# Block diagonally dominant positive definite approximate filters and smoothers

@article{Riedel1993BlockDD, title={Block diagonally dominant positive definite approximate filters and smoothers}, author={Kurt S. Riedel}, journal={Autom.}, year={1993}, volume={29}, pages={779-783} }

We examine stochastic dynamical systems where the transition matrix, ∅, and the system noise, ГQГT, covariance are nearly block diagonal. When HTR−1H is also nearly block diagonal, where R is the observation noise covariance and H is the observation matrix, our suboptimal filter/smoothers are always positive semidefinite, and have improved numerical properties. Applications for distributed dynamical systems with time dependent pixel imaging are discussed.

## Topics from this paper

## 5 Citations

Ooce Note Series on Global Modeling and Data Assimilation Estimation Theory and Foundations of Atmospheric Data Assimilation

- 1999

iii The following is a collection of notes geared to provide an elementary introduction to the topic of data assimilation. The topic is presented with the point of view of estimation theory. As such,…

Citations of Zoran Gajic ’ s Publications

- 2016

1. 207 Gajic and Qureshi, Academic Press , 1995,DoverPublications , 2008. 2. 118 Koskie and Gajic,IEEE/ACM Trancations on Networking , 2005. 3. 87 Gajic, Petkovski, and Shen, Springer Verlag, 1990.…

Journal and Book Citations of Zoran Gajic's Publications excluding Professor Gajic's Self-referencing

- 2015

1. 206 Gajic and Qureshi, Academic Press , 1995,DoverPublications , 2008. 2. 116 Koskie and Gajic,IEEE/ACM Trancations on Networking , 2005. 3. 87 Gajic, Petkovski, and Shen, Springer Verlag, 1990.…

## References

SHOWING 1-10 OF 18 REFERENCES

On optimal ℓ∞ to ℓ∞ filtering

- Mathematics, Computer ScienceAutom.
- 1995

Taking a model matching approach, suboptimal solutions are presented that stem from the resulting l ∞ -induced norm-minimization problem.

Singularly Perturbed and Weakly Coupled Linear Control Systems: A Recursive Approach

- Mathematics
- 1990

Algebraic lyapunov and riccati equations.- Output feedback control of linear singularly perturbed and weakly coupled systems.- Linear stochastic systems.- Recursive approach to finite time singularly…

Quasi Singularly Perturbed and Weakly Coupled Linear Control Systems

- Physics
- 1990

Several structures of the linear-quadratic control problems containing small parameters can be studied efficiently by using the methodology similar to the one presented in the previous chapters. We…

Near-optimum steady state regulators for stochastic linear weakly coupled systems

- Mathematics, Computer ScienceAutom.
- 1990

The proposed method produces the reduction in both off-line and on-line computational requirements and leads to convergence under mild assumptions and only low-order systems are involved in algebraic calculations and no analyticity requirement is imposed on system coefficients.

Discrete-Time Fixed-Lag Smoothing,

- Mathematics
- 1970

Abstract : It has been shown that previously derived algorithms for recursive, optimal, fixed-lag smoothing are unstable under the same assumptions for which the corresponding Kalman filter is…

Nested ε-decompositions and clustering of complex systems

- Mathematics, Computer ScienceAutom.
- 1986

Abstract A graph-theoretic method of extreme simplicity is proposed for decomposition and clustering of complex systems into interconnected subsystems with prescribed interaction strength. The method…

Discrete-time fixed-lag smoothing algorithms

- Mathematics
- 1973

Kalman filtering results are applied to yield alternative computationally stable fixed-lag smoothing algorithms including reduced order and minimal order fixed-lag smoothers. The reduced order…

The Behavior of Forecast Error Covariances for a Kalman Filter in Two Dimensions

- Computer Science
- 1991

Results show that assimilating the profiler wind data leads to a large reduction of forecast/analysis error in heights as well as in winds, over the Profiler region and also downstream, when compared with the results of assimilated the radiosonde data alone.

On the maximum likelihood estimates for linear dynamic systems

- Mathematics, Materials Science
- 1963

A steel slab or bloom containing 0.3 DIFFERENCE 0.15% by weight of C, 0.05 DIFFERENCE 0.60% by weight of Si, 0.60 DIFFERENCE 2.5% by weight of Mn, 0.010 DIFFERENCE 0.15% by weight of Nb, 0.005…

Spectral methods for fluid dynamics

- Mathematics
- 1987

1. Introduction.- 1.1. Historical Background.- 1.2. Some Examples of Spectral Methods.- 1.2.1. A Fourier Galerkin Method for the Wave Equation.- 1.2.2. A Chebyshev Collocation Method for the Heat…