Kalman Filter Design Research Articles

Extended Kalman filter design for compass navigation tool on visual impaired person

Orang normal, robot, dan kendaraan cerdas mengandalkan kombinasi indera visual dan memori ingatan sebagai peta untuk navigasi dalam melakukan mobilitas mandiri. Berbeda dengan tunanetra yang mengandalkan kombinasi indera lain yang masih berfungsi serta tongkat standar maupun elektronik dalam melaksanakan aktifitas mobilitas mandiri. Tongkat masih memiliki kekurangan, diantaranya hanya dapat memberikan informasi isyarat sentuhan, suara, dan getar terhadap jarak objek di lingkungan sekitar. Penelitian ini mengembangkan rancangan dan implementasi produk terapan berupa kompas bicara untuk informasi navigasi tunanetra dengan isyarat suara delapan titik arah mata angin. Produk terapan dibuat mudah dipasang pada sabuk pinggang pengguna dan mudah digunakan. Sistem elektronik arah jam berupa sinyal data 360 derajat yang berasal dari sensor kompas dijadikan masukan sebagai pengganti indera visual untuk mikrokontroler unit (MCU). Sinyal data dari kompas terlebih dahulu dilakukan filter menggunakan Kalman untuk menghilangkan noise dari gangguan lingkungan dan gelombang elektromagnetik. Eksperimen dengan dua skenario berbeda menunjukan sistem dapat berfungsi sempurna dengan menjadi dukungan efektif selama mobilitas mandiri tunanetra. Selain itu, alat ini layak digunakan untuk melatih tunanetra dengan mengkombinasikan terhadap alat bantu perjalanan tongkat standar dengan akurasi lebih besar 0,95% lebih baik dengan filter.

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.

Orthotope-search-expansion-based extended zonotopic Kalman filter design for a discrete-time linear parameter-varying system with a dual-noise term

A novel algorithm utilizing an extended zonotopic Kalman filter based on the orthotope search expansion method is introduced to solve the state estimation problem in discrete-time linear parameter-varying systems when the dual noise of the systems is assumed to be bounded but unknown. First, to identify unknown parameters, an orthotope search expansion method is proposed with a measurement strip constraint. Subsequently, based on the parameter identification orthotopic set, an extended zonotopic Kalman filter algorithm is proposed to derive an estimation interval that wraps the true state of the system. Next, by minimizing the size of the zonotope, the optimal gain matrix for the extended zonotopic Kalman filter algorithm is determined. Finally, the proposed methods are demonstrated for their effectiveness and accuracy through the presentation of two simulation examples.

INS aided spoofing detection of high dynamic GNSS receiver for launch vehicle applications: A loosely coupled approach

Launch vehicle applications require highly accurate and reliable navigation systems that can withstand the high dynamic conditions of the launch and flight phases. GNSS-aided INS (Inertial Navigation System) is the most popular solution for launch vehicle navigation. However, the accuracy of Global Navigation Satellite System (GNSS) receivers can be compromised by malicious spoofing attacks, which can result in significant safety risks and mission failure. This paper presents a method for identifying and mitigating the spoofing attacks on Global Navigation Satellite System (GNSS) receivers using the independent and simultaneous measurements of the Inertial Navigation System (INS). A state space approach is attempted in this paper with an extended Kalman Filter for identifying the spoofed signals. The well-established method of integrating INS and GNSS data for navigation accuracy improvement is taken as the baseline of this algorithm. The proposed method is an extension of a loosely coupled integration algorithm already established for fusing INS and GNSS data. The extended Kalman filter estimated position and velocity of the receiver is used along with the satellite position and velocity computed from ephemeris to find out the range and range rate of each of the satellites to the receiver. The difference between the estimated range and range rate against the measured range and range rate is considered as filter residual. The filter residuals are taken as the parameter to identify the spoofing. The threshold of filter residuals for range and range rates is the critical parameter that decides the false isolation and missing detection. The threshold is decided based on the environment in which the receiver is operated, the dynamics expected, and the noise model. The algorithms envelopment and simulation studies are done. The simulation tests are completed using a GNSS constellation simulator with spoofed signals. The INS and GNSS error model, states selection, Kalman filter design, algorithm details, simulation tests, simulation results, advantages and disadvantages of the new algorithm, and future work are covered in this paper.

