An Extended Kalman Filter for Magnetic Field SLAM Using Gaussian Process Regression

We present a computationally efficient algorithm for using variations in the ambient magnetic field to compensate for position drift in integrated odometry measurements (dead-reckoning estimates) through simultaneous localization and mapping (SLAM). When the magnetic field map is represented with a reduced-rank Gaussian process (GP) using Laplace basis functions defined in a cubical domain, analytic expressions of the gradient of the learned magnetic field become available. An existing approach for magnetic field SLAM with reduced-rank GP regression uses a Rao-Blackwellized particle filter (RBPF). For each incoming measurement, training of the magnetic field map using an RBPF has a computational complexity per time step of O(NpNm2), where Np is the number of particles, and Nm is the number of basis functions used to approximate the Gaussian process. Contrary to the existing particle filter-based approach, we propose applying an extended Kalman filter based on the gradients of our learned magnetic field map for simultaneous localization and mapping. Our proposed algorithm only requires training a single map. It, therefore, has a computational complexity at each time step of O(Nm2). We demonstrate the workings of the extended Kalman filter for magnetic field SLAM on an open-source data set from a foot-mounted sensor and magnetic field measurements collected onboard a model ship in an indoor pool. We observe that the drift compensating abilities of our algorithm are comparable to what has previously been demonstrated for magnetic field SLAM with an RBPF.

Low-Cost and High-Performance Solution for Positioning and Monitoring of Large Structures

Systems for accurate attitude and position monitoring of large structures, such as bridges, tunnels, and offshore platforms are changing in recent years thanks to the exploitation of sensors based on Micro-ElectroMechanical Systems (MEMS) as an Inertial Measurement Unit (IMU). Currently adopted solutions are, in fact, mainly based on fiber optic sensors (characterized by high performance in attitude estimation to the detriment of relevant costs large volumes and heavy weights) and integrated with a Global Position System (GPS) capable of providing low-frequency or single-update information about the position. To provide a cost-effective alternative and overcome the limitations in terms of dimensions and position update frequency, a suitable solution and a corresponding prototype, exhibiting performance very close to those of the traditional solutions, are presented and described hereinafter. The solution leverages a real-time Kalman filter that, along with the proper features of the MEMS inertial sensor and Real-Time Kinematic (RTK) GPS, allows achieving performance in terms of attitude and position estimates suitable for this kind of application. The results obtained in a number of tests underline the promising reliability and effectiveness of the solution in estimating the attitude and position of large structures. In particular, several tests carried out in the laboratory highlighted high system stability; standard deviations of attitude estimates as low as 0.04° were, in fact, experienced in tests conducted in static conditions. Moreover, the prototype performance was also compared with a fiber optic sensor in tests emulating actual operating conditions; differences in the order of a few hundredths of a degree were found in the attitude measurements.

Drift-Free Integration in Inductive Magnetic Field Measurements Achieved by Kalman Filtering

Sensing coils are inductive sensors commonly used to measure magnetic fields, such as those generated by electromagnets used in many kinds of industrial and scientific applications. Inductive sensors rely on integrating the output voltage at the coil's terminals in order to obtain flux linkage, which may suffer from the magnification of low-frequency noise resulting in a drifting integrated signal. This article presents a method for the cancellation of integrator drift. The method is based on a first-order linear Kalman filter combining the data from the coil and a second sensor. Two case studies are presented. In the first one, the second sensor is a Hall probe, which senses the magnetic field directly. In a second case study, the magnet's excitation current was used instead to provide a first-order approximation of the field. Experimental tests show that both approaches can reduce the measured field drift by three orders of magnitude. The Hall probe option guarantees, in addition, one order of magnitude better absolute accuracy than by using the excitation current.

