Implementation Of Kalman Filter Research Articles

Design and implementation of an adaptive unscented Kalman filter with interval Type-3 fuzzy set for an attitude and heading reference system considering gyroscope bias

Low-cost microelectromechanical sensors used in attitude and heading reference systems (AHRS) suffer from unstable on–off biases, scaling errors, and nonlinearities that lead to an increase of navigation errors over time. To damp these errors and uncertainties from ultimate attitude and heading angles, the bias term of gyroscopes is augemented in under estimation state vector for high frequency feedback compensation. In this paper, an adaptive estimation algorithm to combine the strong tracking filter (STF) and interval type-3 fuzzy set (IT3FS) with an unscented Kalman filter (UKF) is proposed to deal with the large uncertainties in the microelectromechanical AHRS. The UKF, involving strong capability of dealing with nonlinearity, is limited by large instable bias uncertainty. By combining the STF to adaptively tuning of the UKF gain matrix and the IT3FS to determine the STF fading factor as well, the new IT3FS-STUKF algorithm is developed for high estimation performance against the significant uncertainties. To validate the proposed IT3FS-STUKF, real experiments are conducted with ground vehicles in urban areas, which show an improved accuracy compared to the extended Kalman filter (EKF) at reasonable computational burden.

A Complex-Valued Stationary Kalman Filter for Positive and Negative Sequence Estimation in DER Systems

In medium- and low-voltage three-phase distribution networks, the load imbalance among the phases may compromise the network voltage symmetry. Inverter-interfaced distributed energy resources (DERs) can contribute to compensating for such imbalances by sharing the required negative sequence current while providing active power synchronized with the positive sequence voltage. However, positive and negative sequences are conventionally defined in a steady state and are not directly observed from the instantaneous voltage and current measurements at the DER unit’s point of connection. In this article, an estimation algorithm for sequence separation based on the Kalman filter is proposed. Furthermore, the proposed filter uses a complex vector representation of the asymmetric three-phase signals in synchronous coordinates to allow for the implementation of the Kalman filter in its stationary form, resulting in a simple dynamic filter able to estimate positive and negative sequences even during transient operation. The proposed stationary complex Kalman filter performs better than state-of-the-art techniques like DSOGI and very similarly to other Kalman filter implementations found in the literature but at a fraction of its computational cost (23.5%).

Generalized Labeled Multi-Bernoulli Filter-Based Passive Localization and Tracking of Radiation Sources Carried by Unmanned Aerial Vehicles

This paper discusses a key technique for passive localization and tracking of radiation sources, which obtains the motion trajectory of radiation sources carried by unmanned aerial vehicles (UAVs) by continuously or periodically localizing it without the active participation of the radiation sources. However, the existing methods have some limitations in complex signal environments and non-stationary wireless propagation that impact the accuracy of localization and tracking. To address these challenges, this paper extends the δ-generalized labeled multi-Bernoulli (GLMB) filter to the scenario of passive localization and tracking based on the random finite-set (RFS) framework and provides the extended Kalman filter (EKF) and unscented Kalman filter (UKF) implementations of the δ-GLMB filter, which fully take into account the nonlinear motion of the radiation source. By modeling the “obstacle scenario” and the influence of external factors (e.g., weather, terrain), our proposed GLMB filter can accurately track the target and capture its motion trajectory. Simulation results verify the effectiveness of the GLMB filter in target identification and state tracking.

An Adaptive Unscented Kalman Filter for the Estimation of the Vehicle Velocity Components, Slip Angles, and Slip Ratios in Extreme Driving Manoeuvres.

This paper presents a novel unscented Kalman filter (UKF) implementation with adaptive covariance matrices (ACMs), to accurately estimate the longitudinal and lateral components of vehicle velocity, and thus the sideslip angle, tire slip angles, and tire slip ratios, also in extreme driving conditions, including tyre-road friction variations. The adaptation strategies are implemented on both the process noise and measurement noise covariances. The resulting UKF ACM is compared against a well-tuned baseline UKF with fixed covariances. Experimental test results in high tyre-road friction conditions show the good performance of both filters, with only a very marginal benefit of the ACM version. However, the simulated extreme tests in variable and low-friction conditions highlight the superior performance and robustness provided by the adaptation mechanism.

