I. Introduction
Recently, active electronically scanned array (AESA) radar systems are being widely employed in advanced airborne platforms to maximize the capability and survivability of missions by facilitating multi-functionality for air-to-air, air-to-ground, and air-to-sea modes [1]. Fourth-generation fighter jets without stealth technology require a reliable system that can help them automatically maintain a low altitude to evade enemy air defense radars [2–5]. Therefore, in recent times, extensive research has been conducted on incorporating terrain-following (TF) capabilities into the flight control of unmanned aerial vehicles performing various missions [6, 7]. Addressing this requirement, an AESA radar can implement the TF mode to rapidly and accurately detect the terrain ahead of the fighter jet, and then provide this information to the flight control system [8]. TF scan coverage in TF mode is determined by a terrain-following computer (TFC), which controls the G-command to maintain a constant terrain clearance height [9]. TF scan coverage is periodically provided to the AESA radar as part of the TF scan command.
However, since a TF scan is primarily conducted along the vertical axis, it offers narrow scan coverage. Consequently, during turning maneuvers, the TF mode is unable to maintain the planned scan coverage compared to other operational modes, such as ground moving target indication (GMTI) and real beam ground mapping (RBGM), which are less affected by such conditions, as shown in Table 1.
To scan the entire TF scan coverage, multiple beams must be emitted and processed within the required time. However, during this period, the fighter jet may have to conduct various maneuvers at very high speeds. In such high-maneuverability situations, the successful execution of the TF scan command depends on the implementation of beam steering control to ensure the proper maintenance of TF scan coverage [10]. This implies that the AESA radar system must control the beam steering angle to align the azimuth center of the TF scan coverage as accurately as possible until the last beam is emitted. This functionality is referred to as full inertial compensation for beam steering commands, as depicted in Fig. 1.
However, the complexity of carrying out full inertial compensation with high accuracy arises from the airborne platform’s ability to move under various maneuvering conditions, including six degrees-of-freedom (6DOF) motion, at speeds of hundreds of knots [11].
Although the navigation system on the airborne platform provides navigation data for high maneuvering, the AESA radar system must predict the navigation data at every single beam transmitting time using the latest navigation data received from the navigation system. This is necessary because the transmitting time of the navigation data differs from its measured time owing to the fixed interval for the exchange of navigation data between the navigation system and the AESA radar system [12, 13], as depicted in Fig. 2.
A previous work studied beam steering and beam stabilization methods for missile guidance using an AESA seeker [14]. This study described the method of using the average angular rate of a body directly fed by the inertial measurement unit (IMU) of the missile system for beam stabilization. However, this study did not account for the interval between the measurement of the angular rate and the actual beam steering control. This interval arises due to the structural limitations of integrating a navigation system into the AESA radar system, which operates independently. Neglecting this interval ultimately means disregarding the angular rate when estimating the attitude at the precise moment of beam emission. This is especially critical in the case of a high-maneuverability aircraft, because such oversight can lead to significant errors and compromise the stabilization of the beam center on the target position.
Furthermore, the coordinate system employed to represent a point of interest (POI) differs from the beam steering angle with respect to the antenna surface. The position of a POI is typically expressed either in relative terms, based on the own-position using the north-east-down (NED) coordinate system, or in absolute terms, based on the latitude, longitude, and mean sea level. However, the antenna surface of an AESA radar system is fixed on the bulkhead, maintaining a certain boresight offset angle from the aircraft centerline to avoid tracking other radar systems [15]. Therefore, the AESA radar system must calculate the beam steering angle in the antenna coordinate system by accounting for the direction angle between the own-position and the POI to align them at every single beam transmitting time.
Notably, the structured analysis and design technique-based architecture design (SADT) method is well suited for managing the inherent complexity of designing full inertial compensation [16]. It is a system architecting approach that involves identifying the functions or activities that a system should perform based on the concept of operation, and then decomposing the concept in a top-down manner. In essence, the SADT method offers an efficient approach to designing the functional architecture of complex systems, enabling traceability from the system’s mission to its physical components.
In this paper, the functional architecture of full inertial compensation for beam steering commands in TF mode operation of airborne AESA radar is designed using the SADT method, which is useful for identifying the effects of external components on the total error in beam steering and for mitigating additional beam steering errors caused by a delay in the exchange of data between the navigation system and the AESA radar system.
Using the system architecting methodology, it is also possible to design the integration of the AESA radar and the airborne platform. Additionally, the interrelationship between requirements and functionalities can be clearly designed using diagrams. In this study, the effects of the design on accuracy between the POI and the point of the beam center are projected onto a flat earth surface and verified through a case study involving various maneuvers of the airborne platform.
