Position Estimation Error Research Articles

Inertial Motion Capture Accuracy Improvement by Kalman Smoothing and Dynamic Networks

Localization-capable inertial motion capture algorithms rely on zero-velocity updates (ZUPT), usually as measurements in a Kalman filtering scheme, for position and attitude error control. As ZUPTs are only applicable during the static phases a link goes through, estimation errors grow during dynamic ones. This error growth may somewhat be mitigated by imposing biomechanical constraints in multi-sensor systems. Error reduction is also possible by optimization-based methods that incorporate the dynamic and static constraints governing the system behavior over a period of time (e.g. the dynamic network algorithm); when this period includes multiple static phases for a link, its estimation accuracy is greatly improved. The current study enhances the error control capabilities of an existing inertial motion capture algorithm by multi-stage smoothing. The base algorithm benefits from imposing biomechanical constraints and is self-calibrating with respect to body geometry and some sensor parameters. The smoothing process, conducted over the stepping periods of each foot, comprises two stages; Kalman smoothing followed by error minimization by dynamic networks. The performance of the algorithm, deployed using both extended and square-root unscented Kalman filtering schemes (EKF and SRUKF, respectively), is experimentally evaluated during a fast-paced walking test using a custom-made inertial motion capture system. A comparison with an optical motion capture system showed that the proposed method decreased pelvis position and attitude estimation errors by 19% and 29%, respectively. Furthermore, compared to the EKF-based smoothing algorithm, the SRUKF-based method proved to be more successful in error reduction and parameter estimation.

A Simple Sensorless Position Error Correction Method for Dual Three-Phase Permanent Magnet Synchronous Machines

In this article, a simple position error correction method is proposed to minimize the influence of parameter deviation on the model-based rotor position estimation, with the help of two sets of windings in a dual 3-phase permanent magnet synchronous machine (PMSM). In the proposed method, when each set of 3-phase windings is individually used for sensorless rotor position estimation, the nominal parameters that are set in each observer are identical but inaccurate, which leads to errors in the estimated rotor position from both observers. Since the error is varied according to the current level, small current pulses are injected respectively into <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</i> - or <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</i> -axis of one set (or both set) of 3-phase windings, which causes the difference between the rotor position estimation errors from two sets of 3-phase windings. This difference is subsequently used as the input of an updated controller to minimize the parameter deviation and the corresponding rotor position error. The proposed method is experimentally validated on a dual 3-phase PMSM system.

Non-initial attitude error analysis of SINS by error closed-loop and energy-level constructing

For the optimization and algorithm design of high precision strapdown inertial navigation system (SINS), a systematic and fine attitude error analysis method is needed. To this end, a closed-loop method and an energy-level method are proposed to analyze the non-initial attitude estimation error of SINS. The closed-loop method is constructed from the basic angular velocity error equation in which angular velocity error is combined with angular velocity and rotation estimate to form a closed loop. This makes it the first time to realize the complete (theoretically unbiased) analysis of SINS rotation estimation error. The energy-level method is constructed from the energy level of angular motion which is expressed as the series expansion of rotation estimate under the defined motion such as coning and maneuvering motion. This enables us to finely analyze the error of any existing multi-sample coning algorithm based on Taylor-series method. The theoretical basis, establishment process and instructions of two methods are given in order in the paper. The detailed process of proof and reasoning of the two methods are given in Appendixes A, B, C and D. Several cases of attitude error analysis based on the proposed methods and simulation examples verify the correctness of the analysis results from the proposed method and the applicability of the proposed method, which provides a systematic analysis tool for the design of SINS and attitude algorithm.

Real time localization solution for land vehicle application using low-cost integrated sensors with GPS

