Search results for: Bayesian approach Kalman filtering approach

Authors: Farhad Asadi, S. Hossein Sadati

Abstract:

Bayesian approach can be used for parameter identification and extraction in state space models and its ability for analyzing sequence of data in dynamical system is proved in different literatures. In this paper, adaptive Kalman filter with Bayesian approach for identification of variances in measurement parameter noise is developed. Next, it is applied for estimation of the dynamical state and measurement data in discrete linear dynamical system. This algorithm at each step time estimates noise variance in measurement noise and state of system with Kalman filter. Next, approximation is designed at each step separately and consequently sufficient statistics of the state and noise variances are computed with a fixed-point iteration of an adaptive Kalman filter. Different simulations are applied for showing the influence of noise variance in measurement data on algorithm. Firstly, the effect of noise variance and its distribution on detection and identification performance is simulated in Kalman filter without Bayesian formulation. Then, simulation is applied to adaptive Kalman filter with the ability of noise variance tracking in measurement data. In these simulations, the influence of noise distribution of measurement data in each step is estimated, and true variance of data is obtained by algorithm and is compared in different scenarios. Afterwards, one typical modeling of nonlinear state space model with inducing noise measurement is simulated by this approach. Finally, the performance and the important limitations of this algorithm in these simulations are explained. 

Keywords: adaptive filtering, Bayesian approach Kalman filtering approach, variance tracking

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Authors: Mohammad Javad Mollakazemi, Farhad Asadi, Aref Ghafouri

Abstract:

Performance of different filtering approaches depends on modeling of dynamical system and algorithm structure. For modeling and smoothing the data the evaluation of posterior distribution in different filtering approach should be chosen carefully. In this paper different filtering approaches like filter KALMAN, EKF, UKF, EKS and smoother RTS is simulated in some trajectory tracking of path and accuracy and limitation of these approaches are explained. Then probability of model with different filters is compered and finally the effect of the noise variance to estimation is described with simulations results.

Keywords: Gaussian approximation, KALMAN smoother, Parameter estimation.

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Authors: S. A. Banani, M. A. Masnadi-Shirazi

Abstract:

This paper presents a new algorithm which yields a nonlinear state estimator called iterated unscented Kalman filter. This state estimator makes use of both statistical and analytical linearization techniques in different parts of the filtering process. It outperforms the other three nonlinear state estimators: unscented Kalman filter (UKF), extended Kalman filter (EKF) and iterated extended Kalman filter (IEKF) when there is severe nonlinearity in system equation and less nonlinearity in measurement equation. The algorithm performance has been verified by illustrating some simulation results.

Keywords: Extended Kalman Filter, Iterated EKF, Nonlinearstate estimator, Unscented Kalman Filter.

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Authors: Othman Maklouf, Ahmed Adwaib

Abstract:

This paper introduces a comparative study between the main GPS\INS coupling schemes, this will include the loosely coupled and tightly coupled configurations, several types of situations and operational conditions, in which the data fusion process is done using Kalman filtering. This will include the importance of sensors calibration as well as the alignment of the strap down inertial navigation system. The limitations of the inertial navigation systems are investigated.

Keywords: GPS, INS, Kalman Filter.

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Authors: Mario Mastriani, Alberto E. Giraldez

Abstract:

In this paper, a new probability density function (pdf) is proposed to model the statistics of wavelet coefficients, and a simple Kalman-s filter is derived from the new pdf using Bayesian estimation theory. Specifically, we decompose the speckled image into wavelet subbands, we apply the Kalman-s filter to the high subbands, and reconstruct a despeckled image from the modified detail coefficients. Experimental results demonstrate that our method compares favorably to several other despeckling methods on test synthetic aperture radar (SAR) images.

Keywords: Kalman's filter, shrinkage, speckle, wavelets.

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Authors: S.K. Satpathy, S.K. Nayak, K. K. Nagwanshi, S. Panda, C. Ardil

Abstract:

Image restoration involves elimination of noise. Filtering techniques were adopted so far to restore images since last five decades. In this paper, we consider the problem of image restoration degraded by a blur function and corrupted by random noise. A method for reducing additive noise in images by explicit analysis of local image statistics is introduced and compared to other noise reduction methods. The proposed method, which makes use of an a priori noise model, has been evaluated on various types of images. Bayesian based algorithms and technique of image processing have been described and substantiated with experimentation using MATLAB.

Keywords: Image Restoration, Probability DensityFunction (PDF), Neural Networks, Bayesian Classifier.

