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Earth-Centered, Earth-Fixed Inertial Navigation System & Error-State Kalman Filter Reference Manual
This is a self-contained reference document that derives the equations necessary to build a combined inertial navigation system and error-state Kalman filter. Coordinate transform, linear time invariant system, inertial sensing, and error-state Kalman filtering theory is built up from first principles. This theory is then leveraged to derive the system equations for two combined inertial navigation system and error-state Kalman filters: (1) a 15-state system modeling white-noise-integrating accelerometer and gyroscope biases, and (2) a 39-state system modeling static and first-order Gauss-Markov accelerometer and gyroscope biases, scale factor errors, and cross-axis sensitivity errors.
Distribution System State Estimation Using a Multiple Iteration Extended Kalman Filter Approach
To support the operation of modern distribution systems, operators require real-time visibility into system states. Due to a lack of measurements and unbalanced operation, the state estimation in distribution systems is challenging as compared to transmission systems. This paper proposes the utilization of a Multiple Iteration - Extended Kalman Filter based approach for the distribution system state estimation. This modified version of the baseline extended Kalman filter iterates over the update step multiple times thereby reducing the estimation error. The proposed algorithm along with the auxiliary algorithms such as bad data detection is integrated into a co-simulation environment. Case studies show that the proposed state estimation method can result in a lesser estimation error as compared to the baseline approach.
Applying the Kalman filter particle method to strange and open charm hadron reconstruction in the STAR experiment
Here, we apply KF Particle, a Kalman Filter package for secondary vertex finding and fitting, to strange and open charm hadron reconstruction in heavy-ion collisions in the STAR experiment. Compared to the conventional helix swimming method used in STAR, the KF Particle method improves the reconstructed Λ, Ω and $D$ 0 significance considerably. At the same time, we demonstrate that Monte Carlo simulation with the STAR detector responses can well reproduce the topological variable distributions reconstructed in real data using the KF Particle method, therefore retaining good control on the reconstruction efficiency uncertainties for strange and open charm hadrons measurements in heavy-ion collisions.
Reduced-order autodifferentiable ensemble Kalman filters
This paper introduces a computational framework to reconstruct and forecast a partially observed state that evolves according to an unknown or expensive-to-simulate dynamical system. Our reduced-order autodifferentiable ensemble Kalman filters (ROAD-EnKFs) learn a latent low-dimensional surrogate model for the dynamics and a decoder that maps from the latent space to the state space. The learned dynamics and decoder are then used within an EnKF to reconstruct and forecast the state. Numerical experiments show that if the state dynamics exhibit a hidden low-dimensional structure, ROAD-EnKFs achieve higher accuracy at lower computational cost compared to existing methods. If such structure is not expressed in the latent state dynamics, ROAD-EnKFs achieve similar accuracy at lower cost, making them a promising approach for surrogate state reconstruction and forecasting.
Covariance operator estimation: Sparsity, lengthscale, and ensemble Kalman filters
This paper investigates covariance operator estimation via thresholding. For Gaussian random fields with approximately sparse covariance operators, we establish non-asymptotic bounds on the estimation error in terms of the sparsity level of the covariance and the expected supremum of the field. We prove that thresholded estimators enjoy an exponential improvement in sample complexity compared with the standard sample covariance estimator if the field has a small correlation lengthscale. As an application of the theory, we study thresholded estimation of covariance operators within ensemble Kalman filters.
Ensemble Kalman filter for data assimilation coupled with low-resolution computations techniques applied in fluid dynamics
This paper presents an innovative Reduced-order model (ROM) for merging experimental and simulation data using data assimilation (DA) to estimate the "True" state of a fluid dynamics system, leading to more accurate predictions. Our methodology introduces a novel approach by implementing the ensemble Kalman filter (EnKF) within a reduced-dimensional framework, grounded in a robust theoretical foundation and applied to fluid dynamics. To address the substantial computational demands of DA, the proposed ROM employs low-resolution (LR) techniques to drastically reduce computational costs. This innovative approach involves downsampling datasets for DA computations, followed by an advanced reconstruction technique based on low-cost singular value decomposition (lcSVD). The lcSVD method, a key innovation in this paper, has never been applied to DA before and offers a highly efficient way to enhance resolution with minimal computational resources. Our results demonstrate significant reductions in both computation time and RAM usage through these LR techniques without compromising the accuracy of the estimations. For instance, in a turbulent test case, for a data compression rate of 15.9, the LR approach can achieve a speed-up of 13.7 and a RAM compression of 90.9% while maintaining a low relative root mean square error (RRMSE) of 2.6%, compared to 0.8% in the high-resolution (HR) reference. Furthermore, we highlight the effectiveness of the EnKF in estimating and predicting the state of fluid flow systems based on limited observations and given low-fidelity numerical data. This paper highlights the potential of the proposed DA method in fluid dynamics applications, particularly for improving computational efficiency in CFD and related fields. Its ability to balance accuracy with low computational and memory costs makes it especially suitable for large-scale and real-time applications, such as environmental monitoring or engineering design. This method will be incorporated into ModelFLOWs-app.
