Constrained Cubature Particle Filter for Vehicle Navigation.

In vehicle navigation, it is quite common that the dynamic system is subject to various constraints, which increases the difficulty in nonlinear filtering. To address this issue, this paper presents a new constrained cubature particle filter (CCPF) for vehicle navigation. Firstly, state constraints are incorporated in the importance sampling process of the traditional cubature particle filter to enhance the accuracy of the importance density function. Subsequently, the Euclidean distance is employed to optimize the resampling process by adjusting particle weights to avoid particle degradation. Further, the convergence of the proposed CCPF is also rigorously proved, showing that the posterior probability function is converged when the particle number N → ∞. Our experimental results and the results of a comparative analysis regarding GNSS/DR (Global Navigation Satellite System/Dead Reckoning)-integrated vehicle navigation demonstrate that the proposed CCPF can effectively estimate system state under constrained conditions, leading to higher estimation accuracy than the traditional particle filter and cubature particle filter.

Limited Memory-Based Random-Weighted Kalman Filter.

The Kalman filter is an important technique for system state estimation. It requires the exact knowledge of system noise statistics to achieve optimal state estimation. However, in practice, this knowledge is often unknown or inaccurate due to uncertainties and disturbances involved in the dynamic environment, leading to degraded or even divergent filtering solutions. To address this issue, this paper presents a new method by combining the random weighting concept with the limited memory technique to accurately estimate system noise statistics. To avoid the influence of excessive historical information on state estimation, random weighting theories are established based on the limited memory technique to estimate both process noise and measurement noise statistics within a limited memory. Subsequently, the estimated system noise statistics are fed back into the Kalman filtering process for system state estimation. The proposed method improves the Kalman filtering accuracy by adaptively adjusting the weights of system noise statistics within a limited memory to suppress the interference of system noise on system state estimation. Simulations and experiments as well as comparison analysis were conducted, demonstrating that the proposed method can overcome the disadvantage of the traditional limited memory filter, leading to im-proved accuracy for system state estimation.

A Transparent Teleoperated Robotic Surgical System with Predictive Haptic Feedback and Force Modelling.

In recent years, robotic minimally invasive surgery has transformed many types of surgical procedures and improved their outcomes. Implementing effective haptic feedback into a teleoperated robotic surgical system presents a significant challenge due to the trade-off between transparency and stability caused by system communication time delays. In this paper, these time delays are mitigated by implementing an environment estimation and force prediction methodology into an experimental robotic minimally invasive surgical system. At the slave, an exponentially weighted recursive least squares (EWRLS) algorithm estimates the respective parameters of the Kelvin-Voigt (KV) and Hunt-Crossley (HC) force models. The master then provides force feedback by interacting with a virtual environment via the estimated parameters. Palpation experiments were conducted with the slave in contact with polyurethane foam during human-in-the-loop teleoperation. The experimental results indicated that the prediction RMSE of error between predicted master force feedback and measured slave force was reduced to 0.076 N for the Hunt-Crossley virtual environment, compared to 0.356 N for the Kelvin-Voigt virtual environment and 0.560 N for the direct force feedback methodology. The results also demonstrated that the HC force model is well suited to provide accurate haptic feedback, particularly when there is a delay between the master and slave kinematics. Furthermore, a haptic feedback approach that incorporates environment estimation and force prediction improve transparency during teleoperation. In conclusion, the proposed bilateral master-slave robotic system has the potential to provide transparent and stable haptic feedback to the surgeon in surgical robotics procedures.

A Force-Feedback Methodology for Teleoperated Suturing Task in Robotic-Assisted Minimally Invasive Surgery.

With robotic-assisted minimally invasive surgery (RAMIS), patients and surgeons benefit from a reduced incision size and dexterous instruments. However, current robotic surgery platforms lack haptic feedback, which is an essential element of safe operation. Moreover, teleportation control challenges make complex surgical tasks like suturing more time-consuming than those that use manual tools. This paper presents a new force-sensing instrument that semi-automates the suturing task and facilitates teleoperated robotic manipulation. In order to generate the ideal needle insertion trajectory and pass the needle through its curvature, the end-effector mechanism has a rotating degree of freedom. Impedance control was used to provide sensory information about needle-tissue interaction forces to the operator using an indirect force estimation approach based on data-based models. The operator's motion commands were then regulated using a hyperplanar virtual fixture (VF) designed to maintain the desired distance between the end-effector and tissue surface while avoiding unwanted contact. To construct the geometry of the VF, an optoelectronic sensor-based approach was developed. Based on the experimental investigation of the hyperplane VF methodology, improved needle-tissue interaction force, manipulation accuracy, and task completion times were demonstrated. Finally, experimental validation of the trained force estimation models and the perceived interaction forces by the user was conducted using online data, demonstrating the potential of the developed approach in improving task performance.

