Square-root Cubature Kalman Filter Research Articles

Joint equalization of RSOP and PMD fused probability-aware with square-root cubature Kalman filter for the PDM PCS-64QAM system under extreme scenarios.

Extreme scenario of lightning strikes would generate ultra-fast rotation of state-of-polarization (RSOP) up to 5.1 Mrad/s and large polarization mode dispersion (PMD) in optical ground wire (OPGW). Unfortunately, the conventional multiple modulus algorithm (MMA) cannot equalize these polarization impairments in polarization division multiplexing (PDM) probabilistic constellation shaping (PCS)-64QAM system. Moreover, due to unavoidable linearization errors and higher modulation order, the extended Kalman filter based on measurement equations of concatenated multiplication (EKF-CM) is highly unstable and fails under such scenarios. To address the above issues, we have proposed a joint equalization scheme of PMD and RSOP, which fuses probability-aware with square-root cubature Kalman filter (PA-SCKF). Firstly, according to the characteristic that the amplitude of PCS signals obeys mixed Rician distribution, the scheme combines maximum a posteriori criterion to obtain the optimal radius of constellation ring which the received symbol belongs to, for the sake of calculating the innovations of SCKF. Secondly, it performs joint equalization of PMD and RSOP impairments based on SCKF and time-frequency conversion architecture. 28GBaud PDM PCS-64QAM simulation results demonstrate that our scheme can jointly equalize maximum impairments of 8.34 Mrad/s RSOP and 90ps DGD under entropy of 4.5bits/symbol. Additionally, only 0.9 dB OSNR penalty is obtained after joint equalization of 6 Mrad/s RSOP with 70ps DGD impairments. Even under entropy of 5.5bit/symbol, it can still jointly equalize impairments of 6.05 Mrad/s RSOP with 60ps DGD. Furthermore, 16GBaud PCS-64QAM experimental results indicate that the maximum joint equalization performances of PA-SCKF scheme under entropy of 4.5bit/symbol and 5bit/symbol are 17 Mrad/s RSOP with 52ps DGD, and 9 Mrad/s RSOP with 52ps DGD, respectively. These results manifest that our PA-SCKF scheme outperforms both MMA and EKF-CM schemes. Importantly, its complexity is on an order of O(Llog2 L), which is comparable to that of EKF-CM scheme.

Model-based monocular 6-degree-of-freedom pose tracking for asteroid

In this paper, we present a novel vision-based framework to track the 6-DoF pose of an asteroid in real time with the 3D contour of the asteroid as a feature. During pose tracking, at the beginning time of tracking, the tracking system is initialized by a pose retrieval method. At each subsequent time instant, given the 3D mesh model of an asteroid, with the initial pose and its covariance given by the square root cubature Kalman Filter (SCKF), the 3D mesh segments constituting the 3D asteroid contour are efficiently extracted from the 3D mesh model. Then, in the input asteroid image, we search the image points corresponding to the extracted 3D segments within the searching range defined by the initial pose and its covariance. After that, the asteroid pose is determined in real time by minimizing the angles between the back-projection lines of the searched image points and the projection planes of the corresponding 3D segments, which is much more robust to the position change of the asteroid and asteroid size. The covariance matrix of the pose is inferred from the Cartesian noise model in the first order. Eventually, the SCKF is derived from the second-order auto regression to generate the final pose estimate and give the initial pose and its covariance for the next time instant. The synthetic trials quantitatively validate the real-time performance, robustness, and accuracy of our algorithm in dark space, different imaging distances, lighting conditions, image noise, model error, and initial pose error, and meanwhile, the real trial qualitatively shows the effectiveness of our method.

