Optimal filtering for systems with unknown inputs via the descriptor Kalman filtering method

Automatica ◽  
2011 ◽  
Vol 47 (10) ◽  
pp. 2313-2318 ◽  
Author(s):  
Chien-Shu Hsieh
Keyword(s):  
Kalman Filtering ◽  
Optimal Filtering ◽  
Filtering Method ◽  
Unknown Inputs

scholarly journals Finite-time and spectral-finite methods of optimal filtering of discrete signals

2021 ◽  
pp. 154-160
Author(s):  
Ю.П. Иванов
Keyword(s):  
Kalman Filtering ◽  
Markov Property ◽  
Estimation Algorithm ◽  
Optimal Filtering ◽  
Filtering Method ◽  
Optimal Processing ◽  
Discrete Signals ◽  
Optimal Linear ◽  
Processing Accuracy ◽  
Interference Models

На основе содержания теоремы ортогонального проецирования излагаются методы оптимальных, линейных рекуррентных оценок, в общем случае, не марковских, сигналов, на фоне произвольных помех. Предлагаемые алгоритмы оптимальной обработки дискретных сигналов являются альтернативными методу фильтрации Калмана, не отличающимися заметно от них по точности обработки и являющимися более универсальными и простыми при их реализации. Универсальность исследуемых методов определяется применимостью их к широкому классу моделей сигналов, не требующих марковского свойства оцениваемого сигнала и изменения структуры алгоритма оценки в зависимости от моделей помех измерения в виде случайного коррелированного процесса или белого шума. Более простые структуры алгоритмов рассматриваемых методов по отношению к фильтрации Калмана объясняются отсутствием необходимости представления модели в пространстве состояний и требования решать нелинейное уравнение Риккати для реализации алгоритма. Спектрально-финитный алгоритм оптимальной оценки сигнала осуществляет сжатие информации в спектральном аспекте на основе использования метода нахождения собственных чисел и векторов и позволяет осуществить понижение размерности векторов результатов измерений вплоть до скалярных величин без заметной потери точности оценки. В качестве исходной информации необходимо знание корреляционной функции и математического ожидания оцениваемого дискретного сигнала и дисперсии и математического ожидания дискретной помехи. Based on the content of the orthogonal projection theorem, methods of optimal, linear recurrent estimates of, in general, non-Markov signals, against the background of arbitrary interference, are presented. The proposed algorithms for optimal processing of discrete signals are alternative to the Kalman filtering method, which do not differ significantly from them in terms of processing accuracy and are more universal and simple to implement. The universality of the studied methods is determined by their applicability to a wide class of signal models that do not require the Markov property of the estimated signal and changes in the structure of the estimation algorithm depending on the measurement interference models in the form of a random correlated process or white noise. The simpler structures of the algorithms of the methods under consideration in relation to Kalman filtering are explained by the absence of the need to represent the model in the state space and the requirement to solve the nonlinear Riccati equation for the implementation of the algorithm.

Reducing Quantitative Fluctuation of Laser-Induced Breakdown Spectroscopy by Kalman Filtering

2013 ◽  
Vol 333-335 ◽  
pp. 243-247 ◽  
Author(s):  
Lan Xiang Sun ◽  
Zhi Bo Cong ◽  
Yong Xin ◽  
Li Feng Qi ◽  
Yang Li
Keyword(s):  
Kalman Filtering ◽  
Elemental Concentration ◽  
Estimation Error ◽  
Laser Induced Breakdown Spectroscopy ◽  
System State ◽  
Large Signal ◽  
Filtering Method ◽  
Breakdown Spectroscopy ◽  
Laser Induced Breakdown ◽  
Quantitative Results

