Discrete Extended Kalman Filter Research Articles

Ultrasonic Time-of-Flight Estimation Through Unscented Kalman Filter

This paper deals with distance or level measurements based on ultrasonic time-of-fight estimation. Moving from a past experience concerning the proposal of a method based on discrete extended Kalman filter (DEKF) to overcome some limitations of already available ultrasonic-based techniques, a new digital signal processing method capable of granting further improvements is presented. The method is based on the unscented Kalman filter (UKF), which is a new extension of the Kalman filter theory mandated to face some DEKF problems, mainly due to its inherent linearization approach. To this aim, UKF is applied to the acquired ultrasonic signal in order to estimate the returned echo envelope as well as to locate its onset more accurately. After describing key features and implementation issues of the new method, the results obtained in a number of tests on simulated and actual ultrasonic signals, which assess its reliability and effectiveness as well as advantages with respect to the previous one, are given.

A Measurement Method Based on Kalman Filtering for Ultrasonic Time-of-Flight Estimation

A new digital signal-processing method for ultrasonic time-of-flight (TOF) estimation is presented. The method applies the discrete extended Kalman filter (DEKF) to the acquired ultrasonic signal in order to accurately estimate the shape factors of the echo envelope as well as locate its onset. It is also possible to assure reduced bias and uncertainty in critical TOF measurements, such as those involving low signal-to-noise ratio (SNR) as well as severe distortion of echo shape. A number of numerical tests are conducted on simulated signals with the aim of highlighting the good performance of the method when operating in critical conditions. Results attained in TOF-based distance measurements finally assess the reliability and efficacy of the method in the presence of actual ultrasonic signals.

Estimation of intracellular phosphate content in plant cell cultures using an extended Kalman filter

Phosphate is an essential nutrient that is usually taken up by plant cells rapidly and stored intracellularly. Currently, there is no convenient means for on-line sensing of the intracellular phosphate content in cultured plant cells. In this study, a state estimator for this important parameter in batch plant cell cultures was developed using extended Kalman filter (EKF) methodology. A non-linear kinetic model was constructed to describe the dynamics of intracellular phosphate uptake and utilization. For intracellular phosphate estimation, this model was found to be most sensitive to three parameters: the maximum specific growth rate (μ max), the maximum phosphate uptake rate (ν max), and the yield coefficient on oxygen ( y o). The EKF algorithm coupled with the kinetic model and on-line oxygen uptake rate ( r o) measurement was used successfully to track the intracellular phosphate content under different initial phosphate concentrations. The state estimator could also accurately predict the biomass concentration. When μ max, ν max, and y o were included in the state vector, tracking of intracellular phosphate was only slightly affected. The estimation system was found very stable as long as the measurement errors of the initial states, the r o measurement error, and the system error were respectively within 30%, 30%, and 50%. With a r o measurement interval as long as 12 h, accurate tracking of the intracellular phosphate content could still be attained using a discrete EKF. Apparently, the slow r o dynamics in plant cell cultures allows the use of a long measurement interval. Considering the difficulties encountered in the on-line sensing of intracellular phosphate using the chemical or nuclear magnetic resonance (NMR) methods, the EKF method coupled with simple on-line oxygen uptake rate measurement provides a promising means for sensing this important culture parameter on-line.

Software sensor for on-line estimation of the microbial activity in activated sludge systems

Abstract This paper considers the design of a software sensor (or soft-sensor) for the on-line estimation of the biological activities of a colony of aerobic micro-organisms acting on activated sludge processes, where the carbonaceous waste degradation and nitrification processes are taken into account. These bioactivities are intimately related to the dissolved oxygen concentration. Two factors that affect the dynamics of the dissolved oxygen are the respiration rate or the oxygen uptake rate (OUR) and the oxygen transfer function (K la). These items are challenging topics for the application of recursive identification due the nonlinear characteristic of the oxygen transfer function, and to the time-varying feature of the respiration rate. In this work, OUR and the oxygen transfer function are estimated through a software sensor, which is based on a modified version of the discrete extended Kalman filter. Numerical simulations are carried out in a predenitrifying activated sludge process benchmark and the obtained results demonstrate the applicability and efficiency of the proposed methodology, which should provide a valuable tool to supervise and control activated sludge processes.