A Novel Tracking Algorithm Based on Waveform Selection for Maneuvering Targets in Clutter

The cognition radar utilizes the dynamic waveform configuration to adapt to the environment to improve tracking performance. A novel tracking algorithm based on waveform selection is proposed to address the maneuvering aircraft tracking problem in clutter. Based on the modified current statistical (MCS) model, the modified probabilistic data association filter (MPDAF) is integrated with the square-root cubature Kalman filter (SCKF) to deal with the nonlinear measurement and the clutter. Additionally, the waveform library is established by applying the fractional Fourier transform (FRFT) to a base waveform, and a direct method is proposed to select the optimal waveform to minimize the posterior state error covariance matrix. The simulation results showed that, compared with the filters with the fixed waveform as well as the state-of-the-art algorithms, the proposed algorithm achieved higher estimation precision and lower track loss percentage while maintaining a low computational burden.

Forecasting-Aided State Estimation in Power Systems During Normal Load Variations Using Iterated Square-Root Cubature Kalman Filter

The main aim is to estimating the voltage profile at all the buses in the system before the arrival of next set of hybrid measurements from field. The effectiveness of the algorithm ISCKF during load variations is evaluated with respect to already implemented Kalman filter approaches for this application. This includes the sudden changes in loads which occurring in practical power systems. The utilization of an iterated square-root cubature Kalman filter (ISCKF) for power system forecasting-aided state estimation (FASE) is being studied during normal load variations. Its implementation involves "Newton-Gauss iterative method being embedded into the square-root cubature Kalman filter (SCKF)" at the measurement update step of Kalman filter. The square-root factor of error covariance matrices is calculated by utilizing QR decomposition to avoid losing of positive definiteness of the matrix. The estimation is carried out utilizing hybrid measurements from remote terminal units and phasor measurement units. The state vector is forecasted using the proposed method in the interval period between two measurement arrivals from the devices. Thereby, caters to state estimation of the voltages at buses in the system even when the measurements are unavailable. The efficacy of the proposed algorithm to FASE is evaluated for IEEE 30-bus system and Northern Region Power Grid (NRPG) 246-bus system. The simulation results show that the proposed ISCKF outperforms the CKF by significant improvement in accuracy of forecasting-aided state estimation. ISCKF will be able to give results before the next set of hybrid data arrives (expected from an estimation algorithm). Therefore, the proposed estimation algorithm is applicable for real-time practical application, with respect to large power systems as well.

Maximum correentropy-based robust Square-root Cubature Kalman Filter for vehicular cooperative navigation

As the core method of cooperative navigation, relative positioning plays a key role in realizing intelligent vehicle driving and vehicle self-assembling network collaboration algorithms. However, when the contamination rate of measurement noise is high, the performance of filtering will be seriously affected. To better address the filtering performance degradation problem due to noise contamination, this paper proposes a vehicular cooperative localization method based on the Maximum Correentropy Robust Square-root Cubature Kalman Filter (MCSCKF). The algorithm not only retains the advantages of Square-root Cubature Kalman Filter (SCKF) but also has strong robustness to non-Gaussian noise. The experimental results of tightly integrated vehicular cooperative navigation show that compared with the Extended Kalman Filter (EKF) and Cubature Kalman Filter (CKF), the localization accuracy of MCSCKF is improved by 35.08% and 31.83%, respectively, which verified the effectiveness in improving the accuracy and robustness of the relative position estimation.

Reliable Estimation of Automotive States Based on Optimized Neural Networks and Moving Horizon Estimator

Accurate estimation of vehicle sideslip angle and attitude angles are essential for the safety control and lateral behaviour of driving performance. In this article, the variation of wheels cornering stiffness is considered for sideslip estimation and addressed by introducing a recursive least squares approach. Based on the nonlinear vehicle dynamic model and the investigated coupling effect between lateral and longitudinal velocity, an optimized moving horizon estimator is proposed to obtain the vehicle sideslip angle, in which an iteration decent algorithm is integrated. Furthermore, a framework, consisting of inertial navigation system measurements, a dual neural network and a square-root cubature Kalman filter, is designed, such that the influence of sensor noise and varied maneuvers are alleviated when estimating the system states. Finally, extensive simulation and field experiments are carried out on different driving scenarios to verify the effectiveness of the developed method. The obtained results clearly indicate the satisfactory estimation accuracy of the designed strategy, superior to the existing estimation methods, such as sole neural networks methods and Kalman-based filters.

