Suboptimal Filtering Algorithm Research Articles

Optimal Estimation in UDP-Like Networked Control Systems With Intermittent Inputs: Stability Analysis and Suboptimal Filter Design

We investigate the optimal estimation problem in lossy networked control systems where the control packets are randomly dropped without acknowledgment to the estimator. Most existing results for this setup are concerned with the design of controller, while the optimal estimation and its performance evaluation have been rarely treated. In this paper, we show that, unlike many other cases such as intermittent observations or TCP-like systems, the system state follows a Gaussian mixture distribution with exponentially increasing terms, which leads to a Gaussian sum filter-based optimal estimation. We develop an auxiliary estimator method to establish necessary and sufficient conditions for the stability of the mean estimation error covariance matrices. It is revealed that the stability is independent of the packet loss rate, and is not affected by the lack of acknowledgment. A suboptimal filtering algorithm with improved computational efficiency is then developed. Numerical examples and simulations are employed to illustrate the theoretical results.

Suboptimal filtering algorithms in the schemes of interconnecting inertial-satellite systems that are based on the method of compensation

Suboptimal filtering algorithms in the schemes of interconnecting inertial-satellite systems that are based on the method of compensation

Conditionally Suboptimal Filtering in Nonlinear Stochastic Differential System

This paper presents a novel conditionally suboptimal filtering algorithm on estimation problems that arise in discrete nonlinear time-varying stochastic difference systems. The suboptimal state estimate is formed by summing of conditionally nonlinear filtering estimates that their weights depend only on time instants, in contrast to conditionally optimal filtering, the proposed conditionally suboptimal filtering allows parallel processing of information and reduce online computational requirements in some nonlinear stochastic difference system. High accuracy and efficiency of the conditionally suboptimal nonlinear filtering are demonstrated on a numerical example.

SUBOPTIMAL STATE ESTIMATION FOR UNCERTAIN MULTISENSOR DISCRETE-TIME LINEAR STOCHASTIC SYSTEMS

The problem of recursive estimation for uncertain multisensor linear discrete-time systems is considered. A new suboptimal filtering algorithm is herein proposed. It is based on the fusion formula for an arbitrary number of local Kalman filters. Each local Kalman filter is fused by the minimum mean square error criterion. The suboptimal gains and weights do not depend on current observations; therefore the proposed filter can easily be implemented in real-time. The examples demonstrate the efficiency and high-accuracy of the proposed filter.

Tracking of multiple maneuvering targets using multiscan JPDA and IMM filtering

The paper considers the problem of tracking multiple maneuvering targets in the presence of clutter using switching multiple target motion models. A novel suboptimal filtering algorithm is developed by applying the basic interacting multiple model (IMM) approach and the joint probabilistic data association (JPDA) technique. Unlike the standard single-scan JPDA approach, the authors exploit a multiscan joint probabilistic data association (mscan-JPDA) approach to solve the data association problem. The algorithm is illustrated via a simulation example involving tracking of four maneuvering targets and a multiscan data window of length two

Suboptimal estimation of signals from uncertain observations using approximations of mixtures

In this paper, we propose a suboptimal filtering algorithm for the estimation of a Gaussian signal from uncertain observations, using covariance information. The suboptimal estimators are obtained as the expectation of the signal, given the observations, when a certain approximation is considered for the conditional distribution. The approximation is carried out via successive approximations of mixtures of Gaussian distributions by Gaussian distributions. On the other hand, by assuming that the uncertainty probability is unknown, a recursive estimation algorithm is proposed for that probability. This algorithm is obtained under a Bayesian viewpoint; specifically, by considering a Beta as the a priori distribution for the unknown parameter, the proposed estimators provide approximations for the mean of the a posteriori distributions.

Tracking of multiple maneuvering targets in clutter using multiple sensors, IMM, and JPDA coupled filtering

We consider the problem of tracking multiple maneuvering targets in clutter using switching multiple target motion models. A novel suboptimal filtering algorithm is developed by applying the basic interacting multiple model (IMM) approach, the joint probabilistic data association (JPDA) technique and coupled target state estimation to a Markovian switching system. The algorithm is illustrated via a simulation example involving tracking of two highly maneuvering, at times closely spaced, targets.

Tracking of multiple maneuvering targets in clutter using IMM/JPDA filtering and fixed-lag smoothing

We consider the problem of tracking multiple maneuvering targets in clutter using switching multiple target motion models. A suboptimal filtering algorithm is developed by applying the basic interacting multiple model (IMM) approach and the joint probabilistic data association (JPDA) technique to a Markovian switching system. A suboptimal fixed-lag smoothing algorithm is developed by applying the IMM and the JPDA approaches to a state-augmented system. The algorithms are illustrated via a simulation example involving tracking of two highly maneuvering targets.

Lumpable hidden Markov models-model reduction and reduced complexity filtering

This paper is concerned with filtering of hidden Markov processes (HMP) which possess (or approximately possess) the property of lumpability. This property is a generalization of the property of lumpability of a Markov chain which has been previously addressed by others. In essence, the property of lumpability means that there is a partition of the (atomic) states of the Markov chain into aggregated sets which act in a similar manner as far as the state dynamics and observation statistics are concerned. We prove necessary and sufficient conditions on the HMP for exact lumpability to hold. For a particular class of hidden Markov models (HMM), namely finite output alphabet models, conditions for lumpability of all HMP representable by a specified HMM are given. The corresponding optimal filter algorithms for the aggregated states are then derived. The paper also describes an approach to efficient suboptimal filtering for HMP which are approximately lumpable. By this we mean that the HMM generating the process may be approximated by a lumpable HMM. This approach involves directly finding a lumped HMM which approximates the original HMM well, in a matrix norm sense. An alternative approach for model reduction based on approximating a given HMM by an exactly lumpable HMM is also derived. This method is based on the alternating convex projections algorithm. Some simulation examples are presented which illustrate the performance of the suboptimal filtering algorithms.

Fault-Tolerant Data Processing in an Integrated Airborne Navigational Equipment

Abstract This paper presents the structure and algorithms of fault - tolerant data processing in an integrated airborne navigational equipment. Failures and malfunctions of different sensors have been described by the additive Gauss-Markov models and by the outliers with the Markov chain properties. For such models suboptimal integrated filtering algorithms have been developed using a problem decomposition, the Gauss approximation method and the generalized likelihood ratio (GLR) approach. It is shown that the system structure contains a GLR failure detector, a multichannel outliers screening procedure and a bias cancellation circuit

Suboptimal sensors location in the state estimation problem for stochastic non-linear distributed parameter systems

The present paper deals with the minimal number sensor choice and their optimal location for the estimation in non-linear stochastic distributed parameter systems described by parabolic and hyperbolic partial differential equations. The necessary condition for the optimal sensor location by using the matrix minimum principle was obtained. In turn, the computational algorithm of the sensors location was determined on the basis of the necessary condition, applying the optimal control theory. The computational efficiency of this algorithm is defined by the suboptimal filtering algorithm which does not require solving of the matrix Riccati equation for the filter error covariance. Finally, one example is given to demonstrate the effectiveness of the present approach.