A Kalman filter clock algorithm for use in the presence of flicker frequency modulation noise

Davis, John; Greenhall, C. A.; Stacey, P. W.

doi:10.1088/0026-1394/42/1/001

Cited by 55 publications

(49 citation statements)

References 13 publications

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“…All of the components in (1), with the exception of flicker noise, are easily represented in a state-space model. Davis et al (2005) showed that flicker noise can be approximated over a finite bandwidth as a linear combination of independent first-order Gauss-Markov (FOGM) processes, yielding what we refer to as finite bandwidth flicker noise (FBFN). Flicker noise has power spectral density…”

Section: Network Noise Estimator (Nne) Descriptionmentioning

confidence: 99%

“…With FBFN the sum of shifted FOGM processes approximates a f −1 spectrum as a combination of f 0 and f −2 segments. Davis et al (2005) recommend a sum of GM processes such that the periods at the corner frequencies, 1/f j of successive FOGM processes, are chosen to increase geometrically with a spacing ratio s, so thatf j+1 =f j /s, and the spectral densities β 2 j are chosen such that β 2 j /2f j are equal (Fig. 1).…”

Section: Network Noise Estimator (Nne) Descriptionmentioning

confidence: 99%

“…Arbitrary offsets for clarity taken account of the fact that for random walk F k = I and Q k = τ 2 δt k (e.g., Segall and Matthews 1997). Davis et al (2005) gives the state transition matrix F FN and process noise covariance matrix Q FN to implement the approximation of flicker noise. (These matrices are found in the Appendix of this paper.…”

Section: Network Noise Estimator (Nne) Descriptionmentioning

confidence: 99%

“…3 High-frequency part of the averaged power spectrum of 100 FBFN components with spacing ratio of 8 (red) and 2 (green) and 100 averaged flicker noise components created using covariance matrix (magenta). The black dashed line indicates the theoretical power spectrum of flicker noise Davis et al (2005) recommend using a multiple of 2 as the spacing ratio. Figure 3 shows the high-frequency part of the power spectrum for FBFN generated with spacing ratios of 8 and 2 as well as the flicker noise generated using the covariance matrix approach (Langbein 2004).…”

Section: Tests Of Fbfnmentioning

confidence: 99%

“…Design matrices for first-order Gauss-Markov process Here, we provide the state-space matrices for FBFN (Davis et al 2005). The state transition matrix for the Gauss-Markov processes representing flicker noise is defined by:…”

Section: Appendixmentioning

confidence: 99%

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Network-based estimation of time-dependent noise in GPS position time series

Dmitrieva

Segall

DeMets

2015

J Geod

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Some estimates of GPS velocity uncertainties are very low, <0.1 mm/year with 10 years of data. Yet, residual velocities relative to rigid plate models in nominally stable plate interiors can be an order of magnitude larger. This discrepancy could be caused by underestimating low-frequency time-dependent noise in position time series, such as random walk. We show that traditional estimators, based on individual time series, are insensitive to low-amplitude random walk, yet such noise significantly increases GPS velocity uncertainties. Here, we develop a method for determining representative noise parameters in GPS position time series, by analyzing an entire network simultaneously, which we refer to as the network noise estimator (NNE). We analyze data from the aseismic central-eastern USA, assuming that residual motions relative to North America, corrected for glacial isostatic adjustment (GIA), represent noise. The position time series are decomposed into signal (plate rotation and GIA) and noise components. NNE simultaneously processes multiple stations with a Kalman filter and solves for average noise components for the network by maximum likelihood estimation. Synthetic tests show that NNE correctly estimates even low-level random walk, thus providing better estimates of velocity uncertainties than conventional, single station methods. To test NNE on actual data, we analyze a heterogeneous 15 station GPS network from the centraleastern USA, assuming the noise is a sum of random walk, flicker and white noise. For the horizontal time series, NNE finds higher average random walk than the standard individual station-based method, leading to velocity uncertainties a factor of 2 higher than traditional methods.

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Section: Network Noise Estimator (Nne) Descriptionmentioning

confidence: 99%

Section: Network Noise Estimator (Nne) Descriptionmentioning

confidence: 99%

Section: Network Noise Estimator (Nne) Descriptionmentioning

confidence: 99%

Section: Tests Of Fbfnmentioning

confidence: 99%

Section: Appendixmentioning

confidence: 99%

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Network-based estimation of time-dependent noise in GPS position time series

Dmitrieva

Segall

DeMets

2015

J Geod

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A novel approach using parallel Kalman filters in time and frequency estimation

Jarlemark

Emardson

2007

Proc Appl Math and Mech

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In the present information based knowledge society, accurate knowledge of time and frequency plays a fundamental role. For many applications, real time estimates of the clocks time and frequency error are required. We have developed a novel approach for estimating time and frequency errors based on an assembly of clocks of varying quality. By using parallel Kalman filters we utilize all available measurements in the estimation. As these measurements are available with different delays, the Kalman filter produces estimates of different quality. One filtermay produce real‐time estimates while another filter waits for delayed measurements. When new information becomes available, the parallel Kalman filters exchange information in order to keep the state matrices updated with the most recent information. In Kalman filtering, accurate modelling of the measurement system is fundamental. All the contributing clocks, as well as the time transfer methods, are modelled as stochastic processes. By using this methodology and by correctly modelling the contributing clocks, we obtain minimum mean square error estimators (MMSE) of the time and frequency errors of a specific clock at every epoch. In addition, we also determine the uncertainty of each time and frequency error estimate. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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