Maximum likelihood-based extended Kalman filter for COVID-19 prediction.

Prediction of COVID-19 spread plays a significant role in the epidemiology study and government battles against the epidemic. However, the existing studies on COVID-19 prediction are dominated by constant model parameters, unable to reflect the actual situation of COVID-19 spread. This paper presents a new method for dynamic prediction of COVID-19 spread by considering time-dependent model parameters. This method discretises the susceptible-exposed-infected-recovered-dead (SEIRD) epidemiological model in time domain to construct the nonlinear state-space equation for dynamic estimation of COVID-19 spread. A maximum likelihood estimation theory is established to online estimate time-dependent model parameters. Subsequently, an extended Kalman filter is developed to estimate dynamic COVID-19 spread based on the online estimated model parameters. The proposed method is applied to simulate and analyse the COVID-19 pandemics in China and the United States based on daily reported cases, demonstrating its efficacy in modelling and prediction of COVID-19 spread.

Sensing and Modelling Mechanical Response in Large Deformation Indentation of Adherent Cell Using Atomic Force Microscopy.

The mechanical behaviour of adherent cells when subjected to the local indentation can be modelled via various approaches. Specifically, the tensegrity structure has been widely used in describing the organization of discrete intracellular cytoskeletal components, including microtubules (MTs) and microfilaments. The establishment of a tensegrity model for adherent cells has generally been done empirically, without a mathematically demonstrated methodology. In this study, a rotationally symmetric prism-shaped tensegrity structure is introduced, and it forms the basis of the proposed multi-level tensegrity model. The modelling approach utilizes the force density method to mathematically assure self-equilibrium. The proposed multi-level tensegrity model was developed by densely distributing the fundamental tensegrity structure in the intracellular space. In order to characterize the mechanical behaviour of the adherent cell during the atomic force microscopy (AFM) indentation with large deformation, an integrated model coupling the multi-level tensegrity model with a hyperelastic model was also established and applied. The coefficient of determination between the computational force-distance (F-D) curve and the experimental F-D curve was found to be at 0.977 in the integrated model on average. In the simulation range, along with the increase in the overall deformation, the local stiffness contributed by the cytoskeletal components decreased from 75% to 45%, while the contribution from the hyperelastic components increased correspondingly.

Set-Membership Based Hybrid Kalman Filter for Nonlinear State Estimation under Systematic Uncertainty.

This paper presents a new set-membership based hybrid Kalman filter (SM-HKF) by combining the Kalman filtering (KF) framework with the set-membership concept for nonlinear state estimation under systematic uncertainty consisted of both stochastic error and unknown but bounded (UBB) error. Upon the linearization of the nonlinear system model via a Taylor series expansion, this method introduces a new UBB error term by combining the linearization error with systematic UBB error through the Minkowski sum. Subsequently, an optimal Kalman gain is derived to minimize the mean squared error of the state estimate in the KF framework by taking both stochastic and UBB errors into account. The proposed SM-HKF handles the systematic UBB error, stochastic error as well as the linearization error simultaneously, thus overcoming the limitations of the extended Kalman filter (EKF). The effectiveness and superiority of the proposed SM-HKF have been verified through simulations and comparison analysis with EKF. It is shown that the SM-HKF outperforms EKF for nonlinear state estimation with systematic UBB error and stochastic error.

A Robust Cubature Kalman Filter with Abnormal Observations Identification Using the Mahalanobis Distance Criterion for Vehicular INS/GNSS Integration.

