Extended Kalman Filter Scheme Research Articles

Admittance boundary conditions and sound pressure field estimation of vibro-acoustic systems using an extended Kalman filter and parametric model order reduction

Time-domain vibro-acoustic finite element simulations have been recently used in auralization and virtual sensing. However, when comparing the transient response based on a finite element model to actual measurements, often discrepancies are seen due to, amongst others, the presence of inaccurate admittance boundary conditions. To achieve accurate time-domain simulations, these uncertainties need to be included in the time-domain simulation. In this paper, the admittance boundary conditions are modelled using the superposition of several passive functions whose parameters are considered as the additional states in an extended Kalman filter scheme. Finite element models for vibro-acoustic systems including admittance boundary conditions have a high computational cost and result in frequency-dependent damping matrices. To get a smaller time-domain model, stability-preserving model order reduction is employed to reduce the number of degrees of freedom while maintaining a good accuracy and stability. Furthermore, to preserve the parameter dependency, parametric model order reduction based on a Taylor series expansion is employed. Experiments are performed on a vibro-acoustic system including a foam layer which can be represented by admittance boundary conditions. These conditions are identified and it is shown that the predicted sound field pressure is improved significantly as compared to the direct time-domain simulation.

Vehicle state and tyre force estimation: demonstrations and guidelines

This paper presents an in-depth analysis of the application of different techniques for vehicle state and tyre force estimation using the same experimental data and vehicle models, except for the tyre models. Four schemes are demonstrated: (i) an Extended Kalman Filter (EKF) scheme using a linear tyre model with stochastically adapted cornering stiffness, (ii) an EKF scheme using a Neural Network (NN) data-driven linear tyre model, (iii) a tyre model-less Suboptimal-Second Order Sliding Mode (S-SOSM) scheme, and (iv) a Kinematic Model (KM) scheme integrated in an EKF. The estimation accuracy of each method is discussed. Moreover, guidelines for each method provide potential users with valuable insight into key properties and points of attention.

An adaptive Kalman filter for extreme polarization effects equalization in coherent optical communication system

The specially designed Kalman filter was proved to be competent to complete the polarization equalization in some extreme environments with the large time-varying polarization mode dispersion (PMD) and the ultrafast rotation of state of polarization (RSOP). But the performance of this kind of Kalman filter is strongly restricted by the initial noise statistics represented by the process noise covariance Q and the measurement noise covariance R which will limit its effectiveness in an actual scene. To solve this problem, this paper proposes an adaptive Kalman filter structure by an adjustable way of estimating the process noise covariance Q and the measurement noise covariance R based on the measurement residual in order to be adaptive to the time-varying environments. The performance of the proposed adaptive Kalman scheme is checked both by the simulation and experiment on the 28 Gbaud PDM-QPSK/16QAM coherent optical communication system platforms. The simulation and experiment results demonstrate that the proposed adaptive Kalman filter scheme has a stable and better performance of the equalization for large PMD combined with ultrafast RSOP, with a greater tolerance the to time-varying extreme polarization environments than that using the extended Kalman filter scheme adopted in our previous work.

Pilot-based extended Kalman filter for phase noise estimation in CO-FBMC/OQAM systems

we proposed a pilot-based extended Kalman filter (P-EKF) scheme for phase noise estimation in offset-QAM-based filterbank multicarrier (FBMC–OQAM) systems with a large number of subcarriers. The performance of the P-EKF scheme with rectangular QAM modulations is evaluated in optical transmission system, including fiber dispersion, nonlinearity, frequency offset and so on. The performance is analyzed in 16-QAM 20Gbaud CO-FBMC/OQAM system with 400 km single mode fiber. The results show that P-EKF can achieve 1.216×10−2 normalized linewidth tolerance (4.48×10−3 of blind-extended Kalman filter (B-EKF) and 2.24×10−3 of modified blind phase search (M-BPS)) at the bit error rate (BER) of 3.8×10−3, while keeping a low amount of calculation (for every iteration, the real multiplication and real addition are both 5). Besides, P-EKF can compensate ∓3500 kHz residual frequency offset at the BER of 3.8×10−3 when the optical signal-to-noise ratio is 25dB, which makes it very suitable to apply to the real DSP module.

An INS-UWB Based Collision Avoidance System for AGV

As a highly automated carrying vehicle, an automated guided vehicle (AGV) has been widely applied in various industrial areas. The collision avoidance of AGV is always a problem in factories. Current solutions such as inertial and laser guiding have low flexibility and high environmental requirements. An INS (inertial navigation system)-UWB (ultra-wide band) based AGV collision avoidance system is introduced to improve the safety and flexibility of AGV in factories. An electronic map of the factory is established and the UWB anchor nodes are deployed in order to realize an accurate positioning. The extended Kalman filter (EKF) scheme that combines UWB with INS data is used to improve the localization accuracy. The current location of AGV and its motion state data are used to predict its next position, decrease the effect of control delay of AGV and avoid collisions among AGVs. Finally, experiments are given to show that the EKF scheme can get accurate position estimation and the collisions among AGVs can be detected and avoided in time.