Sea Surface Temperature Analysis for Fengyun-3C Data Using Oriented Elliptic Correlation Scales

Sea surface temperature (SST) is critical for global climate change analysis and research. In this study, we used visible and infrared scanning radiometer (VIRR) sea surface temperature (SST) data from the Fengyun-3C (FY-3C) satellite for SST analysis, and applied the Kalman filtering methods with oriented elliptic correlation scales to construct SST fields. Firstly, the model for the oriented elliptic correlation scale was established for SST analysis. Secondly, observation errors from each type of SST data source were estimated using the optimal matched datasets, and background field errors were calculated using the model of oriented elliptic correlation scale. Finally, the blended SST analysis product was obtained using the Kalman filtering method, then the SST fields using the optimum interpolation (OI) method were chosen for comparison to validate results. The quality analysis for 2016 revealed that the Kalman analysis with a root-mean-square error (RMSE) of 0.3243 °C had better performance than did the OI analysis with a RMSE of 0.3911 °C, which was closer to the OISST product RMSE of 0.2897 °C. The results demonstrated that the Kalman filtering method with dynamic observation error and background error estimation was significantly superior to the OI method in SST analysis for FY-3C SST data.

Improved Camshift object tracking algorithm in occluded scenes based on AKAZE and Kalman

Camshift algorithm tracking is susceptible to interference when a tracking object is occluded or when its hue is similar to the background. An improved Camshift object-tracking algorithm combining AKAZE (Accelerated-KAZE) feature matching and Kalman filtering is proposed. First, the video channel is converted for processing. Second, AKAZE is used to match the object feature points and Kalman filtering is used to predict the next position. Then different scenes are judged by the threshold and the Camshift and Kalman tracking algorithms are used for object tracking, respectively. Finally, the improved Camshift algorithm is used to test the moving object in a variety of situations and compared with the traditional Camshift algorithm and the Kalman filter improved Camshift algorithm. Experimental results show that the improved joint tracking algorithm can continue tracking under full occlusion. The effective frame rate of recognition is increased by about 20%, and the single-frame image processing time is less than 35 ms, which can meet the real-time tracking requirements.

Underwater Vehicle Positioning by Correntropy-Based Fuzzy Multi-Sensor Fusion

The ability of the underwater vehicle to determine its precise position is vital to completing a mission successfully. Multi-sensor fusion methods for underwater vehicle positioning are commonly based on Kalman filtering, which requires the knowledge of process and measurement noise covariance. As the underwater conditions are continuously changing, incorrect process and measurement noise covariance affect the accuracy of position estimation and sometimes cause divergence. Furthermore, the underwater multi-path effect and nonlinearity cause outliers that have a significant impact on positional accuracy. These non-Gaussian outliers are difficult to handle with conventional Kalman-based methods and their fuzzy variants. To address these issues, this paper presents a new and improved adaptive multi-sensor fusion method by using information-theoretic, learning-based fuzzy rules for Kalman filter covariance adaptation in the presence of outliers. Two novel metrics are proposed by utilizing correntropy Gaussian and Versoria kernels for matching theoretical and actual covariance. Using correntropy-based metrics and fuzzy logic together makes the algorithm robust against outliers in nonlinear dynamic underwater conditions. The performance of the proposed sensor fusion technique is compared and evaluated using Monte-Carlo simulations, and substantial improvements in underwater position estimation are obtained.

A Factor-Graph-Based Approach to Vehicle Sideslip Angle Estimation

Sideslip angle is an important variable for understanding and monitoring vehicle dynamics, but there is currently no inexpensive method for its direct measurement. Therefore, it is typically estimated from proprioceptive sensors onboard using filtering methods from the family of the Kalman filter. As a novel alternative, this work proposes modeling the problem directly as a graphical model (factor graph), which can then be optimized using a variety of methods, such as whole-dataset batch optimization for offline processing or fixed-lag smoothing for on-line operation. Experimental results on real vehicle datasets validate the proposal, demonstrating a good agreement between estimated and actual sideslip angle, showing similar performance to state-of-the-art methods but with a greater potential for future extensions due to the more flexible mathematical framework. An open-source implementation of the proposed framework has been made available online.

