On the properties of reduced order Kalman filters

1989 ◽  
Vol 34 (3) ◽  
pp. 321-324 ◽  
Author(s):  
B. Friedland
Keyword(s):  
Kalman Filters ◽  
Reduced Order

Separate-bias estimation with reduced-order Kalman filters

1998 ◽  
Vol 43 (7) ◽  
pp. 983-987 ◽  
Author(s):  
D. Haessig ◽  
B. Friedland
Keyword(s):  
Kalman Filters ◽  
Bias Estimation ◽  
Reduced Order

Parallel Optimal Kalman Filtering for Stochastic Systems in Multimodeling Form

1999 ◽  
Vol 122 (3) ◽  
pp. 542-550 ◽  
Author(s):  
Cyril Coumarbatch ◽  
Zoran Gajic
Keyword(s):  
Kalman Filter ◽  
Kalman Filtering ◽  
Kalman Filters ◽  
Stochastic Systems ◽  
State Variables ◽  
State Transformation ◽  
Eighth Order ◽  
Reduced Order ◽  
Filtering Technique ◽  
Ill Conditioning

In this paper we show how to completely and exactly decompose the optimal Kalman filter of stochastic systems in multimodeling form in terms of one pure-slow and two pure-fast, reduced-order, independent, Kalman filters. The reduced-order Kalman filters are all driven by the system measurements. This leads to a parallel Kalman filtering scheme and removes ill-conditioning of the original full-order singularly perturbed Kalman filter. The results obtained are valid for steady state. In that direction, the corresponding algebraic filter Riccati equation is completely decoupled and solved in terms of one pure-slow and two pure fast, reduced-order, independent, algebraic Riccati equations. A nonsingular state transformation that exactly relates the state variables in the original and new coordinates (in which the required decomposition is achieved) is also established. The eighth order model of a passenger car under road disturbances is used to demonstrate efficiency of the proposed filtering technique. [S0022-0434(00)01703-2]

LQG/LTR procedure using reduced-order Kalman filters

2017 ◽  
Vol 92 (3) ◽  
pp. 461-475 ◽  
Author(s):  
T. Ishihara ◽  
L. A. Zheng
Keyword(s):  
Kalman Filters ◽  
Reduced Order

scholarly journals Regular design equations for the continuous reduced-order Kalman filter

2011 ◽  
Vol 21 (4) ◽  
pp. 349-361 ◽  
Author(s):  
Peter Hippe
Keyword(s):  
Kalman Filter ◽  
Frequency Domain ◽  
Time Domain ◽  
Matrix Equation ◽  
Kalman Filters ◽  
Polynomial Matrix ◽  
Reduced Order ◽  
Regular Design ◽  
The Time Domain ◽  
Standard Software

Regular design equations for the continuous reduced-order Kalman filter Reduced-order Kalman filters yield an optimal state estimate for linear dynamical systems, where parts of the output are not corrupted by noise. The design of such filters can either be carried out in the time domain or in the frequency domain. Different from the full-order case where all measurements are noisy, the design equations of the reduced-order filter are not regular. This is due to the rank deficient measurement covariance matrix and it can cause problems when using standard software for the solution of the Riccati equations in the time domain. In the frequency domain the spectral factorization of the non-regular polynomial matrix equation does not cause problems. However, the known proof of optimality of the factorization result also requires a regular measurement covariance matrix. This paper presents regular (reduced-order) design equations for reduced-order Kalman filters in the time and in the frequency domains for linear continuous-time systems. They allow to use standard software for the design of the filter, to formulate the conditions for the stability of the filter and they also prove that the existing frequency domain solutions obtained by spectral factorization of a non-regular polynomial matrix equation are indeed optimal.

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