Showing papers on "Invariant extended Kalman filter published in 2018"
TL;DR: Experimental results illustrate that the proposed adaptive extended Kalman filter has better localization accuracy than existing state-of-the-art algorithms.
Abstract: To solve the problem of unknown noise covariance matrices inherent in the cooperative localization of autonomous underwater vehicles, a new adaptive extended Kalman filter is proposed. The predicted error covariance matrix and measurement noise covariance matrix are adaptively estimated based on an online expectation-maximization approach. Experimental results illustrate that, under the circumstances that are detailed in the paper, the proposed algorithm has better localization accuracy than existing state-of-the-art algorithms.
184 citations
TL;DR: A model-free method based on an adaptive Kalman filter is developed to accomplish path tracking for a continuum robot using only pressures and tip position, which shows good robustness against the system uncertainty and external disturbance, and lowers the number of sensors.
Abstract: Continuum robots with structural compliance have promising potential to operate in unstructured environments. However, this structural compliance brings challenges to the controller design due to the existence of considerable uncertainties in the robot and its kinematic model. Typically, a large number of sensors are required to provide the controller the state variables of the robot, including the length of each actuator and position of the robot tip. In this paper, a model-free method based on an adaptive Kalman filter is developed to accomplish path tracking for a continuum robot using only pressures and tip position. As the Kalman filter operates only with a two-step algebraic calculation in every control interval, the low computational load and real-time control capability are guaranteed. By adding an optimal vector to the control law, buckling of the robot can also be avoided. Through simulation analysis and experimental validation, this control method shows good robustness against the system uncertainty and external disturbance, and lowers the number of sensors.
117 citations
TL;DR: A new kinematic calibration method based on the extended Kalman filter (EKF) and particle filter (PF) algorithm that can significantly improves the positioning accuracy of the robot.
Abstract: Precise positioning of a robot plays an very important role in advanced industrial applications, and this paper presents a new kinematic calibration method based on the extended Kalman filter (EKF) and particle filter (PF) algorithm that can significantly improves the positioning accuracy of the robot. Kinematic and its error models of a robot are established, and its kinematic parameters are identified by using the EKF algorithm first. But the EKF algorithm has a kind of linear truncation error and it is useful for the Gauss noise system in general, so its identified accuracy will be affected for the highly nonlinear robot kinematic system with a non-Gauss noise system. The PF algorithm can solve this with non-Gauss noise and a high nonlinear problem well, but its calibration accuracy and efficiency are affected by the prior distribution of the initial values. Therefore, this paper proposes to use the calibration value of the EKF algorithm as the prior value of the PF algorithm, and then, the PF algorithm is used further to calibrate the kinematic parameters of the robot. Enough experiments have been carried out, and the experimental results validated the viability of the proposed method with the robot positioning accuracy improved significantly.
103 citations
TL;DR: In this paper, an extended Kalman filter (HEKF) based on the robust control theory is proposed to track system dynamic state variables, and an approach to tune the parameter of HEKF is presented as well.
Abstract: When implementing Kalman filters to track system dynamic state variables, the dynamical model is assumed to be accurate. However, this assumption may not hold true as power system dynamical model is subjected to various uncertainties, such as varying generator transient reactance in different operation conditions, uncertain inputs, or noise statistics. As a result, the performance of Kalman-type filters can be degraded significantly. To bound the influence of these uncertainties, this letter proposes an $H_\infty$ extended Kalman filter (HEKF) based on the robust control theory. An approach to tune the parameter of HEKF is presented as well. Numerical results on the IEEE 39-bus system demonstrate the effectiveness of the HEKF.
80 citations
TL;DR: A variance-constrained state estimator is developed by using the structure of the extended Kalman filter, where the gain matrix is determined by optimizing an upper bound matrix for the estimation error covariance despite the linearization errors and coupling terms.
Abstract: This paper studies the state estimation problem for nonlinearly coupled complex networks. A variance-constrained state estimator is developed by using the structure of the extended Kalman filter, where the gain matrix is determined by optimizing an upper bound matrix for the estimation error covariance despite the linearization errors and coupling terms. Compared with the existing estimators for linearly coupled complex networks, a distinct feature of the proposed estimator is that the gain matrix can be derived separately for each node by solving two Riccati-like difference equations. By using the stochastic analysis techniques, sufficient conditions are established which guarantees the state estimation error is bounded in mean square. A numerical example is provided to show the effectiveness and applicability of the proposed estimator.