Kalman Filter of Switching System Under Hybrid Cyber Attack

Potential malicious attacks have been a significant security concern for network system applications. However, there are few studies on filtering for hybrid network attacks in switching systems. This paper considers a Kalman filtering problem for the switched systems that suffer from deception attacks and denial-of-service attacks. A new network transmission model for switching systems is established. Then, based on the minimum mean square error criterion, a Kalman filter with low conservatism is designed for the discrete-time switched system. The newly switched Kalman gain matrix is deduced including the random variation of the switching signal after being attacked by the network. Finally, the effectiveness of the proposed filter is verified by the numerical simulation. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —A switching system is considered to be a typical hybrid system. As it often works in a network environment, the switching signal is vulnerable to the network and thus to various cyber-attacks (e.g. spoofing attacks and denial-of-service attacks). Few studies have been conducted on the impact of switching signals in network transmission. To address this problem, this paper proposes a Kalman filter design method with low conservativeness, which describes network attacks and data loss by building a Kalman filter model associated with the switching signal in terms of satisfying Bernoulli random variables. For practitioners, the ability to recover data to a certain extent when the data transmission is affected by different network attacks will save a lot of costs and is important for improving the stability and performance of switching systems. Our future work will aim to improve the performance of different filtering algorithms under different cyber-attacks.

An Extended Kalman Filter Design for State-of-Charge Estimation Based on Variational Approach

State of charge (SOC) is a very important variable for using batteries safely and reliably. To improve the accuracy of SOC estimation, a novel variational extended Kalman filter (EKF) technique based on least square error method is herein provided by establishing a second-order equivalent circuit model for the battery. It was found that when SOC decreased, resistance polarization occurred in the electrochemical model, and the parameters in the equivalent RC model varied. To decrease the modeling error in the equivalent circuit model, the system parameters were identified online depending on the SOC’s estimated result. Through the SOC-estimation process, the variation theorem was introduced, which enabled the system parameters to track the real situations based on the output measured. The experiment results reveal the comparison of the SOC-estimation results of the variational EKF algorithm, the traditional EKF algorithm, the recursive least square (RLS) EKF algorithm, and the forgotten factor recursive least square (FFRLS) EKF algorithm based on different indices, including the mean square error (MSE) and the mean absolute error (MAE). The variational EKF algorithm provided in this paper has higher estimation accuracy and robustness than the traditional EKF, which verifies the superiority and effectiveness of the proposed method.

Extended Kalman Filter design for sensorless sliding mode predictive control of induction motors without weighting factor: An experimental investigation.

Due to their simplicity, cheapness, and ease of maintenance, induction motors (IMs) are the most widely used motors in the industry. However, if they are not properly controlled, the load torque and motor speed will fluctuate in an unsatisfactory fashion. To effectively control the load torque and speed of these IMs, it is necessary to use specialized drives. The entire system (IMs + Drives) will experience uncertainty, nonlinearities, and disruptions, which calls for an outstanding performance control structure. The sensorless sliding mode predictive torque control (SSM-PTC) for both AC-DC converter and DC-AC inverter, which are utilized for feeding the IM, is investigated in this work. The AC-DC converter is controlled using the SSM-PTC method in order to follow the DC-link reference voltage throughout any changes in the operating point of the IM. While the DC-AC inverter is controlled using a sensorless predictive power control (SPPC). Within a unity power factor, this SPPC regulates the reactive power flow between the motor and the supply to account for the undesirable harmonic components of the grid current. In addition, an experimental performance improvement of SSM-PTC of IM supplied by a 5-leg AC-DC-AC power converter using extended Kalman filter (EKF) without weighting factor (WF) is also studied in this work. Design and implantation of the suggested control systems are performed using a dSPACE 1104 card. The experimental results of the proposed converter control demonstrate that the suggested approach effectively regulated the DC link, reducing load torque and speed fluctuations. In the context of inverter control, a prompt active power response yields a motor current waveform that resembles a sinusoidal pattern, exhibiting minimal levels of harmonic distortion.