Simpplified extended Kalman filter phase noise estimation for CO-OFDM transmissions.

We propose a flexible simplified extended Kalman filter (S-EKF) scheme that can be applied in both pilot-aided and blind modes for phase noise compensation in 16-QAM CO-OFDM transmission systems employing a small-to-moderate number of subcarriers. The performance of the proposed algorithm is evaluated and compared with conventional pilot-aided (PA) and blind phase search (BPS) methods via extensive an Monte Carlo simulation in a back-to-back configuration and with a dual polarization fiber transmission. For 64 subcarrier 32 Gbaud 16-QAM CO-OFDM systems with 200 kHz combined laser linewidths, an optical signal-to-noise ratio penalty as low as 1 dB can be achieved with the proposed S-EKF scheme using only 2 pilots in the pilot-aided mode and just 4 inputs in the blind mode, resulting in a spectrally efficient enhancement by a factor of 3 and a computational effort reduction by a factor of more than 50 in comparison with the conventional PA and the BPS methods, respectively.

Joint Device Positioning and Clock Synchronization in 5G Ultra-Dense Networks

In this paper, we address the prospects and key enabling technologies for highly efficient and accurate device positioning and tracking in fifth generation (5G) radio access networks. Building on the premises of ultra-dense networks as well as on the adoption of multicarrier waveforms and antenna arrays in the access nodes (ANs), we first formulate extended Kalman filter (EKF)-based solutions for computationally efficient joint estimation and tracking of the time of arrival (ToA) and direction of arrival (DoA) of the user nodes (UNs) using uplink reference signals. Then, a second EKF stage is proposed in order to fuse the individual DoA and ToA estimates from one or several ANs into a UN position estimate. Since all the processing takes place at the network side, the computing complexity and energy consumption at the UN side are kept to a minimum. The cascaded EKFs proposed in this article also take into account the unavoidable relative clock offsets between UNs and ANs, such that reliable clock synchronization of the access-link is obtained as a valuable by-product. The proposed cascaded EKF scheme is then revised and extended to more general and challenging scenarios where not only the UNs have clock offsets against the network time, but also the ANs themselves are not mutually synchronized in time. Finally, comprehensive performance evaluations of the proposed solutions on a realistic 5G network setup, building on the METIS project based outdoor Madrid map model together with complete ray tracing based propagation modeling, are provided. The obtained results clearly demonstrate that by using the developed methods, sub-meter scale positioning and tracking accuracy of moving devices is indeed technically feasible in future 5G radio access networks operating at sub-6 GHz frequencies, despite the realistic assumptions related to clock offsets and potentially even under unsynchronized network elements.

Extended input estimation method for tracking non‐linear manoeuvring targets with multiplicative noises

In this study, a new input estimation method is proposed for targets with non-linear dynamics and unknown inputs (manoeuvres), where measurement model is corrupted with both additive and multiplicative noises. First, the authors proposed an innovative model by adding unknown inputs as a new state to the original state vector and constructed an augmented state vector. Therefore, manoeuvring model turns into a non-manoeuvring model. The proposed model does not need any manoeuvre detection stage procedure but it causes a correlation between the process and measurement noises. Subsequently, the authors modify the augmented model to deal with the cross-correlation problem. Finally an augmented extended Kalman filter scheme is proposed, which unlike the most existing literature, it can estimate unknown inputs as quickly as possible and copes with the multiplicative noises and the cross-correlation problem. The efficiency of the proposed method is demonstrated in computer simulations for a manoeuvring target with non-linear dynamics through Monte-Carlo simulation.

Estimation Of Global Positioning System Measurement Errors For GAGAN Applications

