International Journal of Antennas and Propagation

Volume 2018, Article ID 6104849, 6 pages

https://doi.org/10.1155/2018/6104849

## Radar Selection Method Based on an Improved Information Filter in the LPI Radar Network

^{1}School of Electronic Information, Jiangsu University of Science and Technology, Zhenjiang, China^{2}CSIC, No. 722 Research & Development Institute, Wuhan Hubei 430079, China

Correspondence should be addressed to Zhenkai Zhang; nc.ude.tsuj@iaknehzgnahz

Received 17 March 2018; Accepted 4 November 2018; Published 17 December 2018

Academic Editor: Atsushi Mase

Copyright © 2018 Zhenkai Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

In order to save the radar resources and obtain the better low probability intercept ability in the network, a novel radar selection method for target tracking based on improved interacting multiple model information filtering (IMM-IF) is presented. Firstly, the relationship model between radar resource and tracking accuracy is built, and the IMM-IF method is presented. Then, the information gain of every radar is predicted according to the IMM-IF, and the radars with larger information gain are selected to track target. Finally, the weight parameters for the tracking fusion are designed after the error covariance prediction of every working radar, in order to improve the IMM-IF. Simulation results show that the proposed algorithm not only saves much more radar resources than other methods but also has excellent tracking accuracy.

#### 1. Introduction

Multiple radar systems have been shown to offer significant advantages over traditional monostatic radars [1]. When it comes to the reasonable configuration of multiple radar systems, the concept of resource scheduling becomes very important and has been drawing more and more attention in recent years.

As we know, low probability intercept (LPI) is one of the important features of modern radars. LPI optimization strategy is proposed in radar network architectures in [2, 3], where transmit power is minimized among netted phased array radars. The paper [4] studies the problem of scheduling the searching, verification, and tracking tasks of the military surveillance radar. The continuous double auction parameter selection algorithm is presented in [5] to solve the problem of allocating resource and selecting operational parameters for phased array radar system. Networked phased array radars that are connected by a communication channel are studied in paper [6], which proposes two types of distributed management techniques for the coordinated radar resource management. Based on sparsity-aware matrix decomposition, an improved method to select informative radars for target tracking in radar networks in proposed in [7], which shows the efficiency and improvement of the tracking performance. The paper [8] presents an optimal solution to the power allocation problem in distributed active multiple-radar systems subject to different power constraints, using a linear fusion rule and a simple objective function. In paper [9], a novel general criterion with the consideration of correlation in the measurement errors from different radars is proposed, which is applicable for a more general sensor network with an excellent tracking performance.

Sensor data fusion techniques are widely used in target tracking of radar network, which can be loosely defined as how to best extract useful information from multiple radar observations. Information filtering, which is essentially a Kalman filter expressed in terms of the inverse of the covariance matrix, has been widely used in multiple sensor estimation [10]. A novel approach to track-to-track fusion in a high-level sensor data fusion architecture for automotive surround environment perception using information matrix fusion (IMF) is presented in [11]. The paper [12] utilizes the iterative joint-integrated probabilistic data association technique for multisensor distributed fusion systems. The paper [13] develops the square-root extensions of unscented information filter and central difference information filter, which have better numerical properties than the original versions. For nonlinear system, the paper [14] presents a new state estimation algorithm called square-root cubature information filter, which is further extended for use in multisensory state estimation. To achieve further improvements in tracking accuracy, a self-adaptive algorithm for maneuver strategy transition probability matrix is proposed in [15], by utilizing the compression ratio of the maneuver strategy error. Many different architectures are presented in [16] for the target tracking in 3D Cartesian coordinates, with the measurements of all the sensors in polar coordinates.

However, those papers focus on the data selection after radar detection and do not consider the difference and accuracy of the sensors. Less working radars means much better LPI performance. In order to save the radar resource with excellent LPI performance, a radar selection algorithm is proposed based on an improved information filtering. The remainder of this paper is organized as follows. Section 2 presents the improved information filtering method and radar selection method. Simulations of the proposed algorithms and comparison results with other methods are provided in Section 3. The conclusions are presented in Section 4.

