Monte Carlo粒子滤波器的一致时间平均一致性
Uniform Time Average Consistency of Monte Carlo Particle Filters
摘要：
证明了当信号遍历且粒子系统满足紧性时，自举型Monte Carlo粒子滤波器在时间平均意义下关于时域一致逼近最优非线性滤波.当信号状态空间是紧的，以及在非紧的设置时，信号是几何遍历和观察满足额外的规律性假设，后者是满足没有进一步的假设。
英文摘要：
We prove that bootstrap type Monte Carlo particle filters approximate the optimal nonlinear filter in a time average sense uniformly with respect to the time horizon when the signal is ergodic and the particle system satisfies a tightness property. The latter is satisfied without further assumptions when the signal state space is compact, as well as in the noncompact setting when the signal is geometrically ergodic and the observations satisfy additional regularity assumptions.
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