Discrete-time filtering for nonlinear stochastic systems has been the subject of considerable research during the past few decades.
Scientific and engineering applications include target tracking, infrastructure monitoring, habitat sensing, and battlefield surveillance.
The objective of nonlinear filtering is to estimate the state of a dynamic process based on noisy observations.To infer the states of the system (position, velocity, attitude, and heading, etc.), certain modalities of measurements such as time of arrival, signal intensity, phase lags or images must be incorporated.
In practical applications, the measurement model is often signal dependent. For instance, in a bearings-only sensor application, the measurement noise is a function of the signal to noise ratio and the incident angle of the signal. Besides, the measurement signals contaminated by the multiplicative noise are common in many systems.
Researchers from Institute of Acoustics of the Chinese Academy of Sciences, Ryerson University (Canada), University of Wisconsin-Madison (USA) have considered a type of multiplicative measurement noise model. It is to facilitate more accurate characterization of measurement errors of sensors.
The main contribution of their research is having presented a generalized iterated Kalman filter for nonlinear stochastic discrete-time system with state-dependent multiplicative observation noise.
Specifically, it is assumed that the measurements of sensors are contaminated by both additive Gaussian noise and multiplicative Gaussian noise.
With this nonlinear state-dependent noise model, the filter update requires the conditional statistics of the observation. That is, the correlation between the state and observation noise must be taken into account.
A maximum a posteriori (MAP) estimation method is adopted to compute the updated state. An approximate MAP estimation can be obtained by an iteration that amounts to re-linearization of the measurement equation.
In the following, an iterated Kalman filter is developed based on Gaussian approximation of the posterior distribution.
Compared with previous research mainly dealing with an additive measurement noise of state-dependent covariance, this research elaborates the theoretical relation between the generalized iterated Kalman filter and the generalized extended Kalman filter, as well as the traditional extended Kalman filter.
It is found that the generalized iterated Kalman filter yields a higher estimation accuracy than the generalized extended Kalman filter and traditional extended Kalman filter in the multiplicative observation noise model.
The error performance of the generalized iterated Kalman filter including the mean square estimation error and the Cramér-Rao lower bound is analyzed as well.
References:
Xiaoqing Hu, Ming Bao, Xiao-Ping Zhang, Senior Member, IEEE, Luyang Guan, and Yu-Hen Hu, Fellow, IEEE. Generalized Iterated Kalman Filter and its Performance Evaluation. Signal Processing, IEEE Transactions on (Vol.63, No. 12, June15, 2015, pp. 3204 - 3217 ). DOI: 10.1109/TSP.2015.2423266
Contact:
Xiaoqing Hu
Institute of Acoustics, Chinese Academy of Sciences, 100190 Beijing, China
Email: auxqhu@gmail.com