The acquisition radar’s detect annulus model of anti-submarine patrol aircraft

Aiming at solving the problem of anti-submarine patrol aircraft(ASPA) detecting different sea-surface and aerial objects, based on the operation performance of acquisition radar, the paper puts forward the concept of detect annulus and establishes the corresponding model, and it gives the manner and method of ASPA detected objects. Through simulation and calculation, it discusses the different pattern of optical axis angle of depression and flight altitude from the width of detect annulus. The paper also provides the basis for the best optical axis angle of depression and flight altitude to meet the operational requirements. At last, the searching method of anti-submarine patrol aircraft using acquisition radar is put forward.


Introduction
Acquisition radar is the main load of the ASPA for searching submarine. For anti-submarine patrol, its mechanical scanning antenna mounted is mounted beneath the prow, on all weather conditions, it can take sea and air target searching and tracking. It uses advanced imaging technology to realize the detection and target recognition of the submarine periscope, the exhaust pipe, and various kinds of ship on the surface, and completes sea anti-submarine and matches up weapon fire control system to complete the anti-submarine task. Due to the structural features of the anti-submarine patrol, the baffle area of the backward body won't emit electromagnetic waves. Before we research how the ASPA uses radar target to search, we must study the effective detection space of the acquisition radar. From the operational use, detect annulus can well describe the problem.
Detect annulus of acquisition radar [1] means that it's possible for the target in the detect annulus to be detected when mechanical scanning antenna of the ASPA scans the area on the sea (or plane of any height ) for a cycle in a given space. To some extent, the detect annulus of acquisition radar reflects the target search efficiency of anti-submarine patrol aircraft.

Basic assumptions
(1) The flight altitude of ASPA is h , flight speed is a v ,uniform linear motion; (2) The angle of acquisition radar beam axis (visual axis) and horizontal plane is  ; (3) Horizontal beam Angle of acquisition radar is a  ,vertical beam Angle is r  ; (4) Ignore the radar beam side lobe. The size of detect annulus is decided by vertical beam Angle of acquisition radar r  and it's described with the width  and the area S  of the detect annulus, as shown in figure 1.

Build the model of detect annulus
Consider that 0 sin r l       , the width of detect annulus  can be nearly described: And the width of detect annulus  can be described with dose the approximate: If the baffle area of the backward body doesn't emit (   ), the area of detect annulu S  will be described: As shown in the formula (3). In any search time, the size of detect annulu has nothing to do with the speed of ASPA flight, and the width of detect annulus is proportional to the flying height, and radar optical axis Angle of depression is inversely proportional to the square of the sine function. Vertical beam Angle is determined by the performance of radar. If the radar model is determined, the vertical beam angle will be determined. Usually, in the view of the conventional radar, high pulse repetition frequency will lead to the distance fuzzy [2][3][4] , as shown in figure 3.We can see that the distance between target 1 P and antenna is .It can result in distance fuzzy.
Instruction: G -antenna gain;  -radar working wavelength; t  -target reflection area; k -Boltzmann constant; 0 T -290K; n F -system noise factor; L -system loss; N S -signal to noise ratio. Most parameters can be obtained directly, but L and N S should be estimated. If the optical axis Angle of depression is minimum, the radius of detect annulus is maximum: As shown in the formula (8). The signal to noise ratio is associated with detection probability d P and false alarm probability fa P [5] .If the testing background noise is gaussian white noise that the corresponding relation is:   Where: av P -average radiation power of radar; t R -separation distance between anti-submarine patrol aircraft and target.
We can see that the maximum width (or coverage) of detect annulus is different when antisubmarine patrol aircraft detects different targets. When anti-submarine patrol aircraft detects the set targets, it can adjust flight altitude and optical axis angle of depression correspondingly to detect targets earlier.
Flight altitude h must meet the flight constraints:

Search method of acquisition radar
Based on the analysis of detect annulus model of acquisition radar, the basic method of anti-submarine patrol aircraft using acquisition radar is parallel flight search and multi-parallel flight search. According to the search manner of radar, the search method of acquisition radar can also be divided into parallel continuous search, parallel discrete search, multi-parallel continuous search and multiparallel discrete search.      Table1 parameter of detect annulus of sea-surface submarine Table 2 Partial parameter of detect annulus of aerial aircraft Where: A1: flight altitude(m); A2:detection range of radar(km); A3: parameter of detect annulus (km); A4:optical axis angle of depression (°).
The simulation results can show that: (1) The maximum detection range of acquisition radar which detect submarine in the surface state is mainly affected by radar range. Within the scope of ceiling height, the bigger anti-submarine patrol aircraft flight level, the higher maximum detection range. Therefore, anti-submarine patrol aircraft should gain flight altitude for increase detective distance.
(2) The optical axis angle of depression has significant influence on the width of detect annulus. The bigger optical axis angle of depression, the smaller width of detect annulus. When detecting the specific low altitude target, the best optical axis angle of depression is 11~13 , this moment the width of detect annulus is largest.It can ensure the targets stay long enough to detect targets more effectively.

Conclusion
From the perspective of operational use, this paper aimed at the operation performance of acquisition radar, put forward the concept of detect annulus, combined the flight constraints of anti-submarine patrol aircraft and operational background, established the corresponding model, obtained the best optical axis angle of depression and flight altitude to meet the operational requirements, provided the basis for the manner and method of anti-submarine patrol aircraft detect different sea-surface and aerial objects, and put forward the searching method of anti-submarine patrol aircraft using acquisition radar.