In this article, we consider the distributed direct target tracking using the received radio signal by exploiting time delay and Doppler for heterogeneous wireless sensor networks. We develop herein a distributed Gaussian particle filtering (D-GPF) algorithm for diffusion networks, along with an adaptive combiners (AC) scheme and a particle number adaptation (PNA) method. We transform the online AC optimization problem into the minimum variance unbiased estimation problem with the nonnegative constraint of the combiners imposed, and solve this constrained problem by establishing the Karush-Kuhn-Tucker (KKT) conditions. Further, we develop a variable bin-size scheme for the PNA method to improve the efficiency of particle filters in conformity with the underlying state uncertainty at each sensor of the heterogeneous networks. Simulations involving heterogeneous networks illustrate i) that the proposed AC method could improve robustness of the D-GPF against the spatial variation of Signal-to-Noise-Ratios over the network, and ii) that the proposed PNA method could achieve a tradeoff between the tracking performance and computational complexity of the D-GPF.

中文翻译：

---

异构网络分布式高斯粒子滤波的直接目标跟踪

在本文中，我们通过利用异构无线传感器网络的时间延迟和多普勒来考虑使用接收到的无线电信号进行分布式直接目标跟踪。我们在此开发了一种用于扩散网络的分布式高斯粒子滤波 (D-GPF) 算法，以及一种自适应组合器 (AC) 方案和一种粒子数自适应 (PNA) 方法。我们将在线 AC 优化问题转化为施加组合器非负约束的最小方差无偏估计问题，并通过建立 Karush-Kuhn-Tucker (KKT) 条件来解决这个约束问题。此外，我们为 PNA 方法开发了一种可变 bin-size 方案，以根据异构网络的每个传感器的潜在状态不确定性来提高粒子滤波器的效率。