Two-stage Extended Kalman Filter Research Articles

Experimental validation of sensor fault estimation for vehicle dynamics with a nonlinear tire model

Sensor fault estimation in an automotive application is crucial for the safe execution and availability of software functions controlling the vehicle. Especially, in situations at the grip limits of the tires the safety of the passengers is most critical and a nonlinear tire model is required for accurate predictions. However, the influence of a nonlinear tire model for sensor fault estimation in an automotive application is not sufficiently analyzed in the literature.In this paper, the influence of a nonlinear tire model on sensor fault estimation during highly dynamic cornering maneuvers is demonstrated. A two-stage Extended Kalman Filter (TSEKF) based on a simple state transformation is used for the estimation of additive and multiplicative faults in longitudinal/lateral acceleration and yaw rate. The proposed estimation algorithm was implemented in real-time on a dSPACE MicroAutoBox II and experimental results with multiple measurements of an Audi S8 (D5) are used for validation of the results. The estimation performance during the measurements, using a linear and a nonlinear tire model, is analyzed and the influence of the state transformation on the accuracy of the filter is investigated.Using a simple nonlinear tire model the state estimation performance under nonlinear operating conditions can be improved by up to 79%, thereby reducing false positive detections significantly. Furthermore, the results show that for the considered system without the use of a state transformation, i.e., neglecting the state-fault cross-covariance, degrades the estimation performance by less than 1%.

Human Motion Capture Based on MEMS Sensor

In order to realize the monitoring of human joint rehabilitation, a human motion capture and recognition system is constructed by using micro electro mechanical system (MEMS) sensor nodes. A two-stage extended Kalman filter algorithm is proposed for multi-sensor data fusion. The error matrix between the coordinate system of sensor node and the coordinate system of body was calculated by using the stationary posture calibration. The root mean squared error (RMSE) of the computed joint angle time series is less than 0.5°. The feature of joint angle time series was extracted and the support vector machine (SVM) classification model based on particle swarm optimization (PSO) was established. The experimental results show that the SVM algorithm optimized by PSO has better recognition effect than BP neural network. The average recognition rate can reach more than 97%. The human motion capture system designed in this paper can effectively realize human motion capture, recognition and joint rehabilitation monitoring.

Performance comparison of representative model-based fault reconstruction algorithms for aircraft sensor fault detection and diagnosis

This article proposes a nonlinear disturbance observer (NDO) based approach for aircraft inertial measurement unit (IMU) fault detection and diagnosis (FDD) by making use of dynamic and kinematic relations of the aircraft. Furthermore, the detailed aircraft IMU FDD design using four representative fault reconstruction algorithms (NDO, sliding mode observer (SMO), iterated optimal two-stage extended Kalman filter (IOTSEKF) and adaptive two-stage extended Kalman filter (ATSEKF)) is presented. More importantly, this paper presents a thorough FDD performance comparison using these four representative methods. Different FDD performance indexes such as fault detection time, minimum detectable faults and fault estimation errors are compared under various situations such as different fault types and noise standard deviations. The advantages, drawbacks and tuning of each method are investigated, which provide useful insights to aircraft sensor FDD.

Two-stage exogenous Kalman filter for time-varying fault estimation of satellite attitude control system

This paper addresses the study of observer-based two-stage extended Kalman filter (TSEKF) estimation problem for the satellite attitude control system (ACS) in the presence of unknown time-varying actuator faults. In the traditional TSEKF methods, the considered faults always refers to constant signal in the propagation of the filter estimation, even though time-varying faults are taken into account in simulation demonstrations. In order to promote the accuracy of the TSEKF algorithm, a nonlinear observer is designed to obtain the fault dynamics and the state estimation with consideration of the nonlinear nature of the satellite ACS, and its estimation results are treated as exogenous signals used for linearizing the nonlinear ACS model. Then based on the observed fault information and the linearized ACS model, the TSEKF estimator is designed to obtain the exogenous filtering scheme, which can simultaneously reconstruct the state and faults accurately. Finally, by using the so called two-stage exogenous Kalman filter (TSXKF), simulation results show that when a time-varying fault occurs, more ideal estimation results can be obtained than those of TSEKF and better dynamic performance can be achieved than that of nonlinear observers.

