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Binary Detection in Gaussian Noise

  1. Feb 7, 2013 #1
    I have a vector signal, [itex]\underline{x}(t)[/itex], which is afflicted with Gaussian noise [itex]\underline{n}(t)[/itex]. I take a finite number, [itex]L[/itex], of discrete observations and (based on those observations) want to determine whether:

    (1) Only Gaussian noise is present, [itex]\left[\text{i.e. } \underline{x}(t) = \underline{n}(t)\right][/itex]
    (2) Gaussian noise plus a "non-noise" term, [itex]\underline{a}m(t)[/itex], are both present. [itex]\left[\text{i.e. } \underline{x}(t) = \underline{a}m(t) + \underline{n}(t)\right][/itex]

    The scalar, [itex]m(t)[/itex], is zero-mean and has unknown power (variance). The elements of [itex]\underline{x}(t)[/itex] are independent of each other and also independent of [itex]m(t)[/itex].

    Given my observations, how can I estimate the probability that the signal is present?

    Many thanks for any help!
  2. jcsd
  3. Feb 7, 2013 #2


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    Science Advisor

    Hey weetabixharry.

    I'm not an expert, but I do recall the subject of Kalman filters:


    Basically you should check out these kind of things where you prefix a structure for your information that assumes some noise model (like White Gaussian) and then uses a filter to not only detect noise, but also the actual non-noisy information.

    There are also non-linear variants of the filter.
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