Information-Based Sensor Placement for Data-Driven Estimation of Unsteady Flows

Estimation of unsteady flowfields around flight vehicles may improve flow interactions and lead to enhanced vehicle performance. Although flowfield representations can be very high-dimensional, their dynamics can sometimes have low-order representations that may be estimated using a few, appropriately placed measurements. This paper presents a sensor-selection framework for the intended application of data-driven, flowfield estimation. This framework combines data-driven modeling, steady-state Kalman filter design, and sparse, sequential sensor selection. This paper also uses the sensor selection framework to design sensor arrays that can perform well for a collection of operating conditions. Flow estimation results on numerical data show that the proposed framework produces arrays that are highly effective at flowfield estimation for the flow behind and an airfoil at a high angle of attack using embedded pressure sensors. Analysis of the flowfields reveals that paths of impinging stagnation points along the airfoil’s surface during a shedding period of the flow are highly informative locations for placement of pressure sensors.

Extended Kalman Filter Design for Tracking Time-of-Flight and Clock Offsets in a Two-Way Ranging System

As radio frequency (RF) hardware continues to improve, two-way ranging (TWR) has become a viable approach for high-precision ranging applications. The precision of a TWR system is fundamentally limited by estimates of the time offset T between two platforms and the time delay τ of a signal propagating between them. In previous work, we derived a family of optimal “one-shot” joint delay–offset estimators and demonstrated that they reduce to a system of linear equations under reasonable assumptions. These estimators are simple and computationally efficient but are also susceptible to channel impairments that obstruct one or more measurements. In this work, we formulate an extended Kalman filter (EKF) for this class of estimators that specifically addresses this limitation. Unlike a generic KF approach, the proposed solution specifically integrates the estimation process to minimize the computational complexity. We benchmark the proposed first- and second-order EKF solutions against the existing one-shot estimators in a MATLAB Monte Carlo simulation environment. We demonstrate that the proposed solution achieves comparable estimation performance and, in the case of the second-order solution, reduces the computation time by an order of magnitude.

Type-2 evolving fuzzy Kalman filter design based on unobservable spectral components space for interval tracking of non-stationary experimental data

In this paper, an interval type-2 evolving fuzzy Kalman filter is designed for processing of unobservable spectral components of uncertain experimental data. The adopted methodology consider the following steps: an initial model of the interval type-2 fuzzy Kalman filter, which is off-line identified from an initial window of the experimental data; the updating of antecedent proposition of interval type-2 fuzzy Kalman filter by using an interval type-2 formulation of evolving Takagi-Sugeno (eTS) clustering algorithm and the updating of consequent proposition by using a type-2 fuzzy formulation of Observer/Kalman Filter Identification (OKID) algorithm, taking into account the multivariable recursive Singular Spectral Analysis of the experimental data. The computational results for tracking the Mackey-Glass chaotic time series illustrate the efficiency of proposed methodology as compared to relevant approaches from literature, and the experimental results for tracking a 2DoF helicopter demonstrate its applicability.

Equivariant Filter (EqF)

The kinematics of many systems encountered in robotics, mechatronics, and avionics are naturally posed on homogeneous spaces; that is, their state lies in a smooth manifold equipped with a transitive Lie group symmetry. This paper proposes a novel filter, the <i>Equivariant Filter (EqF)</i>, by posing the observer state on the symmetry group, linearising global error dynamics derived from the equivariance of the system, and applying extended Kalman filter design principles. We show that equivariance of the system output can be exploited to reduce linearisation error and improve filter performance. Simulation experiments of an example application show that the EqF&#x00A0;significantly outperforms the extended Kalman filter and that the reduced linearisation error leads to a clear improvement in performance.

