# Optimal solution of the two-stage Kalman estimator

@article{Hsieh1995OptimalSO, title={Optimal solution of the two-stage Kalman estimator}, author={Chien-Shu Hsieh and Fu-Chuang Chen}, journal={Proceedings of 1995 34th IEEE Conference on Decision and Control}, year={1995}, volume={2}, pages={1532-1537 vol.2} }

The optimal solution of estimating a set of dynamic state in the presence of a random bias employing a two-stage Kalman estimator is addressed. It is well known that, under an algebraic constraint, the optimal estimate of the system state can be obtained from a two-stage Kalman estimator. Unfortunately, this algebraic constraint is seldom satisfied for practical systems. This paper proposes a general form of the optimal solution of the two-stage estimator, in which the algebraic constraint is…

## 198 Citations

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## References

SHOWING 1-10 OF 21 REFERENCES

### A two-stage Kalman estimator for state estimation in the presence of random bias and for tracking maneuvering targets

- Engineering[1991] Proceedings of the 30th IEEE Conference on Decision and Control
- 1991

The authors provide the optimal solution of a two-stage estimation problem in the presence of random bias. Under an algebraic constraint, the optimal estimate of the system state can be obtained as a…

### A Two-Stage Filter for State Estimation in the Presence of Dynamical Stochastic Bias

- Engineering, Mathematics1992 American Control Conference
- 1992

This paper provides the optimal solution of a two-stage estimation problem of state estimation in the presence of a dynamical stochastic bias driven by a white or colored process noise. It is shown…

### Separating bias and state estimates in a recursive second-order filter

- Mathematics
- 1974

When recursively estimating the state of a nonlinear process using a second-order filter to process data from many sensors, the method of augmenting the state vector with those sensor systematic…

### Separate bias Kalman estimator with bias state noise

- Mathematics
- 1990

A modified decoupled Kalman estimator suitable for use when the bias vector varies as a random-walk process is defined and demonstrated in a practical application consisting of the calibration of a…

### Linear filtering in the presence of time-varying bias

- Mathematics
- 1972

The problem of estimating the state of a linear system subjected to a time-varying bias with sample paths generated from \dot{b} = F^{\astr}b is considered, and an optimal filtering algorithm is…

### Extension of Friedland's separate-bias estimation to randomly time-varying bias of nonlinear systems

- Engineering, MathematicsIEEE Trans. Autom. Control.
- 1993

A pseudo-separate-bias estimation algorithm for randomly time-Varying bias of a class of nonlinear time-varying stochastic systems is obtained and a simulation example is presented to illustrate the effectiveness of the algorithm.

### Interacting acceleration compensation algorithm for tracking maneuvering targets

- EngineeringThe Record of the 1993 IEEE National Radar Conference
- 1993

By testing the bias vector as a target acceleration, the two-stage Kalman estimator can be used for tracking maneuvering targets. The first stage contains a constant velocity motion model and…

### Multistage Estimation of Bias States in Linear Systems.

- Economics
- 1978

Abstract : This paper provides an alternate, constructive derivation of Friedland's method (Ref 1) for recursive bias filtering; and, extends his method to the case where we may wish to increase (or…

### Interacting multiple bias model algorithm with application to tracking maneuvering targets

- Engineering, Computer Science[1992] Proceedings of the 31st IEEE Conference on Decision and Control
- 1992

Simulation results for comparing the performances of the IMM and IMAM algorithms are given, together with a computational count for the two algorithms indicate that the IMAM algorithm requires approximately 43% of the computations of theIMM algorithm when a constant velocity and two constant accelerations models are used.

### Parallel computation in linear discrete filtering

- Engineering
- 1975

Friedland's algorithm for decoupling the bias estimate in the linear optimal filtering is extended to the decoupling of the randomly varying bias terms.