and the transpose of the triangular matrix) approach. Initially, a position estimate is calculated through the use of a recursive least squares (RLS) method with a trilateration algorithm, utilizing raw distance data. This solution is then combined with acceleration data collected from the Marvelmind sensor, resulting in a position solution akin to that of the GPS. The data were initially collected via the ROS (Robot Operating System) platform and then via the Pixhawk development card, with tests conducted using a combination of four fixed and one moving Marvelmind sensors, as well as three fixed and one moving sensors. The designed algorithm is found to produce accurate results for position estimation, and is subsequently implemented on an embedded development card (Pixhawk). The tests showed that the designed algorithm gives accurate results with centimeter precision. Furthermore, test results have shown that the UDU-EKF structure integrated into the embedded system is faster than the classical EKF.

An Improved Method for Swing State Estimation in Multirotor Slung Load Applications

A method is proposed to estimate the swing state of a suspended payload in multirotor drone delivery scenarios. Starting from the equations of motion of the coupled slung load system, defined by two point masses interconnected by a rigid link, a recursive algorithm is developed to estimate cable swing angle and rate from acceleration measurements available from an onboard Inertial Measurement Unit, without the need for extra sensors. The estimation problem is addressed according to the Extended Kalman Filter structure. With respect to the classical linear formulation, the proposed approach allows for improved estimation accuracy in both stationary and maneuvering flight. As an additional contribution, filter performance is enhanced by accounting for aerodynamic disturbance force, which largely affects the estimation accuracy in windy flight conditions. The validity of the proposed methodology is demonstrated as follows. First, it is applied to an octarotor platform where propellers are modeled according to blade element theory and the load is suspended by an elastic cable. Numerical simulations show that estimated swing angle and rate represent suitable feedback variables for payload stabilization, with benefits on flying qualities and energy demand. The algorithm is finally implemented on a small-scale quadrotor and is investigated through an outdoor experimental campaign, thus proving the effectiveness of the approach in a real application scenario.

Online estimation of state-of-charge inconsistency for lithium-ion battery based on SVSF-VBL

It is of great significance to estimate cell inconsistency for improving the service life and safety performance of the power battery pack. To accurately estimate the state-of-charge (SOC) inconsistency of cells with different performance parameters and working states, a method combining adaptive robust unscented Kalman filter and smooth variable structure filter with time-varying smoothing boundary layer (SVSF-VBL) is proposed. The cell mean-difference model is used to simulate the behavior characteristics of the battery module, including the cell mean model expressed by the dual polarization (DP) model and the cell difference model characterized by the hypothetical Rint model. Firstly, the improved forgetting factor recursive least square is applied to identify parameters of the DP model, and the unscented Kalman filter incorporating robust estimation and adaptive filter tuning is employed to estimate the SOC of the battery module. Then, SVSF-VBL is used to estimate the SOC difference between each cell and module based on the Rint model for improving the estimation accuracy and robustness. In addition, the comprehensive inconsistency of the cells can be captured by the secondary performance indicator inherent in SVSF-VBL, which contributes to the in-depth study of cell inconsistency. Finally, a series of tests are carried out to verify the performance of the proposed method, and the results show that the method can improve the estimation accuracy and convergence performance while effectively suppressing the system disturbance.

Scalable recursive state estimation for nonlinear two‐dimensional complex networks with switching topology

SummaryThis paper investigates a scalable recursive state estimation method for nonlinear two‐dimensional (2‐D) stochastic complex networks. In these networks, the switching topology is modelled by random variables generated by the Bernoulli distribution. Considering the Extended Kalman Filter structure, we employ the Taylor series expansion to handle the nonlinear functions in the model. Hence, high‐order terms emerging in the linearization process are modelled by norm‐bounded parameter uncertainties. Due to the uncertainty of such a system, we obtain an upper bound for the estimation error covariance. Furthermore, we obtain an upper bound for the cross covariance to reduce the proposed filter's computational complexity and improve scalability. Within the established setting, next, the proposed filter is designed in such a way that the presented upper bounds are minimized. Finally, a numerical example is provided to illustrate the effectiveness of the proposed state estimation algorithm.