INS/GNSS (inertial navigation system/global navigation satellite system) integration is a promising solution of vehicle navigation for intelligent transportation systems. However, the observation of GNSS inevitably involves uncertainty due to the vulnerability to signal blockage in many urban/suburban areas, leading to the degraded navigation performance for INS/GNSS integration. This paper develops a novel robust CKF with scaling factor by combining the emerging cubature Kalman filter (CKF) with the concept of Mahalanobis distance criterion to address the above problem involved in nonlinear INS/GNSS integration. It establishes a theory of abnormal observations identification using the Mahalanobis distance criterion. Subsequently, a robust factor (scaling factor), which is calculated via the Mahalanobis distance criterion, is introduced into the standard CKF to inflate the observation noise covariance, resulting in a decreased filtering gain in the presence of abnormal observations. The proposed robust CKF can effectively resist the influence of abnormal observations on navigation solution and thus improves the robustness of CKF for vehicular INS/GNSS integration. Simulation and experimental results have demonstrated the effectiveness of the proposed robust CKF for vehicular navigation with INS/GNSS integration.

Constrained Unscented Particle Filter for SINS/GNSS/ADS Integrated Airship Navigation in the Presence of Wind Field Disturbance.

Due to the disturbance of wind field, it is difficult to achieve precise airship positioning and navigation in the stratosphere. This paper presents a new constrained unscented particle filter (UPF) for SINS/GNSS/ADS (inertial navigation system/global navigation satellite system/atmosphere data system) integrated airship navigation. This approach constructs a wind speed model to describe the relationship between airship velocity and wind speed using the information output from ADS, and further establishes a mathematical model for SINS/GNSS/ADS integrated navigation. Based on these models, it also develops a constrained UPF to obtain system state estimation for SINS/GNSS/ADS integration. The proposed constrained UPF uses the wind speed model to constrain the UPF filtering process to effectively resist the influence of wind field on the navigation solution. Simulations and comparison analysis demonstrate that the proposed approach can achieve optimal state estimation for SINS/GNSS/ADS integrated airship navigation in the presence of wind field disturbance.

A Strap-Down Inertial Navigation/Spectrum Red-Shift/Star Sensor (SINS/SRS/SS) Autonomous Integrated System for Spacecraft Navigation.

This paper presents a new Strap-down Inertial Navigation System/Spectrum Red-Shift/Star Sensor (SINS/SRS/SS) system integration methodology to improve the autonomy and reliability of spacecraft navigation using the spectrum red-shift information from natural celestial bodies such as the Sun, Jupiter and the Earth. The system models for SINS/SRS/SS integration are established. The information fusion of SINS/SRS/SS integration is designed as the structure of the federated Kalman filter to fuse the local estimations of SINS/SRS and SINS/SS integrated subsystems to generate the global state estimation for spacecraft navigation. A new robust adaptive unscented particle filter is also developed to obtain the local state estimations of SINS/SRS and SINS/SS integrated subsystems in a parallel manner. The simulation results demonstrate that the proposed methodology for SINS/SRS/SS integration can effectively calculate navigation solutions, leading to strong autonomy and high reliability for spacecraft navigation.

Multi-Sensor Optimal Data Fusion Based on the Adaptive Fading Unscented Kalman Filter.

This paper presents a new optimal data fusion methodology based on the adaptive fading unscented Kalman filter for multi-sensor nonlinear stochastic systems. This methodology has a two-level fusion structure: at the bottom level, an adaptive fading unscented Kalman filter based on the Mahalanobis distance is developed and serves as local filters to improve the adaptability and robustness of local state estimations against process-modeling error; at the top level, an unscented transformation-based multi-sensor optimal data fusion for the case of N local filters is established according to the principle of linear minimum variance to calculate globally optimal state estimation by fusion of local estimations. The proposed methodology effectively refrains from the influence of process-modeling error on the fusion solution, leading to improved adaptability and robustness of data fusion for multi-sensor nonlinear stochastic systems. It also achieves globally optimal fusion results based on the principle of linear minimum variance. Simulation and experimental results demonstrate the efficacy of the proposed methodology for INS/GNSS/CNS (inertial navigation system/global navigation satellite system/celestial navigation system) integrated navigation.

Random Weighting, Strong Tracking, and Unscented Kalman Filter for Soft Tissue Characterization.

This paper presents a new nonlinear filtering method based on the Hunt-Crossley model for online nonlinear soft tissue characterization. This method overcomes the problem of performance degradation in the unscented Kalman filter due to contact model error. It adopts the concept of Mahalanobis distance to identify contact model error, and further incorporates a scaling factor in predicted state covariance to compensate identified model error. This scaling factor is determined according to the principle of innovation orthogonality to avoid the cumbersome computation of Jacobian matrix, where the random weighting concept is adopted to improve the estimation accuracy of innovation covariance. A master-slave robotic indentation system is developed to validate the performance of the proposed method. Simulation and experimental results as well as comparison analyses demonstrate that the efficacy of the proposed method for online characterization of soft tissue parameters in the presence of contact model error.

