# A Sector-Matching Probability Hypothesis Density Filter for Radar Multiple Target Tracking
###### Abstract
Sampling time variety due to radar beam scanning has not been taken into account in PHD filters [36]. In contrast to an optical imaging system, where all measurements within the monitoring space are simultaneously generated at the moment when photos are taken, radar obtains measurements when the beam illuminates the target. It takes a long time for the beam to scan the entire airspace and this causes targets at different locations to be detected at different times. The sampling time difference cannot be ignored, for it leads to a mismatch between multi-target state prediction and measurement, resulting in additional measurement errors, especially when the beam scans large surveillance areas or searches for weak targets and illuminated targets with a long dwell time to obtain a better signal-to-noise ratio (SNR) [13; 37]. [PERSON] previously proposed a time-labeled RFS which has been applied to a number of problems, such as the Bayesian framework [13] and the ET-PHD filter [37]. However, specific measurement time information is generally not included in radar echoes and [PERSON]'s work considered the detection probability as a constant and did not consider the variation in the detection probability with beam dwell time in actual radar operation. In this paper, a novel sector-matching PHD filter is proposed. In order to make the sector-matching framework more suitable for radar real-time MTT in a complex scenario, we combine a real radar system with the LGM-PHD filter [35] and quantify the relationship between beam dwell time, signal-to-noise ratio (SNR), false alarm rate and detection probability. To simplify the problem, we consider a radar one-way electro-scan scenario, in which the target position (in particular, the bearing) and target measurement time correspond one-to-one. The main contributions of this article are as follows:  
* The proposed filter divides the detection space into several small sectors and assumes that the different sectors are independent of each other;Based on these sectors and measurement states, the actual measurement time can be obtained and used to split and derive the prediction and update equations of the PHD filter;
* The quantitative relationship between beam dwell time, false alarm rate, detection probability and SNR is combined with PHD filters;
* Since we interested in the target state at the end of each scan, a state correction step is added before extracting the target state;
* We evaluate the effectiveness of the proposed method using the constant velocity (CV) and constant acceleration (CA) dynamic models, and demonstrate that the proposed filter can solve the problem of high clutter rate and radar sampling time variety when detecting weak targets well, and enables the track maintenance function. The rest of the article is organized as follows. Section 2 presents the technical background. Section 3 presents the specific design of the improved SM PHD multi-filter using its Gaussian mixture implementations. Quantitative simulation experiments are described in Section 4. Section 5 presents our concluding remarks.