Lin Qiongbin, Liu Qiuhua, Lai Tianyue, Wang Wu
College of Electrical Engineering and Automation, Fuzhou University, Fuzhou, Fujian 350116, China.
Fujian Key Lab of Medical Instrument and Pharmaceutical Technology, Fuzhou, Fujian 350116, China.
Comput Math Methods Med. 2017;2017:7837109. doi: 10.1155/2017/7837109. Epub 2017 Jul 26.
The filter problem with missing value for genetic regulation networks (GRNs) is addressed, in which the noises exist in both the state dynamics and measurement equations; furthermore, the correlation between process noise and measurement noise is also taken into consideration. In order to deal with the filter problem, a class of discrete-time GRNs with missing value, noise correlation, and time delays is established. Then a new observation model is proposed to decrease the adverse effect caused by the missing value and to decouple the correlation between process noise and measurement noise in theory. Finally, a Kalman filtering is used to estimate the states of GRNs. Meanwhile, a typical example is provided to verify the effectiveness of the proposed method, and it turns out to be the case that the concentrations of mRNA and protein could be estimated accurately.
研究了基因调控网络（GRNs）存在缺失值时的滤波问题，其中状态动态方程和测量方程中均存在噪声；此外，还考虑了过程噪声与测量噪声之间的相关性。为了解决该滤波问题，建立了一类具有缺失值、噪声相关性和时间延迟的离散时间GRNs。然后提出了一种新的观测模型，以减少缺失值造成的不利影响，并在理论上解耦过程噪声与测量噪声之间的相关性。最后，采用卡尔曼滤波估计GRNs的状态。同时，给出了一个典型例子来验证所提方法的有效性，结果表明mRNA和蛋白质的浓度能够被准确估计。