FPGA Implementation of Kalman Filter for Visible Light

Visible Light (VL) has received significant attention due to its benefits in energy efficiency, wide bandwidth availability, and resistance to electromagnetic interference. This final project discusses VL utilizing the Kalman Filter (KF) to predict and estimate the position of related data. The development of the VL method is carried out using Xilinx FPGA Arty A7 hardware, and the KF implementation is carried out in a two-dimensional framework with the Linear KF approach. The main objective of this Final Project is to implement VL using Photodetectors (Photodiode and Photoresistor LM393) on FPGA. The use of Xilinx FPGA Arty A7 hardware and Xilinx SDK software provides the flexibility and reliability required for system implementation. The results indicate that the implementation of Xilinx FPGA Arty A7-35T with KF and the use of 16 LED and 8 LED configurations yield relatively accurate estimations. While the Photodiode LM393 (PD LM393) sensor does not exhibit superior results compared to the Photoresistor LM393 (PR LM393) sensor, this research effectively optimizes light measurements by utilizing the sensor and KF algorithm. The Root Mean Squared Error (RMSE) results show that for the system with 16 LEDs, KF with PR LM393 has an RMSE of approximately ). This RMSE value indicates that KF with PR LM393 can provide relatively more accurate estimations. Similarly, for the system with 8 LEDs, KF with PR LM393 has an RMSE of around ). In this case, KF with PR LM393 again provides relatively more accurate estimations. Meanwhile, the RMSE result for 2D KF in this system is approximately ), indicating that the KF estimation has a relatively small error value compared to the actual measurement value. This demonstrates that KF effectively reduces noise and measurement data fluctuations in the LM393 Photodetector system with 16 LEDs.

A study on the implementation of nonlinear Kalman filter applying MMG model

Many technologies need to be established to realize autonomous ships. In particular, accurate state estimation in real time is one of the most important technologies. In the ship and ocean engineering fields, there have been many studies on state estimation using nonlinear Kalman filters. Several methods have been proposed for nonlinear Kalman filters. However, there is insufficient verification on the selection of which filter should be applied among them. Therefore, this study aims to validate the filter selection to provide a guideline for filter selection. The effects of modeling error, observation noise, and type of maneuvers on the estimation accuracy of the unscented Kalman filter (UKF) and ensemble Kalman filter (EnKF) used in this study were investigated. In addition, it was verified whether filtering could be performed in real time. The results show that modeling error significantly impacts the estimation accuracy of the UKF and EnKF. However, the observation noise and types of maneuvers did not have an impact like the modeling error. Thus, we obtained the guideline that UKF and EnKF should be used differently depending on the required computation time. We also obtained that keeping the modeling error sufficiently small is essential to improving the estimation accuracy.

Estimation of wheelset equivalent conicity using the dual extended Kalman filter

This paper presents the implementation of the dual extended Kalman filter (DEKF) to estimate wheelset equivalent conicity, an accurate understanding of which can facilitate the implementation of an effective model-based estimator. The estimator is developed to identify the wheelset equivalent conicity of high-speed railway vehicles while negotiating a curve. The designed DEKF estimator employs two discrete-time extended Kalman filters combining state and parameter estimators in parallel. This estimator uses easily available measurements from acceleration sensors measuring at axle boxes and a rate gyroscope measuring bogie frame yaw velocity. Two tests, including linearized and actual wheel-rail geometry, are carried out at a speed of 250 km/h with stochastic and deterministic track features using multibody simulations, SIMPACK. The results with acceptable estimation errors for both track conditions indicate adequate performance and reliability of the designed DEKF estimator. They demonstrate the feasibility of utilizing this DEKF method in rail vehicle applications as the knowledge of time-varying parameters is not only important in achieving an effective estimator for vehicle control but also useful for vehicle condition monitoring.

