INS/GPS Tightly-coupled Integration using Adaptive Unscented Particle Filter

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.

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.

Inherent flaws in the extended Kalman filter (EKF) algorithm were pointed out and unscented Kalman filter (UKF) was put forward as an alternative. Furthermore, a novel adaptive unscented Kalman filter (AUKF) based on innovation was developed. The three data-fusing approaches were analyzed and evaluated in a mathematically rigorous way. Field experiments conducted in lake further demonstrate that AUKF reduces the position error approximately by 65% compared with EKF and by 35% UKF and improves the robust performance.

State of Charge (SOC) estimation plays a crucial role in managing the performance and longevity of electric vehicle (EV) batteries. Various estimation techniques, including various Kalman Filters (KF), have been employed for this purpose. The mathematical process and limits of different KF family algorithms are analysed. In this study, an impact of nonlinear KF parameters on SOC estimation accuracy for EV batteries is analyzed. Specifically, the performance of Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF), and Particle Filter (PF) is examined. EKF is most preferred for SOC estimation whereas introducing sigma points in UKF is the basic difference between EKF and UKF. In comparison to EKF and UKF, PF is more flexible since it applies to nonlinear systems with non-Gaussian distributions. Utilising a sequence of noisy measurements, KF is a recursive method that approximates the state of a dynamic system. It requires accurate parameters such as process noise covariance (Q) and measurement noise covariance (R) to work effectively. In this work, the effect of these parameters on state of charge estimation using nonlinear KFs has been analysed under different settings of noise covariance matrices. Tuning these parameters is essential for optimizing the performance of the KF and ensuring accurate and reliable state estimation in real-world applications. To find parameter values that provide the best balance between accuracy, robustness, and computational efficiency, the tuning process involves experimentation, simulation, and validation using real-world data. According to the results observed, the filter parameters such as three diagonal elements of Q are selected as 2e-8, 0.005, 0.003 and R as 2e-6. By evaluating the state estimation accuracy under different driving scenarios, robustness and sensitivity of filtering technique in estimating SOC for EV batteries has been studied. This analysis contributes to the optimization of SOC estimation algorithms, enhancing the reliability and efficiency of EV battery management systems.

We demonstrate experimentally that inference in a complex hybrid dynamic Bayesian network (DBN) is possible using the 2-time slice DBN (2T-DBN) from (D. Koller et al., Sequential Monte Carlo Methods in Practice: p.445-464, Springer-Verlag, NY, 2000) to model fault detection in a watertank system. In this, a generic particle filter (PF) is used for inference. We extend the experiment and perform approximate inference using The extended Kalman filter (EKF) and the unscented Kalman filter (UKF). Furthermore, we combine these techniques in a 'non-strict' Rao-Blackwellisation framework and apply it to the watertank system. We show that UKF and UKF in a PF framework outperform the generic PF, EKF and EKF in a PF framework with respect to accuracy and robustness in terms of estimation RMSE (root-mean-square error). Especially, we demonstrate the superiority of UKF in a PF framework when our beliefs of how data was generated are wrong. We also show that the choice of network structure is very important for the performance of the generic PF and the EKF algorithms, but not for the UKF algorithms. Furthermore, we investigate the influence of data noise in the watertank simulation. Theory and implementation is based on the theory presented in (R. v.d. Merwe et al., Tech. Rep. CUED/F-INFENG/TR-380, Dept. of Eng., Cambridge Uni., 2000).

The stochastic nature of noise signals affects the vehicle’s internal states and the outputs, resulting in the difficulty in estimation. The unknown or time-varying nature of noise signals if not taken into account for estimation, the results will diverge and be highly deteriorated. In this paper, a maximum likelihood principle (MLP) based adaptive robust extended kalman filter for estimating the states of the adopted non-linear vehicle model is proposed. An observability test is done for the purpose of estimation. A covariance matching (CM) based robust adaptive high forgetting factor based fault tolerant technique is also employed on the robust adaptive extended and unscented kalman filters for comparison purpose. The Robustness of the filter is analyzed by varying the parameter of the vehicle through a local sensitivity analysis. The results show that the MLP based approach to the extended kalman filter performs well in three simulations for sinusoidal steering, Double Lance Change, J-Turn, Fishhook, Slalom maneuver in comparison to robust adaptive unscented kalman filter. Friction coefficient of 0.8 (dry road) and 0.4 (wet road) is chosen for the simulation. The sideslip angle RMSE value for MLP based estimation is obtained as 2.62e-05, 4.545e-06 for Sine and DLC maneuver.

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.

