Nonlinear Kalman Filter Research Articles

Control of DC–DC Converter and DC Motor Dynamics Using Differential Flatness Theory

The article proposes a method for nonlinear control of the dynamical system that is formed by a DC–DC converter and a DC motor, making use of differential flatness theory. First it is proven that the aforementioned system is differentially flat which means that all its state vector elements and its control inputs can be expressed as differential functions of primary state variables which are defined to be the system’s flat outputs. By exploiting the differential flatness properties of the model its transformation to a linearized canonical (Brunovsky) form becomes possible. For the latter description of the system one can design a stabilizing feedback controller. Moreover, estimation of the nonmeasurable state vector elements of the system is achieved by applying a new nonlinear Filtering method which is known as Derivative-free nonlinear Kalman Filter. This filter consists of the Kalman Filter recursion applied on the linearized equivalent model of the system and of an inverse transformation that is based on differential flatness theory and which enables to obtain estimates of the initial nonlinear state-space model. Moreover, to compensate for parametric uncertainties and external perturbations the filter is redesigned as a disturbance observer. By estimating the perturbation inputs that affect the joint model of the DC–DC converter and of the DC motor their compensation becomes possible. The efficiency of the proposed control scheme is further confirmed through simulation experiments.

Sideslip estimation for articulated heavy vehicles at the limits of adhesion

ABSTRACTVarious active safety systems proposed for articulated heavy goods vehicles (HGVs) require an accurate estimate of vehicle sideslip angle. However in contrast to passenger cars, there has been minimal published research on sideslip estimation for articulated HGVs. State-of-the-art observers, which rely on linear vehicle models, perform poorly when manoeuvring near the limits of tyre adhesion. This paper investigates three nonlinear Kalman filters (KFs) for estimating the tractor sideslip angle of a tractor–semitrailer. These are compared to the current state-of-the-art, through computer simulations and vehicle test data. An unscented KF using a 5 degrees-of-freedom single-track vehicle model with linear adaptive tyres is found to substantially outperform the state-of-the-art linear KF across a range of test manoeuvres on different surfaces, both at constant speed and during emergency braking. Robustness of the observer to parameter uncertainty is also demonstrated.

Transient Stability Improvement Through Wide-Area Controlled SVCs

This paper presents a wide-area control approach to improve the transient stability of the power systems while also damping the post-fault inter-area oscillations. The proposed approach employs a nonlinear Kalman filter to estimate the inter-area modes using phasor measurement units (PMUs). The wide-area control system then uses the estimated inter-area dynamics through the developed control algorithms to improve the first swing and damping stability of the system. The performance of the proposed approach is evaluated on the simplified Australian test system with different load models including induction motors and the results show significant improvement in the stability of the system by simply adding the wide-area control signals to the available controllers in the system. The application of the proposed wide-area control system is shown to be feasible on realistic systems by improving the system stability and efficiency.

An efficient estimate and forecast of the implied volatility surface: A nonlinear Kalman filter approach

As suggested by numerous studies, while the implied volatility surface changes over time, its shape tends to pervade. This motivates us to construct a dynamic model for implied volatility surface, which not only captures cross-sectional information of implied volatilities with different strikes and maturities, but also describes how the implied volatility surface evolves over time. In this paper, we use nonlinear parametric function to capture single implied volatility surface, and model the dynamics of implied volatility surface by modeling the dynamics of function coefficients. We introduce unscented Kalman filter to propagate the nonlinear system, which is constructed by the nonlinear parametric function and the dynamics of its coefficients. A dynamic approach is proposed to provide optimal estimation of model parameters and efficient forecast of future implied volatility surface. It shows that our model has a better description of implied volatility surface dynamics than other similar models, and can be used to do volatility surface forecast.

A Three-Dimensional Shape-Based Force and Stiffness-Sensing Platform for Tendon-Driven Catheters.

This paper presents an efficient shape-based three-axial force and stiffness estimator for active catheters commonly implemented in cardiac ablation. The force-sensing capability provides important feedback for catheterization procedures including real-time control and catheter steering in autonomous navigation systems. The proposed platform is based on the introduced accurate and computationally efficient Cosserat rod model for tendon-driven catheters. The proposed nonlinear Kalman filter formulation for contact force estimation along with the developed catheter model provides a real-time force observer robust to nonlinearities and noise covariance uncertainties. Furthermore, the proposed platform enables stiffness estimation in addition to tip contact force sensing in different operational circumstances. The approach incorporates pose measurements which can be achieved using currently developed pose-sensing systems or imaging techniques. The method makes the approach compatible with the range of forces applied in clinical applications. The simulation and experimental results verify the viability of the introduced force and stiffness-sensing technique.

