Backgound
Rogue jogs have been a problem in the past where a jog may significantly overshoot and otherwise produce a poor centering result. These past problems have been largely overcome, such that its been ages since a rogue jog has been detected, so it was rather unexpected that one particular target from last night's session (now known to be AT2022szi) had reported a 'rogue' jog and had pointing errors that progressively increased from 7.05' after the slew to 11.90',  23.50', 93.35' (after final locate frame) to final value of 186.1' for the first main image.

The target lies very close to the RA 0.0 / 24.0 boundary where they have been issues in the past related to incorrect RA values being supplied by TheSky6 to the telescope.
These have been workaround, but there may still hidden issue or a side impact/bug with the workarounds put in place.

Issue
Centering operations for Target AT2022szi were highly anomalous (17:50 to 17:54), Session S1065 (2022-11-29)

Description
For target 2/45 (AT2022szi) the Centering operations were highly anomalous and the target ended up lying outside of the FOV of the main frames.  Issue was identified during investigation which tried to understand why the calculated Scope 2 offset was 93.45' instead of an expected value < 1'.   This was coupled with observation that one particular target (now known to be AT2022szi) had reported a 'rogue' jog and had pointing errors that progressively increased from 7.05' after the slew to 93.35' (after final locate frame) and then to a final value of 186.1' for the first main image. 

Image     Target      Error 1  Error 2  Error 3  Error 4  Error 5
01065010  AT2022szi   7.05     11.90    23.50    93.35    186.1

The first locate frame shows that telescope is pointing only 7' away from the target (shown by blue circle/ the target object is itself faint/not visible) after slewing. There are plenty of stars for plate solution and it should have been a straightforward operation to use guide jogs to automatically brin the telescope onto the target. So what went wrong ?

Analysis

From what can be seen from the Report files it would seem to the problem is associated with RA position and that corrective jogs were being applied in the wrong direction, causing the error to effectively double each time.   It is unclear if this reflects a bug in AstroMain or a particular issue with TheSky6, TeleLink, LX200 in relation to targets RA value which was  RA= 00 01 39.461 (Current Epoch)   ( = 00 00 29.351 (J2000) )  and thus lies very close to the RA 0 / RA 24 boundary where the have previously been issues with TheSky6 sending TPoint Modified RA value to scope which are outside the range 0.0 to 24.0, for which TeleLink.Telescope is now used to warp the invalid RA round before sending the RA onto DeviceHub.Telescope.

  Centering 1                           2022-11-29 17:50  (Local, GMT)
  Taking 5s image (C)...      Ok        [01065010]        (Locate, 3x3 5s C, 17:51:05 UT, Sky 40/+16)
  Linking image (UCA/USNO)... Ok        Solved in 1.0s    (Stars 17, Scale 1.401, Angle 179.5°)
  - Plate Coordinates (RA)    Ok        23 59 55.955      (RA  J2000)
  - Plate Coordinates (Dec)   Ok        +38 09 10.89      (Dec J2000)
  - Pointing Error            Ok        7.05'             (W: -6.56', N: -2.57)
  - Scope Discrepancy         Ok        13.19'
  Review Pointing Error (1)   Ok        7.05'             (W -6.56', N -2.57')
  Adjust Position             Ok        7.05'             (W: 6.56', N: 2.57' jog required)
  Move Scope                  Ok        Jogging scope     (Jogging telescope onto target coordinates)
  - West Jog...               Ok        Jog finished (W)  (30.8s, PulseGuide at x0.90 guide rate)
  - North Jog...              Ok        Jog finished (N)  (12.1s, PulseGuide at x0.90 guide rate)
  Jog Completed               Ok        5.76'             (W: 5.28', N: 2.31' scope change)

  Centering 2                           2022-11-29 17:52  (Local, GMT)
  Taking 5s image (C)...      Ok        [01065011]        (Locate, 3x3 5s C, 17:52:05 UT, Sky 39/+15)
  Linking image (UCA/USNO)... Ok        Solved in 0.8s    (Stars 10, Scale 1.401, Angle 179.5°)
  - Plate Coordinates (RA)    Ok        23 59 28.794      (RA  J2000)
  - Plate Coordinates (Dec)   Ok        +38 11 26.00      (Dec J2000)
  - Pointing Error            Ok        11.90'            (W: -11.90', N: -0.32)
  - Scope Discrepancy         Ok        13.17'
  Review Pointing Error (2)   Ok        11.90'            (W -11.90', N -0.32')
  Adjust Position             Ok        11.90'            (W: 11.90', N: 0.32' jog required)
  Move Scope                  Ok        Jogging scope     (Jogging telescope onto target coordinates)
  - West Jog...               Ok        Jog finished (W)  (16.2s, TheSky6.Jog)
  - North Jog...              Ok        Jog finished (N)  (3.2s, PulseGuide at x0.90 guide rate)
  Jog Completed               Ok        11.79'            (W: 11.74', N: 0.99' scope change)

