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1

The new approach to hybrid Kalman filtering, based on the changed order of filters for state estimation of dynamical systems

Michalski Jacek, Kozierski Piotr, Ziętkiewicz Joanna

Poznan University of Technology Academic Journals. Electrical Engineering

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2019

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No. 97

181--190

EN

The paper presents a new approach to Hybrid Kalman filtering, composed of Extended Kalman Filter and Unscented Kalman Filter. In known algorithms, the Unscented Kalman Filter algorithm is used as first and the result of this is given as an input to the Extended Kalman Filter. The authors checked modified Hybrid Kalman Filter with changed order of filters using theoretical object, which was created on the basis of power system. Besides traditional method, the modification of Hybrid Kalman Particle Filter was evaluated too. Results were compared with Extended Kalman Filter, Unscented Kalman Filter and Bootstrap Particle Filter. For particle filters the authors compared method estimation qualities for a different number of particles. The estimation quality was evaluated by three quality indices. Based on the obtained results, one can see that the changed order of methods in Hybrid Kalman filter can improve estimation quality.

2

Road profile identification using estimation techniques: comparison between independent component analysis and Kalman filter

Chaabane Mariem Miladi, Ben Hassen Dorra, Abbes Mohamed Slim, Baslamisli Selahattin Caglar, Chaari Fakher, Haddar Mohamed

Journal of Theoretical and Applied Mechanics

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2019

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Vol. 57 nr 2

397--409

EN

This paper focuses on the identification of a road profile disturbance acting on vehicles. Vehicles are subjected to many kinds of excitation sources such as road profile irregularities, which constitute a major area of interest when designing suspension systems. Indeed, determining the road profile is important for passive suspension design on the one hand and for determining an appropriate control law for active suspensions on the other. Direct measurement techniques of the road profile are expensive, so solutions based on estimation theory are needed. The aim of this paper is to characterize the road excitation using the Independent Component Analysis (ICA). This proposed method can reconstruct original excitation sources by using physically measurable signals of the system under study. Here, the estimation of road disturbances is considered as output sources and identified from dynamic responses of the vehicle. These responses can be measured via sensors or can be numerically computed. In our case, they are numerically simulated using the Newmark method and consider different types of road profiles. The obtained results are validated after using a comparison with the Kalman filtering. The robustness of the ICA is confirmed via parametric study.

3

Methods of position estimation in parametric navigation

Banachowicz A., Wolski A.

Zeszyty Naukowe. Transport / Politechnika Śląska

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2017

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z. 95

19--25

EN

The estimation of position coordinates of a navigating ship is one of the navigational subprocesses. The methods used in this process are either deterministic (the case of a minimum number of navigational parameters measurements) or probabilistic (in cases where we have access to information redundancy). Naturally, due to the accuracy and reliability of the calculated coordinates, probabilistic methods should be primarily used. The article presents the use of the method of least squares and Kalman filtering in algorithms in integrated navigation for the estimation of position coordinates, taking into account ship movement parameters.

4

The application of Kalman filtering to predict vertical rail axis displacements of the overhead crane being a component of seaport transport structure

Filipiak–Kowszyk D., Kamiński W.

Polish Maritime Research

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2016

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nr 2

64--70

EN

As the devices designed to transport materials, the overhead cranes should meet certain geometric requirements for their operation to be safe. The presently available geodetic equipment, in particular total stations, provides opportunities for precise 3D measurements of coordinates of the controlled points. These coordinates make a basis for correcting the height of crane runway axes. The paper presents a method to calculate position corrections for the crane rail axes in both vertical and horizontal direction, and indicates that these results can find much wider application. Among other goals, the observations of this type, along with the Kalman filtration method, can be used to predict vertical displacements of the crane rail axes. The object of practical considerations in the paper is a crane working in the area with unfavourable geotechnical conditions and the settling limits attributed to this crane and location area in the technical design. The sample practical application has confirmed the validity of the use of the proposed solution for evaluating the operational safety of the crane. Although the tests were performed for the gantry crane, the proposed solution is believed to be applicable for other types of overhead cranes.

5

Application Of Kalman Filter In Navigation Process Of Automated Guided Vehicles

Śmieszek M., Dobrzańska M.

