Aritro Dey

Adaptive Gauss Hermite filter for parameter varying nonlinear systems

This paper presents an adaptive sigma point filter based on Gauss Hermite quadrature rule for estimation of unknown time varying parameters and states of nonlinear systems. An adaptive filter is required for such problems because of the unknown parameter variation which often makes the knowledge of the process noise covariance unavailable. The performance of the proposed filter which adapts to the time varying process noise is evaluated using a case study. The simulation results demonstrate that the proposed filter apart from estimating the states can successfully track and estimate the time varying parameter. From Monte Carlo study it is further observed that the performance of the adaptive Gauss Hermite filter is superior compared with its non adaptive version in the perspective of time varying parameter estimation.

Multiple Sensor Fusion using Adaptive Divided Difference Information Filter

This paper addresses the problem of multiple sensor fusion in situations where the system dynamics suffers from unknown parameter variation. An adaptive nonlinear information filter has been proposed for such multi sensor estimation problems where the process noise covariance becomes unknown as a consequence of unknown parameter variation. The proposed filter, based on the Divided Difference interpolation formula, ensures satisfactory estimation performance by online adaptation of the unknown process noise covariance and makes sensor fusion successful. Efficacy of the proposed filter is demonstrated with the help of a tracking problem in a sensor fusion configuration. Results from Monte Carlo simulation indicate that though the process noise covariance is unknown, the performance of the proposed filter is demonstrably superior to its non adaptive version in the context of joint estimation of parameter and states.

Adaptive divided difference filter for nonlinear systems with non-additive noise

An Adaptive Divided Difference filter has been proposed for the systems with non additive Gaussian noise in the situations when noise statistics is unknown. In face of unknown noise statistics the proposed filter can adapt the unknown measurement noise covariance (Ü) incorporating the steps for adaptation in the non adaptive algorithm of Divided Difference filter. Satisfactory estimation performance of the proposed filter is ensured by online adaptation of the unknown measurement noise covariance with guaranteed positive definiteness of adapted R. Simulation results obtained from the case study demonstrate that the adapted measurement noise covariance converges to its truth value and can also successfully track the truth value when it is time varying. From the Monte Carlo study it is observed that the performance of the proposed filter is superior compared to its non adaptive version when the noises are non additive and the measurement noise statistics remains unknown.

Adaptive divided difference filter for parameter and state estimation of non-linear systems

An adaptive divided difference filter for joint estimation of parameters and states of a non-linear signal model has been proposed. The adaptive non-linear estimator, developed on the framework of second-order divided difference filter is intended for situations where the measurement noise statistics is unknown. Unlike other alternatives, the proposed non-linear adaptive estimator always ensures positive definiteness of the adapted measurement noise covariance. Performance of the evolved filter has been assessed with a bench mark non-linear problem of joint estimation of parameters and states. Simulation with Monte Carlo results demonstrate that the root-mean-square errors of estimated states and parameters are (i) better than those obtained from non-adaptive filters with same initial values of measurement error covariance and (ii) consistent with the estimated error covariance. Furthermore, it is shown that even when the measurement noise covariance varies with time the adapted measurement noise covariance can track the time-varying truth value.

Sliding mode compensation of inverse dynamics velocity control

Direct drive manipulators operate at high speeds, because the reduction gears are eliminated for accurate positioning of the end effector. Obviously, inverse dynamics velocity control is a suitable choice for the control of direct drive manipulator to tackle the dynamic effects due to its high speed operation. However, uncertainty in the dynamic model, and also in the inverse dynamic model, of the manipulator deteriorates its tracking performance. This paper presents a novel approach of inverse dynamics velocity control of direct drive manipulator based on sliding mode compensation technique. The compensated inverse dynamics velocity control scheme is robust against the ill-effects of the model uncertainties and exhibits robust tracking performance of the desired velocity trajectories in the robot joint space. Moreover, the proposed inverse dynamic controller can be designed based on the nominal dynamic model, thus eliminating the need for the online calculation of the computation intensive time varying parameters of the robot dynamic model. The effectiveness of the proposed control algorithm has been validated in the simulation considering a 3 DOF direct drive manipulator model.

