Filter State Estimation Research Articles

GPC-LIVO: Point-wise LiDAR-inertial-visual odometry with geometric and photometric composite measurement model

In the pursuit of precision within Simultaneous Localization and Mapping (SLAM), multi-sensor fusion emerges as a validated strategy with vast potential in robotics applications. This work presents GPC-LIVO, an accurate and robust LiDAR-Inertial-Visual Odometry system that integrates geometric and photometric information into one composite measurement model with point-wise updating architecture. GPC-LIVO constructs a belief factor model to assign different weights on geometric and photometric observations in the measurement model and adopts an adaptive error-state Kalman filter state estimation back-end to dynamically estimate the covariance of two observations. Since LiDAR points have larger measurement errors at endpoints and edges, we only fuse photometric information for LiDAR planar features and propose a corresponding validation method based on the associated image plane. Comprehensive experimentation is conducted on GPC-LIVO, encompassing both publicly available data sequences and data collected from our bespoke hardware setup. The results conclusively establish the better performance of our proposed system compare to other state-of-art odometry frameworks, and demonstrate its ability to operate effectively in various challenging environmental conditions. GPC-LIVO outputs states estimation at a high frequency(1-5 kHz, varying based on the processed LiDAR points in a frame) and achieves comparable time consumption for real-time running.

Integration of Artificial Intelligence within an Advanced Filtering Framework for Real-time System State Estimation and Risk Prediction with Application to a Nuclear Microreactor

Novel nuclear reactor designs, such as Small Modular Reactors and Microreactors, require advanced safety assessment methods to analyze potential threats and hazards, and evaluate the efficacy of the safety systems introduced to cope with them. Then, safety assessment frameworks, embedding simulation models, software tools and artificial intelligence algorithms are envisioned to be integrated in operation for autonomous and semi-autonomous activities, ensuring plant reliability and availability while reducing operational and maintenance costs at the same time. For this, Condition-Based Probabilistic Safety Assessment (CB-PSA) must be enabled to provide real-time estimation of the system health state for up-to-date risk evaluation and operation situational awareness. In this paper, we propose a framework of integration consisting of: i) a Neural Network (NN) surrogate model-based Bayesian filter for real-time state estimation during operation using monitoring data; and ii) a NN model for real-time prediction of safety-related parameters. The effectiveness of the proposed framework is demonstrated through its application to a synthetic case study and to a Nuclear Battery design, with reference to a loss of heat sink (LOHS) accident.

Predictive modeling using Copula Particle Filter and Adaptive Network-Based Fuzzy Inference

This paper introduces a novel prediction algorithm, CPF-ANFIS, designed to overcome the challenges posed by high-dimensional input data in Adaptive Neuro-Fuzzy Inference Systems (ANFIS). ANFIS's performance deteriorates with increasing input dimensionality due to the distortion of its membership functions. To address this limitation, CPF-ANFIS leverages a two-stage approach: A Copula Particle Filter (CPF) for robust state estimation and ANFIS for nonlinear mapping. By incorporating copulas, CPF effectively addresses the impoverishment and degeneracy problems commonly encountered in traditional particle filters. This enhanced robustness allows for more accurate state estimation, which in turn improves the overall performance of the CPF-ANFIS algorithm. By decoupling state estimation from nonlinear modeling, CPF-ANFIS effectively mitigates the curse of dimensionality. The proposed method is evaluated on real-world applications, such as hybrid PV-wind systems and SLAM. Experimental results demonstrate that CPF-ANFIS consistently outperforms ANFIS and the Copula Particle Filter individually, as well as previously proposed methods such as ANFIS-PF, highlighting its effectiveness in achieving accurate predictions under challenging conditions. The results show that the CPF-ANFIS algorithm increases prediction accuracy by at least 5% compared to using each algorithm separately.

