Discrete-time Extended Kalman Filter Research Articles

Integrated Guidance and Control Using Model Predictive Control with Flight Path Angle Prediction against Pull-Up Maneuvering Target.

Integrated guidance and control using model predictive control against a maneuvering target is proposed. Equations of motion for terminal homing are developed with the consideration of short-period dynamics as well as actuator dynamics of a missile. The convex optimization problem is solved considering inequality constraints that consist of acceleration and look angle limits. A discrete-time extended Kalman filter is used to estimate the position of the target with a look angle as a measurement. This is utilized to form a flight-path angle of the target, and polynomial fitting is applied for prediction. Numerical simulation including a Monte Carlo simulation is performed to verify the performance of the proposed algorithm.

A New Continuous Discrete Unscented Kalman Filter

The time and measurement update for the discrete time Kalman filter can be formulated in terms of conditional means and covariances. The unscented Kalman filter can be interpreted as calculating these conditional means and covariances by using the unscented transform. This approach can also be directly applied to nonlinear models as an alternative to the discrete time extended Kalman filter. In this paper, a novel method for computing the unscented Kalman filter for a nonlinear model with continuous time dynamics and discrete time measurements is presented. Compared to the existing approaches, this method is far simpler and less computationally demanding, and it performs at least as well.

Framework design for weight-average molecular weight control in semi-batch polymerization

A framework that embraces a state-of-the-art sensor, multi-objective dynamic optimization, nonlinear state estimation and control, is designed and implemented to achieve target weight-average molecular weight trajectories. The Automatic Continuous Online Monitoring of Polymerization reactions (ACOMP) is combined for the first time with a nonlinear state observer for full polymer characterization and signal processing. A hybrid variation of the discrete-time extended Kalman filter (h-DEKF) is formulated based on an auto-tuning procedure that uses a stochastic global optimization technique. A number of optimal policies are generated and experimentally tested. Results are provided through investigations into the free-radical aqueous polymerization of acrylamide using potassium persulfate as initiator.

Performance Analysis of a DEKF for Available Bandwidth Measurement

The paper presents a characterisation analysis of a measurement algorithm based on a Discrete-time Extended Kalman Filter (DEKF), which has recently been proposed for the estimation and tracking of end-to-end available bandwidth. The analysis is carried out by means of simulations for different rates of variations of the available bandwidth and permits assessing the performance of the measurement algorithm for different values of the filter parameters, that is, the covariance matrixes of the measurement and process noise.

Multi-Variable Integral Sliding Mode Control of a Two Degrees of Freedom Helicopter

In this paper, a multi-variable nonlinear control-oriented model of a twin rotor aerodynamic system (TRAS) is presented. The mathematical description of the multibody system is derived using Lagrange's equations. Based on the resulting state-space representation, a multi-variable integral sliding mode control is designed to accurately track desired trajectories for both the azimuth angle and the pitch angle. Due to unmeasurable states and uncertainties stemming from simplifications at modelling as well as disturbance torques, a discrete-time extended Kalman filter (EKF) is employed and combined with a discrete-time implementation of the nonlinear control law. The proposed control strategy allows for an excellent tracking behaviour as highlighted by experimental results.

Tyre–road friction coefficient estimation based on the discrete-time extended Kalman filter

This paper presents a new algorithm for estimation of the instantaneous value and the maximum value of the tyre–road friction coefficient (the adhesion coefficient) depending on the quality of the road surface. The algorithm applies the discrete-time extended Kalman filter for state estimation. The underlying discrete-time non-linear state-space model was based on a two-wheel longitudinal vehicle dynamics model extended to include the scale factor parameter of the ‘magic formula’ for the longitudinal tyre force introduced by Pacejka. To verify the Kalman-filter-based algorithm, a validated real-time hardware-in-the-loop simulation environment was utilized, and the results were in agreement with the expectations.

Nonlinear Estimation of Fluid Properties using the Time Domain Response of a Vibrating Microcantilever

A novel approach is presented for the modelling and analysis of the dynamic response of a microcantilever beam vibrating in a viscous fluid to determine the properties of the fluid. This new approach is based on modelling the time response of the deflection of the free end of the microcantilever, whereas other methods developed in the field of rheological measurements using vibrating microcantilevers are generally based on the analysis of the frequency response of the deflection of the cantilever. The proposed approach consists of spatially discretizing the beam along its length, approximately representing it with a finite-dimensional state-space model and determining the fluid properties using nonlinear state/parameter estimation techniques. In this work, the discrete-time extended Kalman filter is employed to find estimates of the fluid’s viscosity and density using temporal measurements of the deflection at the free end of the beam. Simulation studies illustrating the validity of the proposed approach are presented.

