# SMC-CPHD Filter with Adaptive Survival Probability for Multiple Frequency Tracking
## 1 Introduction  
Research on multiple target tracking filters has been actively conducted in various fields as well as in the target tracking field [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13]. In particular, multiple target tracking filters based on a random finite set (RFS) can be used in many applications because the filters can track targets, even if the number of targets is unknown or if the number of targets changes over time [14, 15, 16, 17, 18, 19, 20, 21]. Using these characteristics, we have recently conducted research to estimate and to finally mitigate multiple frequencies using the cardinalized probability hypothesis density (CPHD) filter among the RFS-based filters when a global navigation satellite system (GNSS) signal is received with multiple interference signals [22]. Studies have also been conducted to enhance the cardinality estimate performance of the CPHD filter, which results in increasing the performance of frequency estimates [22]. However, the performance is still not perfect, and additional methods are needed to enhance the estimate performance of the filter and the cardinality estimate performance in real situations, especially when clutter is present. As part of these studies, in this paper, the adaptive survival probability is applied to the sequential Monte Carlo-based CPHD (SMC-CPHD) filter. In the initial version of the RFS filters, most of the filters assumed that the probability of survival is constant [7, 8, 10, 23]. However, in a case with clutter in the measurements, fixing the probability of survival to a constant value (relatively large value) prevents the survival intensity from properly reflecting the situation and affects the estimate performance of thefilter. Therefore, it is necessary to adaptively apply the probability of survival according to the measurements including clutter within the specified boundary. To address this problem, the previous paper also suggested adaptively setting the probability of survival to the GM-PHD filter [24]. Here, the authors of [24] defined a simple survival model to adaptively compute the survival probability of the state variable according to moving direction and position. In the paper [25], only the probability of detection was adaptively set. The proposed methods in previous papers were limited in the applicable systems or performed probability adjustment based on the observation area. Based on the existing research results, we propose an adjustment technique of adaptive survival probability to set the appropriate value of survival probability for the multiple frequency tracking system, where the probability of survival is changed to be inversely proportional to the exponential function according to the Euclidean distance between the posterior state and the particles. In order to evaluate whether or not the modified survival probability affects the stability of the filter, the error bounds in the prediction process are analyzed to verify the stability of the filter. In addition to adaptive survival probability, an inverse covariance intersection (ICI)-based compensation technique is added to improve cardinality tracking performance. The ICI method [26; 27] is one of the latest methods in the sensor fusion field. The ICI method provides more precise fusion results than those obtained by conventional covariance intersection (CI) methods [27]. The compensation method with ICI fused two types of cardinality information using the ICI method, which were the cardinality information estimated from the CPHD filter and the cardinality information additionally generated to compensate for the original cardinality estimate. The paper is organized as follows. The processing steps of the SMC-CPHD filter are reviewed in Section 2. The probability of survival points in the SMC-CPHD filter is proposed in Section 3. In addition, the convergence of the mean square estimate is proved in case the proposed survival probability is applied in the existing SMC-CPHD filter.