Non-linear feedback control of the p53 protein-mdm2 inhibitor system using the derivative-free non-linear Kalman filter.

It is proven that the model of the p53-mdm2 protein synthesis loop is a differentially flat one and using a diffeomorphism (change of state variables) that is proposed by differential flatness theory it is shown that the protein synthesis model can be transformed into the canonical (Brunovsky) form. This enables the design of a feedback control law that maintains the concentration of the p53 protein at the desirable levels. To estimate the non-measurable elements of the state vector describing the p53-mdm2 system dynamics, the derivative-free non-linear Kalman filter is used. Moreover, to compensate for modelling uncertainties and external disturbances that affect the p53-mdm2 system, the derivative-free non-linear Kalman filter is re-designed as a disturbance observer. The derivative-free non-linear Kalman filter consists of the Kalman filter recursion applied on the linearised equivalent of the protein synthesis model together with an inverse transformation based on differential flatness theory that enables to retrieve estimates for the state variables of the initial non-linear model. The proposed non-linear feedback control and perturbations compensation method for the p53-mdm2 system can result in more efficient chemotherapy schemes where the infusion of medication will be better administered.

Fixed-Wing UAV Attitude Estimation Using Single Antenna GPS Signal Strength Measurements

This article considers a novel approach to using global positioning system (GPS) signal strength readings and estimated velocity vector for estimating the attitude of a small fixed-wing unmanned aerial vehicle (UAV). This approach has the benefit being able to estimate full position, velocity and attitude states of a UAV using only the data from a single GPS receiver and antenna. Two different approaches for utilizing GPS signal strength within measurement updates for UAV attitude in a nonlinear Kalman filter are discussed and assessed using recorded UAV flight data. Comparisons of UAV pitch and roll estimates against measurements from a high-grade mechanical gyroscope are used to show that approximately 5° error with respect to both mean and standard-deviation on both axes is achievable.

Novel Simplex Kalman Filters

In this paper, a new class of nonlinear Kalman filter is proposed to further improve filtering accuracy and efficiency for high-dimensional state estimation, which is named simplex Kalman filter (SKF). In the proposed SKF, the simplex rules of different numerical accuracy are utilized to generate two sets of sigma points that are applied to numerically compute multivariate moment integrals encountered in nonlinear Kalman filter (NKF). The proposed SKFs can achieve improvement of computational efficiency in state estimation. With the increase in the state dimension, the computational complexity of the new SKFs is lower than that of traditional NKF, which can mitigate the curse of dimension issue in high-dimensional systems. Simulations on nonlinear high-dimensional problem and bearings only tracking demonstrate that in comparison with different NKFs, the new SKFs can improve the filtering performance efficiently.

Extending the Kalman filter for structured identification of linear and nonlinear systems

This paper considers a novel approach to system identification which allows accurate models to be created for both linear and nonlinear multi-input/output systems. In addition to conventional system identification applications, the method can also be used as a black-box tool for model order reduction. A nonlinear Kalman filter is extended to include slow-varying parameter states in a canonical model structure. Interestingly, in spite of all model parameters being unknown at the start, the filter is able to evolve parameter estimates to achieve 100% accuracy in noise-free test cases, and is also proven to be robust to noise in the measurements. The canonical structure ensures a well-conditioned model which simultaneously provides valuable dynamic information to the engineer. After extensive testing of a linear example, the model structure is extended to a generalised nonlinear form, which is shown to accurately identify the handling response of a full vehicle model.

Feedback control of the immune response of renal transplant recipients with inequality constraints

This paper describes a model of the immunologic response of latent viruses and a donor kidney in a renal transplant recipient. An optimal control problem with state variable inequality constraints is considered to maintain the balance between over-suppression where latent viruses are reactivated and under-suppression where the transplanted kidney is rejected. A feedback methodology based on the model predictive control (MPC) method is proposed to design (sub)optimal treatment regimes. In addition, the problem of implementing the MPC methodology and nonlinear Kalman filter with inaccurate or incomplete observation data and long measurement periods is addressed. The results of numerical simulations show that a (sub)optimal dynamic immunosuppression therapy method can help strike a balance between the over-suppression and under-suppression of the immune system.