Wheel-INS2: Multiple MEMS IMU-Based Dead Reckoning System With Different Configurations for Wheeled Robots

A reliable self-contained navigation system is essential for autonomous vehicles. Based on our previous study on Wheel-INS <xref ref-type="bibr" rid="ref1" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[1]</xref> , a wheel-mounted inertial measurement unit (Wheel-IMU)-based dead reckoning (DR) system, in this paper, we propose a multiple IMUs-based DR solution for the wheeled robots. The IMUs are mounted at different places on the wheeled vehicles to acquire various dynamic information. In particular, at least one IMU has to be mounted at the wheel to measure the wheel velocity and take advantage of the rotation modulation. The system is implemented through a distributed extended Kalman filter structure where each subsystem (corresponding to each IMU) retains and updates its own states separately. The relative position constraints between the multiple IMUs are exploited to further limit the error drift and improve the system’s robustness. Particularly, we present the DR systems using dual Wheel-IMUs, one Wheel-IMU plus one vehicle body-mounted IMU (Body-IMU), and dual Wheel-IMUs plus one Body-IMU as examples for analysis and comparison. Field tests illustrate that the proposed multi-IMU DR system outperforms the single Wheel-INS in terms of both positioning and heading accuracy. By comparing with the centralized filter, the proposed distributed filter shows unimportant accuracy degradation while holding significant computation efficiency. Moreover, among the three multi-IMU configurations, the one Body-IMU plus one Wheel-IMU design obtains the minimum drift rate. The position drift rates of the three configurations are 0.82% (dual Wheel-IMUs), 0.69% (one Body-IMU plus one Wheel-IMU), and 0.73% (dual Wheel-IMUs plus one Body-IMU), respectively.

A Novel Federated Structure of Invariant EKF Using Left-/Right-Invariant Observations

In this article, we propose a novel federated structure of the invariant extended Kalman filter (IEKF) using the left- and right-invariant observations. A proper invariant error should be chosen to exploit the trajectory-independent property of the IEKF. For the left- and right-invariant observations, the left-IEKF (LIEKF) and the right-IEKF (RIEKF) are designed, respectively. However, in applications, both left- and right-invariant observations are often used together while using multiple aiding sensors to improve estimation performance. If either the LIEKF or RIEKF is selected and implemented as a centralized filter, the measurement matrix contains current state estimates in mismatched observation-related terms. As a result, as the state estimation error increases, the calculation of the Kalman gain is affected, and the filter cannot properly correct the error. For such situations, we propose a federated structure that updates the left- and right-invariant observations separately in the allocated subfilters. In the subfilter assigned with left-invariant observations, the error is corrected using the LIEKF, and in the subfilter assigned with right-invariant observations, the error is corrected using the RIEKF. Since each subfilter uses trajectory-independent Kalman gain, it is expected to improve the estimation performance compared to the centralized structure. The performance of the proposed method is evaluated and compared to the centralized LIEKF and RIEKF through Monte-Carlo simulations for an inertial navigation example. Also, the proposed method is validated by a publicly available dataset of a ground vehicle equipped with a global positioning system (GPS) and wheel encoders.

Research on Fusion Algorithm of Beidou and AIS Based on Improved Federated Filter

In order to solve the problem of insufficient accuracy and reliability of ship position display in AIS(Automatic Identification System) system, a federated Kalman filter is designed, an open algorithm architecture is built, AIS and BDS positioning information sources are selected for fusion, and the information fusion part of the federated Kalman filter framework is improved by IMMF algorithm and covariance crossover algorithm to obtain more accurate and reliable target position information and ship motion state. Simulation experiments are carried out, and the experimental results show that, compared with GPS positioning or BDS(Bei Dou Navigation Satellite) positioning in AIS alone, AIS/BDS combined positioning based on federated Kalman filter structure has higher system fault tolerance, positioning accuracy and stability, and improves the safety of ship navigation.