Volatility estimation for COVID-19 daily rates using Kalman filtering technique

This paper discusses the use of stochastic modeling in the prognosis of Corona Virus-Infected Disease 2019 (COVID-19) cases. COVID-19 is a new disease that is highly infectious and dangerous. It has deeply shaken the world, claiming the lives of over a million people and bringing the world to a lockdown. So, the early detection of COVID is essential for the patients' timely treatment and preventive measures. A filtering technique with time-varying parameters is presented to predict the stochastic volatility (SV) of COVID-19 cases. The time-varying parameters are estimated using the Kalman filtering technique based on the stochastic component of data volatility. Kalman filtering is essential as it removes insignificant information from the data. We forecast one-step-ahead predicted volatility with ± 3 standard prediction errors, which is implemented by Maximum Likelihood Estimation. We conclude that Kalman filtering in conjunction with the SV model is a reliable predictive model for COVID-19 since it is less constrained by the past autoregressive information.

A Discrete-Time Extended Kalman Filter Approach Tailored for Multibody Models: State-Input Estimation

Model-based force estimation is an emerging methodology in the mechatronic community given the possibility to exploit physically inspired high-fidelity models in tandem with ready-to-use cheap sensors. In this work, an inverse input load identification methodology is presented combining high-fidelity multibody models with a Kalman filter-based estimator and providing the means for an accurate and computationally efficient state-input estimation strategy. A particular challenge addressed in this work is the handling of the redundant state-description encountered in common multibody model descriptions. A novel linearization framework is proposed on the time-discretized equations in order to extract the required system model matrices for the Kalman filter. The presented framework is experimentally validated on a slider-crank mechanism. The nonlinear kinematics and dynamics are well represented through a rigid multibody model with lumped flexibilities to account for localized interaction phenomena among bodies. The proposed methodology is validated estimating the input torque delivered by a driver electro-motor together with the system states and comparing the experimental data with the estimated quantities. The results show the stability and accuracy of the estimation framework by only employing the angular motor velocity, measured by the motor encoder sensor and available in most of the commercial electro-motors.

Bridging GNSS Outages with IMU and Odometry: A Case Study for Agricultural Vehicles

Nowadays, many precision farming applications rely on the use of GNSS-RTK. However, when it comes to autonomous agricultural vehicles, GNSS cannot be used as a stand-alone system for positioning. To ensure high availability and robustness of the positioning solution, GNSS-RTK must be fused with additional sensors. This paper presents a novel sensor fusion algorithm tailored to tracked agricultural vehicles. GNSS-RTK, an IMU and wheel speed sensors are fused in an error-state Kalman filter to estimate position and attitude of the vehicle. An odometry model for tracked vehicles is introduced which is used to propagate the filter state. By using both IMU and wheel speed sensors, specific motion characteristics of tracked vehicles such as slippage can be included in the dynamic model. The presented sensor fusion algorithm is tested at a composting site using a tracked compost turner. The sensor measurements are recorded using the Robot Operating System (ROS). To analyze the achievable accuracies for position and attitude of the vehicle, a precise reference trajectory is measured using two robotic total stations. The resulting trajectory of the error-state filter is then compared to the reference trajectory. To analyze how well the proposed error-state filter is suited to bridge GNSS outages, GNSS outages of 30 s are simulated in post-processing. During these outages, the vehicle's state is propagated using the wheel speed sensors, IMU, and the dynamic model for tracked vehicles. The results show that after 30 s of GNSS outage, the estimated horizontal position of the vehicle still has a sub-decimetre accuracy.

Analyzing the effects of observation function selection in ensemble Kalman filtering for epidemic models

The Ensemble Kalman Filter (EnKF) is a popular sequential data assimilation method that has been increasingly used for parameter estimation and forecast prediction in epidemiological studies. The observation function plays a critical role in the EnKF framework, connecting the unknown system variables with the observed data. Key differences in observed data and modeling assumptions have led to the use of different observation functions in the epidemic modeling literature. In this work, we present a novel computational analysis demonstrating the effects of observation function selection when using the EnKF for state and parameter estimation in this setting. In examining the use of four epidemiologically-inspired observation functions of different forms in connection with the classic Susceptible-Infectious-Recovered (SIR) model, we show how incorrect observation modeling assumptions (i.e., fitting incidence data with a prevalence model, or neglecting under-reporting) can lead to inaccurate filtering estimates and forecast predictions. Results demonstrate the importance of choosing an observation function that well interprets the available data on the corresponding EnKF estimates in several filtering scenarios, including state estimation with known parameters, and combined state and parameter estimation with both constant and time-varying parameters. Numerical experiments further illustrate how modifying the observation noise covariance matrix in the filter can help to account for uncertainty in the observation function in certain cases.