Seamless MEMS-INS/Geomagnetic Navigation System Based on Deep-Learning Strong Tracking Square-Root Cubature Kalman Filter.

To suppress inertial navigation system drift and improve the seamless navigation capability of microelectromechanical system-inertial navigation systems/geomagnetic navigation systems (MEMS-INS/MNS) in geomagnetically unlocked environments, this paper proposes a hybrid seamless MEMS-INS/MNS strategy combining a strongly tracked square-root cubature Kalman filter with deep self-learning (DSL-STSRCKF). The proposed DSL-STSRCKF method consists of two innovative steps: (i) The relationship between the deep Kalman filter gain and the optimal estimation is established. In this paper, combining the two auxiliary methods of strong tracking filtering and square-root filtering based on singular value decomposition, the heading accuracy error of ST-SRCKF can reach 1.29°, which improves the heading accuracy by 90.10% and 9.20% compared to the traditional single INS and the traditional integrated navigation algorithm and greatly improves the robustness and computational efficiency. (ii) Providing deep self-learning capability for the ST-SRCKF by introducing a nonlinear autoregressive neural network (NARX) with exogenous inputs, which means that the heading accuracy can still reach 1.33° even during the MNS lockout period, and the heading accuracy can be improved by 89.80% compared with the single INS, realizing the continuous high-precision navigation estimation.

Enhanced square root CKF with mixture correntropy loss for robust state of charge estimation of lithium-ion battery

The measurement data of lithium-ion battery collected in complex operating conditions may be contaminated by non-Gaussian noises (or outliers), a novel robust state of charge (SOC) estimation approach that enhances the robustness of square-root cubature Kalman filter (SRCKF) by incorporating a mixture correntropy loss (MCL) is proposed to overcome the issue of non-Gaussian measurement noise interference. Although the SRCKF can perform non-destructive state estimation for nonlinear system, it is sensitive to the non-Gaussian noises (or outliers) due to the use of mean square error (MSE) loss. To overcome this limitation, the MCL is used as a cost to replace the MSE in CKF framework, which is constructed by mixture of two Gaussian kernel functions with different kernel widths and has outstanding robustness. Moreover, we establish an effective nonlinear regression model that incorporates noise and state error information into the MCL function, and then a fixed-point iteration method is utilized to update the posterior state estimation. Additionally, to further suppress the influence of abnormal noise on the posterior state estimation, we introduce the exponential function of the innovation vector to adjust the measurement covariance matrix in real-time. Accordingly, an enhanced MCL-SRCKF is developed for SOC estimation considering the measurement noises with non-Gaussian distribution. Results from various simulation environments demonstrate that the proposed method achieves high estimation accuracy in different cases.

Wave Excitation Force Estimation for a Multi-DoF WEC via a Cubature Kalman Filter: Improved Design and Results

