Extended target tracking using an IMM based Rao-Blackwellised unscented Kalman filter (original) (raw)
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This paper consider the nonlinear state estimate problem for tracking maneuvering targets. Two methods are introduced to overcome the difficulty of non-linear model. The first method uses Interacting Multiple Model (IMM) which includes 2, 3, 4 and 10 models. These models are linear, each model stands for an operation point of the nonlinear model. Two model sets are designed using Equal-Distance Model-Set Design for each. The effect of increasing the number of models, separation between them and noise effect on the accuracy is introduced. The second method uses Second order Extended Kalman Filter (EKF2) which is a single nonlinear filter. Both methods are evaluated by simulation using two scenarios. A comparison between them is evaluated by computing their accuracy, change of operation range and computational complexity (computational time) at different measurement noise. Based on this study for small range of variation of nonlinear parameter, and low noise the EKF2 introduced quick and accurate tracking. For a large range of nonlinearity and good separation between models of IMM, at minimum noise large and small numbers of models of IMM introduced best accuracy but as the noise increase large number keeps higher accuracy until the large numbers and small numbers of IMM introduced bad accuracy. At high noise optimizing number of models and separation between model sets, IMM introduces better accuracy.
IMM-UKF algorithm and IMM-EKF algorithm for tracking highly maneuverable target: a comparison
2005
This paper aims to contribute in solving the problem of model-based body motion estimation by using data coming from visual sensors. We consider the case of state estimation in jump Markov nonlinear systems. 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 compare the results given by an IMM algorithm Extended Kalman filter based (IMM-EKF) versus those given by an IMM algorithm Unscented Kalman filter based (IMM-UKF) in tracking target assumed to be highly maneuverable.
Second-order EKF and Unscented Kalman Filter Fusion for Tracking Maneuvering Targets
2007 IEEE International Conference on Information Reuse and Integration, 2007
When dealing with target tracking problem for maneuvering targets, it may be the case that a first order extended Kalman filter can not track the target and diverges due to neglecting the higher order terms of Taylor series. This paper studies two other filters which are more appropriate for maneuvering targets (with nonlinear state space equations). These two filters are entitled as second-order extended Kalman filter (SOEKF) and unscented Kalman filter (UKF). SOEKF uses Hessian matrix (second term of Taylor series) which may help solving the divergence problem. UKF is also useful as it works with the main nonlinear formula without the need to use any approximation. Both of the state space equations (process equation and measurement equation) is assumed to be nonlinear. In order to enhance the accuracy of tracking process sensor fusion approach is also applied for both of the filters. The number of sensors is assumed to be two. A comparison analysis is made between the two filters alone (without fusion approach) and also when sensor fusion is applied.
IMM-LMMSE filtering algorithm for ballistic target tracking with unknown ballistic coefficient
Proceedings of SPIE - The International Society for Optical Engineering, 2006
For ballistic target tracking using radar measurements in the polar or spherical coordinates, various nonlinear filters have been studied. Previous work often assumes that the ballistic coefficient of a missile target is known to the filter, which is unrealistic in practice. In this paper, we study the ballistic target tracking problem with unknown ballistic coefficient. We propose a general scheme to handle nonlinear systems with a nuisance parameter. The interacting multiple model (IMM) algorithm is employed and for each model the linear minimum mean square error (LMMSE) filter is used. Although we assume that the nuisance parameter is random and time invariant, our approach can be extended to time varying case. A useful property of the model transition probability matrix (TPM) is studied which provides a viable way to tune the model probability. In simulation studies, we illustrate the design of the TPM and compare the proposed method with another two IMM-based algorithms where the extended Kalman filter (EKF) and the unscented filter (UF) are used for each model, respectively. We conclude that the IMM-LMMSE filter is preferred for the problem being studied.
A study of a nonlinear filtering problem for tracking an extended target
2004
The paper presents an analysis of a nonlinear filtering problem corresponding to tracking of an extended target whose shape is modelled by an ellipse. The measurements of target extent are assumed to be available in addition to the usual positional measurements. Using Cramer-Rao bounds we establish the best achievable error performance for this highly nonlinear problem. The theoretical bounds are used to examine the performance as a function of measurement accuracy, observer-target geometry and prior knowledge of shape parameters. Finally an extended Kalman filter (KF) and an unscented KF are developed for this application and their performance (consistency and RMS error) are examined.