II. Methodology of Functional Architecting
In principle, system architecting based on a SADT-based architecture design method involves creating an activity model based on structured functions to accomplish the operational concept of a system. In this paper, a functional architecture for full inertial compensation is proposed using a system context diagram, functional decomposition, and activity modeling by employing modeling methods such as IDEF0 or DFD.
Notably, functional architecting involves the following steps: Step 1 involves identifying an operational concept that describes how to accomplish the tasks. To depict the concept of operation, the concept of operation is derived not from a formal procedure but from experience and expertise. Step 2 relates to functional modeling. All functions are first derived from the operational concept and then broken down to the appropriate level to complete the architecture. The result of functional decomposition can be depicted in the form of a function model, which may constitute an activity model created using IDEF0. Notably, IDEF0 is a function modeling method used to describe the implementation of functions, thus offering a functional modeling language for the analysis, development, reengineering, and integration of engineering analysis [17].
III. Results of Functional Architecting
1. Step 1: Operational Concept
During TF flights, the AESA radar transmits an RF signal with a specific waveform to the ground surface while the airborne platform is maneuvering. Given that the antenna beam is illuminated at a POI, the return signals may be reflect primarily by the main-lobe beam projected onto the ground, which is truncated by the half-power beam width (HPBW) [18].
Considering the timing of receiving the navigation data, generating a beam steering command, and transmitting the beam, the radar cannot avoid a certain amount of delay from the command to the POI to the actual beam transmitting due to platform maneuvering. This delay causes an error distance between the POI and the position of the beam center, as shown in Fig. 3.
The operational concept for full inertial compensation involves steering the beam center to the POI while compensating for the 6DOF motion of the platform. Using this function, the user can accomplish the mission of obtaining scanned data covering the region of interest while minimizing the error distance between the POI and the beam center.
2. Step 2: System Context Diagram
To identify the target system’s boundary and its internal/external relationship, the system context diagram should be defined as unambiguously as possible. The system context diagram for achieving full inertial compensation for the AESA radar is illustrated in Fig. 4.
3. Step 3: Activity Model using IDEF0
3.1. Full inertial compensation (A0)
Fig. 5 depicts the activity model for full inertial compensation (A0). The model outputs a beam steering command to the antenna using the latest navigation data, along with the UTC time at which the data were received from the navigation system and the latest TF scan command received from the TFC. This activity is performed through TF mode processing at the system time generated by external interface processing. The beam steering command is then compensated to ensure TF scan coverage in accordance with the TF scan command.
As depicted in Fig. 6, A0 can be decomposed into three subactivities:
- Navigation data prediction (A1): Predicts the navigation data required for beam steering command generation.
- Batch command generation (A2): Generates the batch command required for beam steering command generation.
- Beam steering command generation (A3): Generates the beam steering command, which is output to the antenna.
3.2. Navigation data prediction (A1)
The navigation data is obtained at the time represented by the timetag, which is synchronized with UTC time. Owing to the communication protocol, the AESA radar receives this data with a time delay (e.g., a maximum 20 ms delay for the 1553B Mux Bus). To employ this navigation data for generating a batch command, the AESA radar needs to predict the data at the actual transmit time synchronized with the system time using a proper extrapolation method (e.g., linear extrapolation, Kalman-filter method, etc.). In this paper, linear extrapolation is adopted for this activity, calculated as follows:
- Time difference (ΔT): ΔT = Tsystem_time − TNavigation_data.
- Predicted position PN of own aircraft in the NED coordinate system: PN(N,E,D) = PN−1(N,E,D) + VN−1(N,E,D) × ΔT.
- Predicted attitude of own aircraft: An(Y,R,P) = AN−1(Y,R,P) + AN−1(Ÿ, R̈, P̈) × ΔT , where Y, R, and P refer to the yaw (same as the platform azimuth), roll, and pitch of the aircraft attitude. Meanwhile, Ÿ refers to the yaw rate, R̈ indicates the roll rate, and P̈ represents the pitch rate.
3.3. Batch command generation (A2)
When the TFC inputs a TF scan command, which usually includes information on the required TF scan coverage, the AESA radar generates a batch command to steer the beam center point aligned with the POIs.
To cover a specified TF scan coverage ranging from −25° to 0° in elevation, the AESA radar will produce 10 batches, ensuring that the azimuth center of the TF scan coverage is maintained at intervals of approximately 2°, thus accounting for the overlap of the beams. The POI position T(N,E,D) can be calculated using the following formula:
The relationship between aircraft position and POI is depicted in Fig. 7.
3.4. Beam steering command generation (A3)
If no compensation is necessary for the beam steering angle during maneuvering, every single batch produced by the radar will have the same value as the azimuth center command specified in the TF scan command. Additionally, every single batch will maintain a consistent interval of 2.2°. However, the beam steering angle needs to be compensated, both θaz and θel of every batch will be adjusted based on the most current navigation information of the aircraft [21].