71 citations
TL;DR: The proposed CI-MEKF method is shown to be significantly robust against different uncertainties, such as large body acceleration, magnetic distortion, magnetometer and accelerometer sensors data, and errors, in the initial condition of the attitude.
Abstract: This paper presents an attitude estimation method from uncertain observations of inertial sensors, which is highly robust against different uncertainties. The proposed method of covariance inflated multiplicative extended Kalman filter (CI-MEKF) takes the advantage of non-singularity of covariance in MEKF as well as a novel covariance inflation (CI) approach to fuse inconsistent information. The proposed CI approach compensates the undesired effect of magnetic distortion and body acceleration (as inherent biases of magnetometer and accelerometer sensors data, respectively) on the estimated attitude. Moreover, the CI-MEKF can accurately estimate the gyro bias. A number of simulation scenarios are designed to compare the performance of the proposed method with the state of the art in attitude estimation. The results show the proposed method outperforms the state of the art in terms of estimation accuracy and robustness. Moreover, the proposed CI-MEKF method is shown to be significantly robust against different uncertainties, such as large body acceleration, magnetic distortion, and errors, in the initial condition of the attitude.
66 citations
TL;DR: By utilizing the mathematical induction technique, a new bound function which is dependent on system parameters is proposed and based on such a bound function, the dynamic behaviors, monotonicities, and boundedness problems of error covariance are deeply explored.
Abstract: In this correspondence paper, we provide a new look at the boundedness problems of error covariance of Kalman filtering. First, by utilizing the mathematical induction technique, a new bound function which is dependent on system parameters is proposed. In this manner, the boundedness problems of the error covariance can be converted to the study of the corresponding uniform bounds of the bound function. Second, based on such a bound function, the dynamic behaviors, monotonicities, and boundedness problems of error covariance are deeply explored. Consequently, a few quantitative results under minimal conditions about the uniform bounds on error covariance are obtained. Finally, examples are given to verify the correctness and effectiveness of our theoretical analyses.
61 citations
TL;DR: The DWKFF algorithm with finite length buffers has been developed which has stronger fault-tolerance ability and an optimal local Kalman filter estimator with a buffer of finite length is derived for each subsystem.
Abstract: This paper is concerned with the problem of distributed weighted Kalman filter fusion (DWKFF) for a class of multisensor unreliable networked systems (MUNSs) with correlated noises. The process noise and the measurement noises are assumed to be one-step, two-step cross-correlated, and one-step autocorrelated, and the measurement noises of each sensor are one-step cross-correlated. The stochastic uncertainties in the state and measurements are described by correlated multiplicative noises. The MUNSs suffer measurement delay or loss due to their unreliability. Buffers of finite length are proposed to deal with measurement delay or loss, and an optimal local Kalman filter estimator with a buffer of finite length is derived for each subsystem. Based on the new optimal local Kalman filter estimator, the DWKFF algorithm with finite length buffers has been developed which has stronger fault-tolerance ability. Simulation results illustrate the effectiveness of the proposed approaches.
56 citations
TL;DR: In this article, a 6-DoF dynamic model of an AUV is presented and then some of its parameters including viscous damping, the body lift, and control input coefficients that have the highest effects on the modeling error are identified by augmented state model method.
Abstract: Having an accurate mathematical model is essential in design, control, and navigation process of an autonomous underwater vehicle (AUV) Due to the modeling simplifications, the available mathematical models suffer from the uncertainty of their parameters and they usually need an identification phase for improving the modeling accuracy In case of AUVs, the hydrodynamic coefficients of the model play an important role and they should be identified using the available experimental data In this paper, a 6-DoF dynamic model of an AUV is presented and then some of its parameters including viscous damping, the body lift, and control input coefficients that have the highest effects on the modeling error are identified by augmented state model method The extended Kalman filter (EKF), cubature Kalman filter (CKF), and transformed unscented Kalman filter (TUKF) are used as the estimation filters To verify and compare the three estimation filters with consideration of the predetermined hydrodynamic coefficients and spiral maneuver AUV results, these three methods are evaluated The results indicate that the TUKF identifies the best hydrodynamic model due to solving both the CKF nonlocal sampling problem and the EKF linearization problem
49 citations
01 Jan 2018
TL;DR: This letter derives recursive filter equations that exhibit similar computational complexity when compared to their Kalman filter counterpart—the extended information filter and proposes a filter that employs a purely residual-based modeling of the available information and thus achieves higher modeling flexibility.
