State estimation of nonlinear systems using novel adaptive unscented Kalman filter

The needle puncture technology is one of the simplest minimally invasive medical procedures. Due to the asymmetry of the needle tip, the lateral force exerted by the tissue causes the tip to deflect and reaches the target position. It is important to maintain the needle tip in a desired plane in 2D control. In the process of puncture, the position is measured and the posture of the needle tip needs to be estimated in real time. Three estimation algorithms for estimating the states of the needle tip are employed in this paper. The first algorithm is adaptive Kalman filter (AKF), which is applied to the statistical properties of the noise is not completely known. The second is unscented Kalman filter (UKF). The last one is the combination of AKF and UKF, called adaptive unscented Kalman filter (AUKF) which combines the advantages of both. It should be noted that AKF is based on the feedback linearization model, but UKF and AUKF are directly based on the nonlinear model. On the base of analysis of three estimation algorithms, we study the control method. In this work, we estimate the states via the three methods and analyze the results. The simulation results of the estimation algorithms and the control method illustrate the differences between the three algorithms.

In this paper, an adaptive unscented Kalman filter (AUKF) is developed for state estimation on a tractor-trailer system. For nonlinear systems, the unscented Kalman filter (UKF) is a well-known approach for observer design. Some research has shown the UKF can be more accurate than extended Kalman filter (EKF) with similar computation burden. However, the performance of traditional Kalman filter may deteriorate when process noise changes or sudden disturbance occurs due to the fixed process noise covariance (Q matrix) in the filter. An adaptive gain is calculated to compensate for the mismatch between the actual residual covariance and the deduced value from the filter, ensuring that the sequence of residual is uncorrelated. An estimated Q matrix is referred in the adaptive gain calculation at each sample. Simulation is done in various situations. The positions of trailer are used as measurements. Compared with the standard UKF (SUKF) and another adaptive UKF, the proposed algorithm has better result.

This article introduces an augmented adaptive unscented Kalman filter (KF). The proposed novel technique is suitable to simultaneously estimate both the diagonal process noise covariance matrix and the unknown inputs, thus combining previously reported KF estimators for unknown inputs (dual or joint KF) and for covariance matrices (adaptive KF). A selective scaling method is also introduced to improve the convergence property of the suggested KF. The development of the novel KF is also motivated by a specific estimation problem related to crane systems. Cranes represent a special class of weight handling equipment as they are underactuated and described by nonlinear dynamics such that the load present oscillatory behavior. In addition to the increasing need for their automation in various industrial fields, these features also make them a benchmark system in control engineering with numerous control laws reported in the literature for sway elimination and trajectory tracking. A common issue to realize most of the advanced control laws on real, eventually industrial size cranes is the necessity to know the sway angle and frictions on the configuration variables. It is shown in simulation and also with real experiments on a reduced size overhead crane system that the suggested KF is suitable to estimate both the sway angles and the frictions.

As the requirements on powertrain efficiency of electric vehicles (EVs) are increasing, integrated motor-transmission (IMT) powertrain systems for EVs are becoming a promising solution. For the integration of IMT powertrain systems, the system state information and the actuator status are usually required for the closed-loop controller design or the on-board fault diagnosis. Embracing the demands, an observer for simultaneous estimation of input and system state of an IMT powertrain system is studied in this paper. It is well-known that controller area network (CAN) has been dominant in the vehicle network, which is used to communicate among controllers, sensors, and actuators. However, the CAN bus always induces time-varying delays when there are a number of communication nodes on the bus. The CAN-bus induced delay would result in vibrations in the vehicle powertrain or even deterioration of the entire closed-loop system. To deal with the CAN-bus induced delay in the estimation work for IMT powertrain systems, the potential random delays are considered in a three-state nonlinear model which represents the behavior of an IMT system. To estimate the input and state simultaneously, an adaptive unscented Kalman filter (AUKF) is adopted. As we know, the adopted AUKF has the benefits of dealing with system nonlinearities and calculating the noise covariance matrix automatically. Simulations and comparisons are carried out. We can see from the results that the proposed observer estimates the input and system state well. Moreover, the resulting estimation error is smaller comparing with the estimation error of the observer based on extended Kalman filter algorithm.

Decentralized data-driven estimation of generator rotor speed and inertia constant based on adaptive unscented Kalman filter

For autonomous mobile robots moving in unknown environment, accurate estimation of available power along with the robot power demand for each mission is paramount to successful completion of that mission. Regarding the power consumption, the control unit deals with two tasks simultaneously: 1) it has to monitor the power supply (batteries) state of charge (SoC) constantly. This leads to estimation of robot current available power. Besides, batteries are sensitive to deep discharge or overcharge. The battery SoC is an essential factor in power management of a mobile robot. Accurate estimation of the battery SoC can improve power management, optimize the performance, extend the lifetime, and prevent permanent damage to the batteries. 2) The dynamic characteristics of the terrain the robot traverse requires rapid online modifications in its behaviour. The power required for driving a wheel is an increasing function of its slip ratio. For a wheeled robot moving for driving a wheel is an increasing function of its slip ratio. For a wheeled robot moving on different terrains, slip of the wheels should be checked and compensated for to keep the robot moving with less power consumption. To reduce the power consumption, the target robot moving with less power consumption. To reduce the power consumption, the target of the control system is to keep the slip ratio of the driving wheels around the desired value of the control system is to keep the slip ratio of the driving wheels around the desired value. To fulfill the above mentioned tasks, in this thesis, to increase model validity of lithium-ion battery in various charge/discharge scenarios during the mobile robot operation, the battery capacity fade and internal resistance change are modeled by adding them as state variables to a state space model. Using the output measured data, adaptive unscented Kalman Filter (AUKF) is employed for online model parameters identification of the equivalent circuit model at each sampling time. Subsequently, based on the updated model parameters, SoC estimation is conducted using AUKF. The effectiveness of the proposed method is verified through experiments under different power duties in the lab environment through experiments under different power duties in the lab environment. Better results are obtained both in battery model parameters estimation and the battery SoC estimation in comparison with other Kalman filter extensions. Furthermore, for effective control of the slip ratio, a model-based approach to estimating the longitudinal velocity of the mobile robot is presented. The AUKF is developed to estimate the vehicle longitudinal velocity and the wheel angular velocity using measurements from wheel encoders. Based on the estimated slip ratio, a sliding mode controller is designed for slip control of the uncertain nonlinear dynamical system in the presence of model uncertainties, parameter variations, and disturbances. Experiments are carried out in real time on a four-wheel mobile robot to verify the effectiveness of the estimation algorithm and the controller. It is shown that the controller is able to control the slip ratio of the mobile robot on different terrains while adaptive concept of AUKF leads to better results than the unscented Kalman filter in estimating the vehicle velocity which is difficult to measure in actual practice.