To minimize the error distance between the POI and the actual beam center, the AESA radar calculates the beam steering angle (azimuth and elevation) based on the predicted own-position and own-attitude on activity of “A1” and the position information of the POI from the batch command. In other words, the beam steering angle (azimuth and elevation) can be calculated using the following equations:
- Distance: σd(N,E,D) = Treq(N,E,D) − Tst(N,E,D), where Treq is calculated at the starting position of the TF scan and Tst is calculated at mid-position of the TF scan during maneuvering using the same θaz and θel for nth batch.
- Azimuth angle (δaz) for beam steering in the NED coordinate system:
- Elevation angle (δel) for beam steering in the NED coordinate system:
IV. Analysis of Effectiveness
1. Execution Model
To analyze the effectiveness of the functional architecture presented above, an execution model was employed to examine beam steering cases pertaining to various kinds of aircraft maneuvering. Notably, aircraft velocity can be modeled using the following formula [24], as also depicted in Fig 8:
Information on aircraft position can be obtained by multiplying the velocity components calculated for each axis by the beam steering time. In the case of this study, the initial aircraft position was considered O(0,0,0).
2. Definition of Preconditions
The clearance height, set as a fixed value, must be maintained during TF flight [25]. In this study, the initial true heading and position were considered 0. Turn acceleration was set to the maximum required for the TF flight envelope. The preconditions for the simulation are presented in Table 3 [26]. Notably, the values for attitude and velocity depended on the specific test cases.
3. Definition of Test Cases
3.1. Maneuvering Case #1
This case was considered to compare the maximum bank angle in maximum velocity to the maximum turn rate under level flight, with the pitch angle assumed to be 0°.
The simulation results revealed that without full inertial compensation, errors of 21.24 m (#1.1) and 11.85 m (#1.2) occurred in the north direction. However, upon applying full inertial compensation, errors of 0.12 m (#1.1) and 0.07 m (#1.2) were observed in the north direction, as shown in Figs. 9–12.
3.2. Maneuvering Case #2
This case was examined to compare the maximum bank angle in maximum velocity to the maximum turn rate under ascent flight. The analysis assumed a pitch angle of 15°, considering the TF flight envelope.
The simulation results revealed errors of 176.3 (#2.1) and 101.8 m (#2.2) in the north direction when not using full inertial compensation. In addition, in the case of this maneuver, the error increased significantly when steering the beam over long distances without performing full inertial compensation during ascending maneuvers compared to level flight. In contrast, since the speed in the down direction was about 45 m/s and the moving distance during the time interval of 7 ms was about 0.32 m, a few errors—0.02 m under non-compensation and 0.002 m under compensation—were observed in the down direction.
4. Comparison of Simulation Results
The simulation results indicate that, without performing full inertial compensation, the beam pointing center will shift in accordance with the aircraft’s displacement. In particular, during ascent maneuvers, the error in the beam pointing center increased when steering the beam toward a POI positioned at a distant location as the aircraft’s altitude increased. However, compensating for the aircraft’s maneuvers at beam transmitting time resulted in a significant reduction in errors—within 1 m across all axes— irrespective of the pitch angle, as shown in Table 6.
5. Flight Test Data Results
After installing the AESA radar on a flying test bed (FTB) and performing turn maneuvers (with roll angles varying from −21.7° to −30.3°), a comparison of test result for 123 continuous scans and 1,230 beam steering, as illustrated in Figs. 17 and 18, revealed interesting results. Without full inertial compensation, the following maximum errors were observed: −68.58 m in the north direction, 157.09 m in the east direction, and 0.57 m in the down direction. In contrast, performing full inertial compensation resulted in maximum errors of −3.34 m in the north direction, −8.42 m in the east direction, and 2.21 m in the down direction. These results confirm that full inertial compensation is effective for covering the commanded TF scan coverage in TF mode operation.
V. Conclusion
In this paper, the SADT method is utilized to create the functional architecture of a full inertial compensation system to ensure precise beam steering through accurate TF scan coverage. An operational concept and a system context diagram were employed to meticulously identify the behaviors of the full inertial compensation function as well as the elements and properties of the internal and external interfaces for AESA radar operation. Additionally, the hierarchical activity model facilitated the definition of sub-functional activities, thereby enabling the design of a cohesive functional architecture for the full inertial compensation system. The effectiveness of this approach was demonstrated through simulations conducted using an appropriate execution model and validated through various test cases and flight experiments. Furthermore, the full inertial compensation function was successfully implemented on an actual AESA radar. The simulation and flight test results showed significant improvement in beam steering accuracy and reduction in error by approximately 18.7 times—from 157.09 m to 8.42 m—after compensation.
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