Stochastic Force-based Insertion Depth and Tip Position Estimations of Flexible FBG-Equipped Instruments in Robotic Retinal Surgery

Vitreoretinal surgery is among the most delicate surgical tasks during which surgeon hand tremor may severely attenuate surgeon performance. Robotic assistance has been demonstrated to be beneficial in diminishing hand tremor. Among the requirements for reliable assistance from the robot is to provide precise measurements of system states e.g. sclera forces, tool tip position and tool insertion depth. Providing this and other sensing information using existing technology would contribute towards development and implementation of autonomous robot-assisted tasks in retinal surgery such as laser ablation, guided suture placement/assisted needle vessel cannulation, among other applications. In the present work, we use a state-estimating Kalman filtering (KF) to improve the tool tip position and insertion depth estimates, which used to be purely obtained by robot forward kinematics (FWK) and direct sensor measurements, respectively. To improve tool tip localization, in addition to robot FWK, we also use sclera force measurements along with beam theory to account for tool deflection. For insertion depth, the robot FWK is combined with sensor measurements for the cases where sensor measurements are not reliable enough. The improved tool tip position and insertion depth measurements are validated using a stereo camera system through preliminary experiments and a case study. The results indicate that the tool tip position and insertion depth measurements are significantly improved by 77% and 94% after applying KF, respectively.

Potential of a probabilistic framework for target prediction from surrogate respiratory motion during lung radiotherapy

Purpose.Respiration-induced motion introduces significant positioning uncertainties in radiotherapy treatments for thoracic sites. Accounting for this motion is a non-trivial task commonly addressed with surrogate-based strategies and latency compensating techniques. This study investigates the potential of a new unified probabilistic framework to predict both future target motion in real-time from a surrogate signal and associated uncertainty.Method.A Bayesian approach is developed, based on a Kalman filter theory adapted specifically for surrogate measurements. Breathing motions are collected simultaneously from a lung target, two external surrogates (abdominal and thoracic markers) and an internal surrogate (liver structure) for 9 volunteers during 4 min, in which severe breathing changes occur to assess the robustness of the method. A comparison with an artificial non-linear neural network (NN) is performed, although no confidence interval prediction is provided. A static worst-case scenario and a simple static design are investigated.Results.Although the NN can reduce the prediction errors from thoracic surrogate in some cases, the Bayesian framework outperforms in most cases the NN when using the other surrogates: bias on predictions is reduced by 38% and 16% on average when using respectively the liver and the abdomen for the simple scenario, and by respectively 40% and 31% for the worst-case scenario. The standard deviation of residuals is reduced on average by up to 42%. The Bayesian method is also found to be more robust to increasing latencies. The thoracic marker appears to be less reliable to predict the target position, while the liver shows to be a better surrogate. A statistical test confirms the significance of both observations.Conclusion.The proposed framework predicts both the future target position and the associated uncertainty, which can be valuably used to further assist motion management decisions. Further investigation is required to improve the predictions by using an adaptive version of the proposed framework.

A novel interval type-2 fuzzy Kalman filtering and tracking of experimental data

In this paper, a methodology for design of fuzzy Kalman filter, using interval type-2 fuzzy models, in discrete time domain, via spectral decomposition of experimental data, is proposed. The adopted methodology consists of recursive parametric estimation of local state space linear submodels of interval type-2 fuzzy Kalman filter for tracking and forecasting of the dynamics inherited to experimental data, using an interval type-2 fuzzy version of Observer/Kalman Filter Identification (OKID) algorithm. The partitioning of the experimental data is performed by interval type-2 fuzzy Gustafson-Kessel clustering algorithm. The interval Kalman gains in the consequent proposition of interval type-2 fuzzy Kalman filter are updated according to unobservable components computed by recursive spectral decomposition of experimental data. Computational results illustrate the efficiency of proposed methodology for filtering and tracking the time delayed state variables of Chen's chaotic attractor in a noisy environment, and experimental results illustrate its applicability for adaptive and real time forecasting the dynamic spread behavior of novel Coronavirus 2019 (COVID-19) outbreak in Brazil.