  Centering 3                           2022-11-29 17:52  (Local, GMT)
  Taking 5s image (C)...      Ok        [01065012]        (Locate, 3x3 5s C, 17:52:41 UT, Sky 39/+15)
  Linking image (UCA/USNO)... Ok (1)    Solved in 1.6s    (Stars 19, Scale 1.401, Angle 179.4°)
  - Plate Coordinates (RA)    Ok        23 58 29.834      (RA  J2000)
  - Plate Coordinates (Dec)   Ok        +38 12 41.34      (Dec J2000)
  - Pointing Error            Ok        23.50'            (W: -23.48', N: 0.94)
  - Scope Discrepancy         Ok        13.53'
  Review Pointing Error (3)   Ok        23.50'            (W -23.48', N 0.94')
  Adjust Position             Ok        23.50'            (W: 23.48', N: -0.94' jog required)
  Move Scope                  Ok        Jogging scope     (Jogging telescope onto target coordinates)
  - West Jog...               Ok        Jog finished (W)  (17.0s, TheSky6.Jog)
  - South Jog...              Ok        Jog finished (S)  (5.1s, PulseGuide at x0.90 guide rate)
  Jog Completed               Ok        23.30'            (W: -23.29', N: 0.46' scope change)
  Rogue Jog Detected          Alert     Jog Discrepancy:  46.79' (W: -46.77', N: 1.40')

  Corrective Jog Required
  Adjust Position (3b)        Ok        46.79'            (W: 46.77', N: -1.40' jog required)
  Move Scope                  Ok        Jogging scope     (Jogging telescope onto target coords (attempt 2)
  - West Jog...               Ok        Jog finished (W)  (18.0s, TheSky6.Jog)
  - South Jog...              Ok        Jog finished (S)  (7.0s, PulseGuide at x0.90 guide rate)
  Jog Completed               Ok        69.88'            (W: -69.87', N: 0.89' scope change)

  Centering 4                           2022-11-29 17:53  (Local, GMT)
  Taking 5s image (C)...      Ok        [01065013]        (Locate, 3x3 5s C, 17:53:56 UT, Sky 39/+15)
  Linking image (UCA/USNO)... Ok        Solved in 0.6s    (Stars 20, Scale 1.401, Angle 179.5°)
  - Plate Coordinates (RA)    Ok        23 52 34.262      (RA  J2000)
  - Plate Coordinates (Dec)   Ok        +38 13 02.56      (Dec J2000)
  - Pointing Error            Ok        93.34'            (W: -93.33', N: 1.29)
  - Scope Discrepancy         Ok        13.14'
  Review Pointing Error (4)   Ok        93.35'            (W -93.34', N 1.29')

  Adjust Position             Ok        93.35'            (W: 93.34', N: -1.29' jog required)
  Move Scope                  Ok        Jogging scope     (Jogging telescope onto target coordinates)
  - West Jog...               Ok        Jog finished (W)  (17.3s, TheSky6.Jog)
  - South Jog...              Ok        Jog finished (S)  (6.4s, PulseGuide at x0.90 guide rate)
  Jog Completed               Ok        92.98'            (W: 92.98', N: 0.56' scope change)


  Taking 180s image (C)...    Ok        [01065014]        (Full 3x3 180s C, 17:58:00 UT, Sky 38/+15)
  Linking image (UCA/USNO)... Ok        Solved in 0.8s    (Stars 51, Scale 1.401, Angle 179.5°)
  - Check WCS Centre          Ok        Centres match     (WCS center matches that from image link)
  - Plate Coordinates (RA)    Ok        23 44 41.929      (RA  J2000)
  - Plate Coordinates (Dec)   Ok        +38 12 41.04      (Dec J2000)
  Review Pointing Error (4)   Ok        186.1'            (W -186.1', N 0.93')

Where the Plate Solutions correct ?
Plate solutions were rerun and visually checked comparing match between stars in image and those in TheSky6.  Plate solutions are correct for all the images concerned (1065010-14).

What was required and what did the scope do ?
Examining the first locate frame in detail it was neccessary to jog the telescope east by 7.05' but the scope actually moved west by 4.85' . 

So why did the scope move in the opposite direction ?
The jog was made using a Pulse Guide movement rather than a Telescope Jog (mini-slew) and is therefore more accurate and generally very reliable.  Examining the report and log file shows that the scope was commanded to move west by 6.56' (rather than move east). This would explain why the scope moved west rather than east (the diffference between 6.56 and 4.85 is probably just the error in the drives,  residual backlash etc).   