Sensor Fault Detection and Diagnosis for an Unmanned Quadrotor Helicopter

This paper proposes a new nonlinear fault detection and diagnosis (FDD) scheme for the inertial measurement unit (IMU) sensor of an unmanned quadrotor helicopter (UQH). To mitigate the impact of model uncertainties, the kinematic model of an UQH rather than the dynamic model is employed to design the FDD scheme. A two-stage extended Kalman filter (TSEKF) is developed for detecting, isolating and identifying IMU sensor faults. Considering that the TSEKF is insensitive to time-varying faults, two adaptive two-stage extended Kalman filters are further proposed by integrating TSEKF with different forgetting factor schemes. Several experiments have been designed and implemented on an UQH platform to test the proposed FDD scheme, where bias fault, drift fault and oscillatory fault are considered. The results demonstrate that the proposed FDD methods are effective for detecting and estimating the IMU sensor faults in different fault scenarios.

Novel WiFi/MEMS Integrated Indoor Navigation System Based on Two-Stage EKF.

Indoor navigation has been developing rapidly over the last few years. However, it still faces a number of challenges and practical issues. This paper proposes a novel WiFi/MEMS integration structure for indoor navigation. The two-stage structure uses the extended Kalman filter (EKF) to fuse the information from WiFi/MEMS sensors and contains attitude-determination EKF and position-tracking EKF. In the WiFi part, a partition solution called “moving partition” is originally proposed in this paper. This solution significantly reduces the computation time and enhances the performance of the traditional Weighted K-Nearest Neighbors (WKNN) method. Furthermore, the direction measurement is generated utilizing WiFi positioning results, and a “turn detection” is implemented to guarantee the effectiveness. The navigation performance of the presented integration structure has been verified through indoor experiments. The test results indicate that the proposed WiFi/MEMS solution works well. The root mean square (RMS) position error of WiFi/MEMS is 0.7926 m, which is an improvement of 20.59% and 36.60% when compared to MEMS and WiFi alone. Besides, the proposed algorithm still performs well with very few access points (AP) available and its stability has been proven.

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.

FPGA-Based Implementation of Kalman Filter for Real-Time Estimation of Tire Velocity and Acceleration

Antilock braking systems require accurate vehicle speed and acceleration estimations from wheel speed sensors. Adaptive Kalman filtering is used to estimate wheel speed and acceleration for each wheel. Single core or multicore processor-based embedded systems perform the required estimation using a two-stage extended Kalman filter in many clock cycles, which limits Kalman filter speed and accuracy. In the proposed system, purely arithmetic operations used in the process are simplified and implemented as embedded logic to reduce the overhead delays and increase the update rate by 48%. The proposed system is run sequentially using finite-state machines, while a large number of multiplication and division operations are removed through rewiring and logic reuse. The simplifications not only reduce the amount of logic required to perform the operations by 39.7% but also use simple logic, which can run faster than the replaced logic on field-programmable gate array. The results presented show comparable root-mean-square wheel speed error with a high update rate of 20 MHz when running on a 50-MHz board in all scenarios. The system also provides accurate wheel acceleration estimation, which is crucial for many systems, including the reference system.

Finite Set Model Predictive Control of Interior PM Synchronous Motor Drives With an External Disturbance Rejection Technique

This paper designs a predictive speed controller of interior permanent-magnet synchronous motor (IPMSM) based on finite control set (FCS)–model predictive control (MPC). The proposed predictive speed controller has a cascade-free structure that comprises a single predictive control function for the speed and dq- axis stator currents. The future rotor speed and stator currents are predicted at each sampling interval. Then, the proposed predictive control function is evaluated to determine the optimal switching states for the IPMSM drive. In high-performance speed-controlled drive, the unknown load torque disturbance has to be suppressed. Therefore, the load torque disturbance estimator using the two-stage extended Kalman filter (TSEKF) is proposed to enhance the dynamic performance of the IPMSM drive. The proposed TSEKF simultaneously estimates the system states, which greatly improve the model prediction process. The proposed predictive speed control is simple and compact, which demonstrates a faster transient response and a robust feature to mechanical system parameter variations when compared with the conventional cascaded speed control under a wide speed range and load torque variations. The experimental results on a prototype IPMSM drive built on a Texas Instruments TMS320F28335 floating point digital signal processing (DSP) board are presented considering the constant torque and flux-weakening regions to confirm the feasibility of the proposed FCS-MPC scheme.

A two-stage extended kalman filter method for fault estimation of satellite attitude control systems

This paper presents a two-stage extended Kalman filter (TSEKF) method for actuator and sensor fault estimation problem of satellite attitude control systems. A nonlinear system model with unknown faults is established based on the separate-bias principle. Three kinds of models, namely, ACSs System model without faults, ACSs System model with actuator faults, and ACSs System model with sensor faults are established. A TSEKF strategy for state/fault estimation of nonlinear system is investigated, which are applied to these three models to estimate the system states and faults. The simulation results indicate that the amplitude of additive faults of actuator and sensor can be estimated directly. Moreover, the control effectiveness factors representing the multiplicative faults of actuator can also be estimated. Finally, by using the telemetry data of the on-orbit satellite “TS-1” of Harbin Institute of Technology as the measurement vector, the simulation results show that the proposed TSEKF strategy can be applied directly in engineering to reconstruct the actuator and sensor faults.

