One method to account for parameters errors in the Kalman filter is to ‘consider’ their effect in the so-called Schmidt-Kalman filter. This paper addresses issues that arise when implementing a consider Kalman filter as a real-time, recursive algorithm. A favorite implementation of the Kalman filter as an onboard navigation subsystem is the UDU formulation. A new way to implement a UDU Schmidt-...

The purpose of this paper is to present an alternate derivation of optimal linear filters. The basic technique is the use of a matrix version of the maximum principle of Pontryagin coupled with the use of gradient matrices to derive the optimal values of the ; '1 filter coefficients for minimum variance estimation under the require­ :11" ment that the estimates be unbiased. The optimal filter w...

The Kalman filter is the optimal minimum-variance state estimator for linear dynamic systems with Gaussian noise. In addition, the Kalman filter is the optimal linear state estimator for linear dynamic systems with non-Gaussian noise. For nonlinear systems various modifications of the Kalman filter (e.g., the extended Kalman filter, the unscented Kalman filter, and the particle filter) have bee...

The Kalman filter is the minimum-variance state estimator for linear dynamic systems with Gaussian noise. Even if the noise is non-Gaussian, the Kalman filter is best linear estimator. For nonlinear systems it is not possible, in general, to derive the optimal state estimator in closed form, but various modifications of the Kalman filter can be used to estimate the state. These modifications in...

The Kalman filter is used in this paper as a framework for space time data analysis. Using Kalman filtering it is possible to include physically based simulation models into the data analysis procedure. Attention is concentrated on the development of fast filter algorithms to make Kalman filtering feasible for high dimensional space time models. The ensemble Kalman filter and the reduced rank s...

The focus is on the approximation of solution BSDE in case where forward equation observed presence small Gaussian noise. volatility considered to depend some unknown parameter. This made several steps. First a preliminary estimator obtained, then using Kalman-Bucy filtration equations and Fisher-score device one-step MLE-process this parameter constructed. approximated by means PDE One-step ML...

GPS/INS integrated system is very subject to uncertainties due to exogenous disturbances, device damage, and inaccurate sensor noise statistics. Conventional Kalman filer has no robustness to address system uncertainties which may corrupt filter performance and even cause filter divergence. Based on the INS error dynamic equation, a robust Kalman filter is analyzed and applied in loosely couple...

Report [1] compares the Extended Kalman Filter [2, 3, 4], the Iterated Extended Kalman Filter, IEKF, [2, 3, 4] and the Linear Regression Kalman Filter [5] (e.g. the Unscented Kalman Filter, UKF, [6, 7, 8]) on (i) consistency and (ii) information content of their results (estimates and covariance matrices). The nonlinear filter proposed by Bellaire et al. in [9] is not discussed in report [1]. T...

The basic problem in Target tracking is to estimate the trajectory of a object from noise corrupted measurements and hence becoming very important field of research as it has wider applications in defense as well as civilian applications. Kalman filter is generally used for such applications. When the process and measurements are non linear extensions of Kalman filters like Extended Kalman Filt...

This paper proposes a new radar tracking filter named Noise-estimate Particle Filter (NPF). Kalman filter and particle filter are popular filtering techniques for target tracking. The tracking performance of the Kalman filter severely depends on the setting of several parameters such as system noise and observation noise. However, it is an open problem how to choose proper parameters for variou...