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Authors: E. Ramaraj, A. Padmapriya

Abstract:

In large Internet backbones, Service Providers typically have to explicitly manage the traffic flows in order to optimize the use of network resources. This process is often referred to as Traffic Engineering (TE). Common objectives of traffic engineering include balance traffic distribution across the network and avoiding congestion hot spots. Raj P H and SVK Raja designed the Bayesian network approach to identify congestion hors pots in MPLS. In this approach for every node in the network the Conditional Probability Distribution (CPD) is specified. Based on the CPD the congestion hot spots are identified. Then the traffic can be distributed so that no link in the network is either over utilized or under utilized. Although the Bayesian network approach has been implemented in operational networks, it has a number of well known scaling issues. This paper proposes a new approach, which we call the Pragati (means Progress) Node Popularity (PNP) approach to identify the congestion hot spots with the network topology alone. In the new Pragati Node Popularity approach, IP routing runs natively over the physical topology rather than depending on the CPD of each node as in Bayesian network. We first illustrate our approach with a simple network, then present a formal analysis of the Pragati Node Popularity approach. Our PNP approach shows that for any given network of Bayesian approach, it exactly identifies the same result with minimum efforts. We further extend the result to a more generic one: for any network topology and even though the network is loopy. A theoretical insight of our result is that the optimal routing is always shortest path routing with respect to some considerations of hot spots in the networks.

Keywords: Conditional Probability Distribution, Congestion hotspots, Operational Networks, Traffic Engineering.

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Authors: Chein-Shung Hwang, Ruei-Siang Fong

Abstract:

User-based Collaborative filtering (CF), one of the most prevailing and efficient recommendation techniques, provides personalized recommendations to users based on the opinions of other users. Although the CF technique has been successfully applied in various applications, it suffers from serious sparsity problems. The cloud-model approach addresses the sparsity problems by constructing the user-s global preference represented by a cloud eigenvector. The user-based CF approach works well with dense datasets while the cloud-model CF approach has a greater performance when the dataset is sparse. In this paper, we present a hybrid approach that integrates the predictions from both the user-based CF and the cloud-model CF approaches. The experimental results show that the proposed hybrid approach can ameliorate the sparsity problem and provide an improved prediction quality.

Keywords: Cloud model, Collaborative filtering, Hybridrecommender system

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Authors: H. Bouhamed, A. Rebai, T. Lecroq, M. Jaoua

Abstract:

The objective of our work is to develop a new approach for discovering knowledge from a large mass of data, the result of applying this approach will be an expert system that will serve as diagnostic tools of a phenomenon related to a huge information system. We first recall the general problem of learning Bayesian network structure from data and suggest a solution for optimizing the complexity by using organizational and optimization methods of data. Afterward we proposed a new heuristic of learning a Multi-Entities Bayesian Networks structures. We have applied our approach to biological facts concerning hereditary complex illnesses where the literatures in biology identify the responsible variables for those diseases. Finally we conclude on the limits arched by this work.

Keywords: Data-organization, data-optimization, automatic knowledge discovery, Multi-Entities Bayesian networks, score merging.

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Authors: Davood Shishebori, Mohammad Saber Fallah Nezhad, Sina Seifi

Abstract:

In this paper, a variable multiple dependent state (MDS) sampling plan is developed based on the process capability index using Bayesian approach. The optimal parameters of the developed sampling plan with respect to constraints related to the risk of consumer and producer are presented. Two comparison studies have been done. First, the methods of double sampling model, sampling plan for resubmitted lots and repetitive group sampling (RGS) plan are elaborated and average sample numbers of the developed MDS plan and other classical methods are compared. A comparison study between the developed MDS plan based on Bayesian approach and the exact probability distribution is carried out.

Keywords: MDS sampling plan, RGS plan, sampling plan for resubmitted lots, process capability index, average sample number, Bayesian approach.

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Authors: Amal Jmaii, Damien Rousseliere, Besma Belhadj

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We explore the relationship between internal migration and poverty in Tunisia. We present a methodology combining potential outcomes approach with multiple imputation to highlight the effect of internal migration on poverty states. We find that probability of being poor decreases when leaving the poorest regions (the west areas) to the richer regions (greater Tunis and the east regions).

Keywords: Internal migration, Bayesian approach, poverty dynamics, Tunisia.

