**1. Introduction**

Acoustic signals are used to indirectly obtain information about objects located underwater. Most passive sonar systems use multiple hydrophones in an array for enhanced performance. A horizontal line array (HLA), used for detecting the azimuth angle of an underwater target, receives acoustic signals with a high signal to noise ratio from designated directions using a beamforming technique. If the target signal intensity is high enough in a designated direction, the target direction is detected. The estimated target direction is represented as a conical angle that indicates the direction of the incoming signal measured by the HLA. Unfortunately, it is impossible to distinguish between up and down or right and left from the conical angle. This is called the cone of ambiguity [1].

Sequential processing and batch processing algorithms are used to estimate the target's state, including position and velocity, through bearings-only target motion analysis (BO-TMA). There exist several conventional sequential processing algorithms, including the extended Kalman filter [2], the pseudo-measurement filter [3], and the modified gain extended Kalman filter [4]. In addition to these filters, particle filter approaches [5] and random finite set approaches [6–8] have been recently introduced. If sufficient computational performance is achieved, sequential processing is suitable

for implementation in real time systems. However, good sequential estimation results require small errors in the initial state estimates, and a batch processing algorithm is used for this purpose. Batch processing delivers stable initial values, even though it is not designed to operate in real time because it requires a batch of stored measurements. Robust target localization performance is expected if both types of algorithms are employed properly [9].

In most of the previous studies on sonar systems [2,3,6–9], it is assumed that the received signal arrives at the HLA through the horizontal plane when the distance between the observer and target is large, or when the observer and the target are located at equal depths. Therefore, the cone of ambiguity of the HLA is simplified to left/right ambiguity, which can be easily addressed through a ship maneuver. However, eigenray tracing results show that the received signal can arrive at the HLA with a high elevation angle, especially along a bottom bounce path [10]. The studies in [11,12] consider the elevation angles in BO-TMA for different sensor depths between the observer and the target. They treat only direct paths without considering the reflection of the ray from the waveguide boundaries (i.e., sea surface and bottom) or the refraction of the ray from the vertical sound speed profile. However, bottom bounce paths, which are generated from the reflection of acoustic waves at the ocean bottom, can produce inaccurate target bearings [13] that affect BO-TMA results.

The ray tracing method [14] is used to calculate the elevation angle due to the refraction and reflection of sound waves in underwater waveguides. This method describes the path of each ray as sound waves propagating through the underwater waveguide. In particular, it is possible to calculate the eigenray [15], which represents the path of a ray that propagates from the source to the receiver. The elevation angle of the target signal can be simulated through eigenray tracing, and the conical angle can be calculated using the azimuth angle and the elevation angle.

In this paper, a study is based on the published conference paper [16] and it is conducted to confirm the observability of TMA using the conical angle including the elevation angle of the path reflected from the bottom interface for a given scenario. A discrete target dynamic equation is established with the target state vector, and the conical angle measurement is obtained from the relative geometry of the observer and the target using the ray tracing method in Section 2. Section 3 presents a method of converting the conical angle into a bearing line in Cartesian coordinates using knowledge of the ocean environment (i.e., bottom bathymetry and a sound speed profile). Additionally, a BO-TMA using the particle swarm optimization (PSO) algorithm is proposed. In Section 4, simulation results for the BO-TMA are analyzed using ray tracing. Finally, a summary and conclusion are given in Section 5.