A novel two-stage extended Kalman filter algorithm for reaction flywheels fault estimation

This paper investigates the problem of two-stage extended Kalman filter (TSEKF)-based fault estimation for reaction flywheels in satellite attitude control systems (ACSs). Firstly, based on the separate-bias principle, a satellite ACSs with actuator fault is transformed into an augmented nonlinear discrete stochastic model; then, a novel TSEKF is suggested such that it can simultaneously estimate satellite attitude information and actuator faults no matter they are additive or multiplicative; finally, the proposed approach is respectively applied to estimating bias faults and loss of effectiveness for reaction flywheels in satellite ACSs, and simulation results demonstrate the effectiveness of the proposed fault estimation approach.

State Estimation for Robots with Complementary Redundant Sensors

In this paper, robots equipped with two complementary typologies of redundant sensors are considered: one typology provides sharp measures of some geometrical entity related to the robot pose (e.g., distance or angle) but is not univocally associated with this quantity; the other typology is univocal but is characterized by a low level of precision. A technique is proposed to properly combine these two kinds of measurement both in a stochastic and in a deterministic context. This framework may occur in robotics, for example, when the distance from a known landmark is detected by two different sensors, one based on the signal strength or time of flight of the signal, while the other one measures the phase-shift of the signal, which has a sharp but periodical dependence on the robot-landmark distance. In the stochastic case, an effective solution is a two-stage extended Kalman filter (EKF) which exploits the precise periodic signal only when the estimate of the robot position is sufficiently precise. In the deterministic setting, an approach based on a switching hybrid observer is proposed, and results are analyzed via simulation examples.

Two‐stage robust extended Kalman filter in autonomous navigation for the powered descent phase of Mars EDL

This paper proposed a two-stage robust extended Kalman filter (TREKF) for state estimation of non-linear uncertain system with unknown inputs. In engineering practice, the extended Kalman filter (EKF) with unknown inputs of the non-linear uncertain system may be degraded or even diverged. The optimal two-stage EKF (TEKF) is designed to solve the unknown inputs. The robust EKF (REKF) is considered to solve the non-linear uncertain system for a long time. However, the information about the non-linear uncertain system with unknown inputs is always incorrect. To solve this problem, the TREKF is designed by using the advantages of the TEKF and REKF, furthermore, its stability is proved. Finally, the performances of the TREKF, which are compared with the results of the REKF, TEKF and EKF, are verified by illustrating a numerical example of the powered descent phase of Mars EDL (entry, descent and landing). These also verify that the unfavourable effects of the model uncertainties and the unknown inputs are reduced efficiently by using the TREKF for the miniature coherent altimeter and velocimeter and inertial measurement unit integrated navigation during the powered descent phase of Mars EDL.

Direct Torque Control of Sensorless Induction Machine Drives: A Two-Stage Kalman Filter Approach

Extended Kalman filter (EKF) has been widely applied for sensorless direct torque control (DTC) in induction machines (IMs). One key problem associated with EKF is that the estimator suffers from computational burden and numerical problems resulting from high order mathematical models. To reduce the computational cost, a two-stage extended Kalman filter (TEKF) based solution is presented for closed-loop stator flux, speed, and torque estimation of IM to achieve sensorless DTC-SVM operations in this paper. The novel observer can be similarly derived as the optimal two-stage Kalman filter (TKF) which has been proposed by several researchers. Compared to a straightforward implementation of a conventional EKF, the TEKF estimator can reduce the number of arithmetic operations. Simulation and experimental results verify the performance of the proposed TEKF estimator for DTC of IMs.

Adaptive Two-Stage Extended Kalman Filter Theory in Application of Sensorless Control for Permanent Magnet Synchronous Motor

Extended Kalman filters (EKF) have been widely used for sensorless field oriented control (FOC) in permanent magnet synchronous motor (PMSM). The first key problem associated with EKF is that the estimator requires all the plant dynamics and noise processes are exactly known. To compensate inaccurate model information and improve tracking ability, adaptive fading extended Kalman filtering algorithms have been proposed for the nonlinear system. The second key problem is that the EKF suffers from computational burden and numerical problems when state dimension is large. The two-stage extended Kalman filter (TSEKF) with respect to this problem has been extensively studied in the past. Combining the advantages of both AFEKF and TSEKF, this paper presents an adaptive two-stage extended Kalman filter (ATEKF) for closed-loop position and speed estimation of a PMSM to achieve sensorless operation. Experimental results demonstrate that the proposed ATEKF algorithm for PMSMs has strong robustness against model uncertainties and very good real-time state tracking ability.