Enhanced EKF and SVSF for state of charge estimation of Li‐ion battery in electric vehicle using a fuzzy parameters model

The precision of equivalent circuit model (ECM)-based state of charge (SoC) estimation methods is vulnerable to the variation of the battery parameters, due to several internal and external factors. In this regard, this study proposes a fuzzy logic method for the approximate estimation of the ECM parameters at different temperatures and SoC levels. The fuzzy inference system is designed to handle the non-linear deviation of the battery parameters from their reference values. On this basis, the extended Kalman filter and smooth variable structure filter are used to estimate the SoC. The two algorithms with fuzzy parameters (FP), namely FP-EKF and FP-SVSF, are tested on a 20 Ah Nickel Manganese Cobalt cell with maximum voltage of 4.2 V. The results show that the maximum root mean square error (RMSE) of the estimated SoC is kept within 1.51% with the FP-EKF and 0.68% with the FP-SVSF. Moreover, the reduction of the maximum absolute error may reach 0.34% with the FP-EKF, and 0.82% with the FP-SVSF, compared to the same algorithms without the proposed FP method. The executable codes are implemented on a low-cost controller, and the average computational time is obtained as 215 μs, which confirms the real-time practicality of the proposed method.

Outlier-Resistant Filtering With Dead-Zone-Like Censoring Under Try-Once-Discard Protocol

In this paper, a novel outlier-resistant filtering problem is concerned for a class of networked systems with dead-zone-like censoring under the weighted try-once-discard protocol (WTODP). To describe the phenomenon of dead-zone-like censoring, the sensor output is characterized by the Tobit model in which the censored region is restrained by specified left- and right-censoring thresholds. The WTODP is employed to decide the transmission sequence of sensors so as to alleviate undesirable data collisions. In the case of the measurement outliers, a saturation function is employed in the Tobit Kalman filter structure to constrain the innovations contaminated by the measurement outliers, thereby maintaining satisfactory filtering performance. By resorting to the approach of the matrix inequality, an upper bound is first obtained on the filtering error covariance where the gain matrix of the Tobit Kalman filter is carefully designed to minimize the obtained upper bound. Moreover, the exponential boundedness of the filtering error is analyzed in the mean square sense. Finally, the effectiveness of the proposed outlier-resistant filtering algorithm is verified by three practical examples.

Attitude estimation and control based on modified unscented Kalman filter for gyro-less satellite with faulty sensors

A modified unscented Kalman filter is presented to estimate the quaternion parameters as well as the angular velocities of a rigid gyro-less satellite under faulty sensor conditions. The task is carried out using the Sun sensor and magnetometers as attitude sensors with bounded noise and unknown fault(s). Following the presentation of the satellite attitude dynamics and filtering formulations, a new fault detection and isolation algorithm is proposed. The latter is based on a modified unscented Kalman filter structure for improved fault detection, sensor isolation, and attitude control (AC). A Backtracking Search Algorithm (BSA) is also used to design and optimize the PID controller gains, as well as to optimize sensor installation orientation for residual signal decoupling. In this regard, the paper presents and proves a theory that describes how the proposed optimization process for sensor installation can analytically decouple the faulty orientation signal from the healthy ones. A comparison of attitude and angular velocity estimation approaches using the standard Kalman, extended Kalman, and a proposed modified unscented Kalman filter is also provided. The results show that the proposed filter performs significantly better in closed-loop AC systems and copes adequately with sensor faults.

