8,884 research outputs found
Characterizing and correcting for the effect of sensor noise in the dynamic mode decomposition
Dynamic mode decomposition (DMD) provides a practical means of extracting
insightful dynamical information from fluids datasets. Like any data processing
technique, DMD's usefulness is limited by its ability to extract real and
accurate dynamical features from noise-corrupted data. Here we show
analytically that DMD is biased to sensor noise, and quantify how this bias
depends on the size and noise level of the data. We present three modifications
to DMD that can be used to remove this bias: (i) a direct correction of the
identified bias using known noise properties, (ii) combining the results of
performing DMD forwards and backwards in time, and (iii) a total
least-squares-inspired algorithm. We discuss the relative merits of each
algorithm, and demonstrate the performance of these modifications on a range of
synthetic, numerical, and experimental datasets. We further compare our
modified DMD algorithms with other variants proposed in recent literature
Sparsity-Based Error Detection in DC Power Flow State Estimation
This paper presents a new approach for identifying the measurement error in
the DC power flow state estimation problem. The proposed algorithm exploits the
singularity of the impedance matrix and the sparsity of the error vector by
posing the DC power flow problem as a sparse vector recovery problem that
leverages the structure of the power system and uses -norm minimization
for state estimation. This approach can provably compute the measurement errors
exactly, and its performance is robust to the arbitrary magnitudes of the
measurement errors. Hence, the proposed approach can detect the noisy elements
if the measurements are contaminated with additive white Gaussian noise plus
sparse noise with large magnitude. The effectiveness of the proposed
sparsity-based decomposition-DC power flow approach is demonstrated on the IEEE
118-bus and 300-bus test systems
Estimation of Autoregressive Parameters from Noisy Observations Using Iterated Covariance Updates
Estimating the parameters of the autoregressive (AR) random process is a problem that has been well-studied. In many applications, only noisy measurements of AR process are available. The effect of the additive noise is that the system can be modeled as an AR model with colored noise, even when the measurement noise is white, where the correlation matrix depends on the AR parameters. Because of the correlation, it is expedient to compute using multiple stacked observations. Performing a weighted least-squares estimation of the AR parameters using an inverse covariance weighting can provide significantly better parameter estimates, with improvement increasing with the stack depth. The estimation algorithm is essentially a vector RLS adaptive filter, with time-varying covariance matrix. Different ways of estimating the unknown covariance are presented, as well as a method to estimate the variances of the AR and observation noise. The notation is extended to vector autoregressive (VAR) processes. Simulation results demonstrate performance improvements in coefficient error and in spectrum estimation
- …