Rapid gravitational wave parameter estimation with a single spin: Systematic uncertainties in parameter estimation with the SpinTaylorF2 approximation
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Abstract Since the initial discovery of gravitational waves in 2015, significant developments have been made towards waveform interpretation and estimation of compact binary source parameters. We present herein an implementation of the generalized precession parameter ⟨ χ p ⟩ [Gerosa et al 2021], which averages over all angular variations on the precession timescale, within the RIFT parameter estimation framework. Relative to the precession parameter χ p , which characterizes the single largest dynamical spin in a binary, ⟨ χ p ⟩ has a unique domain 1 < ⟨ χ p ⟩ < 2, which is exclusive to binaries with two precessing spins. After reviewing the physical differences between these two parameters, we describe how ⟨ χ p ⟩ was implemented in RIFT and apply it to all 36 events from the second half of the Advanced LIGO and Advanced Virgo third observing run (O3b). In O3b, ten events show significant amounts of precession ⟨ χ p ⟩ > 0.5. Of particular interest is GW191109_010717; we show it has a ∼ 28 % probability that the originating system necessarily contains two misaligned spins.more » « less
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Equation error and output error are common formulations used in speed and parameter estimation for induction machines. This paper presents a study of the quality of the estimated speed and parameters using local sensitivity analysis. We studied parameter conditioning as a function of input signals and estimation methodology at nominal speed. Simulation results are used to show that output error formulation is better conditioned than equation error for speed and parameter estimation using PWM and six-step voltage inputs.more » « less
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Estimating and quantifying uncertainty in unknown system parameters from limited data remains a challenging inverse problem in a variety of real-world applications. While many approaches focus on estimating constant parameters, a subset of these problems includes time-varying parameters with unknown evolution models that often cannot be directly observed. This work develops a systematic particle filtering approach that reframes the idea behind artificial parameter evolution to estimate time-varying parameters in nonstationary inverse problems arising from deterministic dynamical systems. Focusing on systems modeled by ordinary differential equations, we present two particle filter algorithms for time-varying parameter estimation: one that relies on a fixed value for the noise variance of a parameter random walk; another that employs online estimation of the parameter evolution noise variance along with the time-varying parameter of interest. Several computed examples demonstrate the capability of the proposed algorithms in estimating time-varying parameters with different underlying functional forms and different relationships with the system states (i.e. additive vs. multiplicative).more » « less