A Generalized Unscented Transformation for Probability Distributions

The unscented transform uses a weighted set of samples called sigma points to propagate the means and covariances of nonlinear transformations of random variables. However, unscented transforms developed using either the Gaussian assumption or a minimum set of sigma points typically fall short when the random variable is not Gaussian distributed and the nonlinearities are substantial. In this paper, we develop the generalized unscented transform (GenUT), which uses 2n+1 sigma points to accurately capture up to the diagonal components of the skewness and kurtosis tensors of most probability distributions. Constraints can be analytically enforced on the sigma points while guaranteeing at least second-order accuracy. The GenUT uses the same number of sigma points as the original unscented transform while also being applicable to non-Gaussian distributions, including the assimilation of observations in the modeling of infectious diseases such as coronavirus (SARS-CoV-2) causing COVID-19.

Robust Filtering Techniques for RTK Positioning in Harsh Propagation Environments

Global navigation satellite systems (GNSSs) play a key role in intelligent transportation systems such as autonomous driving or unmanned systems navigation. In such applications, it is fundamental to ensure a reliable precise positioning solution able to operate in harsh propagation conditions such as urban environments and under multipath and other disturbances. Exploiting carrier phase observations allows for precise positioning solutions at the complexity cost of resolving integer phase ambiguities, a procedure that is particularly affected by non-nominal conditions. This limits the applicability of conventional filtering techniques in challenging scenarios, and new robust solutions must be accounted for. This contribution deals with real-time kinematic (RTK) positioning and the design of robust filtering solutions for the associated mixed integer- and real-valued estimation problem. Families of Kalman filter (KF) approaches based on robust statistics and variational inference are explored, such as the generalized M-based KF or the variational-based KF, aiming to mitigate the impact of outliers or non-nominal measurement behaviors. The performance assessment under harsh propagation conditions is realized using a simulated scenario and real data from a measurement campaign. The proposed robust filtering solutions are shown to offer excellent resilience against outlying observations, with the variational-based KF showcasing the overall best performance in terms of Gaussian efficiency and robustness.

A flexible framework for sequential estimation of model parameters in computational hemodynamics

A major challenge in constructing three dimensional patient specific hemodynamic models is the calibration of model parameters to match patient data on flow, pressure, wall motion, etc. acquired in the clinic. Current workflows are manual and time-consuming. This work presents a flexible computational framework for model parameter estimation in cardiovascular flows that relies on the following fundamental contributions. (i) A Reduced-Order Unscented Kalman Filter (ROUKF) model for data assimilation for wall material and simple lumped parameter network (LPN) boundary condition model parameters. (ii) A constrained least squares augmentation (ROUKF-CLS) for more complex LPNs. (iii) A "Netlist" implementation, supporting easy filtering of parameters in such complex LPNs. The ROUKF algorithm is demonstrated using non-invasive patient-specific data on anatomy, flow and pressure from a healthy volunteer. The ROUKF-CLS algorithm is demonstrated using synthetic data on a coronary LPN. The methods described in this paper have been implemented as part of the CRIMSON hemodynamics software package.

Comparing Perimetric Loss at Different Target Intraocular Pressures for Patients with High-Tension and Normal-Tension Glaucoma

PURPOSE

To compare forecasted changes in mean deviation (MD) for patients with normal-tension glaucoma (NTG) and high-tension open-angle glaucoma (HTG) at different target intraocular pressures (IOPs) using Kalman filtering, a machine learning technique.

DESIGN

Retrospective cohort study.

PARTICIPANTS

From the Collaborative Initial Glaucoma Treatment Study or Advanced Glaucoma Intervention Study, 496 patients with HTG; from Japan, 262 patients with NTG.

METHODS

Using the first 5 sets of tonometry and perimetry measurements, each patient was classified as a fast progressor, slow progressor, or nonprogressor. Using Kalman filtering, personalized forecasts of MD changes over 2.5 years' follow-up were generated for fast and slow progressors with HTG and NTG with IOPs maintained at hypothetical IOP targets of 9 to 21 mmHg. Future MD loss with different percentage IOP reductions from baseline (0%-50%) were also assessed for the groups.