Adaptive polynomial Kalman filter for nonlinear state estimation in modified AR time series with fixed coefficients

AbstractThis article presents a novel approach for adaptive nonlinear state estimation in a modified autoregressive time series with fixed coefficients, leveraging an adaptive polynomial Kalman filter (APKF). The proposed APKF dynamically adjusts the evolving system dynamics by selecting an appropriate autoregressive time‐series model corresponding to the optimal polynomial order, based on the minimum residual error. This dynamic selection enhances the robustness of the state estimation process, ensuring accurate predictions, even in the presence of varying system complexities and noise. The proposed methodology involves predicting the next state using polynomial extrapolation. Extensive simulations were conducted to validate the performance of the APKF, demonstrating its superiority in accurately estimating the true system state compared with traditional Kalman filtering methods. The root‐mean‐square error was evaluated for various combinations of standard deviations of sensor noise and process noise for different sample sizes. On average, the root‐mean‐square error value, which represents the disparity between the true sensor reading and estimate derived from the adaptive Kalman filter, was 35.31% more accurate than that of the traditional Kalman filter. The comparative analysis highlights the efficacy of the APKF, showing significant improvements in state estimation accuracy and noise resilience.

Complex‐step derivative‐based extended Kalman filter for state estimation in twin rotor MIMO system

AbstractThis paper presents the design of a complex‐step extended Kalman filter (CS‐EKF) to estimate the states of the twin‐rotor MIMO system (TRMS) which is a non‐linear system. Since the model of TRMS is quite complex and contains discontinuous functions, it is very difficult to calculate the Jacobian matrix in the TRMS analytically by hand. This makes it difficult to implement control methods that require Jacobian matrix calculation for TRMS. Herein, to calculate the Jacobian matrix, the CS‐EKF uses the complex‐step derivative approach, which is a numerical technique and offers near‐analytical accuracy in a single function evaluation. The effectiveness of the CS‐EKF is demonstrated through simulation and real‐time experiments. Also, The CS‐EKF is compared to the finite‐difference extended Kalman filter (FD‐EKF) and the unscented Kalman filter (UKF) in terms of estimation accuracy, computational load, and ease of implementation.

Autonomous Small Body Science Operations Using Reinforcement Learning

This work studies the feasibility of using reinforcement learning for small body science operations subject to resource constraints. Two mission scenarios are considered. In the first scenario, a spacecraft autonomously maneuvers between waypoints about a small body while performing science activities, such as mapping and imaging, and periodically downlinking data and managing on-board resources like battery charge, data buffer storage, and fuel usage. In the second scenario, the spacecraft periodically performs navigation updates to improve its state estimate, ensuring that the collected science is within the specified requirements. A Markov decision process formulation of the mission scenarios is formulated, and reinforcement learning is applied to solve the problem. A range of noisy observation types are tested, demonstrating that a fully observable formulation of the problem trained on direct observations of the state is robust to noisy measurements or a filtered state estimate. A decision-making agent is then trained to manage the state estimate by choosing when to take measurements, demonstrating that near-equivalent policies, in comparison to nominal problem formulation, can be trained with an optional navigation update. Finally, a demonstration is performed in which a ground station outage is simulated. The decision-making agent is shown to be robust to this outage, rapidly adjusting its plan to continue nominal operations.

Quaternion-Based Attitude Estimation of an Aircraft Model Using Computer Vision.

Investigating aircraft flight dynamics often requires dynamic wind tunnel testing. This paper proposes a non-contact, off-board instrumentation method using vision-based techniques. The method utilises a sequential process of Harris corner detection, Kanade-Lucas-Tomasi tracking, and quaternions to identify the Euler angles from a pair of cameras, one with a side view and the other with a top view. The method validation involves simulating a 3D CAD model for rotational motion with a single degree-of-freedom. The numerical analysis quantifies the results, while the proposed approach is analysed analytically. This approach results in a 45.41% enhancement in accuracy over an earlier direction cosine matrix method. Specifically, the quaternion-based method achieves root mean square errors of 0.0101 rad/s, 0.0361 rad/s, and 0.0036 rad/s for the dynamic measurements of roll rate, pitch rate, and yaw rate, respectively. Notably, the method exhibits a 98.08% accuracy for the pitch rate. These results highlight the performance of quaternion-based attitude estimation in dynamic wind tunnel testing. Furthermore, an extended Kalman filter is applied to integrate the generated on-board instrumentation data (inertial measurement unit, potentiometer gimbal) and the results of the proposed vision-based method. The extended Kalman filter state estimation achieves root mean square errors of 0.0090 rad/s, 0.0262 rad/s, and 0.0034 rad/s for the dynamic measurements of roll rate, pitch rate, and yaw rate, respectively. This method exhibits an improved accuracy of 98.61% for the estimation of pitch rate, indicating its higher efficiency over the standalone implementation of the direction cosine method for dynamic wind tunnel testing.