Adaptive Square-Root Unscented Particle Filtering Algorithm for Dynamic Navigation.

This paper presents a new adaptive square-root unscented particle filtering algorithm by combining the adaptive filtering and square-root filtering into the unscented particle filter to inhibit the disturbance of kinematic model noise and the instability of filtering data in the process of nonlinear filtering. To prevent particles from degeneracy, the proposed algorithm adaptively adjusts the adaptive factor, which is constructed from predicted residuals, to refrain from the disturbance of abnormal observation and the kinematic model noise. Cholesky factorization is also applied to suppress the negative definiteness of the covariance matrices of the predicted state vector and observation vector. Experiments and comparison analysis were conducted to comprehensively evaluate the performance of the proposed algorithm. The results demonstrate that the proposed algorithm exhibits a strong overall performance for integrated navigation systems.

Real-time haptic characterisation of Hunt-Crossley model based on radial basis function neural network for contact environment.

Dynamic soft tissue characterisation is an important element in robotic minimally invasive surgery. This paper presents a novel method by combining neural network with recursive least square (RLS) estimation for dynamic soft tissue characterisation based on the nonlinear Hunt-Crossley (HC) model. It develops a radial basis function neural network (RBFNN) to compensate for the error caused by natural logarithmic factorisation (NLF) of the HC model for dynamic RLS estimation of soft tissue properties. The RBFNN weights are estimated according to the maximum likelihood principle to evaluate the probability distribution of the neural network modelling residual. Further, by using the linearisation error modelled by RBFNN to compensate for the linearised HC model, an RBFNN-based RLS algorithm is developed for dynamic soft tissue characterisation. Simulation and experimental results demonstrate that the proposed method can effectively model the natural logarithmic linearisation error, leading to improved accuracy for RLS estimation of the HC model parameters.

Maximum likelihood-based extended Kalman filter for soft tissue modelling.

Realistic modelling of human soft tissue is very important in medical applications. This paper proposes a novel method by dynamically incorporating soft tissue characterisation in the process of soft tissue modelling to increase the modelling fidelity. This method defines nonlinear tissue deformation with unknown mechanical properties as a problem of nonlinear filtering identification to dynamically identify mechanical properties and further estimate nonlinear deformation behaviour of soft tissue. It combines maximum likelihood theory, nonlinear filtering and nonlinear finite element method (NFEM) for modelling of nonlinear tissue deformation behaviour based on dynamic identification of homogeneous tissue properties. On the basis of hyperelasticity, a nonlinear state-space equation is established by discretizing tissue deformation through NFEM for dynamic filtering. A maximum likelihood algorithm is also established to dynamically identify tissue mechanical properties during the deformation process. Upon above, a maximum likelihood-based extended Kalman filter is further developed for dynamically estimating tissue nonlinear deformation based on dynamic identification of tissue mechanical properties. Simulation and experimental analyses reveal that the proposed method not only overcomes the NFEM limitation of expensive computations, but also absorbs the NFEM merit of high accuracy for modelling of homogeneous tissue deformation. Further, the proposed method also effectively identifies tissue mechanical properties during the deformation modelling process.

Extended Kalman filter based on stochastic epidemiological model for COVID-19 modelling.

This paper presents a new stochastic-based method for modelling and analysis of COVID-19 spread. A new deterministic Susceptible, Exposed, Infectious, Recovered (Re-infected) and Deceased-based Social Distancing model, named SEIR(R)D-SD, is proposed by introducing the re-infection rate and social distancing factor into the traditional SEIRD (Susceptible, Exposed, Infectious, Recovered and Deceased) model to account for the effects of re-infection and social distancing on COVID-19 spread. The deterministic SEIRD(R)D-SD model is further converted into the stochastic form to account for uncertainties involved in COVID-19 spread. Based on this, an extended Kalman filter (EKF) is developed based on the stochastic SEIR(R)D-SD model to simultaneously estimate both model parameters and transmission state of COVID-19 spread. Simulation results and comparison analyses demonstrate that the proposed method can effectively account for the re-infection and social distancing as well as uncertain effects on COVID-19 spread, leading to improved accuracy for prediction of COVID-19 spread.

