Article Figures & Data
Figures
- FIGURE 1
A snapshot of the estimation algorithm at time 𝑡𝑘, illustrating the flow of information over a single propagate-update cycle of the recursive steerable-laser TRN filter. The implementation of ray-casting and optimal steering angle selection is discussed in Sections 3 and 4.
- FIGURE 2
Illustration of the ray-casting process and the binary search method used to find a laser beam’s intersection with a DEM. Note: the initial “R” value is either 50 meters (chosen minimum range measurement) or the last valid slant-range value from previous update cycles of the MPF.
- FIGURE 3
Ray-casting Jacobian w.r.t. terrain gradient
- FIGURE 4
Ray-Casting Jacobian w.r.t. slant-angle
- FIGURE 5
Illustration of gimbaling a laser by two different pitch and yaw angles. The measurement Jacobians for each case can be evaluated and compared for information content. The red cone gives the field of view of the laser, and the two black lines show two possible steering angles.
- FIGURE 6
Flat-terrain flight profile over California
- FIGURE 7
Change in ray-casting measurement w.r.t. 30-meter change in North direction. Note the many local minimums and maximums of the function.
- FIGURE 8
Mountainous-terrain flight profile over California
- FIGURE 9
Comparison of North CRLB for three steering strategies over flat terrain described in Section 6
- FIGURE 10
Comparison of North CRLB for three steering strategies over mountainous terrain described in Section 6
- FIGURE 11
Comparison of altitude error CRLB for three steering strategies over mountainous terrain described in Section 6
- FIGURE 12
MPF East error (mountainous case) optimal vs nadir steering
- FIGURE 13
MPF North error (mountainous case) optimal vs nadir steering
- FIGURE 14
MPF Altitude error (mountainous case) optimal vs nadir steering
- FIGURE 15
MPF East error (flat case) optimal vs nadir steering
- FIGURE 16
MPF North error (flat case) optimal vs nadir steering
- FIGURE 17
MPF Altitude error (flat case) optimal vs nadir steering
Tables
INS Specification Value Velocity Random Walk 1 × 10–12 m/sec3/2 Angular Random Walk 
Accelerometer Bias Sigma 9.81×10–6 m/s2 Accelerometer Time Constant 3600 s Gyro Bias Sigma 1.45×10–8 rad/s Gyro Time Constant 3600 s Steer Strategy East 1σ (m) North 1σ (m) Horiz 1σ (m) Nadir 29.1 30.7 44.9 Tri-Pod 15.9 15.94 24.58 Matrix Trace 10.8 7.9 16.01 Steer Strategy East 1σ (m) North 1σ (m) Horiz 1σ (m) Nadir 6.1 6.4 10.8 Tri 2.8 3.0 5.0 Matrix Trace 1.2 1.0 3.1 Case Nadir Steering North RMSE (m) 33.9 7.1 East RMSE (m) 44.7 8.5 Alt (m) RMSE (m) 2.8 2.2 MRSE (m) 56.2 11.2 - TABLE 5
MPF Results: Comparison of optimal steering vs nadir steering on mountainous terrain
Case Nadir Steering North RMSE (m) 3.6 1.9 East RMSE (m) 4.2 1.8 Alt (m) RMSE (m) 2.9 1.8 MRSE (m) 6.2 3.1 Variable Description L Aircraft latitude Ω Earth’s rotation rate Re Earth’s radius νn North velocity νe East velocity νd Down velocity fn Specific force North fe Specific force East fd Specific force Down τα Accelerometer states time constant τg Gyroscope states time constant
Jump to section
- Article
- Abstract
- 1 INTRODUCTION
- 2 SLANT-RANGE TRN NAVIGATION SYSTEM ARCHITECTURE
- 3 RAY-CASTING FOR TERRAIN-REFERENCED NAVIGATION
- 4 OPTIMAL LASER-STEERING STRATEGIES USING THE FISHER INFORMATION MATRIX
- 5 MAXIMIZING THE FIM FOR STEERABLE TRN
- 6 STEERABLE-LASER TRN CRLB RESULTS
- 7 STEERABLE-LASER SIMULATION RESULTS
- 8 CONCLUSIONS
- HOW TO CITE THIS ARTICLE
- AUTHOR CONTRIBUTIONS
- PRODUCT ENDORSEMENT DISCLAIMER
- APPENDIX A: PINSON 15 INS ERROR MODEL
- APPENDIX B: MARGINALIZED PARTICLE FILTER
- Footnotes
- REFERENCES
- Figures & Data
- References
- Info & Metrics
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