정조대왕급(KDX-III Batch-II) 이지스 구축함 해상 기반 탄도탄 요격(BMD) 대기권 밖(Exo-Atmospheric) 람베르트(Lambert) 랑데부 & 키네틱 탄두(KV) DACS 펄스 추진 영거리 오차(ZEM) 직접 요격(Hit-to-Kill) 온디바이스 C# 엔진

using System;
using System.Runtime.CompilerServices;
using System.Runtime.InteropServices;
using System.Runtime.Intrinsics;
using System.Runtime.Intrinsics.X86;

namespace ZeliDesk.Defense.MissileDefense
{
    [StructLayout(LayoutKind.Sequential, Pack = 16)]
    public struct BmdKvState
    {
        public Vector256<float> PosXyz;       // [x, y, z, 0, vx, vy, vz, 0] (m, m/s) ECEF
        public Vector256<float> TargetPosXyz; // [tx, ty, tz, 0, tvx, tvy, tvz, 0]
        public Vector256<float> DacsPulseCmd; // [d1, d2, d3, d4, 0, 0, 0, 0] (ms on-time)
        public float TimeToGo;                // t_go (s)
        public float MissDistance;            // |ZEM| (m)
        public float ClosingSpeed;            // V_rel (m/s)
        public float RemainingDeltaV;         // 잔여 추진력 (m/s)
    }

    public sealed class Kdx3ExoAtmosphericBmdEngine
    {
        private const float MuEarth = 3.986004418e14f; // m^3 / s^2
        private const float J2 = 1.08263e-3f;
        private const float Re = 6378137.0f;           // m
        private const float KvMass = 35.0f;            // kg (경량 키네틱 탄두)
        private const float DacsThrust = 1200.0f;      // N (DACS 다이번트 단일 노즐 추력)
        private const float MinPulseWidthMs = 2.0f;    // 최소 점화 펄스 (ms)

        [MethodImpl(MethodImplOptions.AggressiveInlining | MethodImplOptions.AggressiveOptimization)]
        public void StepHitToKill1000Hz(ref BmdKvState state, float dt)
        {
            // 1. 상태 벡터 분해 (AVX2 벡터 요소 추출)
            float rx = state.PosXyz.GetElement(0);
            float ry = state.PosXyz.GetElement(1);
            float rz = state.PosXyz.GetElement(2);
            float vx = state.PosXyz.GetElement(4);
            float vy = state.PosXyz.GetElement(5);
            float vz = state.PosXyz.GetElement(6);

            float tx = state.TargetPosXyz.GetElement(0);
            float ty = state.TargetPosXyz.GetElement(1);
            float tz = state.TargetPosXyz.GetElement(2);
            float tvx = state.TargetPosXyz.GetElement(4);
            float tvy = state.TargetPosXyz.GetElement(5);
            float tvz = state.TargetPosXyz.GetElement(6);

            // 2. 상대 기하학 및 폐쇄 속도(Closing Velocity) 계산
            float dx = tx - rx;
            float dy = ty - ry;
            float dz = tz - rz;
            float relDist = MathF.Sqrt(dx * dx + dy * dy + dz * dz + 1e-4f);

            float dvx = tvx - vx;
            float dvy = tvy - vy;
            float dvz = tvz - vz;
            float relSpeed = MathF.Sqrt(dvx * dvx + dvy * dvy + dvz * dvz + 1e-4f);
            state.ClosingSpeed = relSpeed;

            // 잔여 비행 시간 t_go (Time-to-Go)
            float vClosingAlongLos = -(dx * dvx + dy * dvy + dz * dvz) / relDist;
            float tGo = (vClosingAlongLos > 100.0f) ? (relDist / vClosingAlongLos) : 0.001f;
            state.TimeToGo = tGo;