State and Parameter Estimation for Retinal Laser Treatment

Adequate therapeutic retinal laser irradiation needs to be adapted to local absorption. This leads to time-consuming treatments as the laser power needs to be successively adjusted to avoid undertreatment and overtreatment caused by too low or too high temperatures. Closed-loop control can overcome this burden by means of temperature measurements. To allow for model predictive control schemes, the current state and the spot-dependent absorption need to be estimated. In this article, we thoroughly compare moving horizon estimator (MHE) and extended Kalman filter (EKF) designs for joint state and parameter estimation. We consider two different scenarios, the estimation of one or two unknown absorption coefficients. For one unknown parameter, both estimators perform very similarly. For two unknown parameters, we found that the MHE benefits from active parameter constraints at the beginning of the estimation, whereas after a settling time, both estimators perform again very similarly as long as the parameters are inside the considered parameter bounds.

GMM-Based Adaptive Extended Kalman Filter Design for Satellite Attitude Estimation under Thruster-Induced Disturbances.

Star images from star trackers are usually defocused to capture stars over an exposure time for better centroid measurements. While a satellite is maneuvering, the star point on the screen of the camera is affected by the satellite, which results in the degradation of centroid measurement accuracy. Additionally, this could result in a worse star vector outcome. For geostationary satellites, onboard thrusters are used to maintain or change orbit parameters under orbit disturbances. Since there is misalignment in the thruster and torque is generated by an impulsive shape signal from the torque command, it is difficult to generate target torque; in addition, it also impacts the star image because the impulsive torque creates a sudden change in the angular velocity in the satellite dynamics. This makes the noise of the star image non-Gaussian, which may require introducing a method for dealing with non-Gaussian measurement noise. To meet this goal, in this study, an adaptive extended Kalman filter is implemented to predict measurement vectors with predicted states. The GMM (Gaussian mixture model) is connected in this sequence, giving weighting parameters to each Gaussian density and resulting in the better prediction of measurement vectors. Simulation results show that the GMM-EKF exhibits a better performance than the EKF for attitude estimation, with 30% improvement in performance. Therefore, the GMM-EKF could be a more attractive approach for use with geostationary satellites during station-keeping maneuvers.

Distributed Consensus Kalman Filter Design with Dual Energy-Saving Strategy: Event-Triggered Schedule and Topological Transformation.

In the distributed information fusion of wireless sensor networks (WSNs), the filtering accuracy is commonly negatively correlated with energy consumption. Therefore, a class of distributed consensus Kalman filters was designed to balance the contradiction between them in this paper. Firstly, an event-triggered schedule was designed based on historical data within a timeliness window. Furthermore, considering the relationship between energy consumption and communication distance, a topological transformation schedule with energy-saving is proposed. The energy-saving distributed consensus Kalman filter with a dual event-driven (or event-triggered) strategy is proposed by combining the above two schedules. The sufficient condition of stability for the filter is given by the second Lyapunov stability theory. Finally, the effectiveness of the proposed filter was verified by a simulation.

Design of a High-Order Kalman Filter for State and Measurement of A Class of Nonlinear Systems Based on Kronecker Product Augmented Dimension

A high-order Kalman filter for full-dimensional variables is proposed for a class of dynamic systems whose state model and measurement model are both nonlinear. The filter requires Taylor expansion of the system equations, and then performs Kronecker product operation on the linear part in the Taylor expansion. Finally, a linear dynamic model is achieved based on the full-dimensional vector formed by the state variables and the high-order dimension expansion variables. After designing the filter, the Kalman filter for the original state variables estimation was selected through the projection operator. The excellent performance of the novel filter is analyzed from the aspects of the information utilization of the state estimation value and the size of the state estimation error covariance matrix. The numerical verification is carried out by computer simulation.

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.