Simplified Control Structure of Fuzzy Logic and Kalman Filter for Induction Motor Drive

The paper deals with the utilization of Kalman filter and fuzzy logic control in induction motor drive with direct torque control (DTC). In order to lower ripple of stator current vector in DTC drive, pulse width modulation technique with high switching frequency is applied. However, the performance of the DTC also depends on the accuracy of both stator resistance and stator current vector. In the paper, the stator resistance and stator current components are assumed to be distorted by Gaussian noises. In order to reduce the effect of noises especially at low speed and very low speed regions, a simple Kalman filter is applied for filtering current components, and fuzzy logic theory is used to increase the flexibility of proportional-integral (PI) compensator in the speed controller of the drive structure. Simulations are implemented in conditions of high-level noises of stator current and stator resistance, and a wide range of load torque. An ITAE-based criterion is utilized to evaluate the performance of drive structures. Results confirmed the expected dynamic properties of the proposed drive structure. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium provided the original work is properly cited.

Joint equalization of CD and RSOP using a time–frequency domain Kalman filter structure in Kramers–Kronig system

Kramers–Kronig (KK) system is a direct detection (DD) optical short-reach interconnection system which is suitable for high capacity data center interconnect (DCI) applications. For this kind of short-reach high capacity polarization-division multiplexing (PDM) optical transmission system, the fiber channel impairments contain chromatic dispersion (CD) and rotation of state of polarization (RSOP) will lead to a severe signal distortion and need to be equalized. This paper proposed a time–frequency domain Kalman filter scheme for joint equalization of CD and RSOP simultaneously in KK system. The proposed scheme is capable of tracking the fast RSOP in time domain and equalizing CD in frequency domain using a window-split structure. The performance of the Kalman scheme is investigated in a 28GBaud PDM 16QAM DD system with KK receivers. The simulation results prove that the proposed Kalman scheme exhibits a good performance of RSOP tracking ability up to speed of 2.5 Mrad/s, with a large accumulated CD tolerance as large as 2040 ps/nm at a low OSNR penalty. The results also show the proposed scheme has a comparable computational complexity compared with a generally used scheme which includes a CD compensation, combined with polarization demultiplexing algorithm constant modulus algorithm (CMA) and multiple modulus algorithm (MMA).

Lidar-aided Autonomous Landing and Vision-based Taxiing for Fixed-Wing UAV

Autonomous UAV technology is limited in its ability to land safely at distinct airfields that have not been precisely surveyed and where GPS is unavailable. In this paper, we present a multi-sensor system for the automatic landing of fixed-wing UAV. The system is composed of a high precision aircraft controller, a range finder (Lidar) and a vision module used for detection and tracking of runways. The estimation of the position of the fixed-wing UAV is by using Lidar and performs gliding till flaring. Then, a federated extended Kalman filter (EKF) structure is costumed and utilizes the solutions of the IMU, GPS and Lidar as independent measurements to estimate the position of the vehicle. The framework can be used to integrate the vision solutions and enables the estimation to be smooth and robust landing. For taxiing, the neural network is used such that from live video stream from the camera trains the UAV to land precisely along the runway.

40 years of sensor fusion for orientation tracking via magnetic and inertial measurement units: Methods, lessons learned, and future challenges

Technological developments over the past two decades have resulted in the development of more accurate and lightweight low-cost magnetic and inertial measurement units (MIMUs). These developments have allowed the extensive application of MIMUs in various fields, specifically tracking the 3D orientation of a rigid body. Despite recent technological improvements, measurements from a tri-axial gyroscope, accelerometer, and/or magnetometer inside the MIMU are characterized by uncertainties. Numerous studies have been conducted to address these uncertainties and develop sensor fusion algorithms (SFAs) to estimate the 3D orientation accurately and robustly. This paper contributes to these efforts by providing a survey of the state-of-the-art SFAs for orientation estimation. We surveyed +250 publications, categorized the SFAs with various structures, identified the modifications proposed to improve their performance, and discussed the strengths and weaknesses of these approaches. We found that, while early SFAs were mostly a vector observation algorithm or an extended Kalman filter, to improve the computational efficiency, more recent works have developed SFAs with a complementary filter or complementary Kalman filter structure. At the same time, to improve the performance of the SFAs, several research teams have proposed various modifications to the basic structure of these filters, such as adaptive gain tuning or imperfect measurement rejection. We also provided an outlook on the lessons learned as well as the main challenges related to SFAs and discussed the practical steps toward developing an effective SFA. We have identified the need for benchmarking studies as the main challenge at the moment. This paper is among the first surveys which provide such breadth of coverage across different SFAs for tracking orientation with MIMUs.