In this paper, we develop a multiple degree-of-freedom (multi-DoF) wave excitation force estimator based on the square-root cubature Kalman filter (SCKF) [1] combined with an online empirical covariance matching technique for a CETO-like, submerged wave energy converter (WEC) device with three PTOs.
 Though wave excitation force estimation is required by many advanced WEC control approaches, the literature is still quite scarce for multi-DoF devices. Indeed, there are several difficulties in designing a multi-DoF excitation force estimator, especially when the full motion of the WEC is considered. The high dimension of the underlying dynamic system leads to difficulties in on-line implementation and in estimator parameter-tuning. Moreover, nonlinearities may significantly deteriorate estimation performance if a linearized model is used by the estimator to reduce computation time. Papers [2-4] present solutions to multi-DoF wave excitation force estimation, ranging from (extended) Kalman filters to feedforward neural networks, but only up to three DoFs, the surge, heave and pitch directions. In [5], results for a CETO-like WEC are presented for all the six DoFs, based on a CKF wave estimator, which uses a linear state-space model. Undesirable large estimation errors on the yaw direction were observed for several sea states, mainly caused by the model errors introduced by linearizing the kinematics linking buoy motion to PTOs motions. Moreover, even though the CKF is known to be relatively easy to calibrate, guessing covariance matrices of the system and measurement model noises remains troublesome.
 In this paper, we propose to use the SCKF, together with an empirical online covariance matching to over overcome the difficulty of parameter tuning. In our estimator, a nonlinear dynamic system of dimension 72 is used to predict the system dynamics at the cubature points, and the 6-dimensional excitation force is estimated. In addition, we show that a careful system state scaling can substantially reduce estimation errors on the yaw direction, even when using the linearized dynamic system. Moreover, thanks to the moderate computation complexity of the SCKF, and its parallelizability, online implementation can be achieved by taking slightly larger sampling time step, at the price of a small degradation in performance.
 REFERENCES
 [1] I. Arasaratnam and S. Haykin. “Cubature kalman filters”. In: IEEE Transactions on automatic control 54.6 (2009).
 [2] Ling, B. A., 2015. “Real-time estimation and prediction of wave excitation forces for wave energy control applications”. Master’s thesis, Oregon State University.
 [3] Hillis, A., Yardley, J., Plummer, A., and Brask, A., 2020. “Model predictive control of a multi-degree-of-freedom wave energy converter with model mismatch and prediction errors”. Ocean Engineering, 212, p. 107724.
 [4] Bonfanti, M., Hillis, A., Sirigu, S. A., Dafnakis, P., Bracco, G., Mattiazzo, G., and Plummer, A., 2020. “Real-time wave excitation forces estimation: An application on the ISWEC device”. Journal of Marine Science and Engineering, 8(10).
 [5] Nguyen, H.-N., Tona, P., Mérigaud, A., Cocho, M., Pichard, A. “Wave Excitation Force Estimation for a Multi-DoF WEC via a Cubature Kalman Filter: Design and Preliminary Results”, In Proc. of OMAE 2021, virtual, online.

Lithium-ion battery state-of-charge estimation based on long-short-term memory neural network and square-root cubature Kalman filter

Due to the widespread use of Li-ion batteries in electric vehicles, battery management systems for monitoring the status and ensuring the safe operation of Li-ion batteries have been extensively studied. Online monitoring of the state of charge (SOC) is crucial for lithium-ion batteries, but achieving precise SOC estimation is a difficult task due to battery dynamics and the influence of factors such as current, temperature, and operating conditions on SOC variability. This paper introduces a novel approach that combines a Long Short-Term Memory (LSTM) network with a square-root cubature Kalman filter (SRCKF) to address this challenge. To tackle the issue at hand, the proposed methodology employs a two-step approach. Initially, the LSTM network is utilized to capture the complex relationship between the state of charge (SOC) and the measured variables, including current, voltage, and temperature. Subsequently, the output of the LSTM network is subjected to smoothing using the SRCKF technique, leading to precise and consistent SOC estimation. A notable advantage of this method is its ability to simplify the arduous task of parameter tuning for the LSTM network, eliminating the need for constructing a battery model. The experimental results demonstrate that the maximum error in estimating the state of charge (SOC) using this particular method is constrained within the 5% threshold. Compared with using a separate LSTM method at different temperatures, by using the combination method, the root mean square error and maximum error of SOC estimation are greatly reduced.