Positioning of a lunar surface rover on the south pole using LCNS and DEMs

With the renewed interest in the lunar surface exploration, the European Space Agency is supporting, as part of the Moonlight program, the development of a dedicated Lunar Communications and Navigation Service (LCNS) infrastructure. This should enable to achieve real time positioning and autonomous navigation in the cislunar space, including, among others, lunar landing and surface operations. One of the services proposed, as part of the LunaNet framework (NASA, 2022), is called the Lunar Augmented Navigation Service (LANS) and it is based on a GNSS-like concept. However, compared to Earth-based GNSS, the expected number of available satellites in lunar orbit will initially be limited, which triggers the interest of coupling these technologies at the receiver level with other navigation data sources. In the case of surface rovers, use of digital elevation model (DEM) data has shown to be a potential other source of information to support positioning. The purpose of this contribution is to look at the actual navigation performances achievable when using a simple (four satellites constellation) lunar radio navigation constellation combined with a DEM, through a state estimation filter, for different rover dynamic and different DEM accuracy levels. It is shown that a 5 meter real-time horizontal position accuracy can be achieved, for 99.7% of the time, using a precise enough DEM (5 m/pixel) and a 4 satellite-constellation under different rover’s dynamic conditions (i.e. velocities).

Sampling free iterative PCE filter for state and parameter estimation of nonlinear dynamical systems

We present a novel filter for state and parameter estimation in non-linear dynamical systems, based on a generalised Kalman filter formulation. To achieve a sampling-free implementation, polynomial chaos expansion (PCE) and a Galerkin projection method are utilized for the propagation of uncertainties through the system dynamics. The non-linear dynamics of the system are then linearised by a sequence of Gauss-Newton iterations in combination with linear Kalman updates. Additionally, we introduce a new square root implementation of the PCE-based filter. The proposed filter is evaluated on the Lorenz-63 and Lorenz-84 models for the task of simultaneous state and parameter estimation and is compared with two related approaches. Finally, the computational complexity of our square-root implementation is compared against two existing square root approaches.

Design, Manufacturing and Testing of a Two-Wheeled Self-Balancing Robot

This work presents a self-balancing robot's modeling, manufacturing, and testing. This study aimed to design and construct a robot capable of maintaining balance while stationary and in motion, employing an effective control strategy. The robot's design incorporates sensors, microcontrollers, actuators, and control algorithms. The control strategy involved implementing an LQR (Linear Quadratic Regulator) controller and a Kalman filter for state estimation. The results demonstrate the robot's ability to effectively maintain balance and navigate flat terrain while controlled by a joystick. This study provides valuable insights into the design and control of self-balancing robots.

A novel residual-based Bayesian expectation–maximization adaptive Kalman filter with inaccurate and time-varying noise covariances

In this study, we introduce a novel residual-based Bayesian expectation–maximization adaptive Kalman filter (RBEMAKF) for dynamic state estimation with inaccurate and time-varying noise covariance matrices. The proposed scheme presents a novel maximum a-posteriori (MAP) estimator for characterizing process and measurement noises, leveraging the residual information derived from the Kalman filter. Simultaneously, the MAP is addressed through the application of the expectation–maximization (EM) algorithm. Subsequently, the standard Kalman filter is executed based on the estimated posterior of process and measurement noises (PMNs) to correct the dynamic state in real-time. Additionally, RBEMAKF is extended to propose Laplacian-RBEMAKF (L-RBEMAKF) and Student’s t-RBEMAKF (ST-RBEMAKF) to accommodate outlier environments. These methods assume Laplacian and Student’s t distributions for the prior of PMNs in RBEMAKF, respectively. Extensive simulations and real-world results demonstrate the effectiveness of the proposed RBEMAKF and its extensions (L-RBEMAKF and ST-RBEMAKF) in dynamic state estimation. The availability of our codes can be found at https://github.com/Gaitxh/RBEMAKF.