Metrology and Measurement Systems

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2015

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Vol. 22, nr 3

443--454

EN

In the paper an example of application of the Kalman filtering in the navigation process of automatically guided vehicles was presented. The basis for determining the position of automatically guided vehicles is odometry – the navigation calculation. This method of determining the position of a vehicle is affected by many errors. In order to eliminate these errors, in modern vehicles additional systems to increase accuracy in determining the position of a vehicle are used. In the latest navigation systems during route and position adjustments the probabilistic methods are used. The most frequently applied are Kalman filters.

6

Multi-layered Bayesian Neural Networks for Simulation and Prediction Stress-Strain Time Series

Krok A.

Journal of Telecommunications and Information Technology

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2015

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nr 3

45--51

EN

The aim of the paper is to investigate the differences as far as the numerical accuracy is concerned between feedforward layered Artificial Neural Networks (ANN) learned by means of Kalman filtering (KF) and ANN learned by means of the evidence procedure for Bayesian technique. The stress-strain experimental time series for concrete hysteresis loops obtained by the experiment of cyclic loading is presented as considered example.

7

SMAC-FDI: A single model active fault detection and isolation system for unmanned aircraft

Ducard G. J. J.

International Journal of Applied Mathematics and Computer Science

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2015

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Vol. 25, no. 1

189--201

EN

This article presents a single model active fault detection and isolation system (SMAC-FDI) which is designed to efficiently detect and isolate a faulty actuator in a system, such as a small (unmanned) aircraft. This FDI system is based on a single and simple aerodynamic model of an aircraft in order to generate some residuals, as soon as an actuator fault occurs. These residuals are used to trigger an active strategy based on artificial exciting signals that searches within the residuals for the signature of an actuator fault. Fault isolation is carried out through an innovative mechanism that does not use the previous residuals but the actuator control signals directly. In addition, the paper presents a complete parameter-tuning strategy for this FDI system. The novel concepts are backed-up by simulations of a small unmanned aircraft experiencing successive actuator failures. The robustness of the SMAC-FDI method is tested in the presence of model uncertainties, realistic sensor noise and wind gusts. Finally, the paper concludes with a discussion on the computational efficiency of the method and its ability to run on small microcontrollers.

8

Model-based techniques for virtual sensing of longitudinal flight parameters

Hardier G., Seren C., Ezerzere P.

International Journal of Applied Mathematics and Computer Science

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2015

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Vol. 25, no. 1

23--38

EN

Introduction of fly-by-wire and increasing levels of automation significantly improve the safety of civil aircraft, and result in advanced capabilities for detecting, protecting and optimizing A/C guidance and control. However, this higher complexity requires the availability of some key flight parameters to be extended. Hence, the monitoring and consolidation of those signals is a significant issue, usually achieved via many functionally redundant sensors to extend the way those parameters are measured. This solution penalizes the overall system performance in terms of weight, maintenance, and so on. Other alternatives rely on signal processing or model-based techniques that make a global use of all or part of the sensor data available, supplemented by a model-based simulation of the flight mechanics. That processing achieves real-time estimates of the critical parameters and yields dissimilar signals. Filtered and consolidated information is delivered in unfaulty conditions by estimating an extended state vector, including wind components, and can replace failed signals in degraded conditions. Accordingly, this paper describes two model-based approaches allowing the longitudinal flight parameters of a civil A/C to be estimated on-line. Results are displayed to evaluate the performances in different simulated and real flight conditions, including realistic external disturbances and modeling errors.

9

Study of the effectiveness of different Kalman filtering methods and smoothers in object tracking based on simulation tests

Malinowski M., Kwiecień J.

Reports on Geodesy and Geoinformatics

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2014

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Vol. 97

1--22

EN

In navigation practice, there are various navigational architecture and integration strategies of measuring instruments that affect the choice of the Kalman filtering algorithm. The analysis of different methods of Kalman filtration and associated smoothers applied in object tracing was made on the grounds of simulation tests of algorithms designed and presented in this paper. EKF (Extended Kalman Filter) filter based on approximation with (jacobians) partial derivations and derivative-free filters like UKF (Unscented Kalman Filter) and CDKF (Central Difference Kalman Filter) were implemented in comparison. For each method of filtration, appropriate smoothers EKS (Extended Kalman Smoother), UKS (Unscented Kalman Smoother) and CDKS (Central Difference Kalman Smoother) were presented as well. Algorithms performance is discussed on the theoretical base and simulation results of two cases are presented.

10

Ekstrakcja sygnałów w wibrodiagnostyce pojazdów

Puchalski A.