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Authors: Chokri Slim

Abstract:

The neural network's performance can be measured by efficiency and accuracy. The major disadvantages of neural network approach are that the generalization capability of neural networks is often significantly low, and it may take a very long time to tune the weights in the net to generate an accurate model for a highly complex and nonlinear systems. This paper presents a novel Neuro-fuzzy architecture based on Extended Kalman filter. To test the performance and applicability of the proposed neuro-fuzzy model, simulation study of nonlinear complex dynamic system is carried out. The proposed method can be applied to an on-line incremental adaptive learning for the prediction of financial time series. A benchmark case studie is used to demonstrate that the proposed model is a superior neuro-fuzzy modeling technique.

Keywords: Neuro-fuzzy, Extended Kalman filter, nonlinear systems, financial time series.

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Authors: O. Nouali, A. Saidi, H. Chahrat, A. Krinah, B. Toursel

Abstract:

This article describes a Web pages automatic filtering system. It is an open and dynamic system based on multi agents architecture. This system is built up by a set of agents having each a quite precise filtering task of to carry out (filtering process broken up into several elementary treatments working each one a partial solution). New criteria can be added to the system without stopping its execution or modifying its environment. We want to show applicability and adaptability of the multi-agents approach to the networks information automatic filtering. In practice, most of existing filtering systems are based on modular conception approaches which are limited to centralized applications which role is to resolve static data flow problems. Web pages filtering systems are characterized by a data flow which varies dynamically.

Keywords: Agent, Distributed Artificial Intelligence, Multiagents System, Web pages filtering.

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Authors: Nicholas D. Assimakis

Abstract:

In linear estimation, the traditional Kalman filter uses the Kalman filter gain in order to produce estimation and prediction of the n-dimensional state vector using the m-dimensional measurement vector. The computation of the Kalman filter gain requires the inversion of an m x m matrix in every iteration. In this paper, a variation of the Kalman filter eliminating the Kalman filter gain is proposed. In the time varying case, the elimination of the Kalman filter gain requires the inversion of an n x n matrix and the inversion of an m x m matrix in every iteration. In the time invariant case, the elimination of the Kalman filter gain requires the inversion of an n x n matrix in every iteration. The proposed Kalman filter gain elimination algorithm may be faster than the conventional Kalman filter, depending on the model dimensions.

Keywords: Discrete time, linear estimation, Kalman filter, Kalman filter gain.

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Authors: Siavash Asadi Ghajarloo

Abstract:

Nowadays predicting political risk level of country has become a critical issue for investors who intend to achieve accurate information concerning stability of the business environments. Since, most of the times investors are layman and nonprofessional IT personnel; this paper aims to propose a framework named GECR in order to help nonexpert persons to discover political risk stability across time based on the political news and events. To achieve this goal, the Bayesian Networks approach was utilized for 186 political news of Pakistan as sample dataset. Bayesian Networks as an artificial intelligence approach has been employed in presented framework, since this is a powerful technique that can be applied to model uncertain domains. The results showed that our framework along with Bayesian Networks as decision support tool, predicted the political risk level with a high degree of accuracy.

Keywords: Bayesian Networks, Data mining, GECRframework, Predicting political risk.

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Authors: Dewan Md. Farid, Nguyen Huu Hoa, Jerome Darmont, Nouria Harbi, Mohammad Zahidur Rahman

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In this paper, we present a new learning algorithm for anomaly based network intrusion detection using improved self adaptive naïve Bayesian tree (NBTree), which induces a hybrid of decision tree and naïve Bayesian classifier. The proposed approach scales up the balance detections for different attack types and keeps the false positives at acceptable level in intrusion detection. In complex and dynamic large intrusion detection dataset, the detection accuracy of naïve Bayesian classifier does not scale up as well as decision tree. It has been successfully tested in other problem domains that naïve Bayesian tree improves the classification rates in large dataset. In naïve Bayesian tree nodes contain and split as regular decision-trees, but the leaves contain naïve Bayesian classifiers. The experimental results on KDD99 benchmark network intrusion detection dataset demonstrate that this new approach scales up the detection rates for different attack types and reduces false positives in network intrusion detection.

Keywords: Detection rates, false positives, network intrusiondetection, naïve Bayesian tree.