Rotor speed estimation for half-broken bar detection in induction motors using Kalman filtering

This study addresses the early detection of half-broken bars in induction motors (IMs). Most research on fault detection focuses on current signature analysis because it can provide online and remote monitoring at a low cost. However, errors caused by spectral leakage around the fundamental frequency supply reduce its reliability for fault diagnosis at the incipient stages. The proposed detection technique is based on a spectral analysis of the motor speed. To detect a half-broken bar, measurements of stator voltages and currents are processed by an adaptive extended Kalman filter for system state estimation. Then, a spectral analysis is applied to the estimated motor speed to obtain its power spectral distribution. Finally, the fault harmonic amplitude at 2sfs is used as fault indicator for fault diagnosis. The proposed approach has three main advantages: (1) speed estimation is unaltered by spectral leakage around the main frequency supply, (2) the cost of speed sensors is avoided, and (3) the absence of connecting shaft couplings prevents corruption of speed data by mechanical interference. Numerical simulations and experimental results were carried out for the squirrel cage IM to provide encouraging validation of the proposed early fault detection technique.

Power System Frequency Dynamics Modeling, State Estimation, and Control using Neural Ordinary Differential Equations (NODEs) and Soft Actor-Critic (SAC) Machine Learning Approaches

With the global energy transition of the electric power system, grid control, supervision, and protection is becoming more challenging. With the increasing integration of renewable energy sources (RES), the system dynamics are changing, causing traditional power system dynamic modeling with swing equation-based modeling approaches to fail. Additionally, the converter-dominated power grid is decreasing the system inertia, making the power system more fragile to the frequency swings. This paper first investigates and compares the application of a model-based Kalman filter state estimation approach with (i) a model-free machine learning approach --- neural ordinary differential equations (NODEs) --- and (ii) a data-driven system identification (SysId) approach to model and infer critical state values of the power system frequency dynamics. Then a model predictive control (MPC) framework is compared to a model-free Soft Actor-Critic (SAC) reinforcement learning (RL) control algorithm in providing efficient fast frequency response (FFR) to the power system frequency dynamics. The approaches are compared in terms of their performance goals as well as their per-timestep computational efficiency. The comparative study for state estimation shows that for the model-free requirement, both NODEs and SysId can provide accurate state estimates; however, with increasing model complexity, NODEs can be a better choice for model identification. Similarly, the results from the FFR comparative study show that the SAC RL-based FFR, once trained, outperforms MPC with better control signals and faster computation time, making the SAC RL-based FFR better option for providing FFR to the power system.

Adaptive Output Feedback Control for Uncertain Nonlinear Systems with Unknown Modeling Errors

AbstractIt is well known that unknown modeling errors cannot be avoided in practice. Such unmeasured uncertainties are usually denoted as unknown nonlinear functions that exist in every channel of the system equation. This paper aims to develop an output feedback adaptive control scheme by constructing state estimation filters to address such unknown modeling errors. In the controller design, these uncertainties caused by modeling errors will be accumulated to the last step for compensation. Unknown parameters existing in the upper bound functions of unknown nonlinear functions and system parameters are estimated synchronously based on tuning function approaches. It is shown that the designed output feedback controller can ensure the stability and tracking performance of the closed‐loop system, and the transient performance in terms of a truncated norm is also established.

Observer‐based residual‐driven dynamic compensation strategy for performance improvement of grid‐forming inverter

SummaryGrid‐forming (GFM) inverters offer stable frequency support for microgrid systems, even in the absence of synchronous generators. However, the GFM inverters have low inertia and vulnerability to system uncertainties and external disturbances. The conventional dual‐loop proportional integral (PI) control strategy, while widely used for its simplicity and robustness, suffers from poor dynamic performance. Motivated by this, this paper presents an observer‐based residual‐driven dynamic compensation (RDDC) strategy based on the coprime factorization technic and the Youla parameterization theory to achieve the primary control of the GFM inverter. The observer‐based RDDC strategy comprises four components: a PI controller for tracking control, a linear quadratic regulator (LQR) controller for dynamic adjustment, a residual generator based on the Kalman filter for state estimation and residual generation, and a residual compensation controller designed using model matching theory and solved through linear matrix inequality (LMI) methods for disturbance suppression. Simulation and experiment results consistently demonstrate that the observer‐based RDDC strategy ensures system robustness, enhances the dynamic and steady‐state performance of the GFM inverter system, and strengthens the ability of the GFM inverter to suppress disturbances.

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.

Real-time prediction of material removal rate for advanced process control of chemical mechanical polishing

Polishing torque holds significance in monitoring the chemical mechanical polishing (CMP) process due to its close correlation with material removal. This study introduces a new model-based technique for estimating the material removal rate (MRR) using in-process data from CMP machines. The proposed method employs either the sequential least squares method or Kalman filter for real-time state estimation. Real-time estimation of MRR enables material removal control without relying on conventional endpoint detection (EDP) technologies. The accuracy of the proposed approach is validated through oxide CMP experiments, demonstrating precise estimation of the center-slowed MRR profile towards the end of the pad life.

