Estimation of noise covariance matrices for a linear time-varying stochastic process

Bélanger, Pierre

doi:10.1016/0005-1098(74)90037-5

Cited by 195 publications

(111 citation statements)

References 5 publications

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“…This allows using targets of opportunity whose behavior is nonstationary in an unpredictable way. Early work for noise statistics identification for stationary systems can be found in [2].…”

Section: Introductionmentioning

confidence: 99%

Radar measurement noise variance estimation with several targets of opportunity

Osborne¹,

Bar‐Shalom²

2006

SPIE Proceedings

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A number of methods exist to track a target's uncertain motion through space using inherently inaccurate sensor measurements. A powerful method of adaptive estimation is the interacting multiple model (IMM) estimator. In order to carry out state estimation from the noisy measurements of a sensor, however, the filter should have knowledge of the statistical characteristics of the noise associated with that sensor. The statistical characteristics (accuracies) of real sensors, however, are not always available, in particular for legacy sensors. This paper presents a method of determining the measurement noise variances of a sensor by using multiple IMM estimators while tracking targets whose motion is not known -targets of opportunity. Combining techniques outlined in [1] and [3], the likelihood functions are obtained for a number of IMM estimators, each with different assumptions on the measurement noise variances. Then a search is carried out to bracket the variances of the sensor measurement noises. The end result consists of estimates of the measurement noise variances of the sensor in question.

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Section: Introductionmentioning

confidence: 99%

Radar measurement noise variance estimation with several targets of opportunity

Osborne¹,

Bar‐Shalom²

2006

SPIE Proceedings

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“…The event-based state estimator equations proposed in the works of Wu et al 18 and Shi et al 24 are equivalent for the case of one sensor with scalar measurements, which follow the sampling scheme of (6) The estimator equations are summarized below.…”

Section: Event-based State Estimatormentioning

confidence: 99%

“…The problem of online noise covariance adaptation has been addressed in numerous studies. 2,[5][6][7][8][9][10][11][12] One of the first and better known methods, innovation-based adaptive estimation (IAE), was developed by Mehra 5 and later perfected by Mohamed and Schwarz. 7 Such methods are based on subtracting the expected measurement from the actual one (which is known as the innovation vector), and testing if the innovation covariance resembles the covariance computed by the filter, and adjusting the noise matrices so that the observed and expected covariances match.…”

Section: Introductionmentioning

confidence: 99%

Online evaluation of the process noise covariance matrix for event‐based state estimators

Martinez-Rey

Santos

Nieto

et al. 2019

Numerical Meth Engineering

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Summary In state estimation, adjusting the process noise covariance matrix is an important and often difficult task. Well‐known methods use the innovation vector to perform an adaptive adjustment, but when using event‐based sensors, the innovation vector is not available for the estimator. We propose an online method for adjusting the process noise covariance matrix using the expected and observed event rates, which is based on the golden section search optimization algorithm. Simulation results confirm the suitability and efficiency of our proposed method. The process noise covariance parameter converges to the actual covariance iteratively, reducing the sensor transmission rate and the estimation error.

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“…This method was corrected by Leathrum [36], and compared to Maybeck's ML estimator [32] in [37], showing that both are equivalent if the system noise is zero-mean. The correlation methods, pioneered by Mehra [29] and Bélanger [38], are the most popular for the estimation of Gaussian noise covariance matrices. These methods are based on the correlation function of the innovation sequence and the derivation of a set of equations which relate this function to the unknown parameters [39].…”

Section: Noise Statistics Estimationmentioning

confidence: 99%

On the identifiability of noise statistics and adaptive KF design for robust GNSS carrier tracking

Vilà‐Valls¹,

Closas²,

Fernández‐Prades³

2015

2015 IEEE Aerospace Conference

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Carrier synchronization is of paramount importance in any communications or positioning system. Mass-market Global Navigation Satellite System (GNSS) receivers typically implement traditional carrier tracking techniques based on well-established phase-locked loop architectures, which are only reliable in quite benign propagation conditions. Under nonnominal harsh propagation conditions, the signal may be affected by shadowing, strong fading, multipath or severe ionospheric scintillation, and thus, traditional architectures are not valid anymore and there exists an actual need for robust tracking solutions. Several approaches to overcome the conventional PLL limitations have appeared during the last decade, being the Kalman filter (KF) based architectures the most promising research line. The main drawback of standard KFs is the assumption of perfectly known process and measurement noise statistics, a knowledge that is always constrained by the system model accuracy. Beyond heuristic solutions, a general framework for the design of adaptive KFs correctly dealing with both process and measurement noises, that would be of capital importance for the practitioner, has not been established. The main goal of this contribution is to provide a clear answer to this fundamental question. It is shown that the main driver on the KF performance is not the adjustment of the measurement noise but the adequate tuning of the process noise statistics. Within this framework, a comprehensive discussion is given for the correct design of adaptive KF architectures for robust carrier tracking applications, where the key idea is to use two independent noise statistics estimation strategies to sequentially adapt both parameters. The design choice is supported by a discussion on the identifiability of the noise statistics' parameters. Simulation results are provided showing the need of fully adaptive solutions, and the achieved performance gain of KF-based architectures when compared to traditional tracking loops.

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Estimation of noise covariance matrices for a linear time-varying stochastic process

Cited by 195 publications

References 5 publications

Radar measurement noise variance estimation with several targets of opportunity

Radar measurement noise variance estimation with several targets of opportunity

Online evaluation of the process noise covariance matrix for event‐based state estimators

On the identifiability of noise statistics and adaptive KF design for robust GNSS carrier tracking

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