Abstract: This letter deals with recursive filtering for dynamic systems where an explicit process model is not easily devisable. Most Bayesian filters assume the availability of such an explicit process model, and thus may require additional assumptions or fail to properly leverage all available information. In contrast, we propose a filter that employs a purely residual-based modeling of the available information and thus achieves higher modeling flexibility. While this letter is related to the descriptor Kalman filter, it also represents a step toward batch optimization and allows the integration of further techniques, such as robust weighting for outlier rejection. We derive recursive filter equations that exhibit similar computational complexity when compared to their Kalman filter counterpart—the extended information filter. The applicability of the proposed approach is experimentally confirmed on two different real mobile robotic state estimation problems.
47 citations
TL;DR: An adaptive extended Kalman filter based on the maximum likelihood is proposed to estimate the instantaneous amplitudes of the travelling waves and the effectiveness of exacting mutation feature using the proposed method has been demonstrated by a simulated instantaneous pulse.
Abstract: The fault location in transmission systems remains a challenging problem, primarily due to the fault location near the substation ends or the weak fault signals. In this study, an adaptive extended Kalman filter (EKF) based on the maximum likelihood (ML) is proposed to estimate the instantaneous amplitudes of the travelling waves. In this method, the EKF algorithm is used to estimate the optimal states (the clean travelling waves) with additive white noise while ML is used to adaptively optimise the error covariance matrices and the initial conditions of the EKF algorithm. Using the proposed method, the singularity points of travelling waves can be detected, and the exact arrival time of the initial wave head at the substations M and N can be easily yielded. Thus the fault distance can be calculated precisely. The effectiveness of exacting mutation feature using the proposed method has been demonstrated by a simulated instantaneous pulse. Also, the proposed method has been tested with different types of faults, such as different fault locations, different fault resistances and different fault inception angles using ATP simulation. The accuracy of fault location using the proposed method has been compared with conventional wavelet transformation scheme.
TL;DR: It is proved that the joint Kalman filter over states and parameters is a natural gradient on top of real-time recurrent learning (RTRL), a classical algorithm to train recurrent models.
Abstract: We cast Amari’s natural gradient in statistical learning as a specific case of Kalman filtering. Namely, applying an extended Kalman filter to estimate a fixed unknown parameter of a probabilistic model from a series of observations, is rigorously equivalent to estimating this parameter via an online stochastic natural gradient descent on the log-likelihood of the observations. In the i.i.d. case, this relation is a consequence of the “information filter” phrasing of the extended Kalman filter. In the recurrent (state space, non-i.i.d.) case, we prove that the joint Kalman filter over states and parameters is a natural gradient on top of real-time recurrent learning (RTRL), a classical algorithm to train recurrent models. This exact algebraic correspondence provides relevant interpretations for natural gradient hyperparameters such as learning rates or initialization and regularization of the Fisher information matrix.
TL;DR: An extended Kalman filter-based method with equality constraints to conduct multi-area DSE and a corrective strategy is proposed to ensure the consistency of the boundary buses in the multiareas.
Abstract: To achieve higher accuracy of estimated dynamic states, phasor measurement unit (PMU) measurements of buses in a network can be used for dynamic state estimation (DSE). However, it is difficult to coordinate the states of boundary buses in different areas when performing multiarea DSE. By using PMU measurements of buses in the network, this paper proposes an extended Kalman filter-based method with equality constraints to conduct multi-area DSE. First, a corrective strategy is proposed to estimate a corrective internal voltage (CIV) and a corrective rotor angle (CRA) of each generator with all PMUs’ measurements. The proposed corrective strategy can also ensure the consistency of the boundary buses in the multiareas. Then, the CIV and the CRA are used to establish equality constraints for updating the dynamic states with the PMU measurements. An IEEE 30-bus system and an IEEE 118-bus system are used to validate the proposed method, with the results showing the feasibility and accuracy of the proposed method.
TL;DR: A novel hybrid estimator consisting of an extended Kalman filter (EKF) and an active power-based model reference adaptive system (AP-MRAS) in order to solve simultaneous estimation problems of the variations in stator resistance and rotor resistance for speed-sensorless induction motor control is presented.