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Authors: Wissem Saidani, Yacine Morsly, Mohand Saïd Djouadi

Abstract:

In this paper, we consider the problem of tracking multiple maneuvering targets using switching multiple target motion models. With this paper, we aim to contribute in solving the problem of model-based body motion estimation by using data coming from visual sensors. The Interacting Multiple Model (IMM) algorithm is specially designed to track accurately targets whose state and/or measurement (assumed to be linear) models changes during motion transition. However, when these models are nonlinear, the IMM algorithm must be modified in order to guarantee an accurate track. In this paper we propose to avoid the Extended Kalman filter because of its limitations and substitute it with the Unscented Kalman filter which seems to be more efficient especially according to the simulation results obtained with the nonlinear IMM algorithm (IMMUKF). To resolve the problem of data association, the JPDA approach is combined with the IMM-UKF algorithm, the derived algorithm is noted JPDA-IMM-UKF.

Keywords: Estimation, Kalman filtering, Multi-Target Tracking, Visual servoing, data association.

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Authors: Zviad Ghadua, Biswa Bhattacharya

Abstract:

The Flash Flood Guidance (FFG) provides the rainfall amount of a given duration necessary to cause flooding. The approach is based on the development of rainfall-runoff curves, which helps us to find out the rainfall amount that would cause flooding. An alternative approach, mostly experimented with Italian Alpine catchments, is based on determining threshold discharges from past events and on finding whether or not an oncoming flood has its magnitude more than some critical discharge thresholds found beforehand. Both approaches suffer from large uncertainties in forecasting flash floods as, due to the simplistic approach followed, the same rainfall amount may or may not cause flooding. This uncertainty leads to the question whether a probabilistic model is preferable over a deterministic one in forecasting flash floods. We propose the use of a Bayesian probabilistic approach in flash flood forecasting. A prior probability of flooding is derived based on historical data. Additional information, such as antecedent moisture condition (AMC) and rainfall amount over any rainfall thresholds are used in computing the likelihood of observing these conditions given a flash flood has occurred. Finally, the posterior probability of flooding is computed using the prior probability and the likelihood. The variation of the computed posterior probability with rainfall amount and AMC presents the suitability of the approach in decision making in an uncertain environment. The methodology has been applied to the Posina basin in Italy. From the promising results obtained, we can conclude that the Bayesian approach in flash flood forecasting provides more realistic forecasting over the FFG.

Keywords: Flash flood, Bayesian, flash flood guidance, FFG, forecasting, Posina.

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Authors: Min Min Swe Zin

Abstract:

This paper introduces the foundations of Bayesian probability theory and Bayesian decision method. The main goal of Bayesian decision theory is to minimize the expected loss of a decision or minimize the expected risk. The purposes of this study are to review the decision process on the issue of flood occurrences and to suggest possible process for decision improvement. This study examines the problem structure of flood occurrences and theoretically explicates the decision-analytic approach based on Bayesian decision theory and application to flood occurrences in Environmental Engineering. In this study, we will discuss about the flood occurrences upon an annual maximum water level in cm, 43-year record available from 1965 to 2007 at the gauging station of Sagaing on the Ayeyarwady River with the drainage area - 120193 sq km by using Bayesian decision method. As a result, we will discuss the loss and risk of vast areas of agricultural land whether which will be inundated or not in the coming year based on the two standard maximum water levels during 43 years. And also we forecast about that lands will be safe from flood water during the next 10 years.

Keywords: Bayesian decision method, conditional binomial distribution, minimax rules, prior beta distribution.

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Authors: Nileshkumar Vaishnav, Aditya Tatu

Abstract:

An algebraic framework for processing graph signals axiomatically designates the graph adjacency matrix as the shift operator. In this setup, we often encounter a problem wherein we know the filtered output and the filter coefficients, and need to find out the input graph signal. Solution to this problem using direct approach requires O(N3) operations, where N is the number of vertices in graph. In this paper, we adapt the spectral graph partitioning method for partitioning of graphs and use it to reduce the computational cost of the filtering problem. We use the example of denoising of the temperature data to illustrate the efficacy of the approach.

Keywords: Graph signal processing, graph partitioning, inverse filtering on graphs, algebraic signal processing.

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Authors: Viliam Makis, Farnoosh Naderkhani, Leila Jafari

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In this paper, we present a model and an algorithm for the calculation of the optimal control limit, average cost, sample size, and the sampling interval for an optimal Bayesian chart to control the proportion of defective items produced using a semi-Markov decision process approach. Traditional p-chart has been widely used for controlling the proportion of defectives in various kinds of production processes for many years. It is well known that traditional non-Bayesian charts are not optimal, but very few optimal Bayesian control charts have been developed in the literature, mostly considering finite horizon. The objective of this paper is to develop a fast computational algorithm to obtain the optimal parameters of a Bayesian p-chart. The decision problem is formulated in the partially observable framework and the developed algorithm is illustrated by a numerical example.

