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Proceedings ArticleDOI

A bearings-only-tracking framework based on the EKF and UKF combined algorithm

Bin Liu1, Xiaochuan Ma1, Chengpeng Hao1, Chaohuan Hou1, Mei Li1 
01 Nov 2007-pp 184-187
TL;DR: This paper delicately compares both of the computing burdens and performances of EKF and UKF in a two-dimensional BOT scenario, and finally proposes a new time-efficiency framework that combines EKFs together to fulfill the estimation process.
Abstract: Bearings-only tracking (BOT) is with the common interest in array signal processing society and is actually a nonlinear estimation process which acts as a posterior one of beamforming. Extended Kalman filter (EKF) which is commonly used in BOT inherits Kalman Filter (KF)'s advantage in having good computational efficiency, but often leads to unstable estimations. Particle filtering (PF) and Unscented Kalman filtering (UKF) are recently suggested for stability improvements, and UKF is suggested more suitable for real-time applications than PF. This paper delicately compares both of the computing burdens and performances of EKF and UKF in a two-dimensional BOT scenario, and finally proposes a new time-efficiency framework that combines EKF and UKF together to fulfill the estimation process. Simulation results and theoretical analyses are included for presenting the new framework.
Citations
More filters
Journal ArticleDOI
TL;DR: A particle filtering algorithm is derived for estimating the model's parameters in a sequential manner and shows that the proposed solution provides a significant benefit over the most commonly used methods, IPDA and IMMPDA.
Abstract: The tracking initiation problem is examined in the context of autonomous bearings-only-tracking (BOT) of a single appearing/disappearing target in the presence of clutter measurements. In general, this problem suffers from a combinatorial explosion in the number of potential tracks resulted from the uncertainty in the linkage between the target and the measurement (a.k.a the data association problem). In addition, the nonlinear measurements lead to a non-Gaussian posterior probability density function (pdf) in the optimal Bayesian sequential estimation framework. The consequence of this nonlinear/non-Gaussian context is the absence of a closed-form solution. This paper models the linkage uncertainty and the nonlinear/non-Gaussian estimation problem jointly with solid Bayesian formalism. A particle filtering (PF) algorithm is derived for estimating the model's parameters in a sequential manner. Numerical results show that the proposed solution provides a significant benefit over the most commonly used methods, IPDA and IMMPDA. The posterior Cramer-Rao bounds are also involved for performance evaluation.

5 citations

Proceedings ArticleDOI
19 Jun 2019
TL;DR: In this paper, an unscented Kalman filter (UKF) was proposed to estimate the moment of inertia for permanent magnet synchronous motors (PMSMs) control system.
Abstract: This paper proposes a novel method to estimate the moment of inertia for permanent magnet synchronous motors (PMSMs) control system. It is based on unscented Kalman filter (UKF). Compared with the conventional method extended Kalman filter(EKF), UKF approximates the probability density distribution of a nonlinear function, rather than using first-order linearization method to approximate. The calculation accuracy of nonlinear distribution statistic based on UKF is able to reach second-order at least, and the validity of the proposed algorithm is proved by computer simulations compared with the conventional method.

4 citations


Cites methods from "A bearings-only-tracking framework ..."

  • ...In order to overcome these shortcomings of EKF, in 1997, Julier and Uhlmann of the University of Oxford in the United Kingdom proposed an evolutionary algorithm for EKF—the unscented Kalman filter (UKF) [9]....

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Proceedings ArticleDOI
01 Jul 2017
TL;DR: A novel approach to an estimator design, the cooperative filter design, for state estimation of nonlinear systems, based on the idea of combining estimates of several different approximate nonlinear filters, which are configured to perform the same task.
Abstract: The paper introduces a novel approach to an estimator design, the cooperative filter design, for state estimation of nonlinear systems. The approach is based on the idea of combining estimates of several different approximate (and thus sub-optimal) nonlinear filters, which are configured to perform the same task. Within the concept, two strategies are proposed, namely the cooperative estimation and cooperative monitoring. The strategies have the potential of an improvement of the estimation performance in terms of accuracy and consistency, which was confirmed by a numerical illustration.

3 citations


Cites background from "A bearings-only-tracking framework ..."

  • ...It is also worth noting, that an EKF and UKF combined algorithm was proposed in [20]....

