### 1. Introduction

### 2. Tracking Method

### 2.1 Unscented Kalman Filter (UKF)

### 2.2 Probabilistic Data Association Filter (PDAF)

#### 2.2.1 Measurement value validation

*k*th measurements and using the selected values for state estimation. The range of validation used during the selection process is known as the validation gate, and the volume of the validation gate is defined as

*q*denotes the dimension of the measurement value and

*γ*

*denotes the threshold of the gate.*

_{G}**S**(k) represents the innovation covariance matrix, which is expressed in Eq. (12).

#### 2.2.2 Data association

*N*denotes the number of valid measurements,

_{v}*θ*

_{i}_{,}

*denotes the*

_{k}*i*th valid measurement at time

*k*, and

*Z*

_{i}_{,}

*denotes the incident observed from the actual target. Moreover,*

_{k}*θ*

_{0,}

*denotes the incident where the valid measurements are obtained from a clutter (reflected signal that obstructs the target detection) instead of the target. Based on the aforementioned equation, it is assumed that only one measurement is derived from a single target. Therefore,*

_{k}*θ*

_{i}_{,}

*(*

_{k}*i*= 0,1,…,

*N*) are exclusive events, and the probability of

_{v}*θ*

_{i}_{,}

*, which is the combination of probability*

_{k}*β*

_{i}_{,}

*that the*

_{k}*i*th measurement will be derived from the actual target and probability

*β*

_{0,}

*that the measurement will be a clutter rather than an observation based on a real target, is defined in Eq. (14).*

_{k}*P*denotes the probability that an accurate measurement exists within the validation gate and

_{G}*P*denotes the probability that an accurate value is observed using the radar sensor. Both values are determined using the sensor. The derived probability of relevance is used in determining the error covariance and UK–PDAF estimation values, and the corresponding process is expressed in Eq. (15).

_{D}### 3. Sensor Fusion

### 3.1 Location Prediction Technique Based on AIS Data

*ϕ*and

_{p}*λ*indicate the predicted latitude and longitude during sensor fusion, respectively.

_{p}*ϕ*and

_{A}*λ*indicate the latitude and longitude of the received AIS signal, respectively.

_{A}*v*denotes the ground speed,

*θ*denotes the course over the ground,

*δ*denotes the angular distance,

*t*denotes the time of sensor fusion, and

_{S}*t*denotes the reception time of the corresponding AIS signal.

_{A}### 3.2 Sensor Fusion Algorithm

### 4. Validation

### 4.1 Result and Abnormal Phenomenon of Case 1

*ΔD*=

*Position*−

_{AIS}*Position*) based on the analytical results of the phenomenon that occurred in Case 1. In the figure, the horizontal axis shows the number of fusion trials, and the vertical axis shows the difference in location. Moreover, the red dotted line presents the distance threshold mentioned in Section 3.2. Owing to abundant AIS data, some are indicated among the reception signals (Fig. 6) (within 500 m based on ARPA radar signal), and distinguishing the indicated symbols and colors becomes difficult. Therefore, the signals over than the red dotted line(200m threshold from the own ship) show that the locations of the traffic ships are at a far distance from the own ship(training ship). What each symbol has a parabola shape means that the traffic ship approached to the own ship in a certain duration and passed to far away.

_{ARPARadar}### 4.2 Result and Abnormal Phenomenon of Case 2

*D*) between the locations of the vessel obtained from the AIS and ARPA signals (based on the analysis results of Case 2).

*D*rapidly increased owing to abnormal occurrences. Fig. 8(b) shows the application of the proposed technique for the same situation.

### 4.3 Result and Abnormal Phenomenon of Case 3

### 4.4 Result and Abnormal Phenomenon of Case 4

*D*) in the locations of the vessel obtained from the AIS and ARPA signals (based on the analysis results of Case 4).

*D*varied within the threshold value. Fig. 10(b) shows the case of updating the signal based on the proposed location prediction and object-tracking algorithms for an identical situation, and the change toward the appearance of a data distributional tendency can be identified. Table 7 lists the fusion success rates with respect to the total number of attempts (189 times) for the aforementioned circumstance, and processing as proposed in this study exhibited higher success rates than sensor fusion without any other additional processing.

### 4.5 Result and Abnormal Phenomenon of Case 5

*D*) between the location of own ship and the locations of the vessel obtained from the AIS and ARPA signals (based on the analysis results of the phenomena of Case 5).

*D*varied within the threshold value with an increase in the measurement time. Fig. 11(b) shows the case of updating the signals using the location prediction algorithm and the proposed object tracking algorithm for the same situation, from which a change toward data having distributional tendency and reduced range of distributed difference between the heterogenous signal locations can be identified.