Keywords: Bayesian control chart, semi-Markov decision process, quality control, partially observable process.

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Authors: Padmakumar S., Vivek Agarwal, Kallol Roy

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With the advent of inexpensive 32 bit floating point digital signal processor-s availability in market, many computationally intensive algorithms such as Kalman filter becomes feasible to implement in real time. Dynamic simulation of a self excited DC motor using second order state variable model and implementation of Kalman Filter in a floating point DSP TMS320C6713 is presented in this paper with an objective to introduce and implement such an algorithm, for beginners. A fractional hp DC motor is simulated in both Matlab® and DSP and the results are included. A step by step approach for simulation of DC motor in Matlab® and “C" routines in CC Studio® is also given. CC studio® project file details and environmental setting requirements are addressed. This tutorial can be used with 6713 DSK, which is based on floating point DSP and CC Studio either in hardware mode or in simulation mode.

Keywords: DC motor, DSP, Dynamic simulation, Kalman Filter

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Authors: Tijani Delleji, Mourad Zribi, Ahmed Ben Hamida

Abstract:

This paper discusses EM algorithm and Bootstrap approach combination applied for the improvement of the satellite image fusion process. This novel satellite image fusion method based on estimation theory EM algorithm and reinforced by Bootstrap approach was successfully implemented and tested. The sensor images are firstly split by a Bayesian segmentation method to determine a joint region map for the fused image. Then, we use the EM algorithm in conjunction with the Bootstrap approach to develop the bootstrap EM fusion algorithm, hence producing the fused targeted image. We proposed in this research to estimate the statistical parameters from some iterative equations of the EM algorithm relying on a reference of representative Bootstrap samples of images. Sizes of those samples are determined from a new criterion called 'hybrid criterion'. Consequently, the obtained results of our work show that using the Bootstrap EM (BEM) in image fusion improve performances of estimated parameters which involve amelioration of the fused image quality; and reduce the computing time during the fusion process.

Keywords: Satellite image fusion, Bayesian segmentation, Bootstrap approach, EM algorithm.

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Authors: Fiona Browne, Huiru Zheng, Haiying Wang, Francisco Azuaje

Abstract:

Recent years have seen a growing trend towards the integration of multiple information sources to support large-scale prediction of protein-protein interaction (PPI) networks in model organisms. Despite advances in computational approaches, the combination of multiple “omic" datasets representing the same type of data, e.g. different gene expression datasets, has not been rigorously studied. Furthermore, there is a need to further investigate the inference capability of powerful approaches, such as fullyconnected Bayesian networks, in the context of the prediction of PPI networks. This paper addresses these limitations by proposing a Bayesian approach to integrate multiple datasets, some of which encode the same type of “omic" data to support the identification of PPI networks. The case study reported involved the combination of three gene expression datasets relevant to human heart failure (HF). In comparison with two traditional methods, Naive Bayesian and maximum likelihood ratio approaches, the proposed technique can accurately identify known PPI and can be applied to infer potentially novel interactions.

Keywords: Bayesian network, Classification, Data integration, Protein interaction networks.

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Authors: Othman Maklouf, Abdurazag Ghila, Ahmed Abdulla, Ameer Yousef

Abstract:

Land vehicle navigation system technology is a subject of great interest today. Global Positioning System (GPS) is a common choice for positioning in such systems. However, GPS alone is incapable of providing continuous and reliable positioning, because of its inherent dependency on external electromagnetic signals. Inertial Navigation is the implementation of inertial sensors to determine the position and orientation of a vehicle. As such, inertial navigation has unbounded error growth since the error accumulates at each step. Thus in order to contain these errors some form of external aiding is required. The availability of low cost Micro-Electro-Mechanical-System (MEMS) inertial sensors is now making it feasible to develop Inertial Navigation System (INS) using an inertial measurement unit (IMU), in conjunction with GPS to fulfill the demands of such systems. Typically IMU’s are very expensive systems; however this INS will use “low cost” components. Unfortunately with low cost also comes low performance and is the main reason for the inclusion of GPS and Kalman filtering into the system. The aim of this paper is to develop a GPS/MEMS INS integrated system, which is able to provide a navigation solution with accuracy levels appropriate for land vehicle navigation. The primary piece of equipment used was a MEMS-based Crista IMU (from Cloud Cap Technology Inc.) and a Garmin GPS 18 PC (which is both a receiver and antenna). The integration of GPS with INS can be implemented using a Kalman filter in loosely coupled mode. In this integration mode the INS error states, together with any navigation state (position, velocity, and attitude) and other unknown parameters of interest, are estimated using GPS measurements. All important equations regarding navigation are presented along with discussion.