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Dissertation
21 Nov 2017
TL;DR: A new type of filter is proposed where particles in addition to a (linearized) Gaussian component are tracked, which can be seen as a parallel solution to the estimation problem, each component can be separately filtered and constituent outputs summed up to form the filtering distribution.
Abstract: Conventional solutions to nonlinear filtering problems fall into two categories, deterministic and stochastic approaches. While the former is heavily used due to low computational demand, approximation error is tied to their initialization, which causes difficulty during long term application. The latter circumvents this but at the cost of a significant increase in computation. An extremely popular stochastic filter termed the particle filter is especially notorious for this. However its superior performance (over the conventional nonlinear filters) and generality of use makes it ideal in environments where high nonlinearity plagues the state-space model. Estimation error and computational complexity for the particle filter are both related to the number of particles utilized. Yet, many researchers have observed that particles in the vicinity of one another, perhaps because they represent the same state, might be redundant. A new type of filter is proposed where particles in addition to a (linearized) Gaussian component are tracked. This can be seen as a parallel solution to the estimation problem, each component can be separately filtered and constituent outputs summed up to form the filtering distribution. This new filter is then used in two classical scenarios used to benchmark nonlinear filters.

3 citations


Cites methods from "A bearings-only-tracking framework ..."

  • ...al proposed an EKF and UKF switching filter, where the accuracy of estimation was fulfilled using a switching mechanism related to the trace of the previous iteration covariance matrix [19]....

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Proceedings ArticleDOI
20 Dec 2008
TL;DR: Simulation results show that STF_UKF is feasible and effective in tracking maneuvering target, especially when initial state deviation and measurement noise are great.
Abstract: The bearings-only tracking problem (BOT) has been studied for many years and UKF has extensively been applied in passive non-maneuvering target tracking. When target takes maneuver, the estimation will diverge. STF can track the abrupt change of state by tuning the gain matrix online. Based on the advantages of STF and UKF, a new method, STF_UKF, is proposed to track maneuvering target with bearings-only measurements from two separate stationary observers. Simulation results show that STF_UKF is feasible and effective in tracking maneuvering target, especially when initial state deviation and measurement noise are great.

2 citations


Cites background from "A bearings-only-tracking framework ..."

  • ...UKF is promising in nonlinear filtering problem and a variety of UKF-type passive tracking filters [1-4] have been reported....

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References
More filters
Journal ArticleDOI
TL;DR: Both optimal and suboptimal Bayesian algorithms for nonlinear/non-Gaussian tracking problems, with a focus on particle filters are reviewed.
Abstract: Increasingly, for many application areas, it is becoming important to include elements of nonlinearity and non-Gaussianity in order to model accurately the underlying dynamics of a physical system. Moreover, it is typically crucial to process data on-line as it arrives, both from the point of view of storage costs as well as for rapid adaptation to changing signal characteristics. In this paper, we review both optimal and suboptimal Bayesian algorithms for nonlinear/non-Gaussian tracking problems, with a focus on particle filters. Particle filters are sequential Monte Carlo methods based on point mass (or "particle") representations of probability densities, which can be applied to any state-space model and which generalize the traditional Kalman filtering methods. Several variants of the particle filter such as SIR, ASIR, and RPF are introduced within a generic framework of the sequential importance sampling (SIS) algorithm. These are discussed and compared with the standard EKF through an illustrative example.

11,409 citations


"A bearings-only-tracking framework ..." refers background in this paper

  • ...But the PF always needs several orders of magnitude more computational effort than that required by an EKF to achieve reliable estimate, so it’s intractable to usage in a real-time setting[4,5]....

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BookDOI
01 Jan 2001
TL;DR: This book presents the first comprehensive treatment of Monte Carlo techniques, including convergence results and applications to tracking, guidance, automated target recognition, aircraft navigation, robot navigation, econometrics, financial modeling, neural networks, optimal control, optimal filtering, communications, reinforcement learning, signal enhancement, model averaging and selection.
Abstract: Monte Carlo methods are revolutionizing the on-line analysis of data in fields as diverse as financial modeling, target tracking and computer vision. These methods, appearing under the names of bootstrap filters, condensation, optimal Monte Carlo filters, particle filters and survival of the fittest, have made it possible to solve numerically many complex, non-standard problems that were previously intractable. This book presents the first comprehensive treatment of these techniques, including convergence results and applications to tracking, guidance, automated target recognition, aircraft navigation, robot navigation, econometrics, financial modeling, neural networks, optimal control, optimal filtering, communications, reinforcement learning, signal enhancement, model averaging and selection, computer vision, semiconductor design, population biology, dynamic Bayesian networks, and time series analysis. This will be of great value to students, researchers and practitioners, who have some basic knowledge of probability. Arnaud Doucet received the Ph. D. degree from the University of Paris-XI Orsay in 1997. From 1998 to 2000, he conducted research at the Signal Processing Group of Cambridge University, UK. He is currently an assistant professor at the Department of Electrical Engineering of Melbourne University, Australia. His research interests include Bayesian statistics, dynamic models and Monte Carlo methods. Nando de Freitas obtained a Ph.D. degree in information engineering from Cambridge University in 1999. He is presently a research associate with the artificial intelligence group of the University of California at Berkeley. His main research interests are in Bayesian statistics and the application of on-line and batch Monte Carlo methods to machine learning. Neil Gordon obtained a Ph.D. in Statistics from Imperial College, University of London in 1993. He is with the Pattern and Information Processing group at the Defence Evaluation and Research Agency in the United Kingdom. His research interests are in time series, statistical data analysis, and pattern recognition with a particular emphasis on target tracking and missile guidance.