Abstract: This paper presents a novel hybrid estimator consisting of an extended Kalman filter (EKF) and an active power-based model reference adaptive system (AP-MRAS) in order to solve simultaneous estimat...
TL;DR: A novel robust extended fractional Kalman filter (REFKF) is developed for states estimation of nonlinear fractional system, by which the states can be estimated accurately even with missing measurements.
Abstract: Accurate and effective state estimation is essential for nonlinear fractional system, since it can provide some vital operation information about the system. However, inevitably missing measurements and additive uncertainty in the gain will affect the performance of estimation result. Thus, in this paper, in order to deal with these problems, a novel robust extended fractional Kalman filter (REFKF) is developed for states estimation of nonlinear fractional system, by which the states can be estimated accurately even with missing measurements. Finally, simulation results are provided to demonstrate that the proposed method can achieve much better estimation performance than the conventional extended fractional Kalman filter (EFKF).
TL;DR: Simulation results show that the presented filter simultaneously provides a superior tracking performance and the correct classification of multiple extended targets, compared to the gamma Gaussian inverse Wishart PHD (GGIW-PHD) filter.
TL;DR: The estimated states and internal parameters showed that the IEKF method was more stable and convergent than the EKF-based method, although the estimated locations, velocities, and altitudes of the two methods were comparable.
Abstract: This research used an invariant extended Kalman filter (IEKF) for the navigation of an unmanned aerial vehicle (UAV), and compared the properties and performance of this IEKF with those of an open-source navigation method based on an extended Kalman filter (EKF). The IEKF is a fairly new variant of the EKF, and its properties have been verified theoretically and through simulations and experiments. This study investigated its performance using a practical implementation and examined its distinctive features compared to the previous EKF-based approach. The test used two different types of UAVs: rotary wing and fixed wing. The method uses sensor measurements of the location and velocity from a GPS receiver; the acceleration, angular rate, and magnetic field from a microelectromechanical system-attitude heading reference system (MEMS-AHRS); and the altitude from a barometric sensor. Through flight tests, the estimated state variables and internal parameters such as the Kalman gain, state error covariance, and measurement innovation for the IEKF method and EKF-based method were compared. The estimated states and internal parameters showed that the IEKF method was more stable and convergent than the EKF-based method, although the estimated locations, velocities, and altitudes of the two methods were comparable.
TL;DR: In this paper, the authors consider identification of all significant vehicle handling dynamics of a test vehicle, including identification of a combined-slip tyre model, using only those sensors currently available on most vehicle controller area network buses.
Abstract: This paper considers identification of all significant vehicle handling dynamics of a test vehicle, including identification of a combined-slip tyre model, using only those sensors currently available on most vehicle controller area network buses. Using an appropriately simple but efficient model structure, all of the independent parameters are found from test vehicle data, with the resulting model accuracy demonstrated on independent validation data. The paper extends previous work on augmented Kalman Filter state estimators to concentrate wholly on parameter identification. It also serves as a review of three alternative filtering methods; identifying forms of the unscented Kalman filter, extended Kalman filter and particle filter are proposed and compared for effectiveness, complexity and computational efficiency. All three filters are suited to applications of system identification and the Kalman Filters can also operate in real-time in on-line model predictive controllers or estimators.
TL;DR: It is proved that the QKF yields a smaller MSE than the traditional extended Kalman filter (EKF) merely based on analog measurements, and the r-Rao lower bound (PCRLB) is introduced as the performance measure.
Abstract: Moving target tracking in directional sensor networks has recently attracted attention by right of special directional sensing features. Unlike omnidirectional sensors, the directional sensor senses the target only in the direction of its orientation. It can provide quantized direction that indicates the presence or absence of the target in the sensing field, rather than just the analog measurement of sensing signal with respect to the detected target. A quantized Kalman filter (QKF) based on both quantized directions and analog ranging measurements is derived in the minimum mean-square error (MMSE) sense. Its performances of mean square estimation error (MSE) and complexity are also analyzed. Then, a reduced-complexity QKF of high-accuracy is pursued to facilitate its implementation. It is proved that the QKF yields a smaller MSE than the traditional extended Kalman filter (EKF) merely based on analog measurements. The posterior Cram $\acute{e}$ r-Rao lower bound (PCRLB) is introduced as the performance measure. The performance advantages of the proposed QKF are demonstrated using Monte Carlo simulations in a target tracking application using ultrasonic ranging sensors.