So why was the scope commanded in the wrong direction ?
Logs shows that the reported pointing error for Locate 1 was  7.05' (W -6.56', N -2.57')
Reviewing the frame the telescope is indeed pointing 2.57" south of the required target, and is indeed 7.05' distant from the target,  but is pointing 6.56' west of the target and not 6.56' east of the target.   Because the pointing error calculation was given RA error opposite to what it should have, this explains why the corrective jog was in the opposite direction. 

Was the issue confirmed to one particular jog ?
Although the 2nd, 3rd and 4th jogs were made using the less dependable TheSky6 jogs which use a mini-slew rather than a pulse guide, the same incorrect pointing error calculations were made and thus the jog commands continued to be made in the opposite direction to that required

So why was the pointing error calculated incorrectly (why was the sign of the RA component incorrect) ?
It it felt unlikely to be coincidence that the issue has arose for this target which lies very close to the RA 0/ RA 24 boundary; there must be some relationship.

With the target's RA coordinates of 00h 00m 29.351s (J2000) and the plate solved RA coordinates for Locate Frame 1 of 23h 59m 55.955s  it is notable the two coordinates straddle the RA 0 / RA 24 line, and it is also certain that the calculation of the RA difference between the two which requires one of the coordinates to be wrapped, has an error.

This is bourne out by examination of code in AstroMain OB.CalculatePointingError() routine which calcuates the W Correction amount (dJogWcorrection) in rotational arc mins and West Pointing error (dErrorW) in arc mins distance

(whilst the routine returns dJogWCorrection the calling routine (OB.CentreTarget) actually uses -dErrorW when calling  the MakeCorrectiveJog() routine to make the actual corrective jog, this MakeCorrectiveJog takes the dWest amount and then calculates the equivalent rotational angle for the RA jog/pulse guide taking Dec into account)

Sub CalculatePointingError(ByRef PointingError_mins As Double, ByRef dErrorN As Double, ByRef dErrorW As Double,
                           ByRef dJogNcorrection As Double, ByRef dJogWcorrection As Double)

  ' in which ........

 ' Calculate West Correction (in rotational arc mins), correcting for cases where Ra1 and Ra2 fall eitherside of the Ra=0 line
 ' -------------------------
 If Ra2 - Ra1 < -12 Then
   dJogWcorrection = ((Ra2 - Ra1) + 24) * 15 * 60
 ElseIf Ra2 - Ra1 > 12 Then
   dJogWcorrection = (24 - (Ra2 - Ra1)) * 15 * 60
 Else
   dJogWcorrection = (Ra2 - Ra1) * 15 * 60
 End If

 ' Calculate West & North Errors (in arc mins)
 ' -----------------------------
 dErrorW = -dJogWcorrection * Math.Cos(Dec1 / DR)

In this routine Ra1 is the Target RA, and Ra2 is the Plate Solved Image RA.

Most of the time the difference between the two RA coordinates is a small number either positive or negative and the calculation

  dJogWcorrection = (Ra2 - Ra1) * 15 * 60

is applied.

The number of cases where the RA values straddles the Ra 0 / Ra 24 line is relatively rare and special handling is used.   The AT2022szi presented one such case.

Subsituting 0.008153 for Ra1 and  23.998876 for Ra2,   Ra2 - Ra1 calculates as 23.990723 which is > 12, and the following calculation was made

  dJogWcorrection = (24 - (Ra2 - Ra1)) * 15 * 60

which gave +8.3493 rotational arc mins and gave dErrorW of -6.56' and lead to a 6.56' jog being commanded to the West (rather than east).

The correct calculation should have been

  dJogWcorrection = ( (Ra2 - Ra1) -24 ) * 15 * 60

Checking the other special conditon where coordinates straddle the boundary but from the opposite position. Lets say Ra1 had been 23.998876 and Ra2 had been 0.008153, then Ra2 - Ra1 would have -23.990723 and the following calculation would have been made

  dJogWcorrection = ((Ra2 - Ra1) + 24) * 15 * 60

this would have given +8.3493 rotational arc mins and give a dErrorW of -6.56' and lead to a 6.56' jog being commanded to the West which would be appropriate.  So this equaton is correct.

Conclusion
Issue was caused by an error in an equation in AstroMain's OB.CalculatePointingError() routine. Only rare cases would have exposed this bug.

Fix
Issue is fixed in AstroMain 3.58.8 (2022-11-30).

Handling of cases straddle Ra0/Ra24 lines also into introduced itno CalculatePointingErrorNewSub() routine and CalculatePointingErrorBrightStar() routines including the new fix. Both of these routines seem to be legacy routines as neither has any references.