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## The shifted Rayleigh mixture filter for bearings-only tracking of maneuvering targets (2007)

Venue: | IEEE Transactions on Signal Processing |

Citations: | 1 - 0 self |

### Citations

778 | A new extension of the Kalman filter to nonlinear systems
- Julier, Uhlmann
- 1997
(Show Context)
Citation Context ...ich the measurements are artificially ordered and regarded as separated in time by an interval of 0 s duration. The performance of the new filter is assessed in simulations. The scenario considered is a variant of the one used by Marrs [10], which describes a target maneuvering through a cluster of sonobuoys, to illustrate the effectiveness of a particle filter (PF) in circumstances when extended Kalman filters fail. Comparisons are made with the generic PF using stratified sampling [11] in the resampling step and also with a modified version of our filter based on the unscented Kalman filter [12]. In this scenario, the performance of the SRMF is comparable to that of the PF, while reducing the computational burden by an order of 1053-587X/$25.00 © 2007 IEEE Authorized licensed use limited to: Imperial College London. Downloaded on February 1, 2010 at 12:09 from IEEE Xplore. Restrictions apply. CLARK et al.: SRMF FOR BEARINGS-ONLY TRACKING OF MANEUVERING TARGETS 3219 magnitude. The SRMF also significantly outperforms the unscented Kalman filter version of the algorithm, with respect to both accuracy and the computational demands. Notation: In Sections II–IV, denotes the subsequence of ... |

267 | Improved particle filter for nonlinear problems
- Carpenter, Clifford, et al.
- 1999
(Show Context)
Citation Context ...multiple sensors. The multiple sensor tracking problem can be treated as a single sensor tracking problem, in which the measurements are artificially ordered and regarded as separated in time by an interval of 0 s duration. The performance of the new filter is assessed in simulations. The scenario considered is a variant of the one used by Marrs [10], which describes a target maneuvering through a cluster of sonobuoys, to illustrate the effectiveness of a particle filter (PF) in circumstances when extended Kalman filters fail. Comparisons are made with the generic PF using stratified sampling [11] in the resampling step and also with a modified version of our filter based on the unscented Kalman filter [12]. In this scenario, the performance of the SRMF is comparable to that of the PF, while reducing the computational burden by an order of 1053-587X/$25.00 © 2007 IEEE Authorized licensed use limited to: Imperial College London. Downloaded on February 1, 2010 at 12:09 from IEEE Xplore. Restrictions apply. CLARK et al.: SRMF FOR BEARINGS-ONLY TRACKING OF MANEUVERING TARGETS 3219 magnitude. The SRMF also significantly outperforms the unscented Kalman filter version of the algorithm, with ... |

223 | Mixture kalman filters,
- Chen, Liu
- 2000
(Show Context)
Citation Context ...inly by the techniques employed to restrict the number of elements in the mixture. Algorithms such as the Generalized Pseudo-Bayes algorithm [2] or the Interacting Multiple Model (IMM) algorithm [2] merge together and retain mixture components. This number is strictly linked to the number of possible mode histories. Other techniques eliminate the least significant terms and allow full flexibility in the choice of . The elimination process can be deterministic (such as in the detection-estimation algorithm [3]), random (such as in the random sampling algorithm [4] and in mixture Kalman filters [5], [6]) or a mixture of both (as proposed by Fearnhead and Clifford [7]). In the case study of Section IV, we use the last method for the mixture reduction step in our implementation of the SRMF, because it is computationally efficient and satisfies certain optimality criteria explained in [7]. The above filters are based on linear/Gaussian models describing the evolution of the state variable and the measurement process, for a given manoeuvre mode history. Hence, the parameters of each mixture component can be obtained from the Kalman filter equations. For bearings-only tracking the measuremen... |