TL;DR: In this article, a finite set model predictive control (FS-MPC) system for active front-end (AFE) converters in combination with an extended Kalman filter (EKF) for on-line parameter estimation is proposed.
Abstract: This paper proposes a finite set model predictive control (FS-MPC) system for active front-end (AFE) converters in combination with an extended Kalman filter (EKF) for on-line parameter estimation to overcome the issues of parameter uncertainty and measurement noise. The FS-MPC performance of such converters is largely affected by variations in the model impedance (filter impedance and grid impedance), especially for systems with low short circuit ratios. Therefore, an EKF is used to estimate these model parameters on-line. Moreover, the EKF is used to filter out measurement noise in the feedback variables. For implementation of the FS-MPC, the discrete-time models of the AFE converter and the filter are derived using two discretization methods (forward Euler method and Taylor series expansion). The observability matrix of the linearized model is computed, and the observability is checked for each time instant to verify that the EKF is working properly. Moreover, the delay time due to the digital calculation is compensated. The performance of the proposed method is illustrated via simulation results.
TL;DR: In this paper, a dynamic mode decomposition (DMD) method based on a Kalman filter is proposed, which can estimate eigenmodes more precisely compared with standard DMD or total least-squares DMD (tlsDMD).
Abstract: A novel dynamic mode decomposition (DMD) method based on a Kalman filter is proposed. This paper explains the fast algorithm of the proposed Kalman filter DMD (KFDMD) in combination with truncated proper orthogonal decomposition for many-degree-of-freedom problems. Numerical experiments reveal that KFDMD can estimate eigenmodes more precisely compared with standard DMD or total least-squares DMD (tlsDMD) methods for the severe noise condition if the nature of the observation noise is known, though tlsDMD works better than KFDMD in the low and medium noise level. Moreover, KFDMD can track the eigenmodes precisely even when the system matrix varies with time similar to online DMD, and this extension is naturally conducted owing to the characteristics of the Kalman filter. In summary, the KFDMD is a promising tool with strong antinoise characteristics for analyzing sequential datasets.
TL;DR: In this article, a generalized total Kalman filter (GTKF) algorithm is proposed to handle all of the random errors in the respective equations of the nonlinear dynamic errors-in-variables (DEIV) model.
Abstract: In this paper, a nonlinear dynamic errors-in-variables (DEIV) model which considers all of the random errors in both system equations and observation equations is presented. The nonlinear DEIV model is more general in the structure, which is an extension of the existing DEIV model. A generalized total Kalman filter (GTKF) algorithm that is capable of handling all of random errors in the respective equations of the nonlinear DEIV model is proposed based on the Gauss–Newton method. In addition, an approximate precision estimator of the posteriori state vector is derived. A two dimensional simulation experiment of indoor mobile robot positioning shows that the GTKF algorithm is statistically superior to the extended Kalman filter algorithm and the iterative Kalman filter (IKF) algorithm in terms of state estimation. Under the experimental conditions, the improvement rates of state variables of positions x, y and azimuth ψ of the GTKF algorithm are about 14, 29, and 66%, respectively, compared with the IKF algorithm.
TL;DR: The simulation results indicate that the proposed filtering algorithm has better navigation precision, can achieve optimal estimation of system state, and can be more flexible at the cost of increased computational burden.
Abstract: This paper explores multiple model adaptive estimation ( MMAE ) method, and with it, proposes a novel filtering algorithm. The proposed algorithm is an improved Kalman filter — multiple model adaptive estimation unscented Kalman filter ( MMAE-UKF ) rather than conventional Kalman filter methods, like the extended Kalman filter ( EKF ) and the unscented Kalman filter ( UKF ). UKF is used as a subfilter to obtain the system state estimate in the MMAE method. Single model filter has poor adaptability with uncertain or unknown system parameters, which the improved filtering method can overcome. Meanwhile, this algorithm is used for integrated navigation system of strapdown inertial navigation system ( SINS ) and celestial navigation system ( CNS ) by a ballistic missile’s motion. The simulation results indicate that the proposed filtering algorithm has better navigation precision, can achieve optimal estimation of system state, and can be more flexible at the cost of increased computational burden.
TL;DR: Through rigorous analytical processes and numerical simulations, it is demonstrated that the new filter provides consistent estimates and the estimation error of the modified UKF is smaller than that of the standard UKF.
