An alternate calculation of the discrete-time Kalman filter gain and Riccati equation solution

1996 ◽  
Vol 41 (12) ◽  
pp. 1817-1819 ◽  
Author(s):  
R. Leland
Keyword(s):  
Kalman Filter ◽  
Riccati Equation ◽  
Discrete Time ◽  
Equation Solution

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.

scholarly journals Kalman Filter Riccati Equation for the Prediction, Estimation, and Smoothing Error Covariance Matrices

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Nicholas Assimakis ◽  
Maria Adam
Keyword(s):  
Kalman Filter ◽  
Riccati Equation ◽  
Discrete Time ◽  
Prediction Error ◽  
Estimation Error ◽  
Riccati Equations ◽  
Covariance Matrices ◽  
Linear Estimation ◽  
Solution Algorithms ◽  
Error Covariance

The classical Riccati equation for the prediction error covariance arises in linear estimation and is derived by the discrete time Kalman filter equations. New Riccati equations for the estimation error covariance as well as for the smoothing error covariance are presented. These equations have the same structure as the classical Riccati equation. The three equations are computationally equivalent. It is pointed out that the new equations can be solved via the solution algorithms for the classical Riccati equation using other well-defined parameters instead of the original Kalman filter parameters.

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.

Distributed Fusion Kalman Self-Turning Filter

2013 ◽  
Vol 760-762 ◽  
pp. 1661-1665
Author(s):  
Ming Bo Zhang
Keyword(s):  
Kalman Filter ◽  
Riccati Equation ◽  
Global Optimal ◽  
Calculated Amount ◽  
Distributed Fusion

This paper puts forward an optimal and distributed fusion Kalman filter based on the Riccati equation, optimal and distributed fusion The Kalman filter has fewer calculated dimensions and less calculated amount than the centralized global optimal Kalman filter. Therefore, it has greater effect in the practice. Present the distributed local self-correcting Kalman filter at the same time. The simulation examples showed its validity.

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