The Global Positioning System (GPS) has been in use for providing positioning, navigation and timing (PNT) services in many parts of the world. There are several errors that affect the positional accuracy of GPS. Prominent among them are ephemeris errors, satellite and receiver clock errors, multipath errors, signal propagation errors such as ionospheric delay, tropospheric delay, and instrumental biases of the satellite and receiver. In this paper, prominent estimation techniques to characterize various GPS measurement errors are reviewed. The GPS data in the Receiver INdependent EXchange (RINEX) format obtained from a Dual frequency GPS receiver is used in this analysis. Among all the errors, ionospheric delay is found to be the most dominant. However, these delay measurements are affected by the satellite and receiver instrumental biases. The instrumental biases exist as the signals at the two GPS frequencies experience different delays inside the satellite and receiver hardware. For estimation of the instrumental biases Extended Kalman filter(EKF) technique is adopted. The user equivalent range error (UERE) obtained due to all the error sources is of the order of few metres. After accounting for various errors, the estimation accuracy is significantly improved.The positional accuracy of the GPS Aided GEO Augmented Navigation (GAGAN) system is basically dependent on ranging errors and the satellite constellation geometry(1). The lineof-sight ionospheric measurements derived from the Global Positioning System (GPS) observables are corrupted by the instrumental biases present in both the GPS satellites and the receivers. The instrumental bias and Total Electron Content (TEC) results (Hyderabad GAGAN station (78.47°E, 17.45°N)) obtained using theExtended Kalman filter technique are presented in this paper. In this work the main focus is towards development of an improved error free approach for aircraft navigation. The existing navigation solutions are based on iterative algorithms and require an initial estimate of the receiver position for computing the navigation solution which is not possible in all conditions. Accurate, reliable and cost effective navigation solution algorithms that suit the Indian geographic area and area of application are proposed in this work. A non-iterative point solution approach algorithm computes the navigation solution based on the available satellite positions and pseudorange measurements(3). The improvement in GPS system has given a feasibility of automated operation of satellite based augmenting system in aircraft navigation can augment GAGAN and improves the positional accuracy of the user. In this paper a communication approach , high, accurate processing using EKF scheme is proposed for GPS aided geo augmented navigation (GAGAN) application. The effectiveness of the proposed approach for higher performance is evaluated under variable conditions.

Application of Extended Kalman Filter Algorithm in SDINS/GPS Integrated Inertial Navigation System

This paper deals with the integrated navigation system based on fusion of data from Strap Down Inertial Navigation System (SDINS) and from Global Position System (GPS). In order to increase the accuracy and reliability of navigation algorithms, these two different systems are combined. The navigation system that be analyzed is basically of INS type while GPS corrective data are obtained less frequently and these are treated as noisy measurements in an extended Kalman filter scheme. The simulation of whole system (SDINS/GPS integrated system with Kalman filter) was modeled using MATLAB package, SIMULINK© tool. The proper choice of Kalman filter parameters had taken to minimize navigation errors for a typical medium range flight scenario (Simulated test trajectory and real trajectory of vehicle motion). A prototype of a SDINS installed on a moving platform in the laboratory to collected data by many experiments to verification our SIMULINK models.

Evaluation of ECMWF's soil moisture analyses using observations on the Tibetan Plateau

AbstractAn analysis is carried out for two hydrologically contrasting but thermodynamically similar areas on the Tibetan Plateau, to evaluate soil moisture analysis based on the European Centre for Medium‐Range Weather Forecasts (ECMWF) previous optimum interpolation scheme and the current point‐wise extended Kalman filter scheme. To implement the analysis, this study used two regional soil moisture and soil temperature networks (i.e., Naqu and Maqu) on the Tibetan Plateau. For the cold‐semiarid Naqu area, both ECMWF soil moisture analyses significantly overestimate the regional soil moisture in the monsoon seasons. For the cold‐humid Maqu network area, the ECMWF products have comparable accuracy as reported by previous studies in the humid monsoon period. The comparisons were made among the liquid soil moisture analysis from ECMWF, the ground station's measurements and the satellite estimates from the Advanced Scatterometer sensor. The results show reasonable performances of the ECMWF soil moisture analyses (i.e., both optimum interpolation and extended Kalman filter products) and the Advanced Scatterometer level 2 products, when compared to the in situ measurements.

Angular Rate Estimation Using a Distributed Set of Accelerometers

A distributed set of accelerometers based on the minimum number of 12 accelerometers allows for computation of the magnitude of angular rate without using the integration operation. However, it is not easy to extract the magnitude of angular rate in the presence of the accelerometer noises, and even worse, it is difficult to determine the direction of a rotation because the angular rate is present in its quadratic form within the inertial measurement system equations. In this paper, an extended Kalman filter scheme to correctly estimate both the direction and magnitude of the angular rate through fusion of the angular acceleration and quadratic form of the angular rate is proposed. We also provide observability analysis for the general distributed accelerometers-based inertial measurement unit, and show that the angular rate can be correctly estimated by general nonlinear state estimators such as an extended Kalman filter, except under certain extreme conditions.

