带相关噪声的观测融合稳态Kalman滤波算法及其全局最优性

Measurement Fusion Steady-State Kalman Filtering Algorithm with Correlated Noises and Global Optimdity

对于带相关的输入白噪声和观测白噪声及相关观测白噪声的多传感器线性离散定常随机系统,用加权最小二乘(WLS)法提出了一种加权观测融合稳态Kalman滤波算法,可处理状态、白噪声和信号融合滤波、平滑、预报问题。基于稳态信息滤波器证明了它完全功能等价于集中式观测融合稳态Kalman滤波算法,因而它具有渐近全局最优性,且可减少计算负担。一个跟踪系统仿真例子验证了它的功能等价性。

For the multisensor linear discrete time-invariant stochastic control systems with correlated input and measurement white noises, and with correlated measurement white muses, a weighted measurement fusion steady-state Kalman filtering algorithm is presented by using the Weighted Least Squares（WLS）method. It can handle the fused filtering, smoothing and prediction problems for the state, white noise and signal. Based on the steady-state information filter, it is proved that it is completely functionally equivalent to the centralized measurement fusion steady-state Kalman filtering algorithm, so that it has asymptotic global optimality, and can reduced the computational burden. A simulation examples for tracking systems verifies its functional equivalence.