# Deep Impact Spacecraft Clock Correlation

**Brian Carcich\
13.April, 2006**

### Abstract

Based on the available spacecraft data and advice from spacecraft
engineering personnel, the earth/flyby clock correlation is good to one
or two seconds, and the inter-spacecraft clock correlation is good to
half a second.

For the purposes of this archive, we have adjusted the earth/flyby
spacecraft clock correlation to agree with an interpolation, over the
encounter period, of available earth/flyby timing correlation data, and
we have adjusted the earth/impactor spacecraft clock correlation to
agree with the flyby correlation on the Time Of Impact to within 60ms.
The spacecraft-to-comet trajectory kernels have been adjusted to agree
with these timing correlations.

It may be possible in the future to adjust the spacecraft clocks\'
correlations up to perhaps two seconds using the available temperature
history of the spacecraft control unit baseplate as an analog for the
spacecraft clocks\' oscillators.

### Introduction

This document summarizes the rationale for the archived correlations
between the Deep Impact (DI) Flyby and Impactor Spacecraft Clocks
(SCLKs) and Dynamical Barycentric Time (TDB) that are encapsulated in
the SPICE SCLK-Kernel files in the PDS archive of DI data. This document
also explains why the clock correlation was changed about 2 seconds,
retroactively, shortly after impact with comet 9P/Tempel 1.

### Background

The correlation between real time TDB and spacecraft clock time is
essential to mission data analysis. The correlation, expressed as rates
between known points in both time systems (SCLK & TDB), is determined
from analysis of spacecraft clock correlation packet data, and made
accessible via a standard SCLK versus SpaceCraft Event Time (SCLKvSCET)
file in the format of a SPICE SCLK-Kernel. A complete explanation of the
SPICE SCLK system is beyond the scope of this document, but is available
at the NAIF web site, <http://naif.jpl.nasa.gov/naif/doc_C.html> as the
Spacecraft Clock Required Reading document (sclk.req).

For the purposes of this document, the clock on either DI spacecraft is
adequately described as two cascading counters. The \"subtick\" counter
runs from 0 to 255 at about 256Hz and therefore overflows about once
every second. The \"tick\" counter runs from 0 to \[2\^32 - 1\] and
increments every time the \"subtick\" counter overflows. This discussion
will mostly focus on the \"tick\" count. However, it should be noted
that the SCLK time is represented as strings of digits representing the
two counters, separated by a period (e.g. \"173727702.100\"). It should
also be noted that the separator is **not** a decimal point, and that
the SCLK string 173727702.1 represents the same time as 1773727702.001,
but a different time than 17727702.100.

In the formal SPICE system, there is also a partition prefix in the SCLK
time (e.g. \"1/0173727702.100\"), but the partition may be ignored for
the purposes of this document. As noted above, more information is
available in the NAIF/SPICE Spacecraft Clock Required Reading document.

Shortly before launch in mid-January, 2006, the mission clocks\' tick
counts were set to be the number of seconds since the J2000 epoch
(01-Jan-2000 12:00:00 UTC or +64.184s TDB). The Flyby clock\'s drift,
i.e. the difference between SCLK tick and TDB rates, was about one
second per day, and the Flyby clock ran slower than TDB. That is, the
difference \[TDB - SCLK ticks\] increased about one second per day.

Based on the appearance of the impact flash in flyby images at
encounter, the Time Of Impact (TOI) was 173727702.218 on the Flyby
clock. Based on geometric analysis by Dennis Wellnitz of the Impactor\'s
final encounter images TOI was 173727875.105 on the Impactor clock.

It should also be noted that there might be a delay between the actual
impact and the appearance of the impact flash; co-investigators on the
project have estimated this delay could be as large as 200ms.

### Discussion

During DI operations, the spacecraft was commanded to generate clock
correlation data from time to time. The periods between successive
correlations ranged from a few days to five weeks.

The Flyby SCLK correlation points closest to TOI are on DOYs 164 and
187, over twenty days before and two days after TOI. The Impactor SCLK
correlation point closest to TOI is on DOY 164, over twenty days before
TOI.

Based on interpolation between the Flyby SCLK correlation points, one of
which is within two days of TOI, the Flyby-determined TOI of

173727702\.218 +/- \~6 subticks

corresponds to

2005-185 05:44:34.265 UTC +/- 25ms

at the Flyby spacecraft. Light travel time means the impact actually
took place 2ms earlier.

Based on that work, the NAV team adjusted the Impactor ephemeris so that
TOI occurs at 05:44:34.200, and the clock rate of the Impactor
SCLK-Kernel was adjusted so that the Impactor-determined TOI of

173727875\.105 +/- \~77 subticks

corresponds to

2005-185 05:44:34.200 +/- 300ms

The 63ms of difference between the final correlations was due to a
slight mis-communication, and it was declared by the Principal
Investigator that this was close enough.

