非寻复域状态-空间滤波

Improper complex-domain state-space filtering

针对实际非平稳海洋声数据存在非寻和非圆特性,在状态-空间模型下,对复信号作增广表示,建立复域状态-空间模型.从观察者的角度,推导了复高斯条件下的最佳瞬变观察者的线性表达式,即复域卡尔曼滤波器.当状态-空间模型为非线性非高斯时,最佳瞬态观察者须通过线性化或数值近似的方法近似得到.给出一种数值近似的方法——复域质点滤波,通过计算机仿真和波导实验证明了在信号非寻的情况下,复域卡尔曼滤波和复域质点滤波比常规的卡尔曼滤波和质点滤波具有更好的估计性能.

The complex-domain state-space model was established, which is developed from that in real- valued space through augmented expression of complex-valued random signals with improper and noncircular properties of non-stationary underwater acoustic data. The optimal transient observer, which termed as complex-domain Kalman filter, was derived under complex Gaussian and linear assumptions with knowledge of complemented covariance. While state-space model is nonlinear and non-Gaussian, the optimal transient observer can be derived by linearization and numerical approximation. A typical numerical approximation method names complex-domain particle filter. Simulation and waveguide experiment show that the complex domain Kalman filter and complex-domain particle filter have better performance compared to the regular Kalman filter and particle filter in improper situation.