This paper designs a new adaptive Kalman filter (KF) to solve the filtering problem of with unknown noise statistics. The estimation error of the process noise covariance matrix will destroy the state estimation, and the state estimation error will reduce the estimation of the process noise covariance matrix, thus affecting the stability and optimality of the filter. In addition, most adaptive KF algorithms adopt the measurement method of single sensor, which is easy to cause the shortage of measurement data and affect the accuracy of the algorithm. Therefore, we propose a measurement sequence fusion adaptive Kalman filter (MSFAKF) algorithm to solve this series of problems. Based on MSFAKF algorithm, the estimation of process noise covariance and measurement noise covariance are obtained by measurement fusion sequence and innovation sequence respectively. Under certain conditions, the stability of MSFAKF algorithm is proved, and the filtering result converges to that of ideal KF with known second moment of noise. Simulation experiment shows that MSFAKF algorithm has the characteristics of fast convergence speed, high accuracy and strong adaptability.

Robust unscented Kalman filter with adaptation of process and measurement noise covariances

A residual based adaptive unscented Kalman filter for fault recovery in attitude determination system of microsatellites

Constrained two-stage Kalman filter for real-time state estimation of systems with time-varying measurement noise covariance

PurposeThis paper aims to develop an adaptive unscented Kalman filter (AUKF) formulation for orientation estimation of aircraft and UAV utilizing low‐cost attitude and heading reference systems (AHRS).Design/methodology/approachA recursive least‐square algorithm with exponential age weighting in time is utilized for estimation of the unknown inputs. The proposed AUKF tunes its measurement covariance to yield optimal performance. Owing to nonlinear nature of the dynamic model as well as the measurement equations, an unscented Kalman filter (UKF) is chosen against the extended Kalman filter, due to its better performance characteristics. The unscented transformation of the UKF is shown to equivalently capture the effect of nonlinearities up to second order without the need for explicit calculations of the Jacobians.FindingsIn most conventional AHRS filters, severe problems can occur once the system suddenly experiences additional acceleration, resulting in erroneous orientation angles. On the contrary in the high dynamic accelerative mode of the new proposed filter the errors would not suddenly increase, since the additional to cruise accelerations are being continuously estimated resulting in substantially more accurate orientation estimation. This feature causes the associated filter errors to gradually increase, in the event of continuous vehicle acceleration, up to a point of zero additional acceleration that subsequently causes a subsidence of the error back to zero.Practical implicationsThe proposed filtering methodology can be implemented for orientation estimation of aircraft and UAV that are equipped with low‐cost AHRSs.Originality/valueTraditional AHRS algorithms utilize the accelerometers output for the computation of roll and pitch angles and magnetometer output for the heading angle. Moreover, these angles are also calculated from the gyroscopes output as well, but with errors that increase with time. Of course for some applications of AHRS system, orientation errors can be damped out with a proportional‐integral controller. In such a case, the filter cut‐off frequency is usually selected experimentally. But, for high accelerating vehicles utilizing AHRS, the system errors can become very large. A possible remedy to this problem could be to use more advanced nonlinear filter algorithms such as the one proposed.

Battery management system (BMS) is an electronic device responsible for all control and management operations of several battery parameters, especially SOH and SOC. The battery SOC acts like an indicator of the internal charge level of the battery, in order to avoid unpredicted system interruption and prevent the batteries from being over-charged or over-discharged. SOC estimation procedure is one of the most complex techniques caused by complex battery chemistry and its strong non linearity. In this paper we have chosen a Kalman filtering algorithm to estimate internal states of Lithium Ion battery and dynamically estimate the SOC by decreasing divergence due to parametric uncertainty of battery model, measurement and process noise by using an Unscented variant of this filter. To further enhance the UKF algorithm, an adaptive calculation of noise covariance is proposed to combine between a better convergence and robust results. Experimental results indicate that the adaptive unscented Kalman filter based algorithm has better performance Battery State of Charge estimation. A comparison with other estimations techniques shows that the proposed SOC estimation method is the best choice in term of accuracy and robustness.

Adaptive unscented Kalman filter for parameter and state estimation of nonlinear high-speed objects

Fusion estimation of lithium-ion battery state of charge and state of health considering the effect of temperature

Kalman filtering is a well-established methodology used in various multi-sensor data fusion applications. In our experiment, we first obtain measurements from the accelerometer and gyroscope and fuse them using Kalman filter in an inertial measurement unit (IMU). We estimate Kalman filter output and estimation error. The affect of process noise and measurement noise on estimation error is tested. It is explored that the measurement noise has significant role to increase estimation error in the data fusion process.