177 | Particle filters for state estimation of jump markov linear systems.
- Doucet, Gordon, et al.
- 2001
(Show Context)
Citation Context ...by the techniques employed to restrict the number of elements in the mixture. Algorithms such as the Generalized Pseudo-Bayes algorithm [2] or the Interacting Multiple Model (IMM) algorithm [2] merge together and retain mixture components. This number is strictly linked to the number of possible mode histories. Other techniques eliminate the least significant terms and allow full flexibility in the choice of . The elimination process can be deterministic (such as in the detection-estimation algorithm [3]), random (such as in the random sampling algorithm [4] and in mixture Kalman filters [5], [6]) or a mixture of both (as proposed by Fearnhead and Clifford [7]). In the case study of Section IV, we use the last method for the mixture reduction step in our implementation of the SRMF, because it is computationally efficient and satisfies certain optimality criteria explained in [7]. The above filters are based on linear/Gaussian models describing the evolution of the state variable and the measurement process, for a given manoeuvre mode history. Hence, the parameters of each mixture component can be obtained from the Kalman filter equations. For bearings-only tracking the measurement pro... |

172 | A general method for approximating nonlinear transformation of probability distributions
- Julier, Uhlmann
- 1994
(Show Context)
Citation Context ...tes than another. One sensible procedure for assigning an order would be to choose measurements according to their predicted error variances, with the most accurate first. Alternatively, the interested reader can find more refined approximation procedures for multiple sensor problems in [9] (Section III), for the nonmaneuvering target case. IV. MULTISENSOR TRACKING OF A SEA-BORNE TARGET In this section, we report on simulation experiments comparing the SRMF with a PF and also with a variant of our algorithm in which the update calculations are computed using the unscented Kalman filter ([12], [16], [17]). We refer to the last filter as the unscented mixture filter (UMF). The bearings-only tracking problem considered here is related to those earlier investigated in [9], [10], and [18]. The motion of a submerged maneuvering target is tracked by three drifting sonobuoys providing noisy bearings measurements of target position, subject to isotropic clutter. A mobile airborne vehicle provides noisy, clutter-free bearings measurements of the sonobuoy positions. 1) Sensor-Target Model: Each of the three sonobuoys is assumed to move as the sum of an independent low-intensity Brownian motion an... |

171 | The unscented Kalman filter for non-linear estimation
- Wan, Merwe
- 2000
(Show Context)
Citation Context ...an another. One sensible procedure for assigning an order would be to choose measurements according to their predicted error variances, with the most accurate first. Alternatively, the interested reader can find more refined approximation procedures for multiple sensor problems in [9] (Section III), for the nonmaneuvering target case. IV. MULTISENSOR TRACKING OF A SEA-BORNE TARGET In this section, we report on simulation experiments comparing the SRMF with a PF and also with a variant of our algorithm in which the update calculations are computed using the unscented Kalman filter ([12], [16], [17]). We refer to the last filter as the unscented mixture filter (UMF). The bearings-only tracking problem considered here is related to those earlier investigated in [9], [10], and [18]. The motion of a submerged maneuvering target is tracked by three drifting sonobuoys providing noisy bearings measurements of target position, subject to isotropic clutter. A mobile airborne vehicle provides noisy, clutter-free bearings measurements of the sonobuoy positions. 1) Sensor-Target Model: Each of the three sonobuoys is assumed to move as the sum of an independent low-intensity Brownian motion and an i... |

163 |
Estimation with applications to Tracking and Navigation, Theory Algorithms and Software
- Bar-Shalom, Li, et al.
- 2001
(Show Context)
Citation Context ...racked by three drifting sonobuoys providing noisy bearings measurements of target position, subject to isotropic clutter. A mobile airborne vehicle provides noisy, clutter-free bearings measurements of the sonobuoy positions. 1) Sensor-Target Model: Each of the three sonobuoys is assumed to move as the sum of an independent low-intensity Brownian motion and an integrated Brownian motion, common to all three, that represents the effect of a bulk drift [10] correlating their behaviour. The model permits three possible modes of manoeuvre for the target ; two are known in the tracking literature [19] as left and right coordinated turns and the third as a nearly constant velocity model. The continuous component of the state (describing the positions and velocities of the target and the observation platforms for each mode) is 12-D (26) Here and denote coordinates of position in the plane, and and the corresponding velocities (at time ). The target and the three sonobuoys are labelled by the superscripts 0, 1, 2, and 3, respectively. The vector describes the bulk drift term common to the equations governing the positions of the three sonobuoys. The model governing the state is a version of (... |