MAIN OUTCOME MEASURES

Mean forecasted MD change at different target IOPs.

RESULTS

The mean (± standard deviation) patient age was 63.5 ± 10.5 years for NTG and 66.5 ± 10.9 years for HTG. Over the 2.5-year follow-up, at target IOPs of 9, 15, and 21 mmHg, respectively, the mean forecasted MD losses for fast progressors with NTG were 2.3 ± 0.2, 4.0 ± 0.2, and 5.7 ± 0.2 dB; for slow progressors with NTG, losses were 0.63 ± 0.02, 1.02 ± 0.03, and 1.49 ± 0.07 dB; for fast progressors with HTG, losses were 1.8 ± 0.1, 3.4 ± 0.1, and 5.1 ± 0.1 dB; and for slow progressors with HTG, losses were 0.55 ± 0.06, 1.04 ± 0.08, and 1.59 ± 0.10 dB. Fast progressors with NTG had greater MD decline than fast progressors with HTG at each target IOP (P ≤ 0.007 for all). The MD decline for slow progressors with HTG and NTG were similar (P ≥ 0.24 for all target IOPs). Fast progressors with HTG had greater MD loss than those with NTG with 0%-10% IOP reduction since baseline (P ≤ 0.01 for all), but not 25% (P = 0.07) or 50% (P = 0.76) reduction since baseline.

CONCLUSIONS

Machine learning algorithms using Kalman filtering techniques demonstrate promise at forecasting future MD values at different target IOPs for patients with NTG and HTG.

Short-term forecasts and long-term mitigation evaluations for the COVID-19 epidemic in Hubei Province, China

As an emerging infectious disease, the 2019 coronavirus disease (COVID-19) has developed into a global pandemic. During the initial spreading of the virus in China, we demonstrated the ensemble Kalman filter performed well as a short-term predictor of the daily cases reported in Wuhan City. Second, we used an individual-level network-based model to reconstruct the epidemic dynamics in Hubei Province and examine the effectiveness of non-pharmaceutical interventions on the epidemic spreading with various scenarios. Our simulation results show that without continued control measures, the epidemic in Hubei Province could have become persistent. Only by continuing to decrease the infection rate through 1) protective measures and 2) social distancing can the actual epidemic trajectory that happened in Hubei Province be reconstructed in simulation. Finally, we simulate the COVID-19 transmission with non-Markovian processes and show how these models produce different epidemic trajectories, compared to those obtained with Markov processes. Since recent studies show that COVID-19 epidemiological parameters do not follow exponential distributions leading to Markov processes, future works need to focus on non-Markovian models to better capture the COVID-19 spreading trajectories. In addition, shortening the infectious period via early case identification and isolation can slow the epidemic spreading significantly.

Nondestructive Damage Testing of Beam Structure Based on Vibration Response Signal Analysis

Nondestructive damage-testing technology based on vibration signal analysis makes full use of the response characteristics of wave and energy. With the advantages of wide bandwidths of response frequency and high sensitivity, the nondestructive testing technology based on vibration signal analysis has a superiority in the application for the detection and characterization of structural defects, and has become one of the important methods for the nondestructive testing of structural material defects and damage. This paper presents a novel method of detection localization and quantitative analysis for local damage in beam structures, based on the response analysis of vibration signals. A damage-detection and -identification algorithm based on a unscented Kalman filter (UKF) was designed, which greatly reduces the computational workload in the process of damage identification over that in conventional methods. The method presented in this paper has significances to widen the application scope of the nondestructive testing method, and increase the recognition efficiency and effectiveness of this kind of method in engineering.

SVM+KF Target Tracking Strategy Using the Signal Strength in Wireless Sensor Networks

Target Tracking (TT) is a fundamental application of wireless sensor networks. TT based on received signal strength indication (RSSI) is by far the cheapest and simplest approach, but suffers from a low stability and precision owing to multiple paths, occlusions, and decalibration effects. To address this problem, we propose an innovative TT algorithm, known as the SVM+KF method, which combines the support vector machine (SVM) and an improved Kalman filter (KF). We first use the SVM to obtain an initial estimate of the target's position based on the RSSI. This enhances the ability of our algorithm to process nonlinear data. We then apply an improved KF to modify this estimated position. Our improved KF adds the threshold value of the innovation update in the traditional KF. This value changes dynamically according to the target speed and network parameters to ensure the stability of the results. Simulations and real experiments in different scenarios demonstrate that our algorithm provides a superior tracking accuracy and stability compared to similar algorithms.