Hybrid State Observer Design for Estimating the Hitch Angles of Tractor-Multi Unit Trailer

In this paper, a new approach of state observer is proposed for the tractor with multi unit trailers. In the case of tractor with two articulated trailers, the dynamic characteristics of the trailers are dominantly determined by the two hitch angles connecting each trailer. A novel estimation system for the hitch angle is introduced by combining the Kalman filter with the deep learning network and transfer function techniques. The Gated Recurrent Unit (GRU) network is constructed to calculate hitch angles and these values are used as the virtual measurement in the Kalman filter. The dynamic characteristics of two trailers with respect to the hitch angles are expressed as the transfer function models and these models are used to calculate the hitch angles as the virtual measurement. The virtual measurements from the two methods are integrated separately into the Kalman filter design. The estimation performance of the hitch angle with the proposed hybrid observer is validated in simulations with various curvature scenarios.

A Novel Adaptive Kalman Filter Based on Credibility Measure

It is quite often that the theoretic model used in the Kalman filtering may not be sufficiently accurate for practical applications, due to the fact that the covariances of noises are not exactly known. Our previous work reveals that in such scenario the filter calculated mean square errors (FMSE) and the true mean square errors (TMSE) become inconsistent, while FMSE and TMSE are consistent in the Kalman filter with accurate models. This can lead to low credibility of state estimation regardless of using Kalman filters or adaptive Kalman filters. Obviously, it is important to study the inconsistency issue since it is vital to understand the quantitative influence induced by the inaccurate models. Aiming at this, the concept of credibility is adopted to discuss the inconsistency problem in this paper. In order to formulate the degree of the credibility, a trust factor is constructed based on the FMSE and the TMSE. However, the trust factor can not be directly computed since the TMSE cannot be found for practical applications. Based on the definition of trust factor, the estimation of the trust factor is successfully modifled to online estimation of the TMSE. More importantly, a necessary and sufficient condition is found, which turns out to be the basis for better design of Kalman filters with high performance. Accordingly, beyond trust factor estimation with Sage-Husa technique (TFE-SHT), three novel trust factor estimation methods, which are directly numerical solving method (TFE-DNS), the particle swarm optimization method (PSO) and expectation max-imization-particle swarm optimization method (EM-PSO) are proposed. The analysis and simulation results both show that the proposed TFE-DNS is better than the TFE-SHT for the case of single unknown noise covariance. Meanwhile, the proposed EM-PSO performs completely better than the EM and PSO on the estimation of the credibility degree and state when both noise covariances should be estimated online.

Strong∗ detectability and observers for linear time-varying systems

This work presents a notion of strong detectability for linear time-varying systems affected by unknown inputs. It is shown that this notion is equivalent to detectability of an auxiliary system without unknown inputs. This allows a straightforward observer design for dependable state estimation in the presence of unknown inputs. The design reduces to a deterministic Kalman filter design problem, where the observer gains can be obtained from the solution of a differential Riccati equation. The efficacy of the proposed approach is demonstrated by means of two examples.

Efficient and Consistent Two Key-Frame Visual-Inertial Navigation Using Matrix Lie Groups

Abstract This paper presents the design of a two key-frame visual-inertial navigation system (2KF-VINS) using a combined Lie group SE2(3) extended Kalman filter (EKF) design framework. The conventional 2KF-VINS filter is unobservable for translations along all three axes and rotation about the gravity direction. As a result, the filter suffers from estimation inconsistencies related to unobservable transformations of the estimation problem. The proposed combined Lie group SE2(3) framework remedies this issue by implicitly preserving the observability consistency property of the filter. Monte Carlo numerical simulations are used to validate the theoretical performance of the right−SE2(3) 2KF-VINS, along with experimental validation using the EuRoC micro aerial vehicle (MAV) dataset to evaluate the performance in real-world scenarios. Additionally, the proposed algorithm is compared with state-of-the-art MSCKF, RI-MSCKF, left−SO(3), and right−SO(3) 2KF-VINS versions with identical and realistic tuning parameters to validate the performance related to the accuracy, consistency, and computational speed of the method.