Extended Kalman filter for online soft tissue characterization based on Hunt-Crossley contact model.

Real-time soft tissue characterization is significant to robotic assisted minimally invasive surgery for achieving precise haptic control of robotic surgical tasks and providing realistic force feedback to the operator. This paper presents a nonlinear methodology for online soft tissue characterization. An extended Kalman filter (EKF) is developed based on dynamic linearization of the nonlinear H-C contact model in terms of system state for online characterization of soft tissue parameters. To handle the resultant linearization modelling error, an innovation orthogonal EKF is further developed by incorporating an adaptive factor in the EKF filtering to adaptively adjust the innovation covariance according to the principle of innovation orthogonality. Simulation and experimental results as well as comparison analysis demonstrate that the proposed methodology can effectively characterize soft tissue parameters, leading to dramatically improved accuracy comparing to recursive least square estimation. Further, the proposed methodology also requires a smaller computational load and can achieve the real-time performance for soft tissue characterization.

Finite-element kalman filter with state constraint for dynamic soft tissue modelling.

This research work proposes a novel method for realistic and real-time modelling of deformable biological tissues by the combination of the traditional finite element method (FEM) with constrained Kalman filtering. This methodology transforms the problem of deformation modelling into a problem of constrained filtering to estimate physical tissue deformation online. It discretises the deformation of biological tissues in 3D space according to linear elasticity using FEM. On the basis of this, a constrained Kalman filter is derived to dynamically compute mechanical deformation of biological tissues by minimizing the error between estimated reaction forces and applied mechanical load. The proposed method solves the disadvantage of costly computation in FEM while inheriting the superiority of physical fidelity.

Extended Kalman Filter Nonlinear Finite Element Method for Nonlinear Soft Tissue Deformation.

BACKGROUND AND OBJECTIVE: Soft tissue modelling is crucial to surgery simulation. This paper introduces an innovative approach to realistic simulation of nonlinear deformation behaviours of biological soft tissues in real time. METHODS: This approach combines the traditional nonlinear finite-element method (NFEM) and nonlinear Kalman filtering to address both physical fidelity and real-time performance for soft tissue modelling. It defines tissue mechanical deformation as a nonlinear filtering process for dynamic estimation of nonlinear deformation behaviours of biological tissues. Tissue mechanical deformation is discretized in space using NFEM in accordance with nonlinear elastic theory and in time using the central difference scheme to establish the nonlinear state-space models for dynamic filtering. RESULTS: An extended Kalman filter is established to dynamically estimate nonlinear mechanical deformation of biological tissues. Interactive deformation of biological soft tissues with haptic feedback is accomplished as well for surgery simulation. CONCLUSIONS: The proposed approach conquers the NFEM limitation of step computation but without trading off the modelling accuracy. It not only has a similar level of accuracy as NFEM, but also meets the real-time requirement for soft tissue modelling.

Neural network modelling of soft tissue deformation for surgical simulation.

This paper presents a new neural network methodology for modelling of soft tissue deformation for surgical simulation. The proposed methodology formulates soft tissue deformation and its dynamics as the neural propagation and dynamics of cellular neural networks for real-time, realistic, and stable simulation of soft tissue deformation. It develops two cellular neural network models; based on the bioelectric propagation of biological tissues and principles of continuum mechanics, one cellular neural network model is developed for propagation and distribution of mechanical load in soft tissues; based on non-rigid mechanics of motion in continuum mechanics, the other cellular neural network model is developed for governing model dynamics of soft tissue deformation. The proposed methodology not only has computational advantage due to the collective and simultaneous activities of neural cells to satisfy the real-time computational requirement of surgical simulation, but also it achieves physical realism of soft tissue deformation according to the bioelectric propagation manner of mechanical load via dynamic neural activities. Furthermore, the proposed methodology also provides stable model dynamics for soft tissue deformation via the nonlinear property of the cellular neural network. Interactive soft tissue deformation with haptic feedback is achieved via a haptic device. Simulations and experimental results show the proposed methodology exhibits the nonlinear force-displacement relationship and associated nonlinear deformation of soft tissues. Furthermore, not only isotropic and homogeneous but also anisotropic and heterogeneous materials can be modelled via a simple modification of electrical conductivity values of mass points.