Applying Particle Swarm Optimization and Extended Kalman Filtering to Model Kaplan Generation Dynamics for Hydropower Systems
Variable renewable generation is increasing the need for hydropower plants to provide fast and flexible grid support, which places new demands on plant-level dynamic models used for monitoring, control, and operational decision-making. This need is especially important for hydroelectric systems, where turbine and generator dynamics are strongly coupled, nonlinear, and time-varying, making accurate real-time representation difficult. To address this problem, this paper develops a digital twin (DT) framework for a synchronous generator–Kaplan turbine system using an explicit separation of slow turbine dynamics and fast generator dynamics. The turbine subsystem is represented by a six-coefficient model, whose parameters are identified offline using particle swarm optimization, while the generator subsystem is updated online through an extended Kalman filter for real-time state and parameter estimation. These models are integrated within a closed-loop simulation that includes a proportional–integral–derivative–double-derivative governor and excitation system, allowing the DT to track plant behavior under realistic operating conditions. Unlike prior studies that treat turbine and generator modeling separately or rely mainly on simulated inputs, the proposed framework is validated using real operational data from a hydropower plant. Results show that the DT reproduces terminal voltage, active power, and reactive power with a normalized root mean square error of approximately 5%. This hybrid offline–online formulation constitutes the main contribution of the work, providing an adaptive and practically deployable DT for hydropower systems with direct relevance to control improvement, performance monitoring, and grid-support applications under high renewable penetration.
Cooperative Navigation within UAV Swarms via Centralized-Unscented Kalman Filtering to Reduce C-SWAP Requirements
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Silent error resilient Kalman filter for inertial navigation using linear algebra checksums
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Cooperative Navigation within UAV Swarms via Centralized-Unscented Kalman Filtering to Reduce C-SWAP Requirements
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Estimation of Power System Frequency Dynamics Using Cubature and Ensemble Kalman Filters
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Experimental validation of a Kalman observer using linearized OpenFAST and a fully instrumented 1:70 model
Abstract To enable real‐time monitoring and control strategies for floating offshore wind turbines, accurate information about the state of the system is needed. This paper details the application of a Kalman filter to the UMaine VolturnUS‐S floating wind platform to provide accurate state estimates in real time using minimal system measurements. The midfidelity nonlinear simulation tool OpenFAST was used to generate the underlying linear state‐space model for the Kalman filter. This linear model and its limitations are demonstrated through comparison with experimental data collected on a 1:70 froude‐scaled model of the floating platform and tower. Using a selection of five measurements from the real system, a Kalman filter was developed to provide estimates for the remaining system states and measurements. These estimates were then validated against the experimental values collected from testing of the scale model. Validation of the Kalman filter produced accurate estimates of surge, heave, and tower base bending moment, measurements of which were not available to the Kalman filter. Performance of the Kalman filter was tested and validated over a range of sea conditions from rated wind speed to storm events and demonstrated robustness in the Kalman filter to maintain accuracy across all operating conditions despite significant error in the underlying linear model for extreme conditions.
Identifying spatiotemporal patterns in opioid vulnerability: investigating the links between disability, prescription opioids and opioid-related mortality
Background: The opioid crisis remains one of the most daunting and complex public health problems in the United States. This study investigates the national epidemic by analyzing vulnerability profiles of three key factors: opioid-related mortality rates, opioid prescription dispensing rates, and disability rank ordered rates. Methods: This study utilizes county level data, spanning the years 2014 through 2020, on the rates of opioid-related mortality, opioid prescription dispensing, and disability. To successfully estimate and predict trends in these opioid-related factors, we augment the Kalman Filter with a novel spatial component. To define opioid vulnerability profiles, we create heat maps of our filter’s predicted rates across the nation’s counties and identify the hotspots. In this context, hotspots are defined on a year-by-year basis as counties with rates in the top 5% nationally. Results: Our spatial Kalman filter demonstrates strong predictive performance. From 2014 to 2018, these predictions highlight consistent spatiotemporal patterns across all three factors, with Appalachia distinguished as the nation’s most vulnerable region. Starting in 2019 however, the dispensing rate profiles undergo a dramatic and chaotic shift. Conclusions: The initial primary drivers of opioid abuse in the Appalachian region were likely prescription opioids; however, it now appears that abuse is sustained by illegal drugs. Additionally, we find that the disabled subpopulation may be more at risk of opioid-related mortality than the general population. Public health initiatives must extend beyond controlling prescription practices to address the transition to and impact of illicit drug use.
Hybrid Cyber-attack Detection in Photovoltaic Farms
Here, to address the cyber-physical security in PV farms, a hybrid cyber-attack detection is proposed in this manuscript. To secure PV farms, the proposed method integrates model-based and data-driven methods by fusing the detection score at the device and system levels. First, a model-based cyber-attack detection method is developed for each PV inverter. A residual between the estimation of the Kalman filter and measurement is calculated. By leveraging the calculated residual from all inverters, a squared Mahalanobis distance is developed for device detection score generation. At the system level, a convolutional neural network (CNN) is proposed to detect cyber-attack using the waveform data at the point of common coupling (PCC) in PV farms. To improve the CNN detection accuracy, a set of well-designed features are extracted from the raw waveform data. Finally, a weighted detection score fusion method is proposed to combine device and system detection scores by using their complementary strength. The feasibility and robustness of the proposed method are validated by testing cases and a comparative experiment.