Robust Gyro‐free Attitude Estimation for a Small Fixed‐wing Unmanned Aerial Vehicle

AbstractThis paper proposes a backup attitude estimation scheme for small fixed‐wing unmanned aerial vehicles (UAVs) in the event of gyroscopic failure. The attitude is propagated in terms of 3 degrees‐of‐freedom (DoF) aircraft dynamics. The errors in attitude propagation are updated using indirect attitude information obtained from accelerations as sensed by onboard accelerometers and a global positioning system (GPS) receiver. In the event of gyroscopic failure, large uncertainties are introduced into the attitude propagation model. Such uncertainties in states and parameters are modeled as norm‐bound uncertainties and a discrete‐time robust extended Kalman filter (REKF) is implemented to estimate the attitude of the UAV.

Nonlinear estimation of ring-down time for a Fabry-Perot optical cavity

This paper discusses the application of a discrete-time extended Kalman filter (EKF) to the problem of estimating the decay time constant for a Fabry-Perot optical cavity for cavity ring-down spectroscopy (CRDS). The data for the estimation process is obtained from a CRDS experimental setup in terms of the light intensity at the output of the cavity. The cavity is held in lock with the input laser frequency by controlling the distance between the mirrors within the cavity by means of a proportional-integral (PI) controller. The cavity is purged with nitrogen and placed under vacuum before chopping the incident light at 25 KHz and recording the light intensity at its output. In spite of beginning the EKF estimation process with uncertainties in the initial value for the decay time constant, its estimates converge well within a small neighborhood of the expected value for the decay time constant of the cavity within a few ring-down cycles. Also, the EKF estimation results for the decay time constant are compared to those obtained using the Levenberg-Marquardt estimation scheme.

Mathematical Modeling of INS/GPS Based Navigation System Using Discrete Time Extended Kalman Filter Schemes for Flapping Micro Air Vehicle

Flapping-wing Micro Air Vehicles (FMAV) comprise a new type of remote-controlled, semi-autonomous or autonomous aircraft that is significantly smaller than conventional aircraft. The concept of flapping-wing flight is inspired by birds and insects, though birds and insects use strikingly different modes of flapping to achieve the same result. Flapping-wing flight has been a large domain of exploration in the last few years, aiming to understand and mimic the ingenious strategies developed by animals during the navigation in three dimensions. While ornithopters deriving all of their lift and thrust from sets of flapping wings, have been demonstrated, applying Micro Electro Mechanical Systems (MEMS) inertial sensors to their navigation systems is an extremely challenging area. This paper presents an approach to designing an INS/GPS based navigation system using a Discrete Time Extended Kalman Filter. Navigation is one of the applications of state estimation techniques, and the reliable determination of attitude, velocity and position of the aircraft is essential for good flight performance during fully autonomous flight. In the current navigation concept, an Inertial Measurement Unit (IMU), providing sensor measurements, is used for this purpose, and the sensors used for navigation system are comprised of a MEMS gyro, a MEMS accelerometer, a MEMS magnetometer and a Global Positioning System. The Kalman filter provides an efficient computational means to estimate the state of a process, as it supports estimations of past, present, and even future states. In this paper three different schemes for a Discrete Time Extended Kalman Filter are used for navigation system. These include a single-stage seven-state discrete time extended Kalman filter, a two-stage cascaded discrete time extended Kalman filter, and a three-stage cascaded discrete time extended Kalman filter. Comparison and analysis of the three schemes are carried out, and it is demonstrated that the proposed algorithm is useful technique for flapping-wing flight.

Double line-of-sight measuring relative navigation for spacecraft autonomous rendezvous

Abstract This paper presents a double line-of-sight (LOS) measuring relative navigation technique for far or medium range (tens of kilometers ∼ several kilometers) autonomous rendezvous. In this new relative navigation technique, two chase spacecraft with inter-spacecraft crosslink form a measuring baseline relative to the target spacecraft in space and, respectively, measure LOS angles of the target and their own inertial states. The processing noise model of the relative navigation system is developed based on the spacecraft relative dynamics equations described in inertial frame. The measurement model including LOS angles of the target and the bearing and length of the measuring baseline is established. A discrete-time extended Kalman filter (EKF) is developed to estimate the relative motion of the target. The degree of observability of the navigation system is analyzed by the condition number. Numerical simulation results indicate that: (1) the relative position and velocity of the target can be estimated with sufficient accuracy using the double LOS measuring relative navigation technique, (2) compared with that of single LOS angles-only navigation, the observability of double LOS measuring relative navigation is improved, (3) the separation angle between two LOS vectors influences the estimation errors and the observability of the navigation system.

