1	6th Joint International Military Sensing Symposium (MSS) Dresden, Germany October 18-21, 2004
2	Combined Optimization of Aircraft Maneuvers and RF Measurements for Passive Air-Air Ranging Prepared by: BAE SYSTEMS Information and Electronics Warfare Systems (IEWS) Nashua, NH (USA) Ronald Yannone & Melvin Carroll PH: 603/885-0454 Email: ronald.m.yannone@baesystems.com
3	Outline Problem Solution approach Math model and assumptions Sample scenario Simulation results Summary
4	Problem Passive Air-to-Air Ranging Passively estimate the range of a target aircraft from an airborne platform at long range quickly and accurately
5	Solution Approach Develop a theoretical range estimate performance model using the Cramer-Rao (CR) lower bound formulation in MATLAB to analyze the problem Develop math models to characterize the passive RF measurements Angle RF Doppler Define, and incorporate, unknown initial conditions with regard to target aircraft (i.e., target aircraft range and speed, and heading with respect to the sensor aircraft) Assess ranging performance across large parametric conditions
6	Potential Approaches IR Sensors Angle-only measurements Slow convergence time due to large sensor aircraft flight excursions Difficult to correlate measurements RF Sensors Angle and frequency measurements Good detection range Potentially fast range convergence RF parameters useful to correlate reports
7	The CR (Cramer-Rao) Lower Bound Provides the Theoretical Performance Limits Based on Measurement Parameter Sets Cramer-Rao lower bound: where: H = partial derivatives of the measurement equations with respect to the states R = measurement covariance matrix and the measurement errors are uncorrelated, jointly Gaussian
8	Math Model and Assumptions
9	Math Model and Assumptions (Cont’d) Angle Measurements where b_i is the cone angle about the interferometer axis at the ith update (i = 1,2,3,…N) r_e is the vector to the emitter from the origin of coordinates. r_pi is the vector from the origin to sensor aircraft position at the ith update d_i is a unit vector in the direction of the interferometer axis at the ith update. (For straight and level flight, d_i is a constant vector.) Superscript T denotes the transpose operation \| x \| denotes magnitude of x. Angle Accuracy Error where s_y is the standard deviation of the phase error in radians. Note that this expression is also the first-order approximation to the interferometer boresight angle-of-arrival error, expressed in radians.
10	Math Model and Assumptions (Cont’d) RF Doppler Measurements For the Doppler method, the measurement variable y is now the received RF, which we denote by f_R and which is related to the state variables by where f _T is the frequency of the signal at the emitter, V_R is the emitter velocity minus the sensor aircraft velocity, and c is the speed of light. The vector r is the range vector from the sensing aircraft to the target aircraft emitter, and r has magnitude r
11	Information On Angle Measurements Measured variable is unambiguous cone angle Since only a single-axis interferometer is used, and up-down ambiguity exists All phase measurement errors are independent of each other and are zero-mean Gaussian Mechanical boresight errors are neglected Cosine of cone angle is provided by unambiguous interferometer Coordinate system origin is at initial position of sensor aircraft Initial headings of sensor aircraft and emitter platform are measured from positive x-axis Initial azimuth of emitter is defined relative to x-axis Port and starboard antennas are available to minimize dropout from field of view This program allows for initial estimates of emitter platform speed, initial range, and heading The estimates are assumed to be normally distributed about the true values Variables to be estimated are horizontal range, azimuth angle To estimate these variables, we must also include emitter velocity vector, which is expressed as a magnitude (speed) and heading relative to the x-axis
12	Range Performance is a Function of Scenario Parameters Sensor aircraft speed Target aircraft speed Initial sensor aircraft heading Initial target aircraft range Initial target aircraft heading Initial target aircraft azimuth Angle measurement accuracy Angle measurement sample interval Initial target aircraft range error assumed Initial target aircraft speed error assumed Initial target aircraft heading error assumed Sensor aircraft maneuver (flight path [2-turn, sinusoid, etc.], time initiated, G’s [“sign” & magnitude], straight-leg lengths [e.g., sinusoidal maneuver], total maneuver duration; total cross-range allowed with respect to initial AZ angle) Sample range estimate requirements (e.g., TBD1% by 15 seconds; TBD2% by 40 seconds)