A Grey Model and Mixture Gaussian Residual Analysis-Based Position Estimator in an Indoor Environment.

As the progress of electronics and information processing technology continues, indoor localization has become a research hotspot in wireless sensor networks (WSN). The adverse non-line of sight (NLOS) propagation usually causes large measurement errors in complex indoor environments. It could decrease the localization accuracy seriously. A traditional grey model considers the motion characteristics but does not take the NLOS propagation into account. A robust interacting multiple model (R-IMM) could effectively mitigate NLOS errors but the clipping point is hard to choose. In order to easily cope with NLOS errors, we present a novel filter framework: mixture Gaussian fitting-based grey Kalman filter structure (MGF-GKFS). Firstly, grey Kalman filter (GKF) is proposed to pre-process the measured distance, which can mitigate the process noise and alleviate NLOS errors. Secondly, we calculate the residual which is the difference between the filtered distance of GKF and the measured distance. Thirdly, a soft decision method based on mixture Gaussian fitting (MGF) is proposed to identify the propagation condition through residual value and give the degree of membership. Fourthly, weak NLOS noise is further processed by unscented Kalman filter (UKF). The filtered results of GKF and UKF are weighted using the degree of membership. Finally, a maximum likelihood (ML) algorithm is applied to get the coordinate of the target. MGF-GKFS is not supported by any of the priori knowledge. Full-scale simulations and an experiment are conducted to compare the localization accuracy and robustness with the state-of-the-art algorithms, including robust interacting multiple model (R-IMM), unscented Kalman filter (UKF) and interacting multiple model (IMM). The results show that MGF-GKFS could achieve significant improvement compared to R-IMM, UKF and IMM algorithms.

A novel adaptive federated filter for GNSS/INS/VO integrated navigation system

In order to solve the problem of decreased navigation performance of the Global Navigation Satellite System (GNSS)/inertial navigation system (INS) integrated navigation systems in GNSS-denied environments, and to improve the navigation accuracy and robustness of the navigation system, a novel adaptive federated filter with a feedback scheme for a GNSS/INS/visual odometry (VO) integrated navigation system is proposed in this paper. A visual-inertial odometry system model with a multi-state constraint Kalman filter structure based on a polar geometry and trifocal tensor geometry between different images is established, which can provide better navigation accuracy in GNSS-denied environments. Moreover, a new method to obtain the information allocation factor according to the different navigation performances of local filters is deduced in this paper, which has low computational complexity and a simple structure. Meanwhile, an abnormal measurement detection algorithm based on fuzzy logic is proposed to detect the abnormal measurements of local filters. The results of the vehicle experiment with the publicly available real-world KITTI dataset show that the proposed algorithm can obtain reliable navigation results in GNSS-denied environments and improve the navigation accuracy and robustness of the GNSS/INS/VO integrated navigation system.

A switched SDRE filter for state of charge estimation of lithium-ion batteries

Lithium-ion (Li-ion) batteries need very precise monitor of the state of charge (SOC) to ensure a long cycle life. Hence, a knowledge of the SOC is important for Li-ion batteries. Although SOC cannot be measured directly, it can be estimated from direct measurement variables based on a model of the battery. Single-Particle-Model (SPM), a reduced-order nonlinear electrochemical model, is commonly used for this purpose. State-dependent-Riccati-equation (SDRE) filter is chosen as the estimator due to its high-flexibility in handling the model’s nonlinearity. However, performance of this filter is limited in presence of uncertainties. To tackle this problem, in this paper, a switching concept is induced into SDRE filter, in the form of switched estimation error covariance matrix with a certain frequency. Thus, by changing the Riccati equation dynamic in SDRE filter and proper adjustment of estimation error covariance matrix eigenvalues, performance and robustness of the common SDRE filter is significantly improved for Li-ion SOC estimation. To analyze the fidelity of such a filter in further applications, stability analysis is carried out on a class of nonlinear systems, and ultimate bound of estimation error is analytically obtained, and the influence of switching is investigated. Simulation results reveal effectiveness of the proposed filter compared to common SDRE filter, extended Kalman filter and variable structure approaches. Furthermore, experimental results verify the effectiveness of the proposed method in practice.