A NARX network optimized with an adaptive weighted square-root cubature Kalman filter for the dynamic state of charge estimation of lithium-ion batteries

Due to the high nonlinearities and unstable working conditions, accurately estimating the state of charge (SOC) by the battery management system (BMS) is a major challenge in ensuring the safety and reliability of lithium-ion batteries in electric vehicles. This paper presents a deep learning network, a nonlinear autoregressive model with exogenous inputs (NARX) network with a closed-loop architecture and transfer learning mechanism, which is optimized using a proposed adaptive weighted square-root cubature Kalman filter (AWSCKF) with a moving sliding window and an adaptive weighing coefficient for SOC estimation of lithium-ion batteries. The proposed AWSCKF method is established through square-root and cubature updates to optimize the statistical value of the state estimate, error covariance, and measurement noise covariance matrices, with the ability to incorporate high nonlinearities to filter out the noise, stabilize, and optimize the final SOC. To evaluate the effectiveness of the optimized NARX network and verify the proposed AWSCKF method, battery tests are carried out using a lithium cobalt oxide battery at various charge-discharge rates and a lithium nickel cobalt manganese oxide battery at temperatures of 0 and 45 °C under five complex working conditions. The SOC accuracy of lithium-ion batteries is enhanced by the hybrid method estimation process, which is based on sensitivity analysis and adaptation to various working conditions. The comprehensive results show that the proposed NARX-AWSCKF model achieves the overall best mean absolute error, root mean square error, and mean absolute percentage error values of 0.07293%, 0.0912%, and 0.40356%, respectively, under various complex conditions. By effectively utilizing battery domain knowledge for real-world BMS applications, the proposed model outperforms other existing methods in terms of high effectiveness, robustness, and potential to boost the NARX performance.

Maximum Correntropy Square-Root Cubature Kalman Filter with State Estimation for Distributed Drive Electric Vehicles

For nonlinear systems, both the cubature Kalman filter (CKF) and square-root cubature Kalman filter (SCKF) can get good estimation performance under Gaussian noise. However, the actual driving environment noise mostly has non-Gaussian properties, leading to a significant reduction in robustness and accuracy for distributed vehicle state estimation. To address such problems, this paper uses the square-root cubature Kalman filter with the maximum correlation entropy criterion (MCSRCKF), establishing a seven degrees of freedom (7-DOF) nonlinear distributed vehicle dynamics model for accurately estimating longitudinal vehicle speed, lateral vehicle speed, yaw rate, and wheel rotation angular velocity using low-cost sensor signals. The co-simulation verification is verified by the CarSim/Simulink platform under double-lane change and serpentine conditions. Experimental results show that the MCSRCKF has high accuracy and enhanced robustness for distributed drive vehicle state estimation problems in real non-Gaussian noise environments.

Research on the High-Speed Collision Avoidance Method of Distributed Drive Electric Vehicles

High-speed autonomous emergency collision avoidance for intelligent vehicles is a challenging task. Many existing studies have not considered the effect of the road adhesion coefficient in the vehicle high-speed collision avoidance planning layer. Additionally, in lateral control, the effect of strong coupling of vehicle motion on the system model is not considered. This effect increases the uncertainty in the collision avoidance process and correlates with driving safety. In this regard, this paper conducted relevant studies. First, a distributed drive electric vehicle (DDEV) with controlled longitudinal speed was selected as the research platform and derived the transformed square-root cubature Kalman filter (T-SCKF) algorithm with cubature point sampling rule transformation to estimate the road adhesion coefficient. Second, the road adhesion coefficient information was used to calibrate the following vehicle safety distance model and the lane change collision avoidance lateral acceleration information was used to determine the vehicle autonomous emergency collision avoidance trajectory and to optimize the planning decision of the vehicle collision avoidance process. Last, the DDEV was laterally controlled to complete the tracking of the high-speed emergency collision avoidance trajectory by the adaptive model predictive control (Adaptive MPC) method with real-time updating of the system model. The relevant validation shows that the T-SCKF algorithm proposed in this paper can effectively estimate the road adhesion coefficient. The tracking control of the high-speed collision avoidance trajectory by the adaptive MPC method has better tracking accuracy and stability than traditional MPC and linear quadratic regulator (LQR) methods.