13	Air-to-Air Passive Ranging Performance is a Multivariable Problem Due to Many Critical “Variations” for the Same Scenario Due to the “Knob Adjustments”
14	Sample Scenario
15	Sensor Aircraft Maneuvers
16	Some Observations in Air-Air Ranging Performance ¾ NNW Scenario The ranging performance has 3 basic regions: transient, transitory steady-state, and longer-term steady-state ¾ corresponding to 15, 40 and 60 second time points, respectively Head-on engagements are best addressed with sensor aircraft maneuvers to right or left Near-perpendicular engagements are best addressed with sensor aircraft maneuvering in the counter (opposite) direction to the target aircraft The desired range error desired at the 3 time points (15, 40, and 60 seconds) for any scenario can be traded by looking at the percent range error curves for the sensor aircraft maneuver/acceleration levels selected Delaying the time to initiate the sensor aircraft maneuver can improve ranging performance for both “opening” and “closing” engagements for either sensor aircraft maneuver because the transient and steady-state responses are improved
17	Some Observations in Air-Air Ranging Performance ¾ NNW Scenario (Cont’d) Given the 45-degree initial veer off the initial sensor aircraft heading: time to initiate the maneuver (particular payoff for “opening” engagements) balance between developing the baseleg [bearing spread] vs. getting in the sensor aircraft turn [angle acceleration “sign” and magnitude change] for steady-state and transient performance, respectively the magnitude and “sign” of the sensor aircraft acceleration deployed (the greater the sensor aircraft acceleration magnitude, the less time spent doing the sensor aircraft turns, thus the more time that can be devoted to the straight leg portion of the maneuver ¾ to thus “extend” the leg length – and increase the baseleg to improve steady-state ranging performance
18	Requirements have to be Driven by Pilot Tactical Maneuvers Ranging performance components ¾ transient (15 sec) and near-steady-state (40 sec) Ranging performance contingent upon the sensor aircraft maneuver with respect to the target aircraft heading and sensor aircraft speed Sensor aircraft maneuver regulates the “observability” needed to estimate range Sensor aircraft maneuver flight path may be sinusoidal, 2-turn, or other defined flight paths Specific tactical sensor maneuver(s) available will be pilot- and scenario-dependent Ranging performance is contingent upon having the target aircraft in the sensor FOV (field-of-view) Need to know the total cross-range excursion permissible by the pilot for different scenarios Need to know the amount of time available to perform the sensor aircraft maneuver The level of a priori information handed-off by onboard Mission Systems directly drives the initialization uncertainty used in any proposed Kalman filter-based tracking algorithm (i.e., initial target aircraft range and speed, and heading with respect to sensor aircraft)
19	Simulation Results 10 percent range error is achievable quickly when the sensor aircraft executes higher G maneuvers To minimize range error at a given time, different sensor aircraft accelerations are required
20	Simulation Results (Cont’d) Initial target aircraft speed errors add a bias to the range error
21	Real-Time Multiple-Hypothesis Passive Ranging Algorithm Initial Conditions Accommodates uncertainties in initial target aircraft range, speed, and heading with respect to the sensor aircraft Several Kalman filter models are seeded with a spread of initial conditions Target Aircraft Dynamics Models Two models used constant velocity, constant heading acceleration (to accommodate heading changes) Maneuver detection logic “built-in” to the IMM (interacting multiple model) formulation
22	Mission Avionics has to “Balance” the Dynamic Requirements of all the Subsystems to Meet Overall Sensor Aircraft Objectives
23	Summary There is no closed-form RF-based passive ranging performance expression that captures all the cited parameters The optimal passive ranging solution is highly parametric and requires accurate received emitter angle and frequency measurements, coupled with the appropriate sensor aircraft acceleration With small (~2 Gs) sensor aircraft sinusoidal or 2-turn maneuvers, 10 percent range accuracy is achievable using angle and RF Doppler measurements Real-time, multiple model Kalman filter-based solutions will adequately perform the passive range calculations by incorporating initial condition uncertainties (i.e., target aircraft speed and range, and heading with respect to the sensor aircraft) The multiple model approach would be augmented by models to accommodate different target aircraft dynamics variations (i.e., to account for target aircraft heading changes with or without concurrent sensor aircraft heading changes)