Abstract: This work, based on the standard unscented Kalman filter (UKF), proposes a modified UKF for highly non-linear stochastic systems, assuming that the associated probability distributions are normal. In the standard UKF with 2n + 1 sample points, the estimated mean and covariance match the true mean and covariance up to the third order, besides, there exists a scaling parameter that plays a crucial role in minimising the fourth-order errors. The proposed method consists of a computationally efficient formulation of the unscented transform that incorporates N − 1 , N ≥ 2 , constant parameters to scale 2 n ( N − 1 ) + 1 sample points such that the 2 N th order errors are minimised. The scaling parameters are obtained by solving a set of algebraic equations. Through rigorous analytical processes and numerical simulations, it is demonstrated that the new filter provides consistent estimates and the estimation error of the modified UKF is smaller than that of the standard UKF. With the help of a well-studied case, univariate non-stationary growth model, the authors evaluate the estimation performance of the new technique using 4n + 1 sample points over 100 independent runs.
TL;DR: In this paper, an inverse optimal control approach based on extended Kalman filter (EKF) algorithm was proposed to solve the optimal control problem of discrete-time affine nonlinear systems.
Abstract: Summary
In this study, we present an inverse optimal control approach based on extended Kalman filter (EKF) algorithm to solve the optimal control problem of discrete-time affine nonlinear systems. The main aim of inverse optimal control is to circumvent the tedious task of solving the Hamilton-Jacobi-Bellman equation that results from the classical solution of a nonlinear optimal control problem. Here, the inverse optimal controller is based on defining an appropriate quadratic control Lyapunov function (CLF) where the parameters of this candidate CLF were estimated by adopting the EKF equations. The root mean square error of the system states is used as the observed error in the case of classical EKF algorithm application, whereas, here, the EKF tries to eliminate the same root mean square error defined over the parameters by generating a CLF matrix with appropriate elements. The performance and the applicability of the proposed scheme is illustrated through both simulations performed on a nonlinear system model and a real-time laboratory experiment. Simulation study demonstrate the effectiveness of the proposed method in comparison with 2 other inverse control approaches. Finally, the proposed controller is implemented on a professional control board to stabilize a DC-DC boost converter and minimize a meaningful cost function. The experimental results show the applicability and effectiveness of the proposed EKF-based inverse optimal control even in real-time control systems with a very short time constant.
TL;DR: In this paper, a least square prediction was proposed for the integrated total Kalman filter (TKF) algorithm for integrated direct geo-referencing with a dynamic errors-in-variables model.
Abstract: We noticed that if INS data is used as system equations of a Kalman filter algorithm for integrated direct geo-referencing, one encounters with a dynamic errors-in-variables (DEIV) model. Although DEIV model has been already considered for observation equations of the Kalman filter algorithm and a solution namely total Kalman filter (TKF) has been given to it, this model has not been considered for system equations (dynamic model) of the Kalman filter algorithm. Thus, in this contribution, for the first time we consider DEIV model for both observation equations and system equations of the Kalman filter algorithm and propose a least square prediction namely integrated total Kalman filter in contrast to the TKF solution of the previous approach. The variance matrix of the unknown parameters are obtained. Moreover, the residuals for all variables are predicted. In a numerical example, integrated direct geo-referencing problem is solved for a GPS–INS system.
TL;DR: In this article, a partial update Kalman filter (PUKF) is proposed for real-time parameter estimation of a dc-dc switch mode power converter, which is based on a novel combination between the classical KF and an M-Max partial adaptive filtering technique.
Abstract: In this paper, a partial update Kalman Filter (PUKF) is presented for the real-time parameter estimation of a dc–dc switch mode power converter. The proposed estimation algorithm is based on a novel combination between the classical Kalman filter (KF) and an M-Max partial adaptive filtering technique. The proposed PUKF offers a significant reduction in computational effort compared to the conventional implementation of the KF, with 50% less arithmetic operations. Furthermore, the PUKF retains comparable overall performance to the classical KF. To demonstrate an efficient and cost effective explicit self-tuning controller, the proposed estimation algorithm (PUKF) is embedded with a Banyasz/Keviczky proportional, integral, derivative (PID) controller to generate a new computationally light self-tuning controller. Experimental and simulation results clearly show the superior dynamic performance of the explicit self-tuning control system compared to a conventional pole placement design based on a precalculated average model.