The focus of this work is the extension of nonlinear state estimation methods to gas-lifted systems. The extended Kalman filter (EKF), unscented Kalman filter (UKF) and particle filter (PF) were used to estimate the nonlinear states. Brief descriptions of the filters were first presented starting from the linear Kalman filter. Hypothesis tests on the expectation of the residuals were performed to show how close to optimal the estimation methods are and it showed the UKF estimates to be slightly better than EKF while PF performs the worst. The PF has poor accuracy using residual visualisation, hypothesis test and the root mean squared error (RMSE) values of the residuals. The gas-lifted system exhibits casing heading instability where the states show oscillatory behaviour depending on the value of the input but the results here do not change in a known way for each filter as the input is changed from the non-oscillatory region to the oscillatory region. Therefore, for this noise distribution and model assumption, either the EKF or UKF can be used for nonlinear state estimation with UKF better preferred if computational cost is not considered when control solutions are used in gas-lifted system.

Many interplanetary mission concepts can benefit from autonomous orbit estimation, particularly during critical mission phases. Previous studies have examined the feasibility of optical navigation using nanosatellite class instruments. While promising, these techniques are not without drawbacks. Convergence of the navigation estimates are often sensitive to errors in initial state estimates. This thesis compares various methods to perform nonlinear estimation for autonomous optical navigation. These methods include an extended Kalman filter (EKF), an unscented Kalman filter (UKF), a particle filter (PF), a fixed-lag smoother (FLS), and moving horizon estimation (MHE). The EKF, UKF, and PF can be implemented in real time, while the FLS and MHE implement a delay into the estimation process. To compare the performance of each state estimator three initial reference scenarios around Mars were considered: a hyperbolic flyby, an elliptic orbit and a orbital maneuver using observations of Mars and its moons. Parameter estimation was also explored, where the mass of Mars was to be estimated as a reference parameter in both the hyperbolic and elliptical trajectories. One last reference scenario included a low Earth orbit (LEO) using observations of satellites in a geosynchronous equatorial orbit. In each case, the FLS and MHE showed similar or better performance over each state estimator but at the cost of an increased computation time with respect to the reference EKF. Similarly the UKF was able to provide improved results withe respect to the EKF. While, the PF provided poor estimates in the Mars trajectories but improvements were seen from the UKF and EKF in the LEO scenario.

Surveillance of underwater for maritime warfare is traditionally being carried out by bearings-only tracking from many decades. The measurements used for state estimation here are nonlinear. Also the noise in the measurements and the process cannot be always Gaussian. The traditional nonlinear filtering algorithms like extended Kalman filter and modified gain extended Kalman filter use the linearisation of the system. The unscented Kalman filter (UKF) uses the sigma point approach based on Gaussian distribution to deal with nonlinearity. The particle filter (PF) uses the randomly generated particles based on the pdf of the state. PF is highly complex to implement and it also suffers from sample impoverishment. Hence, ensemble Kalman filter (EnKF) which is a simplified form of PF will be tried out for bearings-only tracking in this research work. The performance of EnKF is compared with PF and UKF and the results obtained using these filters in Matlab are presented.

On multi-rate fusion for non-linear sampled-data systems: Application to a 6D tracking system

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.

Based on the standard FastSLAM, a new decomposing strategy is proposed in this paper. Although the method involves a little extra computation, it considers fully the relationship between the pose of robot and the individual map feature, and it is better to improve the precision and reliability of SLAM. In addition, a nonlinear adaptive square-root unscented Kalman filter (NASRUKF) is utilized to replace the extended Kalman filter (EKF) and the particle filter (PF) to estimate the pose of robot and the map feature, then several shortcomings of traditional FastSLAM (such as it needs to calculate Jacobian matrix, it is difficult to satisfy the requirement of consistency, and it always yields particle degradation) are overcome, the accuracy and adaptability are improved. In order to verify the concept, one experiment prototype was built. The result proved that the modified FastSLAM algorithm provides a high performance of localization and map building for an autonomous mobile robot (AMR).

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.

This chapter deals with the problem of non-linear and non-Gaussian states and parameters estimation using Bayesian methods. The performances of various conventional and state-of-the-art state estimation techniques are compared when they are utilized to achieve this objective. These techniques include the Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF), and Particle Filter (PF). In the current work, the authors consider two systems (biological model and power system) to perform evaluation of estimation algorithms. The results of the comparative studies show that the UKF provides a higher accuracy than the EKF due to the limited ability of EKF to accurately estimate the mean and covariance matrix of the estimated states through lineralization of the nonlinear process model. The results also show that the PF provides a significant improvement over the UKF because, unlike UKF, PF is not restricted by linear-Gaussian assumptions which greatly extends the range of problems that can be tackled.