A Method of Correcting Estimation Failure in Latent Differential Equations with Comparisons to Kalman Filtering

Studies have used the latent differential equation (LDE) model to estimate the parameters of damped oscillation in various phenomena, but it has been shown that correct, non-zero parameter estimates are only obtained when the latent series exhibits little or no process noise. Consequently, LDEs are limited to modeling deterministic processes with measurement error rather than those with random behavior in the true latent state. The reasons for these limitations are considered, and a piecewise deterministic approximation (PDA) algorithm is proposed to treat process noise outliers as functional discontinuities and obtain correct estimates of the damping parameter. Comprehensive, random-effects simulations were used to compare results with those obtained using a state-space model (SSM) based on the Kalman filter. The LDE with the PDA algorithm (LDEPDA) successfully recovered the simulated damping parameter under a variety of conditions when process noise was present in the latent state. The LDEPDA had greater precision and accuracy than the SSM when estimating parameters from data with sparse jump discontinuities, but worse performance for diffusion processes overall. All three methods were applied to a sample of postural sway data. The basic LDE estimated zero damping, while the LDEPDA and SSM estimated moderate to high damping. The SSM estimated the smallest standard errors for both frequency and damping parameter estimates.

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.

Improved detection of Parkinsonian resting tremor with feature engineering and Kalman filtering

OBJECTIVE

Accurate and reliable detection of tremor onset in Parkinson's disease (PD) is critical to the success of adaptive deep brain stimulation (aDBS) therapy. Here, we investigated the potential use of feature engineering and machine learning methods for more accurate detection of rest tremor in PD.

METHODS

We analyzed the local field potential (LFP) recordings from the subthalamic nucleus region in 12 patients with PD (16 recordings). To explore the optimal biomarkers and the best performing classifier, the performance of state-of-the-art machine learning (ML) algorithms and various features of the subthalamic LFPs were compared. We further used a Kalman filtering technique in feature domain to reduce the false positive rate.

RESULTS

The Hjorth complexity showed a higher correlation with tremor, compared to other features in our study. In addition, by optimal selection of a maximum of five features with a sequential feature selection method and using the gradient boosted decision trees as the classifier, the system could achieve an average F1 score of up to 88.7% and a detection lead of 0.52 s. The use of Kalman filtering in feature space significantly improved the specificity by 17.0% (p = 0.002), thereby potentially reducing the unnecessary power dissipation of the conventional DBS system.

CONCLUSION

The use of relevant features combined with Kalman filtering and machine learning improves the accuracy of tremor detection during rest.

SIGNIFICANCE

The proposed method offers a potential solution for efficient on-demand stimulation for PD tremor.

An adaptive Kalman filtering algorithm based on back-propagation (BP) neural network applied for simultaneously detection of exhaled CO and N2O

A compact high-resolution spectroscopic sensor using a thermoelectrically (TE) cooled continuous-wave (CW) room temperature (RT) quantum cascade laser (QCL) was demonstrated for simultaneous measurements of exhaled carbon monoxide (CO) and nitrous oxide (N₂O). The sampling pressure was optimized to improve the sensitivity, the optimal pressure was determined to be 150 mbar based on an optical density analysis of simulated and measured absorption spectra. An adaptive Kalman filtering algorithm based on back-propagation (BP) neural network was developed and proposed for real-time exhaled breath analysis in order to perform fast and high precision on-line measurements. The detection limits (1σ) of 1.14 ppb and 1.12 ppb were experimentally achieved for CO and N₂O detection, respectively. Typical concentrations of exhaled CO and N₂O from smokers and non-smokers were analyzed. The experimental results indicated that the state-of-the-art CW-QCL based sensor has a great potential for non-invasive, on-line identification and quantification of biomarkers in human breath.