Adaptive IMM-UKF for Airborne Tracking
Aerospace
In this paper, we propose a nonlinear tracking solution for maneuvering aerial targets based on an adaptive interacting multiple model (IMM) framework and unscented Kalman filters (UKFs), termed as AIMM-UKF. The purpose is to obtain more accurate estimates, better consistency of the tracker, and more robust prediction during sensor outages. The AIMM-UKF framework provides quick switching between two UKFs by adapting the transition probabilities between modes based on a distance function. Two modes are implemented: a uniform motion model and a maneuvering model. The experimental validation is performed with Monte Carlo simulations of three scenarios with ACAS Xa tracking logic as a benchmark, which is the next generation of airborne collision avoidance systems. The two algorithms are compared using hypothesis testing of the root mean square errors. In addition, we determine the normalized estimation error squared (NEES), a new proposed noise reduction factor to compare the estimation...
2018
A 3D target model expressed in intrinsic coordinates will be developed in this article. The frame used is the Frenet-Serret frame, that is a practical frame to represent the commands a pilot can have on his aircraft for instance. A quite accurate description of the possible motions of an aircraft is to assume the commands are piecewise constant. Once the target model is derived, a ltering algorithm is needed to perform state estimation. As the target model is not expressed in a vectorial space, but rather in a Lie group setting, a novel algorithm, based on results from the inertial navigation eld has to be established. This new lter is called the Invariant Extended Kalman Filter (IEKF). Résumé: Cet article présente un modèle de cible en 3D et en coordonnées intrinsèques. Le repère de Frenet-Serret est utilisé, il permet de représenter les commandes qu'un pilote peut avoir sur son appareil par exemple. Une description relativement réaliste des mouvements possibles d'un avion ...
An Overview on Target Tracking Using Multiple Model Methods
2008
representativos descritos são o Minimum Mean Square Error Autonomous Multiple Model (MMSE-AMM), o Interacting Multiple Model (IMM) e o Likely Model-Set (LMS). Relativamente ao seguimento de múltiplos objectos, dois algoritmos são descritos e simulados. O primeiro combina o algoritmo IMM com o Joint Probabilistic Data Association Filter (JPDAF); o segundoé um algoritmo novo baseado nos algoritmos LMS e JPDAF. O MMSE-AMMé o mais simples e fraco dos algoritmos para seguimento de um objecto; a complexidade e desempenho do IMM e LMS são semelhantes, mas o LMS tem mais espaço para melhorar e provavelmente irá suplantar o IMM (e o MMSE-AMM). No exemplo simulado na presença de múltiplos objectos, o algoritmo proposto LMS-JPDAF suplanta o desempenho do IMM-JPDAF na presença de incerteza na origem das observações, apesar de mostrar um pior seguimento dos objectos quando estes estão afastados. Palavras-chave: Seguimento de Objectos, Estimação multi-modelo, Data Association iii iv Abstract The aim of this thesis is to present a collection of multiple model (MM) algorithms capable of single or multiple target tracking by solving one or both target motion and measurement origin uncertainties. Furthermore, this thesis introduces a new MM algorithm for multiple target tracking. A single target position estimation is based on MM estimators (composed of Kalman filters banks) with the help of sensor measurements. The three MM generations are presented along with a description and simulation of a representative algorithm. These generations are: i) the Autonomous, ii) the Cooperative and iii) the Variable Structure. The correspondent representative algorithms described are the Minimum Mean Square Error Autonomous Multiple Model (MMSE-AMM), the Interacting Multiple Model (IMM) and the Likely Model-Set (LMS). Regarding the tracking in the presence of the multiple targets two algortihms are described and simulated. The first combines the IMM and Joint Probabilistic Data Association Filter (JPDAF) algorithm, the second is a new algorithm based on the LMS and on the JPDAF. The MMSE-AMM is the simplest and poorer single target tracker; the IMM and LMS complexity and responses are similar but the LMS has further room for improvement and will probabilly surpass the IMM (and the MMSE-AMM) performance. On the multiple target example simulated, the proposed LMS-JPDAF surpassed the IMM-JPDAF tracking performance under measurement origin uncertainty, although provided a worse overall single target tracking when the targets are far apart.
Performance comparison of EKF and particle filtering methods for maneuvering targets
Digital Signal Processing, 2007
Online tracking of maneuvering targets is a highly nonlinear and challenging problem that involves, at every time instant, the estimation not only of the unknown state in the dynamic model describing the evolution of the target, but also the underlying model accounting for the regime of movement. In this paper we review and compare several sequential estimation procedures, that use appropriate strategies for coping with various models that account for the different modes of operation. We focus on the application of the recently proposed cost-reference particle filtering (CRPF) methodology, which aims at the estimation of the system state without using probability distributions. The resulting method has a more robust performance when compared to standard particle filtering (SPF) algorithms or the interactive multiple model (IMM) algorithm based on the use of the well known extended Kalman filter (EKF). Advantages and disadvantages of the considered algorithms are illustrated and discussed through computer simulations.