The Riccati Equation and Its Bounds

  title={The Riccati Equation and Its Bounds},
  author={Richard S. Bucy},
  journal={J. Comput. Syst. Sci.},
  • R. Bucy
  • Published 1 August 1972
  • Mathematics
  • J. Comput. Syst. Sci.

Gramian-based uniform convergent observer for stable LTV systems with delayed measurements

An observer for a linear time-varying system with delayed measurements is developed and it contains nonlinearities that provide a uniform fixed-time convergence to a bounded region in the estimation error coordinates that is new for the addressed class of systems.

On Practical Fixed-Time Convergence for Differential Riccati Equations

Sufficient conditions for fixed-time convergence of matrix differential Riccati equations towards an ellipsoid in the space of symmetric non-negative matrices are proposed. These conditions are based

Process Noise Covariance Design in Kalman Filtering via Bounds Optimization

In terms of estimation accuracy, the Kalman filter with the optimal design outperforms a robust $H_2$ filter designed to cope with an equivalent uncertainty and Monte Carlo simulations illustrate the good convergence, performance, and low sensitivity to initial guesses of the proposed method.

Detectability Conditions and State Estimation for Linear Time-Varying and Nonlinear Systems

A detectability condition for linear time-varying systems based on the exponential dichotomy spectrum guarantees the existence of an observer, whose gain is determined only by the unstable modes of the system.

Nonlinear Observers Design for Vision-Aided Inertial Navigation Systems

A nonlinear observer on SO(3) × R relying on body-frame acceleration, angular velocity and (stereo or monocular) bearing measurements of some landmarks that are constant and known in the inertial frame is proposed.

Appendix: Matrix Equations

The Lyapunov equation and the algebraic Riccati equation are treated in depth. The Lyapunov equation arises as the equation for the asymptotic covariance matrix of the state of a stationary Gaussian

Appendix: State-Variance Matrices

Concepts and results of the geometric structure of the set of state-variance matrices of a time-invariant Gaussian system are provided in this chapter. With respect to a condition, the set is convex

A theoretical analysis of one-dimensional discrete generation ensemble Kalman particle filters

Despite the widespread usage of discrete generation Ensemble Kalman particle filtering methodology to solve nonlinear and high dimensional filtering and inverse problems, little is known about their



Extrapolation, Interpolation, and Smoothing of Stationary Time Series, with Engineering Applications

Extrapolation interpolation and smoothing of stationary, stationary tones interference cancellation using adaptive and stationary time series financial definition of stationary.

Global Theory of the Riccati Equation

  • R. Bucy
  • Mathematics
    J. Comput. Syst. Sci.
  • 1967

A priori bounds for the Riccati equation

Since the appearance of [6] and [7], the theory of linear filtering has experienced a renaissance. This theory, although evidently well known to statisticians in terms of "least squares estimates,"