Estimation of Intracellular Phosphate Content in Plant Cell Cultures Using an Extended Kalman Filter

Phosphate is an essential nutrient that is usually taken up by plant cells rapidly and stored intracellularly. Currently, there is no convenient means for on-line sensing of the intracellular phosphate content in cultured plant cells. In this study, a state estimator for this important parameter in batch plant cell cultures was developed using extended Kalman filter (EKF) methodology. A non-linear kinetic model was constructed to describe the dynamics of intracellular phosphate uptake and utilization. For intracellular phosphate estimation, this model was found to be most sensitive to three parameters: the maximum specific growth rate (mu(max)), the maximum phosphate uptake rate (nu(max)), and the yield coefficient on oxygen (y(o)). The EKF algorithm coupled with the kinetic model and on-line oxygen uptake rate (r(o)) measurement was used successfully to track the intracellular phosphate content under different initial phosphate concentrations. The state estimator could also accurately predict the biomass concentration. When mu(max), nu(max), and y(o) were included in the state vector, tracking of intracellular phosphate was only slightly affected. The estimation system was found very stable as long as the measurement errors of the initial states, the r(o) measurement error, and the system error were respectively within 30%, 30%, and 50%. With a r(o) measurement interval as long as 12 h, accurate tracking of the intracellular phosphate content could still be attained using a discrete EKF. Apparently, the slow r(o) dynamics in plant cell cultures allows the use of a long measurement interval. Considering the difficulties encountered in the on-line sensing of intracellular phosphate using the chemical or nuclear magnetic resonance (NMR) methods, the EKF method coupled with simple on-line oxygen uptake rate measurement provides a promising means for sensing this important culture parameter on-line.

State estimation of batch distillation columns using an extended Kalman filter

Composition monitoring and control play an essential role during a batch distillation cycle, but on-line composition analyzers are expensive, difficult to maintain and give delayed responses. Considering the need and lack of a stochastic estimator for batch distillation columns, a discrete extended Kalman filter (EKF) for binary and multicomponent systems has been developed and tested. The aim of the EKF was to provide reliable and real-time column composition profiles from few temperature measurements and easily available information. Accurate composition estimates and fast convergence were obtained, and the EKF has confirmed its ability to incorporate the effects of noise (from both measurement and modeling). The number of sensors and the observation frequency have shown to be important variables in the design of the EKF, especially for systems with fast dynamics.

A fuzzy neural network based extended Kalman filter

In this paper we construct a discrete extended Kalman filter by using fuzzy neural networks. The constructed filter makes it possible to estimate the states of a nonlinear dynamical system with unknown plant model. The unknown plant is identified by a fuzzy neural network and the modelling error can be compensated by a simple but efficient method that avoids the occurrence of divergence in state estimation. A computer simulation is presented to illustrate the performance and applicability of the proposed filter.

Design and implementation of an extended Kalman filter for the state estimation of a permanent magnet synchronous motor

Practical considerations for implementing the discrete extended Kalman filter in real time with a digital signal processor are discussed. The system considered is a permanent magnet synchronous motor (PMSM) without a position sensor, and the extended Kalman filter is designed for the online estimation of the speed and rotor position by only using measurements of the motor voltages and currents. The algorithms developed to allow efficient computation of the filter are presented. The computational techniques used to simplify the filter equations and their implementation in fixed-point arithmetic are discussed. Simulation and experimental results are presented to demonstrate the feasibility of this estimation process. >

Real time estimator for control of an orbiting single tether system

A real-time estimator is developed for the control of the Tether Dynamics Explorer (TDE) system. TDE is being used in a series of tethered satellite flight experiments whose purpose is to validate existing system models and test proposed control laws. Each experiment consists of an orbiting Delta II second stage which deploys toward the Earth a small box-shaped passive endbody at the end of a flexible tether. A discrete extended Kalman filter (DEKF) is presented which can operate in real time and in conjunction with control laws. This filter estimates the in-plane and out-of-plane tether libration angles and their rates from a proposed three-axis tether tension measurement device in the Delta second stage. The simulation results indicate that the DEKF can estimate the libration angle and their rates from a three-axis tension and length measurement with an acceptable error. The relatively simple computations required make this algorithm particularly well suited for real-time operation. >

Discrete extended Kalman filter for radar point error reduction

A recently proposed method of reducing target glint errors in radar systems is further enhanced with the development of a discrete target model and discrete Kalman filter (DKF). Simulation results demonstrating the DKF are presented, and the limits of the usefulness of this method are investigated. The major advantage of the DKF is that it can be implemented in software in the digital processor of the radar offering flexibility over continuous-time filters. >

Autonomous Satellite Navigation Using Optico-Inertial Instruments

This paper presents an Autonomous and modular Satellite Navigation System. It is based on a discrete extended kalman filter. Two kinds of measurements are taken into account : the first one uses a stellar refraction measurement; the second uses a landmark recognition technique. The forecasted localisation performance of this system is 1 km in LEO and 10 km in GEO.