The handy MDSTraj time savings utility converts a coarse description of a time history trajectory and created higher order states. Often one has description of flight trajectory based on starting position, heading, speed, altitude, roll, pitch, yaw and rate of change and total delta change for each item. Easy to compute and propagate but is generally has issues when used in WGS-84 applications where physics matter such as alignment of velocity vectors.

High rate and fidelity trajectories with linear acceleration, body rates and angular accelerations are automatically derived from the broad scenario definition. The trajectory definitions are parsed, cubic spline interpolated to the Step Size (dt) specified. The MDSTraj calculates the derivatives necessary to form the higher order term trajectory states.

The process builds the 3D vector in ECEF representation using a natural cubic spline interpolator to form velocity and acceleration vector as well as Euler angle rates and accelerations. Finally, body rates and angular accelerations are calculated from the derivatives of the Euler angles.

Cubic spline functions are used to fit the data. A cubic spline is a spline of piecewise third-order polynomials passing through a set of control points (i.e. in this case trajectory points – Position, Attitude, Speed). The resulting spline (segments) curve that spans each trajectory point is a cubic polynomial. With cubic polynomials splines, the adjacent cubic polynomials endpoints must match in location, first and second derivatives.

**The Automated MDSTraj Process to Create Trajectory Files: **

• Calculating the Body Rates relative to NED geographic frame by forming NED-to-Body frame and ECEF to North-East-Down (NED) direction cosines matrices.

• Multiply the ECEF to NED direction cosine by earth rate and transform to defender body frame.

• Add the NED frame rate of change relative to the ECEF frame (a.k.a. Platform Rates).

**Thus we have a 3D Vector of all states needed to generate the Trajectory file directly or for conversion to other formats.**

ASCII Value(s), | Comment:(Event ID Parameter) | Comment:Item | |
---|---|---|---|

Integer | # of Maneuver Events | - | |

Float | Event ID 1 Time | "Time"- | |

Int Int Float | Latitude | "Latitude DD MM SS.SSSSS" | |

Int Int Float | Longitude | "Longitude DD MM SS.SSSSS | |

Float | Heading | "Degrees | |

Float | Heading Rate of Change | "Deg/Secrees | |

Float | Heading Delta | "Degrees | |

Float | Speed | Knots | |

Float | Speed Rate of Change | Knots/Sec | |

Float | Speed Delta | Knots | |

Float | Altitude | Feet | |

Float | Altitude Rate of Change | Feet/Sec | |

Float | Altitude Delta | Feet | |

Float | Roll | Degrees | |

Float | Roll Rate of Change | Degrees/Sec | |

Float | Roll Delta | Degrees | |

Float | Yaw | Degrees | |

Float | Yaw Rate of Change | Degrees/Sec | |

Float | Yaw Delta | Degrees | |

Float | Pitch | Degrees | |

Float | Pitch Rate of Change | Degrees/Sec | |

Float | Pitch Delta | Degrees | |

Float | Pitch Delta | Degrees | |

"0000" | Spare | N/A | |

Float | Event ID 2 Time | N/A | |

Float | Heading | "Degrees | |

Float | Heading Rate of Change | "Deg/Secrees | |

Float | Heading Delta | "Degrees | |

... | ... | "Time"- | |

... | ... | ... | |

"-1" | End of File | n/a | |

Note | A -1000 Value In Parameter value field means no change |

Column | Parameter | Units |
---|---|---|

1 | Time | Seconds |

2 | Longitude | Degrees |

3 | Latitude | Degrees |

4 | Altitude | Meters Relative to WGS84 |

5..7 | ECEF Vel X,Y,Z | Meters/Seconds |

8..10 | ECEF Accel X,Y,Z | Meters/Second^{2} |

11.13 | Roll, Pitch, Yaw (hdg) | Degrees |

14..16 | Body Rate X,Y,Z | Radians/Second |

17..18 | Angular Accel X,Y,Z | Radians/Second^{2} |

Column | Parameter | Units |
---|---|---|

1 | Time | Seconds |

2 | Longitude | Degrees |

3 | Latitude | Degrees |

4 | Altitude | Meters Relative to WGS84 |

5..7 | NEU Velocities | Meters/Seconds |

8 | Total Velocity | Meters/Seconds |

9..11 | NEU Acclerations | Meters/Second^{2} |

12 | Dive Angle | Degrees |

13 | Bearing | Degrees |

14 | Roll | Degrees |

15..17 | Body Rate X,Y,Z | Radians/Second |

18..20 | Angular Accel X,Y,Z | Radians/Second^{2} |

**Note**: Things Change Rapidly! Specifications, Capabilities, Features and Availability Subject to Change Without Notice and May Be Restricted to Certain Users.