This paper is concerned with the estimation problem of a dynamic stochastic variable in a sensor network, where the quantization of scalar measurement, the optimization of the bandwidth scheduling, and the characteristic of transmission channels are considered. For the imperfect channels with missing measurements in sensor networks, two weighted measurement fusion (WMF) quantized Kalman filters based on the quantized measurements arriving at the fusion center are presented. One is dependent on the known message of whether a measurement is received. The other is dependent on the probability of missing measurements. They have the reduced computational cost and same accuracy as the corresponding centralized fusion filter. The approximate solution for the optimal bandwidth-scheduling problem is given under a limited bandwidth constraint. Furthermore, the vector measurement case is also discussed. The simulation research shows the effectiveness.

In recent years, sensor networks have been widely investigated in decentralized estimation, detection, and control due to the significant applications in environmental monitoring, intelligent transportation, space exploration, and so forth [

Various algorithms have been proposed for network estimation, detection, and control [

In this paper, the quantized estimation problem for a dynamic stochastic variable is studied in a sensor network. Due to the limited bandwidth constraint, the measurement of sensors is quantized uniformly according to a given optimal bandwidth scheduling. During the transmission of quantized measurements, there are possible losses due to imperfect channels. Due to the large number of data, the fusion center compresses the received measurements to produce a reduced dimensional fused measurement, based on which, two weighted measurement fusion quantized filters are presented. One is dependent on the knowledge of whether a packet is received. The other is dependent on the probabilities of missing measurements. The front has the better accuracy since more messages are used. They have the same accuracy as the corresponding centralized fusion filters.

Consider the discrete-time system in a sensor network with

The estimation problem considered is shown in Figure

Distributed state estimation scheme based on quantized observations.

Our aim in this paper is to find the weighted measurement fusion quantized Kalman filters (WMF-QKF) under the limited bandwidth by imperfect channels. Two kinds of filters are designed. One is dependent on the values of

We adopt the uniform quantization strategy in [

In sensor networks, the whole bandwidth of communication channels is bounded. Let

When the values of

When

(a) If

(b) If

Then based on systems (

(c) If

Then based on systems (

When

From (

In this section, we will design the filter dependent on the probabilities of

Then the augmented measurements can be expressed as

According to the different cases that the matrix

Two kinds of WMF-QKFs have been proposed. The filter dependent on the values of

WMF-QKF with optimization problems has been solved for systems with scalar measurement in Sections

The system structure is similar to Figure

For the case of multiple dimension measurements of each sensor,

Consider a discrete-time system measured by five sensors:

We solve the optimization problem (

Comparison of tracking for WMF-QKFP and WMF-QKFV under whole bandwidth

The first state component

The second state component

The third state component

Comparison of accuracy of WMF-QKFP, WMF-QKFV, and all LFs under whole bandwidth

The first state component

The second state component

The third state component

The weighted measurement fusion quantized filtering problem is investigated in a sensor network with bandwidth constraint and imperfect channels of missing measurements. Using the knowledge of whether a measurement is lost at the present time or the probabilities of missing measurements, two weighted measurement fusion quantized Kalman filters are developed based on the quantized measurements received, respectively. They have the same accuracy as the corresponding centralized fusion estimators and have the reduced computational cost.

The authors declare that there is no conflict of interests regarding the publication of this paper.

This work is supported by the Natural Science Foundation of China (NSFC-61174139), by Chang Jiang Scholar Candidates Program for Provincial Universities in Heilongjiang (no. 2013CJHB005), by Science and Technology Innovative Research Team in Higher Educational Institutions of Heilongjiang Province (no. 2012TD007), by the Program for New Century Excellent Talents in University for Heilongjiang Province (no. 1154-NCET-01), by the Program for High-qualified Talents (no. Hdtd2010-03), and by Electronic Engineering Provincial Key Laboratory.