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.

中文翻译：

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贝叶斯序列联合检测和估计

摘要 联合检测和估计是指在两个或多个假设之间做出决定，并根据测试结果同时估计潜在分布的未知参数。在对基础随机过程的温和假设下，在顺序框架中研究了这个问题。我们制定了一个无约束的顺序决策问题，其成本函数是预期游程长度和检测/估计误差的加权和。然后，显示了成本函数关于权重的导数（可以解释为拉格朗日乘数）与基础方案的检测/估计误差之间的强联系。此属性用于表征密切相关的顺序决策问题的解决方案，其目标函数是在平均检测/估计误差约束下的预期运行长度。We show that the solution of the constrained problem coincides with the solution of the unconstrained problem with suitably chosen weights. 这些权重被表征为线性程序的解，可以使用高效的现成求解器来求解。理论结果通过两个示例问题进行说明，针对这些问题进行了数值设计，并通过蒙特卡罗模拟验证了其性能。这可以使用高效的现成求解器来解决。理论结果通过两个示例问题进行说明，针对这些问题进行了数值设计，并通过蒙特卡罗模拟验证了其性能。这可以使用高效的现成求解器来解决。理论结果通过两个示例问题进行说明，针对这些问题进行了数值设计，并通过蒙特卡罗模拟验证了其性能。