The Study of Robust Kalman Filter On Linear and Non-Linear Systems

Abstract

Kalman filter is one of the best filter utilized as a part of the state estimation taking into account optimality criteria utilizing system model and observation model. Kalman filtering, otherwise called linear quadratic estimation (LQE), is an algorithm that uses a progression of estimations over time, having noise with different errors, and gives assessments of obscure variables that have a tendency to be more exact than those in view of a single estimation alone. The Kalman Filter is an extremely well known recursive state estimator for linear systems. By and by the calculation is frequently utilized for nonlinear systems by linearizing the system's procedure and estimation capacities. Another Kalman Filter variations linearize the functions in various ways, one of that is Extended Kalman Filter(EKF). While various nonlinear techniques having robust within the sight of outliers and adjusted to non-Gaussian noise, it keeps up high statistical efficiency which is attractive. To deal with this issue, another robust Kalman filter strategy is suggested that limits the impact of structural, innovation, and observation outliers in a linear system. This filter is planned to set up the perceptions and forecasts together, making it amazingly effective in smothering numerous outliers. In development, it contains another pre-whitening methodology that gives a robust multivariable estimator of covariance and location. Besides, the filter gives state estimates that are robust to outliers while keeping up a high statistical effectiveness at the Gaussian appropriation by applying a (GM)Generalised Maximum likelihood estimator. Finally, the filter combines the correct error covariance matrix that is gathered using the influence function of GM-estimator. By simulations, the execution of GM-KF to various outliers and state estimation for the applications: tracking of the vehicle.