6,574 citations


"A bearings-only-tracking framework ..." refers background in this paper

  • ...But the PF always needs several orders of magnitude more computational effort than that required by an EKF to achieve reliable estimate, so it’s intractable to usage in a real-time setting[4,5]....

    [...]

Journal ArticleDOI
08 Nov 2004
TL;DR: The motivation, development, use, and implications of the UT are reviewed, which show it to be more accurate, easier to implement, and uses the same order of calculations as linearization.
Abstract: The extended Kalman filter (EKF) is probably the most widely used estimation algorithm for nonlinear systems. However, more than 35 years of experience in the estimation community has shown that is difficult to implement, difficult to tune, and only reliable for systems that are almost linear on the time scale of the updates. Many of these difficulties arise from its use of linearization. To overcome this limitation, the unscented transformation (UT) was developed as a method to propagate mean and covariance information through nonlinear transformations. It is more accurate, easier to implement, and uses the same order of calculations as linearization. This paper reviews the motivation, development, use, and implications of the UT.

6,098 citations


"A bearings-only-tracking framework ..." refers background in this paper

  • ...Readers can consult [10] for a comparison of accuracy between the two kinds of filters....

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Proceedings ArticleDOI
28 Jul 1997
TL;DR: It is argued that the ease of implementation and more accurate estimation features of the new filter recommend its use over the EKF in virtually all applications.
Abstract: The Kalman Filter (KF) is one of the most widely used methods for tracking and estimation due to its simplicity, optimality, tractability and robustness. However, the application of the KF to nonlinear systems can be difficult. The most common approach is to use the Extended Kalman Filter (EKF) which simply linearizes all nonlinear models so that the traditional linear Kalman filter can be applied. Although the EKF (in its many forms) is a widely used filtering strategy, over thirty years of experience with it has led to a general consensus within the tracking and control community that it is difficult to implement, difficult to tune, and only reliable for systems which are almost linear on the time scale of the update intervals. In this paper a new linear estimator is developed and demonstrated. Using the principle that a set of discretely sampled points can be used to parameterize mean and covariance, the estimator yields performance equivalent to the KF for linear systems yet generalizes elegantly to nonlinear systems without the linearization steps required by the EKF. We show analytically that the expected performance of the new approach is superior to that of the EKF and, in fact, is directly comparable to that of the second order Gauss filter. The method is not restricted to assuming that the distributions of noise sources are Gaussian. We argue that the ease of implementation and more accurate estimation features of the new filter recommend its use over the EKF in virtually all applications.

5,314 citations


Additional excerpts

  • ...it can result in non-stable estimates[3]....

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Proceedings ArticleDOI
01 Oct 2000
TL;DR: The unscented Kalman filter (UKF) as discussed by the authors was proposed by Julier and Uhlman (1997) for nonlinear control problems, including nonlinear system identification, training of neural networks, and dual estimation.
Abstract: This paper points out the flaws in using the extended Kalman filter (EKE) and introduces an improvement, the unscented Kalman filter (UKF), proposed by Julier and Uhlman (1997). A central and vital operation performed in the Kalman filter is the propagation of a Gaussian random variable (GRV) through the system dynamics. In the EKF the state distribution is approximated by a GRV, which is then propagated analytically through the first-order linearization of the nonlinear system. This can introduce large errors in the true posterior mean and covariance of the transformed GRV, which may lead to sub-optimal performance and sometimes divergence of the filter. The UKF addresses this problem by using a deterministic sampling approach. The state distribution is again approximated by a GRV, but is now represented using a minimal set of carefully chosen sample points. These sample points completely capture the true mean and covariance of the GRV, and when propagated through the true nonlinear system, captures the posterior mean and covariance accurately to the 3rd order (Taylor series expansion) for any nonlinearity. The EKF in contrast, only achieves first-order accuracy. Remarkably, the computational complexity of the UKF is the same order as that of the EKF. Julier and Uhlman demonstrated the substantial performance gains of the UKF in the context of state-estimation for nonlinear control. Machine learning problems were not considered. We extend the use of the UKF to a broader class of nonlinear estimation problems, including nonlinear system identification, training of neural networks, and dual estimation problems. In this paper, the algorithms are further developed and illustrated with a number of additional examples.

3,903 citations


"A bearings-only-tracking framework ..." refers result in this paper

  • ...Experimental results indicate that UKFs yield results comparable to a third order Taylor series expansion of the state-model[9], while EKF of course only are accurate to a first order linearization....

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