Experimental evaluation of a real‐time kinematic GPS positioning technique

This paper presents a methodology for observing GPS carrier phase data with the least‐squares algorithm and the extended Kalman filter to improve positioning accuracy of the real‐time kinematic GPS (KGPS). The integer least‐squares method is first employed to solve the GPS integer ambiguities, and the extended Kalman filter scheme is then used to find real‐time kinematic position estimates by incorporating with the vehicle kinematics of the user station. Experimental results show that the proposed KGPS algorithm is not only effective in providing more precise position estimates and reducing the detrimental effect of the cycle slip, but also useful for realtime vehicle navigation and high‐accuracy surveying.

Comparative study of sliding mode speed and position control of a vector-controlled induction machine

This paper demonstrates that high performance speed and position control can be obtained by using sliding mode control methods for a vector-controlled induction machine. Four sliding mode control laws are studied and compared for speed and position control. An extended Kalman filter scheme for rotor resistance estimation is used. Simulation results show that the proposed scheme can achieve accurate speed/position tracking in the presence of load disturbances and rotor resistance variation. Important conclusions are reached regarding the merits and drawbacks of each of the sliding mode techniques.

An extended Kalman filter to assimilate satellite altimeter data into a nonlinear numerical model of the tropical Pacific Ocean: Method and validation

A new implementation of the extended Kalman filter scheme is developed for the purpose of assimilating observations into a high‐resolution nonlinear numerical model of the tropical Pacific Ocean. It is characterized by two successive stages: (1) approximation of the error covariance matrix by a singular low‐rank matrix which leads to making corrections only in those directions for which the error is not naturally attenuated by the system (in this respect it is quite similar to the approach adopted by Cane et al. [1996]), and (2) modification of these directions over time according to the model dynamics, thus reflecting the evolutive nature of the filter. The filter is initialized by a method based on the empirical orthogonal functions obtained from free runs of the model. The reduction of the error covariance matrix avoids the overwhelming burden of computing the temporal evolution of the prediction error with all the degrees of freedom of the full state vector. This assimilation scheme is implemented in the Gent and Cane [1989] primitive equation reduced gravity model. This model has the advantage of using a σ coordinate in the vertical which allows a geographical refinement of the vertical resolution for thermocline gradients. It is forced by the Florida State University database winds, and the Chen et al. [1994] hybrid scheme parameterization is assumed for the mixed layer. The domain of application is the tropical Pacific Ocean basin between 120°E and 80°W longitude and 30°S and 30°N latitude. The resolution is finest at the equator and steadily increases away from the equator. In a first application, validation twin experiments are conducted in which observations are assumed to be synthetic altimeter data sampled according to the TOPEX/POSEIDON mission features. The method is shown to be efficient under various conditions and, in particular, to be capable of transferring information in the vertical from the surface‐only altimeter data to the deepest ocean layers and therefore of adequately constraining the thermal and the velocity profiles within the 300 or 400 m upper ocean. In a second application, real TOPEX/POSEIDON data are used and the results evaluated against independent in situ data, namely, Tropical Ocean‐Global Atmosphere (TOGA)/TAO mooring observations. Improvements in the model behavior are clear in terms of the time variability of the tropical ocean. It therefore seems that the reduced state Kalman filter with empirical orthogonal function (EOF) initialization can be applied with success to such a primitive equation model of the Pacific for the assimilation of altimeter data. However, at this stage the evolutivity of the filter seems to have a limited impact on the performances, which was not the case for tests in the strongly nonlinear midlatitudes [Pham et al., 1998a].

State Estimation in the Control of Integrated Batch Reaction with Distillation Processes

Batch processes involving integrated reaction and fractionation steps call for a higher than normal degree of co-ordination in their control. Ideally, active feedback control action would operate on component concentrations within the reactor/still system but high capital and operating costs, associated with suitable on-line composition sensors, usually preclude this approach. With vapour/liquid equilibrium involved, an alternative is to use temperature measurements to infer underlying component concentrations. As a potential basis for this, the performance of extended Luenberger observer (ELO) and extended Kalman filter (EKF) state estimation strategies is compared in a case study based on an industrial process, for which detailed mathematical models were available. The EKF scheme proves to have superior capability in delivering acceptable estimate accuracy, even in the face of process/model mismatch. This mismatch arose in using a reduced order model in the estimators which cuts computational overheads dramatically but neglects column fluid hold-up and assumes binary rather than true multicomponent VLE.

Incorporating nonlinearities of measurement function in power system dynamic state estimation

Dynamic state estimation in power systems is based on the extended Kalman filter (EKF) scheme. The EKF system uses a linearised measurement equation, neglecting the nonlinearities of the measurement function. Under certain circumstances (e.g. large load changes) this leads to degradation in the filter performance. Two algorithms are proposed for dynamic state estimation which incorporate the measurement function nonlinearities in the EKF scheme. The performance of the schemes are compared with the standard linear EKF scheme under various conditions and comparative results are presented.