Bayesian sequential joint detection and estimation
Bayesian sequential joint detection and estimation
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DOI：
10.1080/07474946.2018.1554899
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发表时间：
2018-07
期刊：
影响因子：
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通讯作者：
Dominik Reinhard;Michael Fauss;A. Zoubir
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文献类型：
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作者：
Dominik Reinhard;Michael Fauss;A. Zoubir
联合检测和估计是指在两个或两个以上的假设之间进行决策，并根据检验结果同时估计潜在分布的未知参数。在对基本随机过程作了较温和的假设下，在序贯框架下研究了该问题。我们建立了一个无约束的序列决策问题，其代价函数是期望行程长度和检测/估计误差的加权和。然后，证明了代价函数关于权重的导数(可被解释为拉格朗日乘子)与基本方案的检测/估计误差之间的强联系。这一性质被用来刻画一个密切相关的序列决策问题的解，其目标函数是在平均检测/估计误差约束下的期望游程长度。证明了在适当选取权重的情况下，约束问题的解与无约束问题的解是一致的。这些权重被描述为线性规划的解，可以使用高效的现成解算器来求解。用数值方法设计了最优序列方案，并通过蒙特卡罗模拟验证了最优序列方案的性能。
Abstract Joint detection and estimation refers to deciding between two or more hypotheses and, depending on the test outcome, simultaneously estimating the unknown parameters of the underlying distribution. This problem is investigated in a sequential framework under mild assumptions on the underlying random process. We formulate an unconstrained sequential decision problem, whose cost function is the weighted sum of the expected run-length and the detection/estimation errors. Then, a strong connection between the derivatives of the cost function with respect to the weights, which can be interpreted as Lagrange multipliers, and the detection/estimation errors of the underlying scheme is shown. This property is used to characterize the solution of a closely related sequential decision problem, whose objective function is the expected run-length under constraints on the average detection/estimation errors. We show that the solution of the constrained problem coincides with the solution of the unconstrained problem with suitably chosen weights. These weights are characterized as the solution of a linear program, which can be solved using efficient off-the-shelf solvers. The theoretical results are illustrated with two example problems, for which optimal sequential schemes are designed numerically and whose performance is validated via Monte Carlo simulations.