Hard-constrained versus soft-constrained parameter estimation

Benavoli, Alessio; Chisci, Luigi; Farina, A.; Ortenzi, L.; Zappa, G.

doi:10.1109/taes.2006.314569

Cited by 16 publications

(5 citation statements)

References 10 publications

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“…Therefore, we argue that the [9]. The mathematical results of the simulations, obtained for the cases k = 0.1, 0.5, 1, 2 are summarized in Table 4 and compared to the unconstrained case.…”

Section: Equality Constraintsmentioning

confidence: 92%

“…This can be modeled by means of inequality constraints on Hand G. Also the trajectory plane, identified by the angle tP' may be known with a certain degree of accuracy based on the location of the possible targets and launch point. In [9] hard constraints versus soft constraints are compared for a general line-fitting problem. In the ballistic case the application of hard constraints on the trajectory characteristics estimation is analyzed.…”

Section: Equality Constraintsmentioning

confidence: 99%

“…This aim can be achieved by the application of constraints on the parameters to be estimated [7][8]. In [9] the application of hard and soft constraints has been analyzed only for a simple line fitting problem. In this paper, the ML estimation accuracy of a parabolic trajectory is improved by the application of equality and inequality (hard) constraints on the trajectory characteristics such as maximum range, maximum height and trajectory plane.…”

Section: Introductionmentioning

confidence: 99%

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MLE in presence of equality and inequality nonlinear constraints for the ballistic target problem

Benavoli

Farina

Ortenzi

2008

2008 IEEE Radar Conference

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This paper focuses on the estimation of the impact point of a ballistic target by means of a batch processing approach which can be applied more specifically when the number of radar measurements is poor. In particular, the Maximum Likelihood (ML) estimator is proposed for the estimation of the ballistic target trajectory approximated to a pure parabolic curve; also the Cramer-Rao Lower Bound (CRLB), which gives the minimum theoretically achievable variance of the estimate, is calculated. The estimator accuracy is improved by the application of equality and inequality constraints on the trajectory characteristics such as maximum range, maximum height and trajectory plane. In the case of application of equality constraints also the CRLB can be computed and the constrained estimator improves strongly its accuracy. In real operational scenarios, a smoothed information can be expressed by means of inequality constraints. The performance of the corresponding estimator has been analyzed by means of Monte Carlo simulation, because of the unavailability of computation of the CRLB for this case.

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“…Therefore, we argue that the [9]. The mathematical results of the simulations, obtained for the cases k = 0.1, 0.5, 1, 2 are summarized in Table 4 and compared to the unconstrained case.…”

Section: Equality Constraintsmentioning

confidence: 92%

Section: Equality Constraintsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

MLE in presence of equality and inequality nonlinear constraints for the ballistic target problem

Benavoli

Farina

Ortenzi

2008

2008 IEEE Radar Conference

Self Cite

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“…The pioneering work in [22] adopted a soft-constraint setting to enforce a slowly varying feature of a state when performing the health estimation of a turbofan engine. In a static parameter estimation problem [23], soft-constraints were used to impose a prior distribution of the parameters to be estimated. In addition, Papi et al [10] considered occasional constraint violation in target tracking problems, but the soft-constraint was simply defined by a prefixed probability regardless of the actual state.…”

Section: Introductionmentioning

confidence: 99%

Particle Filtering With Soft State Constraints for Target Tracking

Liu

Chen

2019

IEEE Trans. Aerosp. Electron. Syst.

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In practice, additional knowledge about the target to be tracked, other than its fundamental dynamics, can often be modeled as a set of soft constraints and utilized in a filtering process to improve the tracking performance. This paper develops a general approach to the modeling of soft inequality constraints, and investigates particle filtering (PF) with soft state constraints for target tracking. We develop two PF algorithms with soft inequality constraints, i.e., a sequential-importance-resampling particle filter and an auxiliary sampling mechanism. The latter probabilistically selects the candidate particles from the soft inequality constraints of the state variables so that they are more likely to comply with the soft constraints. The performances of the proposed algorithms are evaluated using Monte Carlo simulations in a target tracking scenario.

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“…Bai and Ye (1999) proposed a constrained logarithmic least squares estimator for system identification. Benavoli et al (2006) studied two alternative methods of using a priori knowledge on the estimated parameters; these methods are the hardconstrained estimation approach and the soft-constrained estimation approach. Benavoli et al (2007) tackled the problem of parameter estimation in linear regression models when the parameters are under polytopic constraints; the proposed estimator is an improvement over the standard least square estimator.…”

Section: Introductionmentioning

confidence: 99%

A multiple projection approach for constrained system identification

Hassan

Zribi

Alazemi

et al. 2011

IJCAT

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This paper deals with the constrained system identification problem of linear discrete time dynamical systems. It is assumed that the parameters of the system are constrained due to physical limitations. Using a multiple projection approach, a minimum variance estimator and its associated recursive version are developed to estimate the constrained parameters of the system. The most important feature of the developed technique is that it gives estimates of the system parameters once the first set of measurements is received. Therefore, there is no need to wait till sufficient number of measurements are collected to start the algorithm. The simulation results of illustrative examples are presented to show the effectiveness of the proposed estimation scheme.

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Hard-constrained versus soft-constrained parameter estimation

Cited by 16 publications

References 10 publications

MLE in presence of equality and inequality nonlinear constraints for the ballistic target problem

MLE in presence of equality and inequality nonlinear constraints for the ballistic target problem

Particle Filtering With Soft State Constraints for Target Tracking

A multiple projection approach for constrained system identification

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