Przegląd Mechaniczny

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2014

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nr 11

34--38

PL

W pracy przedstawiono nowe, autorskie podejście do analizy informacji pochodzących z diagnostycznych systemów monitorujących sygnały przyspieszenia drgań na przykładzie pojazdów. Przedmiotem badań i eksperymentów były układy stochastyczne o losowym przebiegu procesu i pomiaru oraz zakłóceniach mających postać szumów białych Gaussa. Zaproponowano oryginalne rozwiązania łączące filtrację modelową Kalmana z metodami podprzestrzeni obserwacji, prowadzące do utworzenia residuów statystycznych i miar detekcji uszkodzeń. Przydatność opracowanej metodyki zweryfikowano w czasie testów obejmujących różne stany spotykane w eksploatacji układów zaworowych silnika ZI.

EN

The paper presents a new approach to the analysis of information derived from the monitoring systems of vibrations accelerations signal: the case of vehicles. The subject of the research and experiments were stochastic systems with process and measurement uncertainty modeled by white Gaussian noises. The novel solution that combines Kalmahs filtering with the observation subspace methods which leads to the generation of residuals and indexes of faults detection was proposed in the paper The technique was verified during experimental tests of different maintenance states of valve systems of the SI engine.

11

Wybrane algorytmy wygładzania w aplikacjach nawigacyjnych

Gil R., Kaniewski P.

Pomiary Automatyka Kontrola

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2014

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R. 60, nr 9

726--728

PL

W artykule przedstawiono wyniki badań algorytmów wygładzania w układzie liniowym dyskretnym. Przeprowadzone badania pozwoliły na wyznaczenie błędów średniokwadratowych (RMS) położenia dla systemu z filtrem Kalmana oraz optymalnym estymatorem wygładzającym. Zaprezentowano jakościową poprawę, redukcję błędu RMS, oceny stanu układu wynikającą z zastosowania wygładzania. Przeprowadzone badania potwierdziły wartość użytkową algorytmów wygładzania.

EN

The paper presents the results of testing smoothing algorithms for a linear discrete system. Three types of smoothing algorithms are analyzed in the paper: fixed-interval smoothing, fixed-point smoothing, fixed-lag smoothing. The performance of the above smoothing algorithms was experimentally tested for a selected system model. There was assumed the dynamics model called in the literature as PVA (Position-Velocity-Acceleration). It describes the rate of change in the position, velocity and acceleration of the object in time. The research allowed determining the root mean square errors (RMS) of the position for a system with Kalman filter and the optimal smoothing estimator. It was shown that the use of smoothing improved the estimation of the state of the system significantly. The quality improvement, that is the decrease in the RMS errors of the system state estimates as a result of using smoothing algorithms, is presented in the paper. The investigations performed proved the usefulness of smoothing algorithms. The obtained results allowed determining the level of improvement in the state estimation when using the optimal smoothing estimators. Moreover, there was shown the improvement in the estimation accuracy with the increase in the time interval between the instants of state estimation and measurement.

12

Analiza różnych odmian filtru Kalmana przy lokalizacji obiektów mobilnych w oparciu o testy symulacyjne

Malinowski M., Kwiecień J.

Logistyka

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2014

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nr 6

7040--7050

PL

W praktyce nawigacyjnej stosowane są różne architektury i strategie integracji przyrządów pomiarowych, które wpływają na dobór algorytmu filtracji Kalmana. Na podstawie przedstawionych w artykule testów symulacyjnych wykonano analizę różnych metod filtracji Kalmana stosowanych przy lokalizacji obiektów mobilnych. W porównaniu zastosowano filtr EKF (Extended Kalman Filter) wymagający aproksymacji przy użyciu (jakobianów) pochodnych cząstkowych oraz filtry pozbawione tego wymogu jak UKF (Unscented Kalman Filter) i CDKF (Central Difference Kalman Filter). Przedyskutowano własności algorytmów na podstawie teoretycznej oraz wyników symulacji jednego zagadnienia w dwóch wariantach.

EN

One of tasks in navigation practice is determination the position of the object based on measurement of its attitude. On the grounds of simulation tests of algorithms designed and presented in this paper, the analysis of different methods of Kalman filtration applied in object tracing was made. EKF (Extended Kalman Filter) filter based on approximation with (jacobians) partial derivations and derivative-free filters like UKF (Unscented Kalman Filter) and CDKF (Central Difference Kalman Filter) were implemented in comparison. The two cases were carried out to verify the correctness and quality of work of developed modular library of estimation algorithms in practice. Filtering performance is discussed on the theoretical base and simulation results of example in two variants are presented.

