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.

scholarly journals Global Systems for Mobile Position Tracking Using Kalman and Lainiotis Filters

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Nicholas Assimakis ◽  
Maria Adam
Keyword(s):  
Kalman Filter ◽  
Steady State ◽  
Impulse Response ◽  
Finite Impulse Response ◽  
Position Tracking ◽  
Computational Burden ◽  
Time Invariant ◽  
Global Systems

We present two time invariant models for Global Systems for Mobile (GSM) position tracking, which describe the movement inx-axis andy-axis simultaneously or separately. We present the time invariant filters as well as the steady state filters: the classical Kalman filter and Lainiotis Filter and the Join Kalman Lainiotis Filter, which consists of the parallel usage of the two classical filters. Various implementations are proposed and compared with respect to their behavior and to their computational burden: all time invariant and steady state filters have the same behavior using both proposed models but have different computational burden. Finally, we propose a Finite Impulse Response (FIR) implementation of the Steady State Kalman, and Lainiotis filters, which does not require previous estimations but requires a well-defined set of previous measurements.

The Design of a Robust Weighted Measurement Fusion Steady-State Kalman Filter

2014 ◽  
Vol 701-702 ◽  
pp. 624-629
Author(s):  
Wen Qiang Liu ◽  
Xue Mei Wang ◽  
Zi Li Deng
Keyword(s):  
Kalman Filter ◽  
Steady State ◽  
Lyapunov Equation ◽  
Model Parameters ◽  
Invariant System ◽  
Parameter Uncertainties ◽  
Worst Case ◽  
Uncertain Model ◽  
Time Invariant ◽  
Time Invariant System

For the linear discrete-time multisensor time-invariant system with uncertain model parameters and measurement noise variances, by introducing fictitious noise to compensate the parameter uncertainties, using the minimax robust estimation principle, based on the worst-case conservative multisensor system with conservative upper bounds of measurement and fictitious noises variances, a robust weighted measurement fusion steady-state Kalman filter is presented. By the Lyapunov equation approach, it is proved that when the region of the parameter uncertainties is sufficient small, the corresponding actual fused filtering error variances are guaranteed to have a less-conservative upper bound. Simulation results show the effectiveness and correctness of the proposed results.

scholarly journals Iterative and Algebraic Algorithms for the Computation of the Steady State Kalman Filter Gain

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Nicholas Assimakis ◽  
Maria Adam
Keyword(s):  
Kalman Filter ◽  
Steady State ◽  
Prediction Error ◽  
Covariance Matrices ◽  
Asymptotically Stable ◽  
System Parameters ◽  
Estimation And Prediction ◽  
Error Covariance ◽  
Algebraic Algorithms ◽  
Time Invariant

The Kalman filter gain arises in linear estimation and is associated with linear systems. The gain is a matrix through which the estimation and the prediction of the state as well as the corresponding estimation and prediction error covariance matrices are computed. For time invariant and asymptotically stable systems, there exists a steady state value of the Kalman filter gain. The steady state Kalman filter gain is usually derived via the steady state prediction error covariance by first solving the corresponding Riccati equation. In this paper, we present iterative per-step and doubling algorithms as well as an algebraic algorithm for the steady state Kalman filter gain computation. These algorithms hold under conditions concerning the system parameters. The advantage of these algorithms is the autonomous computation of the steady state Kalman filter gain.

A Relationship between Parameters of Two Representations of Discrete LTI ARMA System Model and the Corresponding Device Fingerprints

2013 ◽  
Vol 416-417 ◽  
pp. 1267-1273 ◽  
Author(s):  
Hong Lin Yuan ◽  
Zhi Hua Bao ◽  
Yan Yan
Keyword(s):  
Discrete Time ◽  
Digital Communication ◽  
Linear Time ◽  
Moving Average ◽  
System Model ◽  
Autoregressive Moving Average ◽  
Linear Time Invariant ◽  
Time Invariant ◽  
The Relationship ◽  
Time Linear

Device fingerprints has potential to identify the source of digital communication information. Although identifying transmitters with their fingerprints remains an arduous question, fusion identification with multiple device fingerprints is a feasible methodology. In this paper, a relationship between parameters of two representations of discrete-time linear time-invariant (LTI) autoregressive moving average (ARMA) system model is derived which has definite physical meaning. With the relationship, a novel linear device fingerprints is proposed which may enlarge the inter-class distance of the transmitters to be identified. The proposed device fingerprints can be used for fusion identification of network devices and the corresponding ARMA systems especially for that with slight differences.

scholarly journals On the Asymptotic Stability of Linear Discrete Time Delay Systems

Volume 1 ◽  
2004 ◽  
Author(s):  
S. B. Stojanovic ◽  
D. Lj. Debeljkovic
Keyword(s):  
Time Delay ◽  
Asymptotic Stability ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Numerical Example ◽  
Discrete Time Delay ◽  
Time Invariant ◽  
Working Out

This paper extends some of the basic results in the area of Lyapunov (asymptotic) to linear, discrete, time invariant time-delay systems. These results are given in the form of only sufficient conditions and represent other generalisation of some previous ones or completely new results. In the latter case it is easy to show that, in the most cases, these results are less conservative then those in existing literature. A numerical example has been working out to show the applicability of results derived. To the best knowledge of the authors, such results have not yet been reported.

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