56 |
Mixture reduction algorithms for target tracking,” State Estimation in Aerospace and Tracking Applications,
- Salmond
- 1989
(Show Context)
Citation Context ...tively. The pair is the mean and covariance of the two-fold mixture. Other variables appearing in the algorithm description are associated with weight calculations. TABLE II ALGORITHM The precise form that the SRMF takes in a particular application depends on the manner in which —fold Gaussian mixtures are approximated to —fold Gaussian mixtures in Step 3. A variety of approaches have been proposed for tackling “mixture reduction” problems of this type. Some involve both the elimination of some elements from the mixture and also the combination of other, in some sense similar, components (see [13] or [14]). This procedure, which involves a careful analysis and modification of the spatial distribution of the elements in the mixture, has a heavy computational overhead. For this reason, the most commonly used mixture reduction methods leave the constituent densities unaltered and retain or reject the mixture components, depending on the size of their weights. In this latter category, available methods include purely deterministic selection procedures (as in the detection-estimation algorithm [3]), purely randomized selection procedures (as in the random-sampling algorithm [4]), and “parti... |

53 |
Random sampling approach to state estimation in switching environments.
- Akashi, Kumamoto
- 1977
(Show Context)
Citation Context ...y. These mixture filters differ mainly by the techniques employed to restrict the number of elements in the mixture. Algorithms such as the Generalized Pseudo-Bayes algorithm [2] or the Interacting Multiple Model (IMM) algorithm [2] merge together and retain mixture components. This number is strictly linked to the number of possible mode histories. Other techniques eliminate the least significant terms and allow full flexibility in the choice of . The elimination process can be deterministic (such as in the detection-estimation algorithm [3]), random (such as in the random sampling algorithm [4] and in mixture Kalman filters [5], [6]) or a mixture of both (as proposed by Fearnhead and Clifford [7]). In the case study of Section IV, we use the last method for the mixture reduction step in our implementation of the SRMF, because it is computationally efficient and satisfies certain optimality criteria explained in [7]. The above filters are based on linear/Gaussian models describing the evolution of the state variable and the measurement process, for a given manoeuvre mode history. Hence, the parameters of each mixture component can be obtained from the Kalman filter equations. For bea... |

43 |
On-line inference for hidden Markov models via particle filters,”
- Fearnhead, Clifford
- 2003
(Show Context)
Citation Context ...the mixture. Algorithms such as the Generalized Pseudo-Bayes algorithm [2] or the Interacting Multiple Model (IMM) algorithm [2] merge together and retain mixture components. This number is strictly linked to the number of possible mode histories. Other techniques eliminate the least significant terms and allow full flexibility in the choice of . The elimination process can be deterministic (such as in the detection-estimation algorithm [3]), random (such as in the random sampling algorithm [4] and in mixture Kalman filters [5], [6]) or a mixture of both (as proposed by Fearnhead and Clifford [7]). In the case study of Section IV, we use the last method for the mixture reduction step in our implementation of the SRMF, because it is computationally efficient and satisfies certain optimality criteria explained in [7]. The above filters are based on linear/Gaussian models describing the evolution of the state variable and the measurement process, for a given manoeuvre mode history. Hence, the parameters of each mixture component can be obtained from the Kalman filter equations. For bearings-only tracking the measurement process equation is nonlinear. The novelty of the SRMF lies in the w... |