13

Asynchronous distributed state estimation for continuous-time stochastic processes

Kowalczuk Z., Domżalski M.

International Journal of Applied Mathematics and Computer Science

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2013

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Vol. 23, no. 2

327--339

EN

The problem of state estimation of a continuous-time stochastic process using an Asynchronous Distributed multi-sensor Estimation (ADE) system is considered. The state of a process of interest is estimated by a group of local estimators constituting the proposed ADE system. Each estimator is based, e.g., on a Kalman filter and performs single sensor filtration and fusion of its local results with the results from other/remote processors to compute possibly the best state estimates. In performing data fusion, however, two important issues need to be addressed namely, the problem of asynchronism of local processors and the issue of unknown correlation between asynchronous data in local processors. Both the problems, along with their solutions, are investigated in this paper. Possible applications and effectiveness of the proposed ADE approach are illustrated by simulated experiments, including a non-complete connection graph of such a distributed estimation system.

14

A comparison between numerical differentiation and Kalman filtering for a LEO satellite velocity determination

Sharifi M. A., Seif M. R., Hadi M. A.

Artificial Satellites : Journal of Planetary Geodesy

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2013

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Vol. 48, No. 3

103--110

EN

The kinematic orbit is a time series of position vectors generally obtained from GPS observations. Velocity vector is required for satellite gravimetry application. It cannot directly be observed and should be numerically determined from position vectors. Numerical differentiation is usually employed for a satellite’s velocity, and acceleration determination. However, noise amplification is the single obstacle to the numerical differentiation. As an alternative, velocity vector is considered as a part of the state vector and is determined using the Kalman filter method. In this study, velocity vector is computed using the numerical differentiation (e.g., 9-point Newton interpolation scheme) and Kalman filtering for the GRACE twin satellites. The numerical results show that Kalman filtering yields more accurate results than numerical differentiation when they are compared with the intersatellite range-rate measurements.

15

Niskokosztowe sensory MEMS w systemach nawigacji inercyjnej

Sawicki M., Sondej T.

Pomiary Automatyka Kontrola

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2012

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R. 58, nr 8

701-703

PL

W artykule zaprezentowano system pozycjonowania zbudowany przy użyciu sensorów nawigacji inercyjnej (INS) oraz odbiornika GPS. Jako czujniki inercyjne zastosowano niskokosztowe, powszechnie dostępne akcelerometry i żyroskopy wykonane w technologii MEMS. Omówiono sposób kalibracji akcelerometru oraz metody przetwarzania sygnałów z sensorów MEMS. Przedstawiono również wyniki przeprowadzonych badań eksperymentalnych.

EN

The paper presents a positioning system with GPS and inertial sensors. The system is based on commercial solutions described in [1, 3]. The designed system consists of a GPS receiver, a MEMS accelerometer, a MEMS gyroscope, an electronic compass and a pressure sensor. Data processing was carried out by use of a microcontroller with ARM Cortex-M3 core. Designated positions are recorded on a microSD memory card and transmitted by the UART interface according to the NMEA standard. The experimental tests consisting in driving on city roads were performed. The measurement results were recorded directly from the GPS receiver and the system output. Characteristic places such as a tunnel or railway traction were analysed. The results obtained show that MEMS sensors improve the accuracy of determining the position during short-term GPS signal outages. They allow setting the positions more accurately in difficult terrain such as dense urban areas and underground tunnels. In addition, application of low-cost sensors gives a possibility to use the system in popular car navigation systems or mobile phones.

16

Novel optimal recursive filter for state and fault estimation of linear stochastic systems with unknown disturbances

Khémiri K., Ben Hmida F., Ragot J., Gossa M.

International Journal of Applied Mathematics and Computer Science

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2011

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Vol. 21, no 4

629-637

EN

This paper studies recursive optimal filtering as well as robust fault and state estimation for linear stochastic systems with unknown disturbances. It proposes a new recursive optimal filter structure with transformation of the original system. This transformation is based on the singular value decomposition of the direct feedthrough matrix distribution of the fault which is assumed to be of arbitrary rank. The resulting filter is optimal in the sense of the unbiased minimum-variance criteria. Two numerical examples are given in order to illustrate the proposed method, in particular to solve the estimation of the simultaneous actuator and sensor fault problem and to make a comparison with the existing literature results.

17

Algorytm sterowania czterowirnikowcem

Barański P., Polańczyk M., Strumiłło P.