A Distributed Implementation of Steady-State Kalman Filter

This paper studies the distributed state estimation in sensor network, where <formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex>$m$</tex></formula> sensors are deployed to infer the <formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex>$n$</tex></formula> -dimensional state of a Linear Time-Invariant (LTI) Gaussian system. By a lossless decomposition of the optimal steady-state Kalman filter, we show that the problem of distributed estimation can be reformulated as that of the synchronization of homogeneous linear systems. Based on such decomposition, a distributed estimator is proposed, where each sensor node runs a local filter using only its own measurement, alongside with a consensus algorithm to fuse the local estimate of every node. We prove that the average of estimates from all sensors coincides with the optimal Kalman estimate, and under certain condition on the graph Laplacian matrix and the system matrix, the consensus error is bounded and the asymptotic error covariance is derived. As a result, the distributed estimator is stable for each single node. We further show that the proposed algorithm has a low message complexity of min( <formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex>$m$</tex></formula> , <formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex>$n$</tex></formula> n). Numerical examples are provided in the end to illustrate the efficiency of the proposed algorithm.

Fast and Accurate Estimation of Evapotranspiration for Smart Agriculture

AbstractThe ability to quantify evapotranspiration (ET) is crucial for smart agriculture and sustainable groundwater management. Efficient ET estimation strategies often rely on the vertical‐flow assumption to assimilate data from soil‐moisture sensors. While adequate in some large‐scale applications, this assumption fails when the horizontal component of the local flow velocity is not negligible due to, for example, soil heterogeneity or drip irrigation. We present novel implementations of the ensemble Kalman filter (EnKF) and the maximum likelihood estimation (MLE), which enable us to infer spatially varying ET rates and root water uptake profiles from soil‐moisture measurements. While the standard versions of EnKF and MLE update the predicted soil moisture prior to computing ET, ours treat the ET sink term in Richards' equation as an updatable observable. We test the prediction accuracy and computational efficiency of our methods in a setting representative of drip irrigation. Our strategies accurately estimate the total ET rates and root‐uptake profiles and do so up to two‐orders of magnitude faster than the standard EnKF.

Evaluation of Low-Complexity Adaptive Full Direct-State Kalman Filter for Robust GNSS Tracking.

This paper evaluates the implementation of a low-complexity adaptive full direct-state Kalman filter (DSKF) for robust tracking of global navigation satellite system (GNSS) signals. The full DSKF includes frequency locked loop (FLL), delay locked loop (DLL), and phase locked loop (PLL) tracking schemes. The DSKF implementation in real-time applications requires a high computational cost. Additionally, the DSKF performance decays in time-varying scenarios where the statistical distribution of the measurements changes due to noise, signal dynamics, multi-path, and non-line-of-sight effects. This study derives the full lookup table (LUT)-DSKF: a simplified full DSKF considering the steady-state convergence of the Kalman gain. Moreover, an extended version of the loop-bandwidth control algorithm (LBCA) is presented to adapt the response time of the full LUT-DSKF. This adaptive tracking technique aims to increase the synchronization robustness in time-varying scenarios. The proposed tracking architecture is implemented in an GNSS hardware receiver with an open software interface. Different configurations of the adaptive full LUT-DSKF are evaluated in simulated scenarios with different dynamics and noise cases for each implementation. The results confirm that the LBCA used in the FLL-assisted-PLL (FAP) is essential to maintain a position, velocity, and time (PVT) fix in high dynamics.

Discrete-time Kalman filter for heave motion estimation

This paper addresses the problem of estimating the heave motion of a platform using biased measurements of an accelerometer. We develop a general framework wherein convenient and well-known properties of trigonometric functions are exploited to devise a linear system whose state encompasses implicit representations of wave amplitudes and phase shifts, as well as a constant sensor bias. The observability of the system is analyzed, followed naturally by the implementation of a discrete-time linear time-varying Kalman filter with global asymptotic stability guarantees. Our proposed methodology is validated with realistic numerical examples, including an accurate representation of a continuous wave spectrum within an ocean context.