The technique proposed in this research demonstrates a real time nonlinear data fusion solution based on extremely low-cost and grade inertial sensors for land vehicle navigation. Here, the utilized nonlinear multi-sensor data fusion (MSDF) is based on the combination between extremely low-cost micro electrical mechanical systems (MEMS) inertial, heading, pressure, and speed sensors in addition to satellite-based navigation system. The integrated navigation system fuses position and velocity states from the Global Positioning System (GPS), the velocity measurements from an odometer, heading angle observation from a magnetometer and navigation states from an inertial navigation system (INS). The implemented system performance is assessed through the post-processing of collected raw measurements and real time experimental work. The system that runs the real-time experiments is established on three connected platforms, two of them are based on a 32-bit ARMTM core and the third one is based 16-bit AVR ATMEL microcontroller. This microcontroller is connected to an on-board diagnostics (OBD) shield to collect the vehicle speed measurements. The raw data obtained from the integrated sensors is saved and post processed in MATLAB®. In normal conditions, the estimated position errors are reduced through the usage of INS/GPS integration with heading observation angle from a magnetometer. In GPS-denied environments, the integrated system uses the observations from INS, magnetometer in addition to the velocity from odometer to ensure a continuous and accurate navigation solution. A complementary filter (CF) is implemented to estimate and improve the pitch and roll angles calculations. In addition to that, an unscented Kalman filter (UKF) is used cascaded with the designed CF to complete the designed sensors fusion algorithm. Experimental results show that the designed MSDF can achieve a good level of accuracy and a continuous localization solution of a land vehicle in different GPS availability cases and can be implemented on the available in the market processors to be run in real time.

Bipolar-Voltage-Injection-Based Position Estimation Method of Planar Switched Reluctance Motors Using Improved Flux Linkage Model

This article proposes a new position estimation method based on an unsaturated flux linkage model for planar switched reluctance motors (PSRMs). The bipolar-voltage-injection method is used to measure the flux linkage, and it is found that ripples caused by iron loss and aluminum eddy current with different amplitudes appear at the troughs of the flux curve. The effect of the losses on the flux linkage measurement is revealed in this article, and the loss compensation models are built based on the analysis. The improved flux linkage model is proposed with the loss compensation models. Then, the position estimation method is given with the improved flux linkage model. Flux linkage measurement result shows that the model with loss compensation has higher accuracy than the conventional model. Initial and planar-motion position estimation experiments are carried out for the PSRM. The initial position estimation error is from -0.4 to 0.4 mm. The planar-motion position estimation errors are from -1.1 to 1.1 mm in the X-axis and from -1.2 to 1.0 mm in the {Y-axis, and the effectiveness of the proposed flux linkage model is verified.

Passive and Explicit Attitude and Gyro-Bias Observers Using Inertial Measurements

This article addresses the problem of estimating the attitude and gyro bias using biased gyro and inertial vector measurements. Two nonlinear observers are presented. One of the two is the passive observer evolving on the semisphere of quaternion, which decouples the gyro measurements from the reconstructed attitude. The other is the explicit observer evolving on the SO(3), which uses directly body-frame measurements of known inertial vectors. The proposed observers achieve faster convergence for large attitude estimation errors than similar observers in literature, guarantee asymptotical stability for almost arbitrary initial conditions, achieve similar steady-state performance with lower computational cost than multiplicative extended Kalman filter, which is the workhorse of attitude estimation, and are suitable for implementation using a low-cost inertial measurement unit. Simulation and experimental results prove the fast convergence and steady-state performance of the proposed observers.

Realization of the Neural Fuzzy Controller for the Sensorless PMSM Drive Control System

A neural fuzzy controller (NFC)-based speed controller for the sensorless permanent magnet synchronous motor (PMSM) drive control system is realized in this paper. The NFC is a fuzzy logic controller (FLC), which adjusts the RBFNN-based (radial basis function neural network) parameter by adapting the dynamic system characteristics. For sensorless PMSM drive, the integration of sliding mode observer (SMO) and phase-locked loop (PLL) is executed to estimate the rotor position and speed. To eliminate the initial rotor position estimation and overcome the conventional PLL-based position estimation error in the direction reversion transition, the I-f control strategy is applied to start up the motor and change the rotational direction effectively. The system performance was verified in various experimental conditions. The simulation and experimental results indicate that the proposed control algorithm is implemented efficiently. The motor starts up with diverse external loads, operates in a wide speed range for both positive and negative directions, and reverses the rotational direction stably. Furthermore, the system presents robustness against disturbance and tracks the command speed properly.