Dynamic State Estimation of Synchronous Machines Using Iterated Square-Root Cubature Kalman Filter and Synchrophasor Measurements

Power system dynamic state estimation is the first prerequisite for control and stability prediction under transient conditions. For a stable and reliable power system, it is crucial and helpful to have accurate, precise, and up-to-date information on the states of the synchronous machines- rotor angle and rotor speed deviation. This paper proposes an application of the Iterated Square-root Cubature Kalman filter (ISCKF) to estimate these main states of synchronous generators. The ISCKF method consists of two step modification - one is the square-root step modification of CKF and the next step is the addition of iterative approach to the square-root CKF method. To demonstrate the performance of the proposed approach during a three-phase short circuit fault, the simulation results, are compared with that of Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF) and Cubature Kalman Filter (CKF). The test systems considered are a single machine infinite bus (SMIB) system, an IEEE 9-bus system and a 19-generator 42-bus test system. The estimation accuracy of the rotor angle using ISCKF method is increased by 6.8–36.54% when compared to that of the CKF method. Similarly, the improvement in accuracy is 4.4–28.57% for estimation of speed deviation.

A Robust Hierarchical Estimation Scheme for Vehicle State Based on Maximum Correntropy Square-Root Cubature Kalman Filter

Accurate acquisition of vehicle dynamics state information is essential for vehicle active safety control systems. However, these states cannot be easily measured, and the measurement is expensive. Conventional Kalman filters perform well for vehicle state estimation in Gaussian environments but exhibit low accuracy and robustness under practical non-Gaussian noise. Vehicle model parameter ingestion, inaccurate tire force calculation, and non-Gaussian noise from on-board sensors cause great challenges to the estimation of vehicle driving states. Therefore, this paper presents a robust hierarchical estimation scheme for vehicle driving state based on the maximum correntropy square-root cubature Kalman filter (MCSCKF) using easily measurable on-board sensor information. First, the vehicle mass is dynamically updated based on the recursive least squares (FRLS) method with a forgetting factor. Then, an adaptive sliding mode observer (ASMO) is designed to estimate the longitudinal and lateral tire forces. Ultimately, the vehicle states are estimated based on the MCSCKF under non-Gaussian noise. Two typical operating situations are carried out to verify the validity of the proposed estimation scheme. The results prove that the proposed estimation scheme can estimate the vehicle's driving state accurately compared to other common methods. And the MCSCKF algorithm has better accuracy and robustness than the traditional Kalman filters for vehicle state estimation in non-Gaussian situations.

Cooperative Strategy of Trajectory Tracking and Stability Control for 4WID Autonomous Vehicles Under Extreme Conditions

Trajectory tracking and stability control are two essential functions of autonomous vehicles, and there is inevitable mutual interference between them, especially under extreme conditions. Towards addressing this challenge, this paper proposes a novel cooperative strategy of trajectory tracking and stability control for four-wheel independent drive (4WID) autonomous vehicles. An adaptive trajectory tracking controller is designed based on the model predictive control (MPC) theory, in which the tire cornering stiffness is modified in real-time leverages the lateral force estimated by the square-root cubature Kalman filter (SCKF). Then, the vehicle stability controller is designed based on the sliding mode control (SMC), in which the tire force saturation constraint and the relative weight of yaw rate and sideslip angle are considered. Furthermore, a weight adaptive criterion with normalized stability index is defined to develop the cooperative strategy of trajectory tracking and stability control. The feasibility and adaptability of the proposed method to different extreme conditions are verified by hardware-in-the-loop (HIL) test and CarSim-Simulink co-simulation. Finally, an experimental case is presented to demonstrate the realizability of the proposed method.