An experimental comparative study of adaptive sigma-point Kalman filters: Case study of a rigid–flexible four-bar linkage mechanism and a servo-hydraulic actuator

This paper investigates the application, design, and implementation of different adaptive sigma-point Kalman filters for nonlinear dynamic systems. It is a well-known fact that the performance of nonlinear Kalman filters depends on a prior knowledge of system noise statistics. In real-time applications, this knowledge is difficult and in some cases impossible to predefine. Therefore, an adaptation mechanism based on the random weighting method is proposed in this work to estimate, simultaneously, noise covariance and the state of the system. On the other hand, for real time execution, the computational efficiency of such filters should also be considered to minimize the burden on computational resources. Based on these two factors, in this paper, four different variants of the adaptive sigma-point Kalman filter are studied in detail: (I) an Adaptive Unscented Kalman filter (AUKF), (II) an Adaptive Square-root Unscented Kalman filter (ASr-UKF) with an Unscented Transformation sigma-point selection strategy, (III) an Adaptive Scaled Spherical Simplex Unscented Kalman filter (AS3UKF), and (IV) an Adaptive Square-root Scaled Spherical Simplex Unscented Kalman filter (ASr-S3UKF) with scaled spherical simplex sigma-point selection strategy. The performance of these adaptive sigma-point Kalman filters is analyzed here in depth and discussed for application to a simulated rigid–flexible four-bar linkage mechanism and a practical servo-hydraulic actuator setup under different scenarios. The simulation and the experimental results indicated that, for the cases studied in this article, the filters are competitive and present advantages and disadvantages that should be dealt with according to the requirements of the problem.

Implementation and Performance Analysis of Kalman Filters with Consistency Validation

This paper provides a useful supplement note for implementing the Kalman filters. The material presented in this work points out several significant highlights with emphasis on performance evaluation and consistency validation between the discrete Kalman filter (DKF) and the continuous Kalman filter (CKF). Several important issues are delivered through comprehensive exposition accompanied by supporting examples, both qualitatively and quantitatively for implementing the Kalman filter algorithms. The lesson learned assists the readers to capture the basic principles of the topic and enables the readers to better interpret the theory, understand the algorithms, and correctly implement the computer codes for further study on the theory and applications of the topic. A wide spectrum of content is covered from theoretical to implementation aspects, where the DKF and CKF along with the theoretical error covariance check based on Riccati and Lyapunov equations are involved. Consistency check of performance between discrete and continuous Kalman filters enables readers to assure correctness on implementing and coding for the algorithm. The tutorial-based exposition presented in this article involves the materials from a practical usage perspective that can provide profound insights into the topic with an appropriate understanding of the stochastic process and system theory.

Cooperative decentralized navigation algorithms based on bearing measurements for arbitrary measurement topologies

This work presents and compares several cooperative navigation solutions for formations of autonomous underwater vehicles, equipped with depth sensors and capable of taking bearing measurements to their neighbors under a certain measurement topology. Two approaches based on the extended Kalman filter are described, one centralized and the other decentralized, which has the advantage of requiring much less communication and computational complexity with minimal degradation of the produced estimates. Additionally, four other Kalman filter implementations, based on systems with linear dynamics using artificial measurements, are also described, one centralized and the remaining ones decentralized. The performance of these algorithms, under both acyclical and cyclical measurement topologies, is compared using Monte Carlo simulations, whereby both the mean error and root-mean-squared-error (RMSE) of the computed navigation estimates are presented.

Accounting for simulation errors in continuous-discrete Kalman filtering

In continuous-discrete Kalman filter implementations there is a tradeoff between the computational requirements for real time implementation, and errors incurred by selection of step size and method order in the simulation of the continuous time system model between sampling instances. Because the Kalman filter corrects errors in the state vector using output measurements, a systematic approach to account for the effects of simulation errors in the continuous-discrete Kalman filter allows the filter to be designed to deal with simulation errors in addition to conventional process (state) and measurement (output) noise.

Treatment of Extended Kalman Filter Implementations for the Gyroless Star Tracker.