An Overall System Delay Compensation Method for IPMSM Sensorless Drives in Rail Transit Applications

In rail transit application, the multimode pulsewidth modulation (PWM) is used to take full advantage of the dc-bus voltage in wide speed range. To improve the sensorless control performance of interior permanent magnet synchronous motor (IPMSM) drives in this condition, an overall system delay compensation method is proposed for a hybrid position observer that combines a simple square-wave voltage injection with a nonsingular terminal sliding mode observer. Due to the delay effect, the currents and position estimation performance are deteriorated, such as more severe dq-axis currents coupling and fluctuation of estimated position error. In order to solve these problems, the analysis of delay characteristics in the IPMSM sensorless drives is first presented. For carrier-based modulation, the compensation time is obtained through a self-tuning PI regulator based on predictive q-axis voltage error. Then, the three-phase reference currents are utilized to judge the direction near zero-crossing point and the parameters robustness is also analyzed. For optimal PWM modulation, the voltage vector angle and modulation depth are predicted in a simple way, and the delay effect can be eliminated. Furthermore, the harmonics distribution in sensorless control is described by power spectral density. Finally, the effectiveness of proposed strategy is verified by experimental results with a 3.7-kW IPMSM sensorless drive platform.

Two-Step Continuous-Control Set Model Predictive Current Control Strategy for SPMSM Sensorless Drives

Integration of model predictive current control (MPCC) and the existing position estimation method is an attractive and promising strategy for surface-mounted permanent magnet synchronous machines (SPMSMs) sensorless drives. However, its system control performance is severely weakened by the filter delay and position estimation errors in the position estimation process because the conventional MPCC requires accurate rotor position information. In order to effectively resolve these problems, a two-step continuous-control-set MPCC (TS-CCS-MPCC) strategy is proposed in this paper. By adopting the two-step prediction to complete the machine mathematical model, the predictive currents can be obtained without the estimated rotor position. Meanwhile, a new proportional cost function is developed to obtain the optimal voltage vector. With the proposed control strategy, the necessary position estimation process in the conventional MPCC can be removed, and the MPCC-based sensorless control can be achieved rapidly and steadily, which not only simplifies the whole implementation process but also dramatically improves the system dynamic performance. Besides, the one-beat delay compensation and machine parameter identification are deduced to enhance the control performance of the proposed scheme. Finally, the experiments validate that the proposed sensorless control scheme can achieve excellent control performance for both steady-state and dynamic operations.

Improving the accuracy of permanent magnet rotor position estimation for stepper motors using magnetic induction and harmonic rejection

To improve the accuracy of permanent magnet (PM) rotor position estimation for a hybrid stepper motor (HSM), the authors propose a sensorless control design based on the back electromagnetic force (back-EMF) caused by magnetic induction and harmonic rejection via an orthogonal third-order phase-locked loop (PLL3rd) and an integral harmonic filter (IHF). The accuracy of estimation is analysed considering PM rotor position estimation errors. The harmonics of the back-EMF signal are eliminated by the IHF before entering the PLL3rd, which synchronises and decreases position estimation error. This technique is a simple, reliable, and effective method for implementing sensorless control of an HSM. An industrial test-bench was used to implement the proposed scheme. The experimental results are presented to validate the effectiveness of the proposed estimation method.

Analysis of Optimal Range Sensor Placement for Tracking a Moving Target

To improve target tracking performance, it is necessary not only to model target dynamics well, but also to employ high accuracy sensors. In addition to this, the geometry between the sensors and the target also significantly affects the tracking performance. In this letter, we give a closed-form formula for the optimal range sensor placement problem, by minimizing the errors both in the position and velocity estimates when there are two sensors. Using the formula, the effects of errors in a prior position and velocity estimates of a target and tracking filter parameters on the optimal sensor placement are analyzed.

Underwater square-root cubature attitude estimator by use of quaternion-vector switching and geomagnetic field tensor

This paper presents a kind of attitude estimation algorithm based on quaternion-vector switching and square-root cubature Kalman filter for autonomous underwater vehicle (AUV). The filter formulation is based on geomagnetic field tensor measurement dependent on the attitude and a gyro-based model for attitude propagation. In this algorithm, switching between the quaternion and the three-component vector is done by a couple of the mathematical transformations. Quaternion is chosen as the state variable of attitude in the kinematics equation to time update, while the mean value and covariance of the quaternion are computed by the three-component vector to avoid the normalization constraint of quaternion. The square-root forms enjoy a continuous and improved numerical stability because all the resulting covariance matrices are guaranteed to stay positively semidefinite. The entire square-root cubature attitude estimation algorithm with quaternion-vector switching for the nonlinear equality constraint of quaternion is given. The numerical simulation of simultaneous swing motions in the three directions is performed to compare with the three kinds of filters and the results indicate that the proposed filter provides lower attitude estimation errors than the other two kinds of filters and a good convergence rate.

