A deterministic approach for general discrete-time Kalman filter for singular systems

2005 ◽  
Author(s):  
A.F. Bianco ◽  
J.Y. Ishihara ◽  
M.H. Terra
Keyword(s):  
Kalman Filter ◽  
Discrete Time ◽  
Singular Systems ◽  
Deterministic Approach

Analisis Kestabilan Kalman Filter Sistem Singular dengan Pendekatan Deterministik

2019 ◽  
Vol 2 (2) ◽  
Author(s):  
Budi Rudianto
Keyword(s):  
Kalman Filter ◽  
State Space ◽  
Riccati Equation ◽  
Discrete Time ◽  
Simple Structure ◽  
Descriptor Systems ◽  
Deterministic Approach ◽  
Optimal Form

Makalah ini membahas Kalman filter dan Persamaan Aljabar Ricatti (PAR) untuk waktu diskrit. Lebih lanjut, sistem deskriptor varian waktu ditampilkan dalm bentuk formulasi umum. Pendekatan deterministik digunakan untuk menentukan bentuk optimum menjadi formulasi 9-block. Pernyataan 9-block selain menyatakan tahapan kondisi ruang, juga menampilkan struktur sederhana yang menarik dan simetris. Kemudian, kami akan menunjukkan bahwa Persamaan Aljabar Ricatti (PAR) memiliki semidefinit dan menstabilkan sistem.   In this paper will discuss the Kalman filter and Riccati equation for discrete-time. Furthermore, time-variant descriptor systems presented in a common formulation. Deterministic approach used to determine the optimal form into the formulation "9-block". The expression "9-block", besides stating stages pending state space, also presents a simple structure that is interesting and symmetrical. And then, we will show that the Aljabar Riccati Eqution has a stabilizing semi-definit.

Estimation of Steady-State Optimal Filter Gain From Nonoptimal Kalman Filter Residuals

1994 ◽  
Vol 116 (3) ◽  
pp. 550-553 ◽  
Author(s):  
Chung-Wen Chen ◽  
Jen-Kuang Huang
Keyword(s):  
Kalman Filter ◽  
Steady State ◽  
Finite Number ◽  
Discrete Time ◽  
Stochastic System ◽  
Moving Average ◽  
Ar Model ◽  
Numerical Example ◽  
Measurement Noises ◽  
Time Invariant

This paper proposes a new algorithm to estimate the optimal steady-state Kalman filter gain of a linear, discrete-time, time-invariant stochastic system from nonoptimal Kalman filter residuals. The system matrices are known, but the covariances of the white process and measurement noises are unknown. The algorithm first derives a moving average (MA) model which relates the optimal and nonoptimal residuals. The MA model is then approximated by inverting a long autoregressive (AR) model. From the MA parameters the Kalman filter gain is calculated. The estimated gain in general is suboptimal due to the approximations involved in the method and a finite number of data. However, the numerical example shows that the estimated gain could be near optimal.

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