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.

scholarly journals Distributed Periodic Steady State Kalman Filter

2022 ◽  
Vol 16 ◽  
pp. 668-674
Author(s):  
Nicholas Assimakis ◽  
Maria Adam ◽  
Christos Massouros
Keyword(s):  
Kalman Filter ◽  
Steady State ◽  
Impulse Response ◽  
Distributed Algorithm ◽  
Finite Impulse Response ◽  
Idle Time ◽  
Parallel Structure ◽  
Distributed Implementation ◽  
Periodic Steady State

In this paper a distributed implementation for the periodic steady state Kalman filter is proposed. The distributed algorithm has parallel structure and can be implemented using processors in parallel without idle time. The number of processors is equal to the model period. The resulting speedup is also derived. The Finite Impulse Response (FIR) form of the periodic steady state Kalman filter is derived.

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.

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 Response of a swirl flame to inertial waves

2017 ◽  
Vol 10 (4) ◽  
pp. 277-286 ◽  
Author(s):  
Alp Albayrak ◽  
Deniz A Bezgin ◽  
Wolfgang Polifke
Keyword(s):  
Steady State ◽  
Impulse Response ◽  
Finite Impulse Response ◽  
Reactive Flow ◽  
Inertial Waves ◽  
Mean Flow ◽  
Flow Equations ◽  
Flame Response ◽  
Inertial Wave ◽  
The Impact

Acoustic waves passing through a swirler generate inertial waves in rotating flow. In the present study, the response of a premixed flame to an inertial wave is scrutinized, with emphasis on the fundamental fluid-dynamic and flame-kinematic interaction mechanism. The analysis relies on linearized reactive flow equations, with a two-part solution strategy implemented in a finite element framework: Firstly, the steady state, low-Mach number, Navier–Stokes equations with Arrhenius type one-step reaction mechanism are solved by Newton’s method. The flame impulse response is then computed by transient solution of the analytically linearized reactive flow equations in the time domain, with mean flow quantities provided by the steady-state solution. The corresponding flame transfer function is retrieved by fitting a finite impulse response model. This approach is validated against experiments for a perfectly premixed, lean, methane-air Bunsen flame, and then applied to a laminar swirling flame. This academic case serves to investigate in a generic manner the impact of an inertial wave on the flame response. The structure of the inertial wave is characterized by modal decomposition. It is shown that axial and radial velocity fluctuations related to the eigenmodes of the inertial wave dominate the flame front modulations. The dispersive nature of the eigenmodes plays an important role in the flame response.

Exact Deadbeat Controller Design From N Impulse Response Samples

1986 ◽  
Vol 108 (1) ◽  
pp. 65-68 ◽  
Author(s):  
R. E. Rink
Keyword(s):  
Steady State ◽  
Impulse Response ◽  
Controller Design ◽  
Open Loop ◽  
Step Response ◽  
Simple Method ◽  
Arbitrary Type ◽  
Pi Controllers ◽  
State Tracking ◽  
Time Invariant

A simple method is given for the design of exact deadbeat regulators and PI controllers when only N impulse or step response samples from the process are available. It is required that the process be linear, controllable, observable, time invariant, and that N≥2n, where n is the degree of the process. It is not required that the process be open-loop stable, in distinction with previously-given simple methods. This makes it easy to include any number of integrations in the controller to achieve steady-state tracking properties of arbitrary type.

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.

scholarly journals An Improved Initial Alignment Method for Rocket Navigation Systems

2013 ◽  
Vol 66 (5) ◽  
pp. 737-749 ◽  
Author(s):  
Lihua Zhu ◽  
Xianghong Cheng
Keyword(s):  
Kalman Filter ◽  
Impulse Response ◽  
Finite Impulse Response ◽  
Wind Effect ◽  
Navigation Systems ◽  
Alignment Method ◽  
Initial Alignment ◽  
Online Estimation ◽  
Sensor Errors ◽  
Lever Arm Effect

This paper proposes an algorithm for the initial alignment method for rocket navigation systems. It uses the inertial freezing alignment to resolve the attitude matrix with respect to its fast and robust characteristics. Due to disturbances from the swaying base environment, such as people walking and wind effect, which would consequently result in a great lever arm effect, a Finite Impulse Response (FIR) filter is utilized to decrease the noise in the accelerometers' measurement. In addition, there are sensor errors in the system; the online estimation of gyroscopes' drift with a Kalman filter is adopted to achieve compensation. Numerical results from a simulated rocket initial alignment experiment are reported to demonstrate the effectiveness of the method.

scholarly journals Single-agent Finite Impulse Response Optimizer vs Simulated Kalman Filter Optimizer

Mekatronika ◽  
2019 ◽  
Vol 1 (2) ◽  
pp. 15-22
Author(s):  
Tasiransurini Ab Rahman ◽  
Nor Azlina Ab. Aziz ◽  
Nor Hidayati Abdul Aziz
Keyword(s):  
Kalman Filter ◽  
Impulse Response ◽  
Optimization Algorithm ◽  
Applied Research ◽  
Finite Impulse Response ◽  
Single Agent ◽  
Optimal Solution ◽  
Optimal Estimation ◽  
Performance Comparison ◽  
Repetition Number

Single-agent Finite Impulse Response Optimizer (SAFIRO) is a new estimation-based optimization algorithm which mimics the work procedure of the ultimate unbiased finite impulse response (UFIR) filter. In a real UFIR filter, the horizon length, N, plays an important role to obtain the optimal estimation. In SAFIRO, N represents the repetition number of estimation part that needs to be done in find-ing an optimal solution. On the other hand, Simulated Kalman Filter (SKF) is also an estimation- based optimization algorithm inspired by the estimation capability of Kalman filtering. In literature, substantial amount of works has been devoted to SKF, both in applied research and fundamental enhancements. Thus, in this paper, a performance comparison of both SAFIRO and SKF is presented. It is found that the SAFIRO outperforms the SKF significantly.

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