Adaptive Gauss Hermite filter for parameter and state estimation of nonlinear systems

This paper presents an adaptive Gauss Hermite filter for nonlinear signal models in the situation when the measurement noise statistics is unknown. The proposed nonlinear filter, based on the Gauss Hermite quadrature rule, can ensure satisfactory estimation performance despite the problem of unknown measurement noise statistics by online adaptation. Results of Monte Carlo Simulation demonstrate the efficacy of the proposed filter for joint estimation of parameters and states using an object tracking problem.

Square Root Quadrature Information Filters for Multiple Sensor Fusion

This paper presents new algorithms for square root quadrature information filers which are intended for multiple sensor fusion. The use of recently proposed quadrature rules for numerical approximation of Bayesian integrals enables these filters to demonstrate improved estimation accuracy over their competing algorithms. Additionally, these newly proposed estimators are numerically stable as they incorporate square root framework of filtering and advocated for the applications with limited bit precision. With the help of an aircraft tracking problem in presence of multiple sensor measurements the efficacy of the proposed filters are exemplified in a sensor fusion configuration.

Adaptive Nonlinear Information Filters for Multiple Sensor Fusion

This paper addresses the problem of multiple sensor fusion in situations when the system dynamics is affected by unknown parameter variation and proposes a set of adaptive nonlinear information filters. For the above estimation problem complete knowledge of the process noise covariance (Q) remains unavailable due to unknown parameter variation. The proposed varieties of adaptive nonlinear information filters are so designed that they can present satisfactory estimation performance in the face of parametric uncertainty by online adaptation of unknown \({{\varvec{Q}}}\). The adaptation steps incorporated in the algorithms have been formulated using Maximum Likelihood Estimation method. Superiority of the adaptive information filters over their non adaptive counterparts is demonstrated in simulation considering a case study where a maneuvering aircraft is to be tracked using multiple radars. Additionally, comparison of performance of proposed alternative adaptive filters is also carried out to appreciate the relative advantages of the proposed variants of adaptive information filters for multiple sensor fusion.

Adaptive Unscented Kalman Filter at the Presence of Non-additive Measurement Noise

This paper proposes an Adaptive Unscented Kalman Filter (AUKF) for nonlinear systems having non-additive measurement noise with unknown noise statistics. The proposed filter algorithm is able to estimate the nonlinear states along with the unknown measurement noise covariance (R) online with guaranteed positive definiteness. By this formulation of adaptive sigma point filter for non-additive measurement noise, the need of approximating non-additive noise as additive one (as is done in many cases) may be waived. The effectiveness of the proposed algorithm has been demonstrated by simulation studies on a nonlinear two dimensional bearing-only tracking (BOT) problem with non-additive measurement noise. Estimation performance of the proposed filter algorithm has been compared with (i) non adaptive UKF, (ii) an AUKF with additive measurement noise approximation and (iii) an Adaptive Divided Difference Filter (ADDF) applicable for non-additive noise. It has been found from 10000 Monte Carlo runs that the proposed AUKF algorithm provides (i) enhanced estimation performance in terms of RMS errors (RMSE) and convergence speed, (ii) almost 3-7 times less failure rate when prior measurement noise covariance is not accurate and (iii) relatively more robust performance with respect to the initial choice of R when compared with the other nonlinear filters involved herein.

Joint Estimation of States and Parameters of a Reentry Ballistic Target Using Adaptive UKF

The problem of joint estimation of states and parameters of a reentry ballistic target in the situation where the measurement noise covariance is unknown or incorrectly known has been addressed here and towards that end an Adaptive Unscented Kalman Filter (AUKF) based joint estimation technique has been presented. The presented AUKF algorithm has utilized (i) residual sequences for the adaptation of measurement noise covariance matrix (R) to guarantee positive definiteness and (ii) an iterative measurement update step to further improve the estimation performance. Simulation results demonstrate that adapted measurement noise covariance converges to its truth value and can also successfully track the truth value when it is time varying. From Monte Carlo studies it is assessed that the joint estimation performance of the presented adaptive estimator is superior compared to its non adaptive counter part.