Huber-based high-degree cubature Kalman tracking algorithm

In recent decades, nonlinear Kalman filtering based on Bayesian theory has been intensively studied to solve the problem of state estimation in nonlinear dynamical system. Under the Gaussian assumption, Bayesian filtering can provide a unified recursive solution to the estimation problem that is described as the calculation of Gaussian weighted integrals. However it is typically intractable to directly calculate these integrals. The numerical integration methods are required from a practical perspective. Therefore, nonlinear Kalman filters are generated by different numerical integrations. As a representative of nonlinear Kalman filter, cubature Kalman filter (CKF) utilizes a numerical rule based on the third-degree spherical-radial cubature rule to obtain better numerical stability, which is widely used in many fields, e.g., positioning, attitude estimation, and communication. Target tracking can be generalized as the estimations of the target position, the target velocity and other parameters. Hence, nonlinear Kalman filters can also be used to perform target tracking, effectively. Since the CKF based on the third-degree cubature rule has a limited accuracy of estimation, it is necessary to find a CKF based a cubature rule with higher accuracy in the case of target tracking system with a large uncertainty. High-degree cubature Kalman filter is therefore proposed to implement state estimation due to its higher numerical accuracy, which is preferred to solve the estimation problem existing in target tracking. To improve the filtering accuracy and robustness of high-degree cubature Kalman filter, in this paper we present a new filtering algorithm named Huber-based high-degree cubature Kalman filter (HHCKF) algorithm. After approximating nonlinear measurements by using the statistical linear regression model, the measurement update is implemented by the Huber M estimation. As a mixed estimation technique based on the minimum of l1-norm and l2-norm, the Huber estimator has high robustness and numerical accuracy under the assumption of Gaussian measurement noises. Therefore, the Huber-based high-degree cubature Kalman tracking algorithm is generated by combining the state prediction based on the fifth-degree spherical radial rule. In this paper, the influence of tuning parameter on the tracking performance is discussed by simulations. Simulations in the context of bearings only tracking and reentry vehicle tracking demonstrate that the new HHCKF can improve the tracking performance significantly.

The Nonsequential Fusion Method for Localization from Unscented Kalman Filter by Multistation Array Buoys

Based on special features of array buoy and the research field of location and tracking of underwater target, the research combines the highly adaptive nonlinear filtering algorithm unscented Kalman filter with the nonlinear programming of multistation array buoy positioning system. In accordance with the model of nonsequential target location, the research utilizes Unscented Transformation to update the measuring error and covariance matrix of state error, aiming at estimating the filtering of state variable and acquiring the object’s current state of motion. The research analyzes the positioning performance of algorithm, pursuit path, astringency, and other performance indexes of target-relevant parameter through numerical simulation experiment. From the result, the conclusion that multistation array buoy can complete the task of tracing target track very well can be reached, which provides theoretical foundation for putting the algorithm into engineering practice.

Mobile Localization And Tracking With Los And Nlos Identification In Wireless Sensor Networks

Abstract This paper addresses the problem of mobile sensor localization and tracking in an obstructed environment. To solve this problem, a combination of three approaches is proposed: a nonlinear Kalman Filter to estimate the mobile position, a sub filter used jointly with the nonlinear filter to estimate the bias due to the Non-Line Of Sight (NLOS) effect and a low complexity method for Line Of Sight (LOS) and NLOS identification. Based on hypothesis testing, this method discriminates between the LOS and NLOS situations using a sequence of estimated biases. Simulation results show that the proposed method provides good positioning accuracy

On the use of shape constraints for state estimation in reaction systems

State estimation techniques are used for improving the quality of measured signals and for reconstructing unmeasured quantities. In chemical reaction systems, nonlinear estimators are often used to improve the quality of estimated concentrations. These nonlinear estimators, which include the extended Kalman filter, the receding-horizon nonlinear Kalman filter and the moving-horizon estimator, use a state-space representation in terms of concentrations. An alternative to the representation of chemical reaction systems in terms of concentrations consists in representing these systems in terms of extents. This paper formulates the state estimation problem in terms of extents, which allows imposing additional shape constraints on the sign, monotonicity and concavity/convexity properties of extents. The addition of shape constraints often leads to significantly improved state estimates. A simulated example illustrates the formulation of the state estimation problem in terms of concentrations and extents, and the use of shape constraints.

Real-time nowcasting of nominal GDP with structural breaks

This paper provides early assessments of current U.S. Nominal GDP growth, which has been considered as a potential new monetary policy target. The nowcasts are computed using the exact amount of information that policy makers have available at the time predictions are made. However, real time information arrives at different frequencies and asynchronously, which poses the challenge of mixed frequencies, missing data, and ragged edges. This paper proposes a multivariate state space model that not only takes into account asynchronous information inflow it also allows for potential parameter instability (DYMIBREAK). We use small scale confirmatory factor analysis in which the candidate variables are selected based on their ability to forecast nominal GDP. The model is fully estimated in one step using a nonlinear Kalman filter, which is applied to obtain simultaneously both optimal inferences on the dynamic factor and parameters. Differently from principal component analysis, the proposed factor model captures the comovement rather than the variance underlying the variables. We compare the predictive ability of the model with other univariate and multivariate specifications. The results indicate that the proposed model containing information on real economic activity, inflation, interest rates, and Divisia monetary aggregates produces the most accurate real time nowcasts of nominal GDP growth.