A Novel and Robust Calibration Method for the Underwater Transponder Position

This article addresses the transponder position calibration problem for the ultrashort baseline (USBL) system. Calibration is an important technique for the positioning of the USBL and the calibration of the installation error. The estimation error of the transponder position is greatly affected by the slant distance error in the traditional method. Furthermore, the calibration accuracy depends heavily on the slant distance error and it has poor robustness in the presence of outliers. Thus, a robust calibration model combining slant distance and bearings is developed, which overcomes the disadvantage of poor robustness of the traditional method. The transponder position can be estimated in real time by the adaptive fault-tolerant Kalman filter designed in this article. Some experiments are carried out to prove the superiority of the proposed algorithm. The USBL positioning accuracy is also improved with the novel calibration method.

Performance, Accuracy and Generalization Capability of RFID Tags' Constellation for Indoor Localization.

Indoor localization has recently witnessed an increase in interest due to its wide range of potential services. Further, the location information is very important in many applications, such as the Internet of Things, logistics, library management and so on. Hence, different technologies and techniques have been proposed in the literature for indoor localization systems. Most of these systems present the disadvantages of a poor performance, low accuracy and high cost. However, thanks to its low cost, high accuracy and non-line-of-sight detection, radio frequency identification (RFID)-based localization has increasingly become the most used technology for indoor localization. In this paper, we propose an innovative approach based on the multiple input single output (MISO) protocol to improve the accuracy of a low-cost RFID localization system. Whereas most traditional systems use a single tag for localization, the proposed architecture encourages the use of a group of RFID tags named as a constellation. According to experimental results and based on the signals’ diversity, the location accuracy is improved to get an estimated position error of 81 cm at the cumulative distribution function of 90%.

Dynamic modeling of soft continuum manipulators using lie group variational integration.

This paper presents the derivation and experimental validation of algorithms for modeling and estimation of soft continuum manipulators using Lie group variational integration. Existing approaches are generally limited to static and quasi-static analyses, and are not sufficiently validated for dynamic motion. However, in several applications, models need to consider the dynamical behavior of the continuum manipulators. The proposed modeling and estimation formulation is obtained from a discrete variational principle, and therefore grants outstanding conservation properties to the continuum mechanical model. The main contribution of this article is the experimental validation of the dynamic model of soft continuum manipulators, including external torques and forces (e.g., generated by magnetic fields, friction, and the gravity), by carrying out different experiments with metal rods and polymer-based soft rods. To consider dissipative forces in the validation process, distributed estimation filters are proposed. The experimental and numerical tests also illustrate the algorithm’s performance on a magnetically-actuated soft continuum manipulator. The model demonstrates good agreement with dynamic experiments in estimating the tip position of a Polydimethylsiloxane (PDMS) rod. The experimental results show an average absolute error and maximum error in tip position estimation of 0.13 mm and 0.58 mm, respectively, for a manipulator length of 60.55 mm.

Initial Rotor Position Estimation by Detecting Vibration of Permanent Magnet Synchronous Machine

The principal methods of initial rotor position estimation of permanent magnet synchronous machine (PMSM), such as high-frequency rotating signal injection methods and high-frequency pulsating signal injection methods, are implemented by calculating the voltage equations of the stator winding. However, these methods have low adaptability to the PMSMs with different saliency properties and high sensitivity to electrical parameter variations. In this article, an initial rotor position estimation method based on the dynamical equations of the PMSM is proposed to solve the abovementioned problems. First, a series of vibration signals of the PMSM is generated by applying a high-frequency voltage to the rotating virtual d-axis of the rotor. Then, the relationship between the vibration signals and the rotating virtual d-axis position is established. Next, the initial d-axis rotor position of the PMSM is estimated by analyzing the vibration response. Finally, the rotor magnetic polarity is identified on account of the saturation saliency effect. The theoretical analysis and simulation, as well as experiments, are carried out to verify the effectiveness and accuracy of the innovation method. The results demonstrate that the proposed method has the advantages of easy implementation, high adaptability, and strong robustness; also, the maximum initial rotor position estimation error of the proposed method is 1.7 electrical degrees, which is lower than other methods.