Laser-induced breakdown spectroscopy (LIBS) is excellent for its potential of online compositional analysis. Large signal fluctuation is the major obstacle of LIBS for quantitative analysis application. A kalman filtering method is proposed to estimate the elemental concentration and smooth the quantitative results. The system state model and the measurement model are deduced. The relation matrix between the measured values and system state is estimated based on calibration curve built on some standard samples, and the measurement noise matrix is estimated by the variance of multiple measurements of the spectral intensity. In order to make Kalman filter follow the changes of elemental concentration, the initial value of the covariance matrix of estimation error is reset as a certain rule. The experimental results show that the Kalman filtering method can greatly reduce the fluctuation of quantitative results and improve the measurement accuracy.

scholarly journals Globally Optimal Distributed Kalman Filtering for Multisensor Systems with Unknown Inputs

Sensors ◽  
2018 ◽  
Vol 18 (9) ◽  
pp. 2976 ◽  
Author(s):  
Yali Ruan ◽  
Yingting Luo ◽  
Yunmin Zhu
Keyword(s):  
State Estimation ◽  
Kalman Filtering ◽  
Optimal Algorithm ◽  
The State ◽  
Unknown Input ◽  
Initial Value ◽  
State Estimate ◽  
Multisensor Systems ◽  
Unknown Inputs ◽  
Augmented State

In this paper, the state estimation for dynamic system with unknown inputs modeled as an autoregressive AR (1) process is considered. We propose an optimal algorithm in mean square error sense by using difference method to eliminate the unknown inputs. Moreover, we consider the state estimation for multisensor dynamic systems with unknown inputs. It is proved that the distributed fused state estimate is equivalent to the centralized Kalman filtering using all sensor measurement; therefore, it achieves the best performance. The computation complexity of the traditional augmented state algorithm increases with the augmented state dimension. While, the new algorithm shows good performance with much less computations compared to that of the traditional augmented state algorithms. Moreover, numerical examples show that the performances of the traditional algorithms greatly depend on the initial value of the unknown inputs, if the estimation of initial value of the unknown input is largely biased, the performances of the traditional algorithms become quite worse. However, the new algorithm still works well because it is independent of the initial value of the unknown input.

scholarly journals Three Revised Kalman Filtering Models for Short-Term Rail Transit Passenger Flow Prediction

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Pengpeng Jiao ◽  
Ruimin Li ◽  
Tuo Sun ◽  
Zenghao Hou ◽  
Amir Ibrahim
Keyword(s):  
Real Time ◽  
Nonparametric Regression ◽  
Kalman Filtering ◽  
Rail Transit ◽  
Correction Coefficient ◽  
Short Term ◽  
Transit System ◽  
Filtering Method ◽  
Passenger Flow ◽  
Model Based

Short-term prediction of passenger flow is very important for the operation and management of a rail transit system. Based on the traditional Kalman filtering method, this paper puts forward three revised models for real-time passenger flow forecasting. First, the paper introduces the historical prediction error into the measurement equation and formulates a revised Kalman filtering model based on error correction coefficient (KF-ECC). Second, this paper employs the deviation between real-time passenger flow and corresponding historical data as state variable and presents a revised Kalman filtering model based on Historical Deviation (KF-HD). Third, the paper integrates nonparametric regression forecast into the traditional Kalman filtering method using a Bayesian combined technique and puts forward a revised Kalman filtering model based on Bayesian combination and nonparametric regression (KF-BCNR). A case study is implemented using statistical passenger flow data of rail transit line 13 in Beijing during a one-month period. The reported prediction results show that KF-ECC improves the applicability to historical trend, KF-HD achieves excellent accuracy and stability, and KF-BCNR yields the best performances. Comparisons among different periods further indicate that results during peak periods outperform those during nonpeak periods. All three revised models are accurate and stable enough for on-line predictions, especially during the peak periods.

An improved Kalman filtering method for indoor location

2016 ◽  
Author(s):  
Tingting Guo ◽  
Feng Qiao ◽  
Mingzhe Liu ◽  
Aidong Xu ◽  
Qinning Liu ◽  
...  
Keyword(s):  
Kalman Filtering ◽  
Indoor Location ◽  
Filtering Method
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