### Abstract

An interval error-based method (MIE) of predicting mean squared error (MSE) performance of maximum-likelihood estimators (MLEs) is extended to the case of signal parameter estimation requiring intermediate estimation of an unknown colored noise covariance matrix; an intermediate step central to adaptive array detection and parameter estimation. The successful application of MIE requires good approximations of two quantities: 1) interval error probabilities and 2) asymptotic (SNR → √) local MSE performance of the MLE. Exact general expressions for the pairwise error probabilities that include the effects of signal model mismatch are derived herein, that in conjunction with the Union Bound provide accurate prediction of the required interval error probabilities. The Cramér-Ran Bound (CRB) often provides adequate prediction of the asymptotic local MSE performance of MLE. The signal parameters, however, are decoupled from the colored noise parameters in the Fisher Information Matrix for the deterministic signal model, rendering the CRB incapable of reflecting loss due to colored noise covariance estimation. A new modification of the CRB involving a complex central beta random variable different from, but analogous to the Reed, Mallett, and Brennan beta loss factor provides a working solution to this problem, facilitating MSE prediction well into the threshold region with remarkable accuracy.

Original language | English (US) |
---|---|

Title of host publication | Bayesian Bounds for Parameter Estimation and Nonlinear Filtering/Tracking |

Publisher | John Wiley and Sons Inc. |

Pages | 306-324 |

Number of pages | 19 |

ISBN (Electronic) | 9780470544198 |

ISBN (Print) | 0470120959, 9780470120958 |

DOIs | |

State | Published - Jan 1 2007 |

Externally published | Yes |

### Fingerprint

### Keywords

- Bayesian methods
- Colored noise
- Error probability
- Maximum likelihood estimation
- Parameter estimation
- Signal to noise ratio

### ASJC Scopus subject areas

- Computer Science(all)

### Cite this

*Bayesian Bounds for Parameter Estimation and Nonlinear Filtering/Tracking*(pp. 306-324). John Wiley and Sons Inc.. https://doi.org/10.1109/9780470544198.ch26

**Mean-Squared Error and Threshold SNR Prediction of Maximum-Likelihood Signal Parameter Estimation With Estimated Colored Noise Covariances.** / Richmond, Christ.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Bayesian Bounds for Parameter Estimation and Nonlinear Filtering/Tracking.*John Wiley and Sons Inc., pp. 306-324. https://doi.org/10.1109/9780470544198.ch26

}

TY - CHAP

T1 - Mean-Squared Error and Threshold SNR Prediction of Maximum-Likelihood Signal Parameter Estimation With Estimated Colored Noise Covariances

AU - Richmond, Christ

PY - 2007/1/1

Y1 - 2007/1/1

N2 - An interval error-based method (MIE) of predicting mean squared error (MSE) performance of maximum-likelihood estimators (MLEs) is extended to the case of signal parameter estimation requiring intermediate estimation of an unknown colored noise covariance matrix; an intermediate step central to adaptive array detection and parameter estimation. The successful application of MIE requires good approximations of two quantities: 1) interval error probabilities and 2) asymptotic (SNR → √) local MSE performance of the MLE. Exact general expressions for the pairwise error probabilities that include the effects of signal model mismatch are derived herein, that in conjunction with the Union Bound provide accurate prediction of the required interval error probabilities. The Cramér-Ran Bound (CRB) often provides adequate prediction of the asymptotic local MSE performance of MLE. The signal parameters, however, are decoupled from the colored noise parameters in the Fisher Information Matrix for the deterministic signal model, rendering the CRB incapable of reflecting loss due to colored noise covariance estimation. A new modification of the CRB involving a complex central beta random variable different from, but analogous to the Reed, Mallett, and Brennan beta loss factor provides a working solution to this problem, facilitating MSE prediction well into the threshold region with remarkable accuracy.

AB - An interval error-based method (MIE) of predicting mean squared error (MSE) performance of maximum-likelihood estimators (MLEs) is extended to the case of signal parameter estimation requiring intermediate estimation of an unknown colored noise covariance matrix; an intermediate step central to adaptive array detection and parameter estimation. The successful application of MIE requires good approximations of two quantities: 1) interval error probabilities and 2) asymptotic (SNR → √) local MSE performance of the MLE. Exact general expressions for the pairwise error probabilities that include the effects of signal model mismatch are derived herein, that in conjunction with the Union Bound provide accurate prediction of the required interval error probabilities. The Cramér-Ran Bound (CRB) often provides adequate prediction of the asymptotic local MSE performance of MLE. The signal parameters, however, are decoupled from the colored noise parameters in the Fisher Information Matrix for the deterministic signal model, rendering the CRB incapable of reflecting loss due to colored noise covariance estimation. A new modification of the CRB involving a complex central beta random variable different from, but analogous to the Reed, Mallett, and Brennan beta loss factor provides a working solution to this problem, facilitating MSE prediction well into the threshold region with remarkable accuracy.

KW - Bayesian methods

KW - Colored noise

KW - Error probability

KW - Maximum likelihood estimation

KW - Parameter estimation

KW - Signal to noise ratio

UR - http://www.scopus.com/inward/record.url?scp=85036510928&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85036510928&partnerID=8YFLogxK

U2 - 10.1109/9780470544198.ch26

DO - 10.1109/9780470544198.ch26

M3 - Chapter

SN - 0470120959

SN - 9780470120958

SP - 306

EP - 324

BT - Bayesian Bounds for Parameter Estimation and Nonlinear Filtering/Tracking

PB - John Wiley and Sons Inc.

ER -