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Efficent Generation of Fractional Brownian Motion for Simulation of Infrared Focal-plane Array Calibration Drift

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Abstract

Infrared focal-plane arrays suffer from a type of 1/f noise which leads to slow drifts in detected radiation levels following calibration. This noise can be modeled by fractional Brownian motion (FBM), with an empirical Hurst parameter (H) in the range 0 < H < 1 / 2. For such noise we examine the statistics of both the maximum deviation from the calibration point during a fixed time, and the time to reach a fixed deviation from the calibration point. We employ analytical and numerical means; for the latter, we provide a new algorithm for generating a discrete-time version of FBM with 0 < H ≤ 1 / 2 which is fast (order N log N), and exact. Statistics of the maximum deviation show the same qualitative behavior for different values of H, and rapidly approach a limit as the length N increases. Results for first passage times, in contrast, vary markedly with H, but not with N.

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Authors and Affiliations

  1. McLean Hospital, USA

    Steven B. Lowen

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  1. Steven B. Lowen
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Lowen, S.B. Efficent Generation of Fractional Brownian Motion for Simulation of Infrared Focal-plane Array Calibration Drift. Methodology and Computing in Applied Probability 1, 445–456 (1999). https://doi.org/10.1023/A:1010027211901

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