Position Control Using Trajectory Tracking and State Estimation of a Quad-rotor

Quad-rotor aircrafts are unmanned aerial vehicles that have gained significant popularity in recent years and have been developed for use in many areas. Such vehicles are capable of vertical take-off and landing and are used in various applications. To operate a quad-rotor aircraft efficiently and safely, fundamental issues such as mathematical modeling, control, and state estimation need to be studied. Mathematical modeling involves creating a holistic model of the various subsystems of the aircraft including aerody-namic, kinematic, dynamic and control systems. The control system is a mechanism used for the aircraft to perform the desired movements. State estimation techniques are used to obtain and predict information about the state of the aircraft. This study includes position control using a trajectory generation algorithm. Attitude estimation of the quad-rotor is improved with the Explicit Complementary Filter (ECF) and the state estimations is improved with the Extended Kalman Filter (EKF). Different from other studies, the results are obtained by feeding the model with a state estimation filter. The performances of the filters used for state estimation are compared.

Adaptive Fuzzy Decentralized Output-Feedback Control of Large-Scale Systems With Sensor Faults: A Multichannel Asynchronous Triggering Approach

This paper proposes an adaptive fuzzy decentralized output feedback control scheme for large-scale systems with multichannel asynchronous event-triggering. Uncertain system dynamics, unknown interconnections and time-varying sensor faults are handled simultaneously, even though only the corrupted measured local output is available for the design procedure. First, local state estimation filters are designed to estimate the unmeasured states. Then, considering that the resource-limited communication and computation may exist in all three types of channels including state estimation filter-to-controller channel, parameter estimator-to-controller channel and controller-to-actuator channel, an asynchronous event-triggering framework with time-varying triggering threshold is developed for multiple channels to release the communication and computation burden. Compared with the existing synchronous triggering mechanism, the proposed asynchronous one has several advantages: 1) the redundant signal transmission is reduced, 2) the triggering conditions for different channels are uncorrelated, which enables the designer to adjust the signal transmission frequency of each channel independently, and 3) the robustness could be improved in the face of noise as ideal synchronous triggering is not easy to be achieved in practice. In addition, both gain and bias faults, which are allowed to be unknown and time-varying, are covered in a unified sensor fault model. It is proved that, with the proposed control scheme, all the closed-loop signals are semi-globally uniformly ultimately bounded and the output tracking error converges into an adjustable residual set without Zeno behavior. Finally, simulation and comparison results illustrate the effectiveness and advantages of the proposed control scheme.

Robust Bayesian state and parameter estimation framework for stochastic dynamical systems with combined time-varying and time-invariant parameters

We consider the joint state and parameter estimation for dynamical systems having both time-varying and time-invariant parameters. For systems with time-invariant parameters, it has previously been demonstrated that although nonlinear filters may be used for concurrent state and parameter estimation, employing the Markov Chain Monte Carlo (MCMC) algorithm for estimating time-invariant parameters with nested nonlinear filters for state estimation provides more reliable estimates. Following established methods for parameter estimation using filters, we augment the state vector to include the original system states in addition to the subset of the parameters that are known to vary in time. Conventionally, both time-varying and time-invariant parameters would be appended in the state vector, and thus for the purpose of estimation, both would free to vary in time. However, allowing parameters that are known to be time-invariant to change in time introduces non-physical dynamics into the original system. To avoid inducing artificial dynamics, the time-invariant parameters are estimated using MCMC. Furthermore, by estimating the time-invariant parameters by MCMC, the dimensionality of the augmented state is smaller and the nonlinearity in the ensuing state space model will tend to be weaker compared to the conventional approach. The time-varying parameters are perturbed by random noise processes, and the amplitude of the artificial noise is estimated alongside the time-invariant system parameters using MCMC. Estimating the noise strength in this procedure circumvents the need for manual tuning. We illustrate the above-described approach for a simple dynamical system in which some model parameters are time-varying, while the remaining parameters are time-invariant. We adopt the extended Kalman filter (EKF) for state estimation and the estimation of the time-varying system parameters, but reserve the task of estimating time-invariant parameters, including the model noise strength and the artificial noise strength associated with the time-varying parameter to the MCMC algorithm.