23 | Cost-Function-Based Gaussian Mixture Reduction for Target Tracking
- Williams, Maybeck
- 2003
(Show Context)
Citation Context ...The pair is the mean and covariance of the two-fold mixture. Other variables appearing in the algorithm description are associated with weight calculations. TABLE II ALGORITHM The precise form that the SRMF takes in a particular application depends on the manner in which —fold Gaussian mixtures are approximated to —fold Gaussian mixtures in Step 3. A variety of approaches have been proposed for tackling “mixture reduction” problems of this type. Some involve both the elimination of some elements from the mixture and also the combination of other, in some sense similar, components (see [13] or [14]). This procedure, which involves a careful analysis and modification of the spatial distribution of the elements in the mixture, has a heavy computational overhead. For this reason, the most commonly used mixture reduction methods leave the constituent densities unaltered and retain or reject the mixture components, depending on the size of their weights. In this latter category, available methods include purely deterministic selection procedures (as in the detection-estimation algorithm [3]), purely randomized selection procedures (as in the random-sampling algorithm [4]), and “partial rando... |

6 | The shifted Rayleigh filter: A new algorithm for bearings-only tracking,”
- Clark, Vinter, et al.
- 2007
(Show Context)
Citation Context ...ia explained in [7]. The above filters are based on linear/Gaussian models describing the evolution of the state variable and the measurement process, for a given manoeuvre mode history. Hence, the parameters of each mixture component can be obtained from the Kalman filter equations. For bearings-only tracking the measurement process equation is nonlinear. The novelty of the SRMF lies in the way that it deals with this nonlinearity. To generate Gaussian approximations to the conditional densities of the state, associated with each manoeuvre mode history, it employs the shifted Rayleigh filter [8] based on an exact calculation of the first and second moments of the conditional density of the state. The proposed algorithm takes account of clutter by associating with each manoeuvre mode an additional clutter mode (cf. [9]). The algorithm can be adapted also to take account of multiple sensors. The multiple sensor tracking problem can be treated as a single sensor tracking problem, in which the measurements are artificially ordered and regarded as separated in time by an interval of 0 s duration. The performance of the new filter is assessed in simulations. The scenario considered is a va... |

6 |
Asynchronous multi-sensor tracking in clutter with uncertain sensor locations using Bayesian sequential Monte Carlo methods,” in
- Marrs
- 2001
(Show Context)
Citation Context ...of the first and second moments of the conditional density of the state. The proposed algorithm takes account of clutter by associating with each manoeuvre mode an additional clutter mode (cf. [9]). The algorithm can be adapted also to take account of multiple sensors. The multiple sensor tracking problem can be treated as a single sensor tracking problem, in which the measurements are artificially ordered and regarded as separated in time by an interval of 0 s duration. The performance of the new filter is assessed in simulations. The scenario considered is a variant of the one used by Marrs [10], which describes a target maneuvering through a cluster of sonobuoys, to illustrate the effectiveness of a particle filter (PF) in circumstances when extended Kalman filters fail. Comparisons are made with the generic PF using stratified sampling [11] in the resampling step and also with a modified version of our filter based on the unscented Kalman filter [12]. In this scenario, the performance of the SRMF is comparable to that of the PF, while reducing the computational burden by an order of 1053-587X/$25.00 © 2007 IEEE Authorized licensed use limited to: Imperial College London. Downloaded... |

5 |
The shifted Rayleigh filter for bearings only tracking,” presented at the 8th.
- Clark, Vinter, et al.
- 2005
(Show Context)
Citation Context ...mponent can be obtained from the Kalman filter equations. For bearings-only tracking the measurement process equation is nonlinear. The novelty of the SRMF lies in the way that it deals with this nonlinearity. To generate Gaussian approximations to the conditional densities of the state, associated with each manoeuvre mode history, it employs the shifted Rayleigh filter [8] based on an exact calculation of the first and second moments of the conditional density of the state. The proposed algorithm takes account of clutter by associating with each manoeuvre mode an additional clutter mode (cf. [9]). The algorithm can be adapted also to take account of multiple sensors. The multiple sensor tracking problem can be treated as a single sensor tracking problem, in which the measurements are artificially ordered and regarded as separated in time by an interval of 0 s duration. The performance of the new filter is assessed in simulations. The scenario considered is a variant of the one used by Marrs [10], which describes a target maneuvering through a cluster of sonobuoys, to illustrate the effectiveness of a particle filter (PF) in circumstances when extended Kalman filters fail. Comparisons... |