            // 3. 중력 가속도 계산 (J2 섭동 고려)
            float rNorm = MathF.Sqrt(rx * rx + ry * ry + rz * rz);
            float rNorm3 = rNorm * rNorm * rNorm;
            float rNorm5 = rNorm3 * rNorm * rNorm;

            float zSq = rz * rz;
            float rSq = rNorm * rNorm;
            float j2Factor = 1.5f * MuEarth * J2 * Re * Re / rNorm5;

            float gx = -MuEarth * rx / rNorm3 - j2Factor * rx * (1.0f - 5.0f * zSq / rSq);
            float gy = -MuEarth * ry / rNorm3 - j2Factor * ry * (1.0f - 5.0f * zSq / rSq);
            float gz = -MuEarth * rz / rNorm3 - j2Factor * rz * (3.0f - 5.0f * zSq / rSq);

            // 4. 영거리 오차(Zero-Effort-Miss, ZEM) 산출
            // ZEM = (r_tgt + v_tgt * t_go) - (r_kv + v_kv * t_go + 0.5 * g * t_go^2)
            float tGoSq = tGo * tGo;
            float zemX = (tx + tvx * tGo) - (rx + vx * tGo + 0.5f * gx * tGoSq);
            float zemY = (ty + tvy * tGo) - (ry + vy * tGo + 0.5f * gy * tGoSq);
            float zemZ = (tz + tvz * tGo) - (rz + vz * tGo + 0.5f * gz * tGoSq);

            float missDistance = MathF.Sqrt(zemX * zemX + zemY * zemY + zemZ * zemZ);
            state.MissDistance = missDistance;

            // 5. 비례항법 기반 최적 가속도 명령: a_cmd = (3 / t_go^2) * ZEM
            float nPrime = 3.5f;
            float scale = nPrime / MathF.Max(tGoSq, 0.001f);
            float aCmdX = Math.Clamp(scale * zemX, -250.0f, 250.0f); // DACS 최대 횡가속도 한계
            float aCmdY = Math.Clamp(scale * zemY, -250.0f, 250.0f);
            float aCmdZ = Math.Clamp(scale * zemZ, -250.0f, 250.0f);

            // 6. 4채널 DACS 다이번트 추력기 펄스 폭 매핑 (PWM)
            // 요격체 횡축 (Y_b, Z_b) 투영
            float reqForceY = aCmdY * KvMass;
            float reqForceZ = aCmdZ * KvMass;

            float pulseD1 = 0f, pulseD2 = 0f, pulseD3 = 0f, pulseD4 = 0f;
            float maxDtMs = dt * 1000.0f; // 1.0 ms

            // Y축 추력기 (+Y: D1, -Y: D2)
            if (reqForceY > 10.0f)
                pulseD1 = Math.Clamp((reqForceY / DacsThrust) * maxDtMs, MinPulseWidthMs, maxDtMs);
            else if (reqForceY < -10.0f)
                pulseD2 = Math.Clamp((-reqForceY / DacsThrust) * maxDtMs, MinPulseWidthMs, maxDtMs);

            // Z축 추력기 (+Z: D3, -Z: D4)
            if (reqForceZ > 10.0f)
                pulseD3 = Math.Clamp((reqForceZ / DacsThrust) * maxDtMs, MinPulseWidthMs, maxDtMs);
            else if (reqForceZ < -10.0f)
                pulseD4 = Math.Clamp((-reqForceZ / DacsThrust) * maxDtMs, MinPulseWidthMs, maxDtMs);

            state.DacsPulseCmd = Vector256.Create(pulseD1, pulseD2, pulseD3, pulseD4, 0f, 0f, 0f, 0f);

            // 실제 적용 추력 가속도
            float appliedAy = (pulseD1 - pulseD2) / maxDtMs * (DacsThrust / KvMass);
            float appliedAz = (pulseD3 - pulseD4) / maxDtMs * (DacsThrust / KvMass);

            // 7. RK2 궤도 적분 (고도 궤도 갱신)
            float newVx = vx + gx * dt;
            float newVy = vy + (gy + appliedAy) * dt;
            float newVz = vz + (gz + appliedAz) * dt;

            float newRx = rx + 0.5f * (vx + newVx) * dt;
            float newRy = ry + 0.5f * (vy + newVy) * dt;
            float newRz = rz + 0.5f * (vz + newVz) * dt;

            state.PosXyz = Vector256.Create(newRx, newRy, newRz, 0f, newVx, newVy, newVz, 0f);
        }
    }
}