In experiment 6, the goal is to show that the hierarchical gating network (HGN) can correctly differentiate between an unmodeled impulsive maneuver, an unmodeled solar radiation pressure (SRP) change, and an unmodeled change in the measurement noise variance statistic. In this scenario, 1173 recorded MPF two way doppler measurements are processed with the best available post mission solution (including Todd Ely's genetic algorithm tuned SRP model) in the ARTSN extended Kalman filter (EKF).

The EKF's in the various experiments are initialized with the estimated state and error covariance at the end of this data set but without the small maneuver that occurs on March, 25 1997. To allow for the new filter configurations to stabilize, the second data set submitted to the HGN contains 49 doppler measurements before this maneuver. In all, 438 measurements are processed in each HGN structure below.

The specific filter dynamic and measurement configurations and the HGN settings and structures used are detailed below. Note that because of a legacy "copy and paste" error from previous experiments, the "Poly-Accel" legend label in plots in fact represents the impulsive maneuver identification filters. These filters do NOT include polynomial accelerations.

Experiment 6 A

In this experiment, the filters in the 0th bank model maneuvers at the time the actual burn occurs but with magnitudes that are not the same as the actual maneuver. The 0th bank utilizes the MPF nav team SRP model and nominal noise statistic and is the only bank to include states and initial values for the March 25 maneuver. Thus the filters in the 0th bank are inferior to the filter in the 1st bank running with the tuned Ely SRP model EXCEPT at the time of the maneuver. The 2nd bank varies the noise statistic but uses the suboptimal MPF nav team SRP model.

Bank Number	Purpose	Mar 25 Burn	SRP Model	Obs. Noise Statistic
0	Burn Detection	Included with same t, varying mags	MPF Nav Team	0.01 (nom)
1	SRP Model Change	not included	MPF #2, Ely, MPF #4	0.01 (nom)
2	Noise Statistic Change	not included	MPF Nav Team	x0.333, x1, x3 nom

• Measurement Residuals for all 9 Filters (for 5 days)
• Original GN Formulation
  • Varying eta 3 banks: On the top HGN level there is a brief selection of bank 0 followed by dominance of bank 2. Internally, filters (0,0), (1,1) and (0,2) dominate their respective banks. In open competition among all filters these three also share the majority of the gating weight.
  • Eta = 10.0 3 banks: Bank 0 is selected after initial indication of banks 2 and 1 on the top level. This switch corresponds to the unmodeled event. Internally, (0,0) dominates after the event in bank 0; (1,1) dominates for 20 days in bank 1 when (2,1) outperforms it; and the nominal noise filter (1,2) dominates from the event on. In open competition, (0,2) is initially selected, (0,0) is switched to after the unmodeled event, and then (1,1) dominates from the next pass on.
  • Varying eta noise bank excluded: Essentially the same as the fixed learning rate 3 bank sequence.
  • Eta = 10.0 noise bank excluded: Essentially the same as the fixed learning rate 3 bank sequence.
• Normed GN Formulation
  • Varying eta 3 banks: On the top level, bank 1 switches to bank 0 after the unmodeled event and bank 2 dominates from the 3rd data pass on. Internally, (0,0) dominates bank 0; (2,1) is selected but a switch is made to (1,1) after the second data pass; and the noise bank switches from (2,2) for most of the data set to (0,2) and (1,2) late. In open competition, (2,2) dominates from the 2nd data pass on.
  • Eta = 10.0 3 banks: Essentially the same as the varying learning rate case before, except the dominant filters are more clearly defined for all banks except the SRP bank. Also , the (0,0) filter dominates vs. all other filters towards the end of the data set.
  • Varying eta noise bank excluded: The impulse identification bank dominates from the time of the maneuver onward on the top level (with the exception of the 16th mission day pass). Internally, (0,0) and (1,1) dominate from the event time on in their respective banks. In open competition, (0,0) dominates from the unmodeled event on.
  • Eta = 10.0 noise bank excluded: On the top level, bank 0 briefly dominates after the vent occurs but bank 1 is otherwise the selected model. Internally, (0,0) and (1,1) dominate as before. In open competition (2,1) yields to (0,0) after the event which in turn switches to (1,1) on the very next data pass.

Summary of 6A Results

In experiment set 6A the filters in bank 0 that contain impulsive maneuver states are suboptimal in their SRP models. Thus, the switch to bank 0 and then back to bank 1 after the unmodeled impulse is an accurate identification of the system behavior. This behavior is exhibited by all of the original GN formulation test sequences. However, the varying learning rate approach in the three bank sequence did not give as clean and clear a selection as the other three test sequences.

The normed residual approach inappropriately selected measurement noise as the cause of suboptimality in both of the three bank test sequences. This error prompted the 2-bank analysis that left the measurement noise bank out of the HGN architecture. In the two bank mode with varying learning rate the maneuver identification bank was selected for the entire data set...in error. However, the fixed learning rate normed GN test correctly switched back to the bank 1 with the optimal SRP and noise configuration after the unmodeled burn.

The (0,0) filter was clearly preferred within bank 0 for all tests run in 6A. This reflects a sensitivity toward the particular test impulse magnitude in the filter which was selected arbitrarily and does not match the actual unmodeled impulse.

Experiment 6 B

The maneuvers are again modeled only in the 0th bank as in Experiment 6 A; however, now all of the filters in banks 0 and 2 use the optimal SRP model. The 2nd bank does NOT model the nominal statistic but uses 1/3, 3, and 9 times the nominal variance. In this scenario, the filters in the 0th bank are identical up until the unmodeled maneuver and are nominal as is the middle filter of bank 1.

