## 1 Introduction  
Terrain Referenced Navigation (TRN) is a technique for estimating the position of an aircraft by comparing the Digital Elevation Model (DEM) with the altitude of the terrain measured by an altimeter. This technique is used to correct the position error of the inertial navigation system, which increases as the navigation time becomes longer. The Global Navigation Satellite System (GNSS) is more accurate than TRN for correction of position error of the inertial navigation system and is used in various fields. However, GNSS has the disadvantage that it cannot be used if it receives a hostile jamming signal. On the other hand, TRN has the advantage of being able to operate normally regardless of hostile jamming signals. Because of this advantage, TRN is applied to various weapon systems such as Tomahawk and TAURUS missiles [1, 2]. According to previous research results, the fundamental performance limitation of TRN is the Radar Altimeter (RA) beam width problem [3]. TRN expects an RA to measure a relative distance to a terrain point directly below the vehicle. However, RA measures the relative distance to the closest point in the beam footprint. The difference between the two altitudes is the RA error, which causes performance degradation of TRN. The smaller the RA beam width, the better the accuracy of TRN. There are methods of reducing the RA beam width problem by lowering the flight altitude as much as possible or making the angle of the beam width smaller by increasing the frequency of the radio wave used in the RA. However, these methods cannot be applied to objects flying at high altitude. To overcome these problems, an Interferometric Radar Altimeter (IRA) has been developed as a more accurate altimeter [4]. The IRA outputs not only the relative distance (slant range, \(R\)) but also the cross-track angle (look angle, \(\theta\)) of the closest point on the zero Doppler line by using the principle of interferometry and two or more antennas. Since the IRA provides a three-dimensional measurement of the closest point, the beam width problem is no longer a problem. In the 2000s, Honeywell developed a TRN system using an IRA called Precision Terrain Aided Navigation (PTAN). The published brochure states that PTAN has a position accuracy of about 3 m at altitudes up to about 1.5 km and about 30 m accuracy at altitudes up to about 9 km [5]. However, detailed papers or materials on PTAN have not been disclosed. Based on the findings on the IRA [4; 6; 7], many studies on TRN using IRA [8; 9; 10; 11] have been conducted. Recently, with Hanwha Systems, we developed a TRN system using IRA. The IRA was designed with reference to [PERSON]'s paper [4]. We carried out several flight tests with the developed TRN system. To perform TRN using the IRA, the 3D relative position of the closest point should be calculated. In previous research, the relative position measurement equation for the closest point was presented [8]. However, when the equation was applied to an actual aircraft loading flight test, the altitude error was larger than expected. Analysis of the altitude error showed that the relative position of the closest point must be calculated using the angle of attack, the side slip angle and \"the effective look angle\" rather than the Euler angles, in an actual flight environment in which the influence of wind exists. This paper is an extension of work originally presented in reference [12]. In this paper, we propose a new relative position measurement equation that can be used in real flight environments where wind effects exist. We also prove the equation mathematically. To obtain real data for the TRN simulation, we carried out a flight test and analyzed the results. We evaluated the performance of the proposed equation and conventional equation by TRN simulation. This paper is organized as follows. Section 2 describes differences between TRN using RA and TRN using IRA.