BeyondPlanck VI. 噪声特性表征与建模
BeyondPlanck VI. Noise characterization and modelling
AI总结：
本文提出一种贝叶斯方法在BeyondPlanck框架内估计Planck LFI噪声参数并传播不确定性，发现30和44GHz频段需额外对数正态分量，并揭示了噪声PSD参数的显著时变性及额外相关噪声。
摘要：
我们提出了一种贝叶斯方法，用于估计仪器噪声参数并在全局 BeyondPlanck 吉布斯采样框架内传播噪声不确定性，并将其应用于 Planck 低频仪器（LFI）时序数据。遵循先前文献，我们最初采用 $1/f$ 模型作为噪声功率谱密度（PSD），但发现 30 和 44 GHz 频段的噪声模型需要额外的对数正态分量。我们实现了最优维纳滤波（或约束实现）间隙填充程序来处理被掩蔽的数据。随后，我们利用该程序在时域估计无间隙相关噪声 $n_\mathrm{corr}$，并对噪声 PSD 参数 $ξ^n = \{σ_0, f_\mathrm{knee}, α, A_\mathrm{p}\}$ 进行采样。与先前的 Planck 分析不同，我们仅在每个指向周期（PID）内假设分段平稳噪声，而非整个任务期间，但采用 LFI 数据处理中心（DPC）结果作为 $α$ 和 $f_\mathrm{knee}$ 的先验。平均而言，我们发现最佳拟合相关噪声参数与先前结果基本一致，但有少数显著例外。然而，对时间相关结果的详细检查揭示了许多重要发现。首先，我们发现所有噪声 PSD 参数存在统计上显著的时变性的有力证据，其中许多与卫星遥测数据直接相关。其次，虽然简单的 $1/f$ 模型对 LFI 70 GHz 通道拟合极佳，但 30 和 44 GHz 通道存在 $1/f$ 模型无法描述的额外相关噪声，包括在 0.1--1 Hz 的主要科学频率范围内。（节选）
英文摘要：
We present a Bayesian method for estimating instrumental noise parameters and propagating noise uncertainties within the global BeyondPlanck Gibbs sampling framework, and apply this to Planck Low Frequency Instrument (LFI) time-ordered data. Following previous literature, we initially adopt a $1/f$ model for the noise power spectral density (PSD), but find the need for an additional lognormal component in the noise model for the 30 and 44\,GHz bands. We implement an optimal Wiener-filter (or constrained realization) gap-filling procedure to account for masked data. We then use this procedure to both estimate the gapless correlated noise in the time-domain, $n_\mathrm{corr}$, and to sample the noise PSD parameters, $ξ^n = \{σ_0, f_\mathrm{knee}, α, A_\mathrm{p}\}$. In contrast to previous \textit{Planck} analyses, we assume piecewise stationary noise only within each pointing period (PID), not throughout the full mission, but we adopt the LFI Data Processing Center (DPC) results as priors on $α$ and $f_\mathrm{knee}$. On average, we find best-fit correlated noise parameters that are mostly consistent with previous results, with a few notable exceptions. However, a detailed inspection of the time-dependent results reveals many important findings. First and foremost, we find strong evidence for statistically significant temporal variations in all noise PSD parameters, many of which are directly correlated with satellite housekeeping data. Second, while the simple $1/f$ model appears to be an excellent fit for the LFI 70 GHz channel, there is evidence for additional correlated noise not described by a $1/f$ model in the 30 and 44 GHz channels, including within the primary science frequency range of 0.1--1 Hz. (Abridged)
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