### The Two-Second Shift

During mission operations, the project generated updated versions of the
SCLK-Kernel files as clock correlation data became available. Due to
operational restrictions, interpolation could not be used in these
project kernels between the most recent correlation point and the
previous point. Instead, the project used extrapolation, which process,
when coupled with other restriction, caused artifacts in the
correlation.

Here is a brief summary of the origin of the artifacts from the DI Flyby
SCLK-Kernel file by Boris Semenov of JPL:

> Traditionally the SCLK correlation function provided in the SCLKvSCET
> file had to comply with two requirements (in order to maintain correct
> tagging/sorting by UTC in the ground system):

1)  The correlation must be continuous, and

2)  The must be backward compatible (meaning that drift rates for the
    past epochs must not change).

> To achieve that every update of SCLKvSCET introduced two points: one
> \"real\" data point with actual estimated drift and one \"artificial\"
> data point about 5000 seconds before the actual point with a bogus
> drift rate, just to connect the previous trend with the new one in a
> continuous fashion.
>
> Arguably, the right thing to do to make the SCLK kernel better reflect
> real clock trend was to have the \`\`artificial\'\' points dropped and
> change coefficients of the \`\`real\'\' points to \`\`connect\'\' the
> real points into a continuous piece-wise line function. This way the
> drift rates that were initially estimated slightly incorrectly would
> be changed to make the correlation match the reality better.
>
> Exactly this was done to the final official SCLKvSCET to get the
> modified version that used to produce this SCLK kernel.

Figure 1 presents a plot of (TDB - SCLK ticks) illustrates these
processes graphically; it shows TDB advancing about one second per day
relative to the flyby SCLK, as noted above.

![](media/image1.png){width="5.992361111111111in"
height="4.497916666666667in"}

**Figure 1.** A plot of the TDB minus SCLK ticks, showing the TDB
advancing about one second per day relative to the flyby SCLK.

The white curves and points show what Boris Semenov calls the \"right
thing to do\" i.e. a piecewise linear interpolation between known
points.

The cyan plots represent the project\'s synthetic approach to the data
points. For more details of how this was done, see \"Operational
Approach to SCLKvSCET File Creation\" below.

During encounter, the white segment \"ef\" represents the interpolated
science correlation, and the cyan segment \"eg\" represents the
extrapolated project correlation. At the Time Of Impact (TOI), the
difference is about two seconds between the extrapolated and
interpolated correlations.

### Operational Approach to SCLKvSCET File Creation

Focusing on the interval from DOY 095 through 129, the actual
correlation points available to the project during that interval were
\"a\" on DOY 083 and \"b\" on DOY 095. Using those two points, the
project calculated the segment \"ab\" by interpolation, and extrapolated
that line forward in time past DOY 095 (cyan segment \"bd\" and beyond)
for operational use. When the correlation point \"c\" became available
on DOY 129, they created the correlation point \"d\" about 5000 seconds
before \"c\" as an artifice to (1) maintain backward compatibility as
noted above (i.e. to not change any SCLK to SCET conversions performed
using segment \"bd\"), and (2) terminate the previous extrapolation from
\"b\". They also created the segment \"cd\" to (1) bring the operational
correlation back to a real datum, and (2) maintain a continuous
correlation.

### The Temperature Monkey Wrench

The SCLK oscillator rates are dependent on temperature, and Figure 2
presents two plots that indicate the approach and encounter temperature
history of the SCUs. The time coverage is from about DOYs 170 through
187.

![](media/image2.jpeg){width="5.969444444444444in"
height="3.6756944444444444in"}

**Figure 2.** Two plots illustrating the temperature history of the SCUs
for the approach and encounter phases of the mission.

There are also ground-based data that show the effect of temperature on
the oscillator frequencies. The Figure 3 presents a plot that show the
relative offset between the two spacecraft clocks during approach and
encounter. Note that this plot is the offset of one spacecraft\'s SCLK
relative to the other, and does not involve TDB or UTC. The point to be
made here, however, is that both Amy Walsh and Brian Carcich have
verified that the temperature variations around encounter, coupled with
the effect of temperature on oscillator frequency, may account for the
single blue point labeled \"Possible bad point \...\" and one second or
more of uncertainty with respect to TDB and UTC.

![](media/image3.jpeg){width="5.959027777777778in"
height="5.2340277777777775in"}

**Figure 3.** A plot showing the relative offset between the two
spacecraft clocks during approach and encounter.