2 |
Sequential Monte Carlo tracking schemes for maneuvering targets with passive ranging,” in
- Malcolm, Doucet, et al.
- 2002
(Show Context)
Citation Context ...hms, particle filter (PF), shifted Rayleigh filter, unscented Kalman filter. I. INTRODUCTION I N THIS paper, we propose the shifted Rayleigh mixturefilter (SRMF) for tracking a maneuvering target, given noisy bearing measurements of target position relative to a sensor platform. The design of the filter is based on a description of the motion of the target and the sensor platform using a discrete time linear system driven by Gaussian inputs with a discrete set of random coefficients describing the current maneuvering mode. Such models, referred to as jump Markov linear models, are widely used [1], [2] because of their versatility in describing a wide range of maneuvering target motions. For the tracking problem considered, the conditional density of the target state given the available measurements, is a mixture of probability densities. Each mixture component can be regarded as the density of the target state conditioned on the available measurements and on a mode history. The number of components in the mixture grows in time because the number of possible mode histories increases geometrically. Our approach is to obtain estimates of target state using Gaussian mixture approximations... |

2 |
Bearings-only tracking with sea trial sonar data from multiple asynchronous sonobuoys,” presented at the
- Karan, Wang
- 1998
(Show Context)
Citation Context ... interested reader can find more refined approximation procedures for multiple sensor problems in [9] (Section III), for the nonmaneuvering target case. IV. MULTISENSOR TRACKING OF A SEA-BORNE TARGET In this section, we report on simulation experiments comparing the SRMF with a PF and also with a variant of our algorithm in which the update calculations are computed using the unscented Kalman filter ([12], [16], [17]). We refer to the last filter as the unscented mixture filter (UMF). The bearings-only tracking problem considered here is related to those earlier investigated in [9], [10], and [18]. The motion of a submerged maneuvering target is tracked by three drifting sonobuoys providing noisy bearings measurements of target position, subject to isotropic clutter. A mobile airborne vehicle provides noisy, clutter-free bearings measurements of the sonobuoy positions. 1) Sensor-Target Model: Each of the three sonobuoys is assumed to move as the sum of an independent low-intensity Brownian motion and an integrated Brownian motion, common to all three, that represents the effect of a bulk drift [10] correlating their behaviour. The model permits three possible modes of manoeuvre for the... |

1 |
Sequential Monte Carlo Methods
- Fearnhead
- 1998
(Show Context)
Citation Context ...tic selection procedures (as in the detection-estimation algorithm [3]), purely randomized selection procedures (as in the random-sampling algorithm [4]), and “partial randomization” procedures Authorized licensed use limited to: Imperial College London. Downloaded on February 1, 2010 at 12:09 from IEEE Xplore. Restrictions apply. 3222 IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 55, NO. 7, JULY 2007 where some elements are chosen deterministically and some randomly. In the simulations reported in Section IV, we employ a partial randomization algorithm, proposed by Fearnhead and Clifford [7], [15]. A distinctive feature of [7] and [15] is that the threshold on weight magnitude, determining whether an index value and its accompanying weight is automatically retained, is adapted to the distribution of weights, in a manner which is optimal as defined in [7] and [15]. III. MULTIPLE SENSORS Consider now a variant of the tracking problem of Section II, in which a total of sensors provide independent, simultaneous bearing measurements of target position. In this problem, the state (1) and mode transition matrix (6) remain the same, but the measurement (2)–(5) are replaced by equations for the... |