Sensorless Synchronous Reluctance Motor Drives: A Projection Vector Approach for Stator Resistance Immunity and Parameter Adaptation

This article presents a general projection vector framework for the analysis of flux and position observers applied to sensorless control of synchronous reluctance (SyR) machines, with emphasis to parametric errors sensitivity. The stator resistance immunity property of Adaptive Projection vector for Position error estimation (APP) technique is demonstrated in maximum torque per ampere (MTPA) conditions. Out of MTPA, additional resistance adaption is devised for accurate estimation of stator flux and torque. Alternatively, inductance adaptation might be preferred to resistance's, when dealing with inaccurate motor flux-maps. Inductance adaptation is shown to decrease the steady-state position error. All the proposed APP observers with adaptation techniques are subjected to stability analysis. The merit and the feasibility of the proposed scheme are experimentally demonstrated on a 1.1-kW SyR machine test bench.

An Autonomous RSSI Filtering Method for Dealing with Human Movement Effects in an RSSI-Based Indoor Localization System

In this paper, an experimental evaluation of received signal strength indicator (RSSI-based) localization methods in an indoor wireless network is studied. The major contributions of this work are twofold. First, the well-known and widely used min–max and trilateration methods are tested in the cases of without and with human movement effects. By this purpose, how RSSI data during human movements affect the accuracy of such methods and which method shows the best position estimation result, have been investigated. Second, we also design and develop a new RSSI filter to automatically reduce RSSI variation and the position estimation error caused by human movements. Experiments are carried out in a parking building. An LPC2103F microcontroller interfaced with a CC2500 RF transceiver as a low-cost, low power, 2.4 GHz radio module is used as a wireless node. Results demonstrate that without human movement effects, the performances by both localization methods are not much different. However, with human movement effects, the min–max method shows better accuracy than the trilateration method in handling the RSSI variation problem. The results also indicate that by applying the proposed RSSI filter, it can directly cope with the RSSI variation problem caused by humans. The localization error decreases by 69.87% for the case of the min–max method, and it decreases by 72.74% for the case of the trilateration method (the best case). Compared with the case of employing the moving average filter as the commonly used filter, the localization error only decreases by 18.67% and 12.99%, respectively.

A Realistic Simulation Environment for MRI-Based Robust Control of Untethered Magnetic Robots With Intra-Operational Imaging

Dual-use of magnetic resonance imaging (MRI) devices for robot tracking and actuation has transformed them into potential medical robotics platforms for targeted therapies and minimally invasive surgeries. In this letter, we present the dynamic simulations of an MRI-based tracking and actuation scheme, which performs intra-operational imaging while controlling untethered magnetic robots. In our realistic rigid-body simulation, we show that the robot could be controlled with a 1D projection-based position feedback while performing intra-operational echo-planar imaging (EPI). From the simulations, we observe that the velocity estimation error is the main source of the controller instability for low MRI sequence frequencies. To minimize the velocity estimation errors, we constrain the controller gains according to maximum closed-loop rates achievable for different sequence durations. Using the constrained controller in simulations, we confirm that EPI imaging could be introduced to the sequence as an intra-operational imaging method. Although the intro-operational imaging increases the position estimation error to 2.0 mm for a simulated MRI-based position sensing with a 0.6 mm Gaussian noise, it does not cause controller instability up to 128 k-space lines. With the presented approach, continuous physiological images could be acquired during medical operations while a magnetic robot is actuated and tracked inside an MRI device.

Method of estimating initial rotor position for IPMSMs using subdivided voltage vectors based on inductance variation

This paper proposes a method for estimating the initial rotor position for an interior permanent-magnet synchronous motor (IPMSM) using subdivided voltage vectors based on inductance variation. Since the stator inductance of an IPMSM varies depending on the rotor position, the current that flows through the entire IPMSM drive system can be different depending on the rotor position when a voltage vector is applied to the stator winding of the IPMSM. Therefore, the rotor position can be estimated using the differences in the currents. In the conventional method, which uses six voltage vectors to estimate the initial rotor position, the estimated position error is increased in specific regions where the phase angle of the applied voltage vector is remarkably different from that of the N pole of the rotor. This paper presents an advanced method using subdivided voltage vectors to estimate the initial rotor position more precisely in a specific region. The effectiveness of the advanced estimation method is verified by simulation and experimental results.