CRLB and ML for parametric estimate: New results

The modified Riccati equation arises in the implementation of Kalman filter in target tracking under measurement uncertainty and it cannot be transformed into an equation of the form of the Riccati equation. An iterative solution algorithm of the modified Riccati equation is proposed. A method is established to decide when the proposed algorithm is faster than the classical one. Both algorithms have the same behavior: if the system is stable, then there exists a steady-state solution, while if the system is unstable, then there exists a critical value of the measurement detection probability, below which both iterative algorithms diverge. It is established that this critical value increases in a logarithmic way as the system becomes more unstable.

show abstract

“…It is remarkable that the following special cases are implied by (5). (ii) Setting p d = 0 in (5), the classical Lyapunov equation is derived:…”

Section: Matrix Operationmentioning

confidence: 99%

“…It plays an important role in target tracking [1][2][3][4][5][6][7][8][9][10]. Theoretical properties of the modified Riccati equation have been derived in [2,3].…”

Section: Introductionmentioning

confidence: 99%

On the Convergence of the Modified Riccati Equation

Assimakis

Αδάμ

2012

ISRN Signal Processing

View full text Add to dashboard Cite

show abstract

“…The estimator and the pertinent CRLB computation for this specific case has been calculated in [6]; for sake of brevity the mathematical details are not reported here. The accuracy of the unconstrained estimator will be taken as reference to evaluate the results presented in the sequel.…”

Section: Model Of the Data: Reference Geometrymentioning

confidence: 99%

“…The CRLB, computed by the inversion of the Fisher Information Matrix (FIM), gives the minimum theoretically achievable variance of the estimate [4]. The ML estimation of a parabolic trajectory and the CRLB computation have already been approached in [5] and [6]. In [5] the improvement of estimator accuracy was achieved by the fusion of the measurements of few radars.…”

Section: Introductionmentioning

confidence: 99%

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

Benavoli

Farina

Ortenzi

2008

2008 IEEE Radar Conference

Self Cite

View full text Add to dashboard Cite

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.

show abstract

“…For this purpose, we exploit the enumeration approach of [9–11] that is here extended and applied to the case of a multistatic passive radar. This is appropriately considered to derive a CRLB with P d < 1, able to yield a realistic evaluation of the achievable positioning accuracy that fully includes the effects both of the system geometry and of the SNR.…”

Section: Introductionmentioning

confidence: 99%

Cramér‐Rao lower bound with P _d < 1 for target localisation accuracy in multistatic passive radar

Anastasio

Farina

Colone

et al. 2014

IET Radar, Sonar & Navigation

View full text Add to dashboard Cite

CRLB and ML for parametric estimate: New results

Cited by 11 publications

References 7 publications

On the Convergence of the Modified Riccati Equation

On the Convergence of the Modified Riccati Equation

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

Cramér‐Rao lower bound with P _d < 1 for target localisation accuracy in multistatic passive radar

Contact Info

Product

Resources

About

CRLB and ML for parametric estimate: New results

Cited by 11 publications

References 7 publications

On the Convergence of the Modified Riccati Equation

On the Convergence of the Modified Riccati Equation

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

Cramér‐Rao lower bound with P d < 1 for target localisation accuracy in multistatic passive radar

Contact Info

Product

Resources

About

Cramér‐Rao lower bound with P _d < 1 for target localisation accuracy in multistatic passive radar