Nonlinear Kalman filter based on duality relations between continuous and discrete-state stochastic processes.

An alternative application of duality relations of stochastic processes is demonstrated. Although conventional usages of the duality relations need analytical solutions for the dual processes, here I employ numerical solutions of the dual processes and investigate the usefulness. As a demonstration, estimation problems of hidden variables in stochastic differential equations are discussed. Employing algebraic probability theory, a little complicated birth-death process is derived from the stochastic differential equations, and an estimation method based on the ensemble Kalman filter is proposed. As a result, the possibility for making faster computational algorithms based on the duality concepts is shown.

Control and disturbances compensation in underactuated robotic systems using the derivative-free nonlinear Kalman filter

SUMMARYThe Derivative-free nonlinear Kalman Filter is used for developing a robust controller which can be applied to underactuated MIMO robotic systems. The control problem for underactuated robots is non-trivial and becomes further complicated if the robot is subjected to model uncertainties and external disturbances. Using differential flatness theory it is shown that the model of a closed-chain 2-DOF robotic manipulator can be transformed to linear canonical form. For the linearized equivalent of the robotic system it is shown that a state feedback controller can be designed. Since certain elements of the state vector of the linearized system cannot be measured directly, it is proposed to estimate them with the use of a novel filtering method, the so-called Derivative-free nonlinear Kalman Filter. Moreover, by redesigning the Kalman Filter as a disturbance observer, it is shown that one can estimate simultaneously external disturbance terms that affect the robotic model or disturbance terms which are associated with parametric uncertainty. The efficiency of the proposed Kalman Filter-based control scheme is tested in the case of a 2-DOF planar robotic manipulator that has the structure of a closed-chain mechanism.

Wide‐area damping control for inter‐area oscillations using inverse filtering technique

In this study, a non-linear excitation controller using inverse filtering is proposed to damp inter-area oscillations. The proposed controller is based on determining generator flux value for the next sampling time which is obtained by maximising reduction rate of kinetic energy of the system after the fault. The desired flux for the next time interval is obtained using wide-area measurements and the equivalent area rotor angles and velocities are predicted using a non-linear Kalman filter. A supplementary control input for the excitation system, using inverse filtering approach, to track the desired flux is implemented. The inverse filtering approach ensures that the non-linearity introduced because of saturation is well compensated. The efficacy of the proposed controller with and without communication time delay is evaluated on different IEEE benchmark systems including Kundur's two area, Western System Coordinating Council three-area and 16-machine, 68-bus test systems.

Pilotless flight vehicle motion control in the conditions of uncertainty

The article is devoted to the problem of pilotless airplane motion parameters adaptive regulator synthesis on the basis of the identification approach. For the solution of identification task the application possibility of various observers algorithms was considered.One of them is the algorithm of a nonlinear Kalman filter. It allows to estimate simultaneously state vector and parameters of state matrix. Application of this algorithm demands presence of a separate assortment of metres for state vector derivative. Researches have shown, that for various uncertainty level of motion mathematical model of pilotless airplane it ensures too low accuracy of control, even in comparison with the proportional regulator with the constant factors, received for nominal model. The algorithm of the linear optimum observer has appeared as more effective instrument of identification in the problem of flight adaptive control. It allows to increase accuracy of control in comparison with non adaptive regulators. Thus the best outcomes turn out at use of the separate observer for model parameters and the separate observer of motion parameters vector, and also in the presence of the information on air velocity of flight. In algorithm of an adaptive control sequentially to observers the proportional feedback on state vector with variable factors was used. Factors of functional for all observers corresponded to the factors received for not adaptive linearly- quadratic optimum regulator.

A Practical Robust Long Term Yield Curve Model

This paper describes the development and initial testing of the Black-corrected version of a workhorse 3-factor Gaussian yield curve (term structure) model, the economic factor model (Dempster et al., 2010) which we have used for many years with Monte Carlo scenario simulation for structured derivative valuation, investment modelling and asset liability management with various time steps and currencies. In common with most alternative approaches in the literature to generating non-negative yieldsusing Black's idea, we propose a simple approximation to the Black mathematical model using the nonlinear unscented Kalman filter (UKF). However, model calibration, unlike that of the current computationally intensive alternatives, requires not significantly more computing time than is needed for the linear Kalman filter with the underlying affine shadow rate model. Initial empirical testing of the new Black EFM model both in- and out-of-sampleshows acceptable accuracy, improved over that of the affine EFM model, which can be further improved by UKF tuning in future research. Migration of the system to the cloud can reduce calibration times for both models from a few hours to a few minutes by exploiting massive parallelization of the computationally intensive step.