The literature since Apollo contains exhaustive material on attitude filtering, usually treating the problem of two sensors, a combination of state measuring and inertial devices. More recently, it has become popular for a sole attitude determination device to be considered. This is especially the case for a star tracker given its unbiased stellar measurement and recent improvements in optical sensor performance. The state device indirectly estimates the attitude rate using a known dynamic model. In estimation theory, two main attitude filtering approaches are classified, the additive and the multiplicative. Each refers to the nature of the quaternion update in the filter. In this article, these two techniques are implemented for the case of a sole star tracker, using simulated and real night sky image data. Both sets of results are presented and compared with each other, with a baseline established through a basic linear least square estimate. The state approach is more accurate and precise for measuring angular velocity than using the error-based filter. However, no discernible difference is observed between each technique for determining pointing. These results are important not only for sole device attitude determination systems, but also for space situational awareness object localisation, where attitude and rate estimate accuracy are highly important.

Square-Root Extended Information Filter for Visual-Inertial Odometry for Planetary Landing

A novel sequential information filter formulation for computationally efficient visual-inertial odometry and mapping is developed in this work and applied to a realistic moon landing scenario. Careful construction of the square-root information matrix, in contrast to the full information or covariance matrix, provides easy and exact mean and covariance recovery throughout operation. Compared to an equivalent extended Kalman filter implementation, which provides identical results, the proposed filter does not require explicit marginalization of past landmark states to maintain constant-time complexity. Whereas measurements to opportunistic visual features only provide relative state information, resulting in drift over time unless a priori mapped landmarks are identified and tracked, the tight coupling of the inertial measurement unit provides some inertial state information. The results are presented in a terrain-relative navigation simulation for both a purely orbital case (with no active propulsion) and a landing case with a constant thrust.

Comparison of EKF and TSO for Health Monitoring of a Textile-Based Heater Structure and its Control

In this article, the conception, design, and implementation of a discrete extended Kalman filter and a Takagi–Sugeno observer are introduced, and an innovative model description of an embroidered heater structure is presented. The observers are compared based on the algorithm complexity with the indicator of the number of arithmetic operations and the parameter error of the textile-based heater structure for health monitoring through virtual sensing. The proposed schemes allow an estimation of the heater temperature to guarantee safety by preventing overheating without a direct measurement. An estimation strategy is necessary because measurements of the temperature of the whole heater structure are usually not available, but this knowledge is vital for health monitoring purposes or for a safe shutdown if necessary. A cascaded sliding-mode control strategy using an integral surface for the electrical current and the temperature is presented. Measurements validate the utilized model. The effectiveness of the observers is justified by hardware-in-the-loop simulations and measurements.

LCNS Positioning of a Lunar Surface Rover Using a DEM-Based Altitude Constraint

With the renewed interest in lunar surface exploration, the European Space Agency envisions to stimulate the creation of lunar communications and navigation services (LCNS) to enable, among others, autonomous navigation capabilities for lunar rovers. As the number of satellites foreseen in such a service is much smaller compared to Earth-based global navigation satellite systems, different complementary technologies are pursued to improve the attainable navigation accuracy for lunar rovers. One way to improve the position accuracy provided by the LCNS satellites is to constrain their vertical position using a high resolution digital elevation model (DEM). This article presents the results of a variance covariance analysis of an extended Kalman filter implementation in which the LCNS ranging measurements are used together with the altitude provided by a DEM from the Lunar Orbiter Laser Altimeter instrument of the Lunar Reconnaissance Orbiter. Assuming a realistic orbit determination and time synchronization accuracy of the LCNS satellites, the usage of a navigation-grade inertial measurement unit and an oven-controlled crystal oscillator, a 3-sigma position accuracy of less than 10 m can be obtained. Furthermore, the availability is substantially improved as the DEM-aided solution enables a position solution in case of only 3 visible satellites.

TensorGraphicalModels: A Julia toolbox for multiway covariance models and ensemble Kalman filter

<h2>Abstract</h2> The increasing availability of high dimensional multi-indexed data has created an opportunity for the development of graphical modeling software that bridges the gap between second order statistical and computational models. In this paper, we introduce TensorGraphicalModels, a suite of Julia tools for statistical estimation of high-dimensional multiway (tensor-variate) covariance and precision matrices, with applications to ensemble Kalman filtering. The Julia package implements several state-of-the-art multiway covariance and precision matrix estimators. These are illustrated in the context of a physics-driven forecasting example with an integrated implementation of a tensor ensemble Kalman filter (EnKF).