Bank Number	Purpose	Mar 25 Burn	SRP Model	Obs. Noise Statistic
0	Burn Detection	Included with same t, varying mags	Ely	0.01 (nom)
1	SRP Model Change	not included	MPF #2, Ely, MPF #4	0.01 (nom)
2	Noise Statistic Change	not included	Ely	x0.333, x3, x9 nom

• Measurement Residuals for all 9 Filters (for 5 days)
• Original GN Formulation
  • Varying eta 3 banks: At the top level, bank 0 is selected for the first 11 days (5 data passes), after which a noise-impulse-SRP bank switching occurs. Internally, (0,0) dominates in bank 0; (1,1) initially builds a majority before switching to (2,1) around 17 days into the data set; and (0,2) slowly builds to dominance before switching to (1,2) at 17 days. In open filter competition, (0,0) dominates after the unmodeled event for one pass, (0,2) dominates for the next pass, and (0,0) dominates thereafter.
  • Eta = 10.0 3 banks: Bank 0 dominates at the top level until the last pass, when bank 2 is selected. Internally, (0,0) dominates after the unmodeled event; (1,1) holds a modest majority throughout; and (0,2) builds to dominate bank 2. In open competition, (0,2) switches to (0,0) after the unmodeled event which is dominant throughout.
  • Varying eta noise bank excluded: On the top level, bank 0 dominates throughout. Internally, the filters (0,0) and (1,1) behave as in the previous sequence. In open competition (1,1) switches to (0,0) which dominates thereafter.
  • Eta = 10.0 noise bank excluded: Essentially, this is a more separated version of the previous sequence.
• Normed GN Formulation
  • Varying eta 3 banks: Bank 2 builds to dominate by the time of the event and maintains this position at the top level of the HGN. Internally, (0,0) holds g = 0.6 from the event time on; (1,1) slowly builds to a 0.65 gating weight; and (2,2) dominates throughout the noise bank. In open competition, (2,2) dominates.
  • Eta = 10.0 3 banks: Noise dominates and no clear selection is made internally in banks 0 and 1.
  • Varying eta noise bank excluded: On the top level, bank 0 is selected after the vent. Internally, (0,0) dominates after the event in bank 0; no clear filter is selected in bank 1.
  • Eta = 10.0 noise bank excluded: Same as before with more separation between filters internally.

Summary of 6B Results

In experiment set 6B the filters in bank 0 that contain impulsive maneuver state now also use the optimal SRP and noise model. Therefore, if they are selected at the time of the maneuver they should outperform all other filters for the remainder of the data set.

The original GN formulation test sequences perform as expected by originally assigning more weight to bank 0 and then allowing almost all of the gating weight to be assigned to this bank. While this does not provide the dramatic switch on the top level that was seen in 6A it is thought to be the correct interpretation of the filter models and data set. Switching is more pronounced in the open competition among filters where no clear winner was selected until the time of the unmodeled maneuver when (0,0) is chosen in the two bank cases (noise was selected first in the 3 bank cases).

As in 6A the normed residual GN formulations incorrectly select measurement noise as the dominant change in the measurement residual environment. However, the 2 bank runs with the normed residual formulation actually show a more marked environment change at the time of the unmodeled event. This result is interesting as it may show that the normed formulation might play a role operating in parallel with the original formulation without an included noise bank. In this manner, two separate indicators of environment change are available: (1) the original formulation which is very sensitive to picking a filter that performs even slightly better than its peers and (2) the normed formulation which is not as sensitive but indicates a dramatic change with more definitiveness. In this approach the normed formulation could be viewed as conservative and resistant to small differences among filters while the original formulation is more sensitive and responsive.

Experiment 6 C

The maneuvers are modeled only in the 0th bank as zero magnitude events (with estimated correction states in the EKF) but at a half day before, at the time of , and a half day after the actual maneuver occurs. The 1st and 2nd banks are identical to those in 6B.

Bank Number	Purpose	Mar 25 Burn	SRP Model	Obs. Noise Statistic
0	Burn Detection	- .5 day, 0, +.5 day, zero initial mag	Ely	0.01 (nom)
1	SRP Model Change	not included	MPF #2, Ely, MPF #4	0.01 (nom)
2	Noise Statistic Change	not included	Ely	x0.333, x3, x9 nom

• Measurement Residuals for all 9 Filters (for 5 days)
• Original GN Formulation
  • Varying eta 3 banks: On the top level, bank 0 is dominant except for a brief switching to bank 2 at 12 days. Internally, (1,0) dominates after the event; (1,1) builds to g = .85 in bank 1; and (0,2) dominated bank 2. In open competition, a switch from (0,2) to (1,0) occurs at event time. Filter (1,0) remains dominant except for the pass at 11-12 days.
  • Eta = 10.0 3 banks: Much the same, more separation in some cases.
  • Varying eta noise bank excluded: See above. Also there is a marked selection of (1,0) from an even field after the time of the unmodeled event in open competition.
  • Eta = 10.0 noise bank excluded: See above. There is again the marked selection of (1,0) in the open competition at the event time.
• Normed GN Formulation
  • Varying eta 3 banks: Noise bank and filter (2,2) dominate.
  • Eta = 10.0 3 banks: See above.
  • Varying eta noise bank excluded: See above.
  • Eta = 10.0 noise bank excluded: See above.

Summary of 6C Results

In experiment set 6C the filters in bank 0 that contain impulsive maneuver state still contain the optimal SRP and noise models but now use impulsive maneuver states of initially zero magnitude. These impulses are scattered about the actual burn time at half day intervals. Therefore, the (1,0) filter should be the best match to the data coming in.

These tests were successful in much the same way as the tests in 6B (with the reminder that the normed test sequences that included noise were not accurate). The ability to disperse the impulsive maneuver identifiers in time with zero initial magnitude indicates that the identification of impulsive maneuvers once suboptimality has been detected may give this approach a certain degree of robustness.