Elektronika : konstrukcje, technologie, zastosowania

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2011

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Vol. 52, nr 9

135-138

PL

W artykule omówiono prosty algorytm sterowania platformą latającą złożoną z czterech silników i śmigieł o stałym skoku. Stanowi to dużą zaletę w porównaniu do helikopterów gdzie wymagane są skomplikowane i drogie śmigła o zmiennym skoku. W algorytmie sterowania platformy zastosowano kontroler PID. Do pomiaru położenia platformy latającej wykorzystywany jest czujnik przyśpieszenia oraz żyroskop. Informacje z tych dwóch czujników są integrowane za pomocą filtracji Kalmana w celu uzyskania lepszej estymacji położenia platformy.

EN

The article presents a simple algorithm for controlling a quadcopter composed of four engines an constant pitch propellers. The algorithm is based on a PID controller. The posture of the quadcopter is estimated on the base of an accelerometer and a gyroscope. The data is integrated by a Kalman filter to achieve accurate estimates of the vehicle posture.

18

An improved Neural Kalman Filtering Algorithm in the analysis of cyclic behaviour of concrete specimens

Krok A.

Computer Assisted Mechanics and Engineering Sciences

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2011

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Vol. 18, no. 4

275-282

EN

The article is related to the results of research on Node Decoupled Extended Kalman Filtering (NDEKF) as a learning method for the training of Multilayer Perceptron (MPL). Developments of this method made by the author are presented. The application of NDEKF and MPL and other methods (pruning of MLP, Gauss Process model calibrated by Genetic Algorithm and Bayesian learning methods) are discussed on the problem of hysteresis loop simulations for tests of compressed concrete specimens subjected to cyclic loading.

19

Sensitivity analysis of multiple fault test and reliability measures in integrated GPS/INS systems

Almagbile A., Wang J., Ding W., Knight N.

Archiwum Fotogrametrii, Kartografii i Teledetekcji

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2011

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Vol. 22

25--37

EN

Based on Kalman filtering, multi-sensor navigation systems, such as the integrated GPS/INS system, are widely accepted to enhance the navigation solution for various applications. However, such integrated systems do not always provide robust and stable navigation solutions due to unmodelled measurements and system dynamic errors, such as faults that degrade the performance of Kalman filtering for such integration. Single fault detection methods based on least squares (snapshot) method were investigated extensively in the literature and found effective to detect the fault at either sensor level or integration level. However, the system might be contaminated by multiple faults simultaneously. Thus, there is an increased likelyhood that some of the faults may not be detected and identified correctly. This will degrade the accuracy of positioning. In this paper multiple fault test and reliability measures based on a snapshot method were implemented in both the measurement model and the predicted states model for use in a GPS/INS integration system. The influences of the correlation coefficients between fault test statistics on the performances of the faults test and reliability measures were also investigated. The results indicate that the multiple fault test and reliability measures can perform more effectively in the measurement model than the predicted states model due to weak geometric strength within the predicted states model.

20

A cooperative positioning algorithm for DSRC enabled vehicular networks

Efatmaneshnik M., Kealy A., Alam N., Dempster A.

Archiwum Fotogrametrii, Kartografii i Teledetekcji

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2011

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Vol. 22

117--129

EN

Many of the safety related applications that can be facilitated by Dedicated Short Range Communications (DSRC), such as vehicle proximity warnings, automated braking (e.g. at level crossings), speed advisories, pedestrian alerts etc., rely on a robust vehicle positioning capability such as that provided by a Global Navigation Satellite System (GNSS). Vehicles in remote areas, entering tunnels, high rise areas or any high multipath/ weak signal environment will challenge the integrity of GNSS position solutions, and ultimately the safety application it underpins. To address this challenge, this paper presents an innovative application of Cooperative Positioning techniques within vehicular networks. CP refers to any method of integrating measurements from different positioning systems and sensors in order to improve the overall quality (accuracy and reliability) of the final position solution. This paper investigates the potential of the DSRC infrastructure itself to provide an intervehicular ranging signal that can be used as a measurement within the CP algorithm. In this paper, time-based techniques of ranging are introduced and bandwidth requirements are investigated and presented. The robustness of the CP algorithm to inter-vehicle connection failure as well as GNSS dropouts is also demonstrated using simulation studies. Finally, the performance of the Constrained Kalman Filter used to integrate GNSS measurements with DSRC derived range estimates within a typical VANET is described and evaluated.