Kaiman Filter And The Applied Research Of Suppressing The Narrowband Interference In UWB Systems

Kalman solved the discrete linear filtering problem by mathematical equations in1960. From thenon, with the rapid development of computer information technology, Kalman filter has been extensivelystudied and used. Kalman filtering is a time domain state spatial filtering method. Its data storagecapacity is small, and the mean square error estimated is the optimal. It can also handle one-dimensionalor multidimensional stationary or non-stationary random signal. Because of its simple design and easysimulation realizable on the computer, it has been widely used in multiple fields, such as navigation,communications, industrial control, geological exploration, wireless positioning and so on. It becomesthe subject of current concern.In this paper, combined with the characteristics of ultra-wideband communication technology, theKalman filter for the interference suppression applications in ultra-wideband (UWB) communication isresearched meticulously and thoroughly based on the Kalman filter estimation theory. We describemainly from two major aspects. On the one hand, the application of Kalman filter about the narrowbandstationary signal in ultra-wideband communication is discussed. According to the smooth characteristicsof linear time series, we regard the narrowband stationary signal as the state equation of the system,while the received signal in ultra-wideband system is considered as the observation equation. Then weestablish a time domain basic Kalman filtering equation, and simulate on computer. However,simulation results indicate that this algorithm can’t simulation narrowband stationary random signalwhen parameters of narrowband stationary signal of the AR (p) model are few. Therefore, it isrecommended that the above Kalman filter algorithm should be improved, which is compared withKalman filter method improved before by simulation experiments. On the other hand, multi-scaleKalman filter algorithm for the fractal noise signal in UWB system is studied. Firstly, brief introduces ofthe basic theory of wavelet transform and fractal noise signal are given. Secondly, the multi-scalewavelet decomposition of the non-stationary fractal noise signal is received. And the waveletcoefficients on each scale wavelet coefficients are modeled as the corresponding stationary time seriesmodel under its stationary nature. Finally, combined with the discrete observation signal of the UWBsystem, we obtain the state space model of the Kalman filter by using the computer Matlab software tosimulate.