Joint equalization of linear impairments using two-stage cascade Kalman filter structure in coherent optical communication systems

In this paper, instead of adopting different algorithms to deal with the different impairments separately based on different signal processing structures, we proposed a joint linear impairment equalization scheme using a two-stage cascade Kalman structure in which the first stage solves the residual chromatic dispersion (rCD), the rotation of state of polarization (RSOP) and polarization mode dispersion (PMD), and the second stage compensates for the carrier frequency offset (CFO) and carrier phase noise (CPN). The structures of the two stages are similar with a seamless connection and possess a clear logic architecture. The stages are compatible with each other and achieve excellent performance. We aim to use this two-stage Kalman scheme as a comprehensive DSP equalization scheme to replace the combined algorithms of the constant modulus algorithm (CMA), improved Mth-power algorithm (IMP), and blind phase search (BPS). Simulations based on a 28 Gbaud polarization division multiplexed quadrature-phase shift keying coherent optical communication system show that the proposed two-stage Kalman scheme comprehensively outperforms the CMA-IMP-BPS scheme in solving the problems of RSOP, PMD, rCD, CFO, and CPN. The experimental results confirm the simulation results. In addition, the complexity of the proposed Kalman scheme is relatively less than the CMA-IMP-BPS scheme.

Joint equalization scheme of ultra-fast RSOP and large PMD compensation in presence of residual chromatic dispersion.

Polarization demultiplexing is generally carried out by a multiple-input multiple-output (MIMO) based algorithm in polarization division multiplexing (PDM) coherent systems. However, in some extreme environments, the MIMO algorithm becomes inapplicable due to the ultra-fast rotation of the state of polarization (RSOP) and large polarization mode dispersion (PMD). In addition, the residual chromatic dispersion (RCD) is always present because of the mismatch of the compensated chromatic dispersion and real value induced in the optical fiber channel. According to the literature, the Kalman filter-based polarization demultiplexing algorithms possess very weak RCD tolerance. Faced with this dilemma, in this paper, a new Kalman filter structure is proposed, which can jointly compensate ultra-fast RSOP, large PMD and RCD. This Kalman filter structure enables the equalization of the RSOP in the time domain and compensation for RCD and PMD in the frequency domain. We verified the performance of the proposed Kalman scheme in the 28 Gbaud PDM-QPSK/16 QAM coherent system, with a comparison to constant modulus algorithm/multiple modulus algorithm (CMA/MMA). The simulation results confirm that, compared with CMA/MMA, the proposed Kalman scheme can provide a significant performance enhancement to cope with ultra-fast RSOP (up to 3 Mrad/s) and large PMD (more than 200 ps) with a large tolerance to RCD (over the range of ± 820 ps/nm in PDM-QPSK and ± 500 ps/nm in PDM-16 QAM).

A Parallel Attitude-Heading Kalman Filter Without State-Augmentation of Model-Based Disturbance Components

This paper proposes an inertial and magnetic sensing-based parallel orientation Kalman filter (KF), which is composed of two separate KFs: one for attitude estimation with an external acceleration model as presented in author's previous work and the other for heading estimation with a magnetic disturbance model. The novelty of the proposed attitude-heading KF, compared to other model-based KFs, is that the disturbance models are implemented by inserting them into the measurement equations without state-augmentation. In this case, there is no increase in the matrix size of the corresponding KF structure, which is advantageous as the computational cost is approximately halved when compared with the state-augmentation type approaches. The proposed KF has been experimentally verified in magnetically disturbed conditions. The proposed method has advantages over the KF with state-augmentation in the calculation efficiency and ease of use.