#### 2. Radar Selection Based on Improved Information Filter

Interacting multiple model (IMM) method is used for tracking maneuvering target. Information filter (IF), which is the dual Kalman filter, has attracted much attention for tracking fusion using multiple sensors [17]. But it cannot present excellent tracking performance for maneuvering target. In order to accomplish tracking fusion of maneuvering targets in radar network, a novel radar selection method based on interacting multiple model information filtering (IMMIF) is proposed in this section.

##### 2.1. Tracking Models and Measurement Noise in Radar Network

All the dynamic models are , is the th model used at time , the switch probability from model to model is , , , . is the probability of model , . Let and represent the state vector and the observation vector, respectively; the state equation and transfer equation at time are where and are stationary white noise processes with covariance matrices and . is the transition matrix and is the observation matrix. Every recurrence of the IMM algorithm contains interacting of input, model’s filtering, update of model probability, and interacting of output.

The covariance matrix of measurement noise is controlled by the emitted power. As we know, radar equation at time is as follows: where is the single dwelling time of the beam from the normal direction at time , is the average radiated power, is the receiver gain, is the radar cross section (RCS) of the target, is Boltzmann constant, and are, respectively, effective noise temperature and radar system loss, is the detection range, is the transmit gain, represents the signal to noise ratio of the system at time .

The single pulse signal is radiated by the radar, and the covariance of the measurement noise can be denoted as: where is the pulse width, is the wave velocity, and is the carrier frequency. We can see that different can lead to different .

##### 2.2. Information Filtering for Every Model

Utilizing all the states and model probabilities from last recurrence, the computation of input state and covariance of model can be express as

Using information state and Fisher information replace state estimate and covariance , we can obtain information filtering result based on Kalman filter. The definition of information state and Fisher information is

Prediction and estimation of and and can be obtained by recursive iteration, combining with and . The prediction of information state and Fisher information are given as

In the light of observation data from different sensors in the sensor network, the estimation of information state and Fisher information for every model are as follows: where and are the contributions that measurements make to and , respectively, which can be represented as follows.

The model probability is recursively updated by the ^{th} radar as
where is the likelihood function of model at time .

In the radar network, every radar will update a model probability, the final model probability can be calculated as

##### 2.3. Emitted Radar Selection Based on Information Computation

According to formula (2) and (3), the covariance of the measurement noise can be predicted based on the prediction of target distance and target RCS. So in (2) is replaced by which is predicted by and . is presented as

and are the target’s range and velocity which are estimated by the IMM tracking algorithm at time and is the tracking interval. RCS is supposed to be the same as , which has been measured by the fusion center according to the echo.

There are radars in the network. When the observation noise is predicted by the ^{th} radar, the information can be calculated using
where is the information gain which can be predicted by (9).

An information vector can be represented as

is the mean value of , which can be represented as

There are radars whose information gain are larger than , which will be selected as the working radars at next time, .

##### 2.4. Tracking Fusion Based on the Prediction for Error Covariance Matrix

The selected radars are used for target tracking. Then, the observation vector will be obtained. Using information filter for every model, the final estimation of the th radar can be represented as where .

Different radars have different predicted covariance matrix. The predicted covariance matrix is given as where is model probability at time , the predicted covariance matrix of every model can be represented as .

Then estimations and predicted covariance matrices and its trace will be obtained, *TR*_{n} = trace . Then, the reciprocal vector is computed. The weight of the radar tracking data can be formulated as

The final fusion result can be obtained at last:

#### 3. Simulation Results

In this section, Monte Carlo simulations are performed to analyze the performance of the proposed resource scheduling method.

##### 3.1. Trajectory Design

Figure 1 shows the target trajectory with its measurement results in 100 s. RCS of every radar is produced randomly during target tracking. All the radar positions are shown in Figure 1, which can be used to evaluate the LPI performance of the fusion methods.