Keywords: GPS, IMU, Kalman Filter.

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Authors: Jian Shi, Baoguo Yu, Haonan Jia, Meng Liu, Ping Huang

Abstract:

Adapting to the flexibility of war, a large number of guided weapons launch from aircraft. Therefore, the inertial navigation system loaded in the weapon needs to undergo an alignment process in the air. This article proposes the following methods to the problem of inaccurate modeling of the system under large misalignment angles, the accuracy reduction of filtering caused by outliers, and the noise changes in GPS signals: first, considering the large misalignment errors of Strapdown Inertial Navigation System (SINS)/GPS, a more accurate model is made rather than to make a small-angle approximation, and the Unscented Kalman Filter (UKF) algorithms are used to estimate the state; then, taking into account the impact of GPS noise changes on the fine alignment algorithm, the innovation adaptive filtering algorithm is introduced to estimate the GPS’s noise in real-time; at the same time, in order to improve the anti-interference ability of the air fine alignment algorithm, a robust filtering algorithm based on outlier detection is combined with the air fine alignment algorithm to improve the robustness of the algorithm. The algorithm can improve the alignment accuracy and robustness under interference conditions, which is verified by simulation.

Keywords: Air alignment, fine alignment, inertial navigation system, integrated navigation system, UKF.

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Authors: Anant Oonsivilai, Kenedy A. Greyson

Abstract:

The growth and interconnection of power networks in many regions has invited complicated techniques for energy management services (EMS). State estimation techniques become a powerful tool in power system control centers, and that more information is required to achieve the objective of EMS. For the online state estimator, assuming the continuous time is equidistantly sampled with period Δt, processing events must be finished within this period. Advantage of Kalman Filtering (KF) algorithm in using system information to improve the estimation precision is utilized. Computational power is a major issue responsible for the achievement of the objective, i.e. estimators- solution at a small sampled period. This paper presents the optimum utilization of processors in a state estimator based on KF. The model used is presented using Petri net (PN) theory.

Keywords: Kalman filters, model, Petri Net, power system, sequential State estimator.

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Authors: Moulay A. Akhloufi, Abdelhakim Bendada

Abstract:

Face recognition in the infrared spectrum has attracted a lot of interest in recent years. Many of the techniques used in infrared are based on their visible counterpart, especially linear techniques like PCA and LDA. In this work, we introduce a probabilistic Bayesian framework for face recognition in the infrared spectrum. In the infrared spectrum, variations can occur between face images of the same individual due to pose, metabolic, time changes, etc. Bayesian approaches permit to reduce intrapersonal variation, thus making them very interesting for infrared face recognition. This framework is compared with classical linear techniques. Non linear techniques we developed recently for infrared face recognition are also presented and compared to the Bayesian face recognition framework. A new approach for infrared face extraction based on SVM is introduced. Experimental results show that the Bayesian technique is promising and lead to interesting results in the infrared spectrum when a sufficient number of face images is used in an intrapersonal learning process.

Keywords: Face recognition, biometrics, probabilistic imageprocessing, infrared imaging.

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Authors: Seok Hyoung Lee, Vladimir Shin

Abstract:

An optimal mean-square fusion formulas with scalar and matrix weights are presented. The relationship between them is established. The fusion formulas are compared on the continuous-time filtering problem. The basic differential equation for cross-covariance of the local errors being the key quantity for distributed fusion is derived. It is shown that the fusion filters are effective for multi-sensor systems containing different types of sensors. An example demonstrating the reasonable good accuracy of the proposed filters is given.

Keywords: Kalman filtering, fusion formula, multi-sensor, mean-square error.

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Authors: Gaurav Kumar, Dharmbir Prasad, Rudra Pratap Singh

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In the current work, adaptive extended Kalman filter (AEKF) is presented for solution of ground radar based ballistic missile (BM) tracking problem in re-entry phase with unknown ballistic coefficient. The estimation of trajectory of any BM in re-entry phase is extremely difficult, because of highly non-linear motion of BM. The estimation accuracy of AEKF has been tested for a typical test target tracking problem adopted from literature. Further, the approach of AEKF is compared with extended Kalman filter (EKF). The simulation result indicates the superiority of the AEKF in solving joint parameter and state estimation problems.

Keywords: Adaptive, AEKF, ballistic missile, EKF, re-entry phase, target tracking.

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