State-of-charge estimation of lithium-ion batteries based on fractional-order modeling and adaptive square-root cubature Kalman filter

This paper mainly studies the state of charge (SOC) estimation of lithium batteries based on a fractional-order adaptive square-root cubature Kalman filter (FO-ASRCKF). Firstly, a fractional-order model (FOM) of lithium battery is established by using fractional-order derivative theory. In order to meet the identification accuracy, an improved adaptive genetic algorithm is applied to the process of multi-parameter model identification. Then, the FO-ASRCKF algorithm based on FOM and adaptive rules is proposed, and a comparative experiment with Fractional-order adaptive iterative extended Kalman filter (FO-AIEKF) and Integer-order adaptive square-root cubature Kalman filter (IO-ASRCKF) is carried out. The experimental results show that the proposed FO-ASRCKF can work normally under various working conditions, and it has higher SOC estimation accuracy, with the mean absolute error (MAE) being less than 0.5%. Moreover, it can also overcome the divergence caused by noise and wrong initial values, indicating a better robustness.

Estimation of state parameters and road adhesion coefficients for distributed drive electric vehicles based on a strong tracking SCKF

To address the difficulties in accurately measuring driving state parameters and the road adhesion coefficient, in this paper, the permanent magnet synchronous motor (PMSM) was selected as the automotive in-wheel motor, and the distributed drive electric vehicle (DDEV) simulation model was built based on CarSim and MATLAB/Simulink software. PMSM speed estimation by Adaptive Sliding Mode Observer (ASMO) was used as input information for subsequent studies of state parameters and road adhesion coefficient estimation. Next, this paper established a nonlinear three-degrees-of-freedom whole-vehicle dynamics reference model based on the Dugoff tire model. We derived a suboptimal fading factor using strong tracking theory (STT) and introduced it into the square root of the prediction error covariance of the square-root cubature Kalman filter (SCKF) algorithm. A strong tracking square-root cubature Kalman filter (ST-SCKF) observer was constructed. Improved algorithm estimation accuracy and the ability to cope with sudden changes in operating conditions improve the estimation accuracy of the DDEV driving state parameters and road adhesion coefficient. Finally, a joint CarSim and MATLAB/Simulink simulation and experiments on real vehicles were carried out. The results show that, compared to the traditional CKF (cubature Kalman filter, CKF) and SCKF algorithms, the ST-SCKF algorithm is able to estimate vehicle state parameters and road adhesion coefficients more accurately while maintaining good estimation accuracy for docked road conditions with sudden changes in the road adhesion coefficient.

Measurement of Hand Joint Angle Using Inertial-Based Motion Capture System

The inertial sensor motion capture system has significant advantages over the classical optical motion capture system, including its high versatility, portability, and affordability. However, its accuracy is over one order of magnitude lower than the optical system. The measurement error of the finger joint angle is mainly due to sensor drift and misalignment of sensor to finger segment. In this article, we propose a method that includes both orientation estimation and calibration for accurate joint angle estimation. Specifically, at first, the accuracy of the sensor orientation is greatly improved using the square root cubature Kalman filter (SRCKF) to fuse the magnetic and inertial measurement units (MIMUs) data. Second, the kinematic restrictions of the finger joints are used for initial and in-process calibration to achieve sensor-to-segment (StoS) calibration throughout the process. Finally, the difference between the orientation of the two adjacent segments is the joint angle. Experiments show that our proposed system improves joint measurement accuracy compared with the existing inertial sensor-based systems. Evaluation of ten participants showed that the average root mean square error (RMSE) of finger joint measurements is <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$5.5^{\circ }(\pm 4.0^{\circ })$ </tex-math></inline-formula> . Our proposed system provides accurate information in measuring hand joint angles and quantifying hand movement function in clinical practice.

An Improved IMM-GPDA Tracking Algorithm

To improve the accuracy and efficiency of multi-maneuvering target tracking in dense clutter environments, an improved interactive multi-model generalized probabilistic data association (IMM-GPDA) algorithm is proposed in this paper. The algorithm introduces Doppler information into the measurement data. Firstly, the measurement data is pre-processed by double-threshold regional density clutter elimination, and then the pre-processed data is put into the improved IMM-GPDA algorithm with square-root cubature Kalman filter (SRCKF) and model transition probability adaptation for interaction, association, and filtering. Simulation results show that the algorithm has advanced accuracy, instantaneity, and robustness in tracking environments with multi-maneuvering targets and dense clutters.