Stochastic Stability of the Extended Kalman Filter With Intermittent Observations

In this technical note, we analyze the error behavior of the discrete-time extended Kalman filter for nonlinear systems with intermittent observations. Modelling the arrival of the observations as a random process, we show that, given a certain regularity of the system, the estimation error remains bounded if the noise covariance and the initial estimation error are small enough. We also study the effect of different measurement models on the bounds for the error covariance matrices.

Stochastic stability of the discrete-time constrained extended Kalman filter

In this paper, stability of the projection-based constrained discrete-time extended Kalman filter (EKF) as applied to nonlinear systems in a stochastic framework has been studied. It has been shown that like the unconstrained EKF, the estimation error of the EKF with known constraints on the states remains bounded when the initial error and noise terms are small, and the solution of the Riccati difference equation remains positive definite and bounded. Stability results are verified and performance of the constrained EKF is demonstrated through simulations on a nonlinear engineering example.

Stability of the Extended Kalman Filter When the States are Constrained

In this note, stability of the projection-based constrained discrete time extended Kalman filter (EKF) when applied to deterministic nonlinear systems has been studied. It is proved that, like the unconstrained case, under certain assumptions, the EKF with state equality constraints is an exponential observer, i.e., it keeps the dynamics of its estimation error exponentially stable. Also, it has been shown that a simple modification to the general definition of the EKF with exponential weighting increases the filter's degree of stability and convergence speed with or without state constraints.

Process Fault Monitoring Using Data Fusion Based on Extended Kalman Filter Incorporated with Time-Delayed Measurements

A model-based process fault monitoring approach is proposed in this paper which utilizes a multi-sensor data fusion technique. The fusion algorithm is based on a discrete-time extended Kalman filter (EKF). The presented EKF is modified to incorporate the asynchronous sensor measurements. The resulting approach will be evaluated for a variety of conditions including synchronous/asynchronous measurements, full-state and non full-state measurements and time-varying dynamics for monitoring single, double, triple and quadruple process faults. The simulation studies on a CSTR benchmark problem demonstrate the effectiveness of the proposed fault monitoring approach to deal with different circumstances.

Adaptive extended Kalman filtering for visual motion estimation of 3D objects

An algorithm for the real-time estimation of the position and orientation of a moving object of known geometry is presented in this paper. An estimation algorithm is adopted where a discrete-time extended Kalman filter computes the object pose on the basis of visual measurements of the object features. The scheme takes advantage of the prediction capability of the extended Kalman filter for the pre-selection of the features to be extracted from the image at each sample time. To enhance the robustness of the algorithm with respect to measurement noise and modelling error, an adaptive version of the extended Kalman filter, customized for visual applications, is proposed. Experimental results on a fixed single-camera visual system are presented to test the performance and the feasibility of the proposed approach.

Stability Properties of the Discrete-Time Extended Kalman Filter

In this paper the stability conditions for the discrete-time extended Kalman filter (EKF) are considered. Explicit upper bounds are given for the estimation error in both the noiseless and the general case. The results published so far generally requires that the state belongs to a compact subset of Rn. In this paper it is proved that this can be relaxed to only require the state to belong to a open convex subset of Rn, provided that the Hessian matrix of the output map is bounded in Rn.

Gain-scheduled control of an electrostatic levitator

A simple gain-scheduling approach to the position control of electrostatically levitated materials is presented. An electrostatic levitator is currently being constructed at the German Aerospace Center (DLR). It can be used for containerless processing of metals and nonconducting materials. Time-varying sample charges and the fact that the plant is open-loop unstable make this a difficult and challenging control problem. The nonlinear parameter-dependent system is approximated by two local linear models. Based on these models, two local linear controllers are designed. LMI-based pole region assignment is used to reduce the design procedure to the tuning of three parameters with intuitive meaning. The sample charge is estimated with a discrete-time extended Kalman filter and used as scheduling parameter. Experimental results demonstrate that gain-scheduled control achieves a significantly better performance than fixed-gain, observer-based state feedback control.

Stochastic stability of the discrete-time extended Kalman filter

The authors analyze the error behavior for the discrete-time extended Kalman filter for general nonlinear systems in a stochastic framework. In particular, it is shown that the estimation error remains bounded if the system satisfies the nonlinear observability rank condition and the initial estimation error as well as the disturbing noise terms are small enough. This result is verified by numerical simulations for an example system.

Factorized extended Kalman filter for optical processing

Kalman filtering represents formidable linear algebra computational requirements for each new input measurement vector. An architecture-motivated implementation of a discrete-time extended Kalman filter algorithm is presented. This particular formulation takes advantage of the following features of the optical processor architecture: the ability to perform matrix–vector operations, floating-point capabilities, and specially designed matrix–vector L U decomposition operations. A factorized L D LT algorithm is used to propagate the covariance matrices between sample times. The air-to-air missile guidance problem is used as a case study wherein an extended Kalman filter is required due to the nonlinear nature of the measurement equations.