scholarly journals Minimax-robust filtering problem for stochastic sequences with stationary increments and cointegrated sequences

10.19139/56 ◽  
2014 ◽  
Vol 2 (3) ◽  
Author(s):  
Maksym Luz ◽  
Mikhail Moklyachuk
Keyword(s):  
Robust Filtering ◽  
Stationary Increments ◽  
Filtering Problem

scholarly journals Linear filtering of systems with memory and application to finance

2006 ◽  
Vol 2006 ◽  
pp. 1-26 ◽  
Author(s):  
A. Inoue ◽  
Y. Nakano ◽  
V. Anh
Keyword(s):  
Linear Filtering ◽  
Partial Observations ◽  
Filtering Algorithm ◽  
Stationary Increments ◽  
Parameter Estimations ◽  
Portfolio Problem ◽  
Systems With Memory ◽  
Two Parameters ◽  
With Memory ◽  
Filtering Problem

We study the linear filtering problem for systems driven by continuous Gaussian processes V(1) and V(2) with memory described by two parameters. The processes V(j) have the virtue that they possess stationary increments and simple semimartingale representations simultaneously. They allow for straightforward parameter estimations. After giving the semimartingale representations of V(j) by innovation theory, we derive Kalman-Bucy-type filtering equations for the systems. We apply the result to the optimal portfolio problem for an investor with partial observations. We illustrate the tractability of the filtering algorithm by numerical implementations.

scholarly journals A Robust Recursive Filter for Nonlinear Systems with Correlated Noises, Packet Losses, and Multiplicative Noises

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Hua-Ming Qian ◽  
Wei Huang ◽  
Biao Liu ◽  
Chen Shen
Keyword(s):  
Nonlinear Systems ◽  
Random Variables ◽  
Robust Filtering ◽  
Packet Losses ◽  
Recursive Filter ◽  
Bernoulli Random Variables ◽  
Multiplicative Noises ◽  
Measurement Noises ◽  
Correlated Noises ◽  
Filtering Problem

A robust filtering problem is formulated and investigated for a class of nonlinear systems with correlated noises, packet losses, and multiplicative noises. The packet losses are assumed to be independent Bernoulli random variables. The multiplicative noises are described as random variables with bounded variance. Different from the traditional robust filter based on the assumption that the process noises are uncorrelated with the measurement noises, the objective of the addressed robust filtering problem is to design a recursive filter such that, for packet losses and multiplicative noises, the state prediction and filtering covariance matrices have the optimized upper bounds in the case that there are correlated process and measurement noises. Two examples are used to illustrate the effectiveness of the proposed filter.

scholarly journals Robust Filtering for Linear Equality Constrained Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-16
Author(s):  
Chuanbo Wen ◽  
Yunze Cai ◽  
Xiaoming Xu
Keyword(s):  
Discrete Time ◽  
Constrained Systems ◽  
Linear Filter ◽  
Robust Filtering ◽  
Orthogonal Factorization ◽  
Numerical Example ◽  
Linear Equality ◽  
Error System ◽  
Filtering Problem

This paper deals with the robust filtering problem for linear discrete-time constrained systems. The purpose is the design of a linear filter such that the resulting error system is bounded. An orthogonal factorization is used to decompose the original robust filtering problem into stochastic and deterministic parts, which are then solved separately. Finally, a numerical example is presented to demonstrate the applicability of the proposed method.

scholarly journals Robust Filtering Techniques for RTK Positioning in Harsh Propagation Environments

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1250
Author(s):  
Daniel Medina ◽  
Haoqing Li ◽  
Jordi Vilà-Valls ◽  
Pau Closas
Keyword(s):  
Intelligent Transportation Systems ◽  
Robust Statistics ◽  
Real Data ◽  
Transportation Systems ◽  
Global Navigation Satellite Systems ◽  
Mixed Integer ◽  
Robust Filtering ◽  
Precise Positioning ◽  
The Impact ◽  
Filtering Techniques

Global navigation satellite systems (GNSSs) play a key role in intelligent transportation systems such as autonomous driving or unmanned systems navigation. In such applications, it is fundamental to ensure a reliable precise positioning solution able to operate in harsh propagation conditions such as urban environments and under multipath and other disturbances. Exploiting carrier phase observations allows for precise positioning solutions at the complexity cost of resolving integer phase ambiguities, a procedure that is particularly affected by non-nominal conditions. This limits the applicability of conventional filtering techniques in challenging scenarios, and new robust solutions must be accounted for. This contribution deals with real-time kinematic (RTK) positioning and the design of robust filtering solutions for the associated mixed integer- and real-valued estimation problem. Families of Kalman filter (KF) approaches based on robust statistics and variational inference are explored, such as the generalized M-based KF or the variational-based KF, aiming to mitigate the impact of outliers or non-nominal measurement behaviors. The performance assessment under harsh propagation conditions is realized using a simulated scenario and real data from a measurement campaign. The proposed robust filtering solutions are shown to offer excellent resilience against outlying observations, with the variational-based KF showcasing the overall best performance in terms of Gaussian efficiency and robustness.

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