A Two-stage Kalman Filter for Sensorless Direct Torque Controlled PM Synchronous Motor Drive

This paper presents an optimal two-stage extended Kalman filter (OTSEKF) for closed-loop flux, torque, and speed estimation of a permanent magnet synchronous motor (PMSM) to achieve sensorless DTC-SVPWM operation of drive system. The novel observer is obtained by using the same transformation as in a linear Kalman observer, which is proposed by C.-S. Hsieh and F.-C. Chen in 1999. The OTSEKF is an effective implementation of the extended Kalman filter (EKF) and provides a recursive optimum state estimation for PMSMs using terminal signals that may be polluted by noise. Compared to a conventional EKF, the OTSEKF reduces the number of arithmetic operations. Simulation and experimental results verify the effectiveness of the proposed OTSEKF observer for DTC of PMSMs.

Design of a Fault-Tolerant Controller Based on Observers for a PMSM Drive

This paper presents a specific controller architecture devoted to obtain a permanent-magnet synchronous motor (PMSM) drive that is robust to mechanical sensor failure. In order to increase the reliability which is a key issue in industrial and transportation applications (electric or hybrid ground vehicle or aerospace actuators), two virtual sensors (a two-stage extended Kalman filter and a back-electromotive-force adaptive observer) and a maximum-likelihood voting algorithm are combined with the actual sensor to build a fault-tolerant controller (FTC). The observers are evaluated through simulation and experimental results. The FTC feasibility is proved through simulations and experiments on a 1.1-kW PMSM drive.

A novel robust two-stage extended Kalman filter for bearings-only maneuvering target tracking

A novel robust filter is proposed via embedding extended Kalman filter into an optimal two-stage Kalman filter, which is improved through a modified Sage-Husa noise statistics estimator. Meanwhile, strong tracking multiple fading factors are introduced in this paper to improve the tracking performance for high maneuvering targets. The new method provides an optimal estimation of the target state through a combination of the output of the first stage (a “bias-free” filter) and that of the second stage (a “bias-compensating” filter). Furthermore, the unknown statistical parameters of virtual noises are estimated online, and the predicted covariance can be adjusted in real time by fading factors when high maneuvers occur. Simulation results of tracking a maneuvering target by 3 passive sensors show that the proposed algorithm has advantages over the conventional method in terms of the numerical accuracy with only a little additional computational cost. Key words: Target tracking, two-stage Kalman filter, noise statistics estimator, multiple fading factors.

Two-Stage Extended Kalman Filters with Derivative-Free Local Linearizations

This paper proposes a derivative-free two-stage extended Kalman filter (2-EKF) especially suited for state and parameter identification of mechanical oscillators under Gaussian white noise. Two sources of modeling uncertainties are considered: (1) errors in linearization, and (2) an inadequate system model. The state vector is presently composed of the original dynamical/parameter states plus the so-called bias states accounting for the unmodeled dynamics. An extended Kalman estimation concept is applied within a framework predicated on explicit and derivative-free local linearizations (DLL) of nonlinear drift terms in the governing stochastic differential equations (SDEs). The original and bias states are estimated by two separate filters; the bias filter improves the estimates of the original states. Measurements are artificially generated by corrupting the numerical solutions of the SDEs with noise through an implicit form of a higher-order linearization. Numerical illustrations are provided for a few ...

Speed and rotor flux estimation of induction machines using a two-stage extended Kalman filter

This paper presents an effective implementation of an extended Kalman filter used for the estimation of both rotor flux and rotor velocity of an induction motor. An algorithm proposed by Hsieh and Chen in [Hsieh, C.S., & Chen, F.C. (1999). Optimal solution of the two-stage Kalman estimator. IEEE Transactions on automatic control, 44(1), 194–199] for linear parameter estimation is extended to non-linear estimation, where parameters such as the velocity of an induction machine are present in the transition matrix and in the augmented state space. Compared to a straightforward implementation of an extended Kalman filter, our modified optimal two-stage Kalman estimator reduces the number of arithmetic operations by 25%, allowing higher sampling rate or the use of a cheaper microcontroller.