We consider non-linear state space models in high-dimensional situations, where the two common tools for state space models both have difficulties. The Kalman filter variants are seriously biased due to non-Gaussianity and the particle filter suffers from the “curse of dimensionality”. Inspired by a regression perspective on the Kalman filter, a novel approach is developed by combining the Kalm...

This paper presents a new robust fault and state estimation based on recursive least square filter for linear stochastic systems with unknown disturbances. The novel elements of the algorithm are : a simple, easily implementable, square root method which is shown to solve the numerical problems affecting the unknown input filter algorithm and related information filter and smoothing algorithms;...

This paper studies the effect of targeted observations on state and parameter estimates determined with Kalman filter data assimilation (DA) techniques. We first provide an analytical result demonstrating that targeting observations within the Kalman filter for a linear model can significantly reduce state estimation error as opposed to fixed or randomly located observations. We next conduct ob...

—The so-called constrained least mean-square algorithm is one of the most commonly used linear-equality-constrained adaptive filtering algorithms. Its main advantages are adaptability and relative simplicity. In order to gain analytical insights into the performance of this algorithm, we examine its mean-square performance and derive theoretical expressions for its transient and steady-state me...

In this paper, a mechanism is designed for integration of inertial navigation system information (INS) and global positioning system information (GPS). In this type of system a series of mathematical and filtering algorithms with Tightly Coupled techniques with several objectives such as application of integrated navigation algorithms, precise calculation of flying object position, speed and at...

This paper discusses the behavior of the second-order modes (Hankel singular values) of linear continuous-time systems under typical frequency transformations, such as lowpass-lowpass, lowpasshighpass, lowpass-bandpass, and lowpass-bandstop transformations. Our main result establishes the fact that the second-order modes are invariant under any of these typical frequency transformations. This m...

Filters of some sort are essential to the operation of most electronic circuits. It is therefore in the interest of anyone involved in electronic circuit design to have the ability to develop filter circuits capable of meeting a given set of specifications. delay time steady state error, operating frequency, and wavelength, damping frequency, and wavelength the major interesting design paramete...

—The so-called constrained least mean-square algorithm is one of the most commonly used linear-equality-constrained adaptive filtering algorithms. Its main advantages are adaptability and relative simplicity. In order to gain theoretical insights into the performance of this algorithm, we examine its mean-square convergence and derive an expression for its steady-state mean-square deviation. Ou...