BDA Support in MeasurementSets¶

The information below was written during the implementation of baseline-dependent averaging in Dp3 and WSClean, and describes how BDA is stored in a measurement set.

Rationale¶

The MeasurementSet (MS) format is generic enough to support Baseline Dependent Averaging (BDA) in time. It is in fact generic enough to support any kind of time averaging applied to every row in the measurement set.

Averaging in frequency is also possible in the MS. However, it requires creating a Spectral Window per frequency averaging (as the metadata about frequency is stored in the SPECTRAL_WINDOW subtable).

No restrictions are imposed on averaging by the MeasurementSet format. Therefore, time integrations can overlap, any ordering of rows is allowed, and the integration times do not need to have any similarity over the rows. In practice, however, no tools exist that allow this full flexibility.

We suggest to add keywords to the MS that allow tools to determine (without going through all the data) some of the characteristics of the BD averaging method applied. In particular, tools that support BDA should be quickly able to determine:

If the data is BDA;
How much memory is needed to hold all data for a certain interval of data (e.g. a 30 sec calibration interval); and
Whether and how the data can be expanded back to a fully regular MS. That is, if the BDA is simple enough (as in the normal use-case) it should be possible to recover the original time and frequency axis.

A specific tool may work only on a subset of the MS, e.g. only on the calibrator scans. Those may be BD averaged differently than e.g. the target scans. We therefore suggest to record the regularity on a finer level than on the entire MS.

Suggested implementation¶

Time and frequency direction BDA are treated differently. We will describe each.

We assume that the same averaging has been applied to all columns (DATA, WEIGHT_SPECTRUM, FLAGS but also CORRECTED_DATA and other data columns). We think that this assumption is compatible with BDA use-cases.

BDA_TIME_AXIS: Metadata for time table¶

We suggest to add an optional structured set of meta information that specify the regularity of the MS. These keywords are stored in a subtable called BDA_TIME_AXIS of the main table, and specify for each subset of the MS the characteristics of if and how BDA is applied. Absence of the table implies no BDA is applied in the time direction. The table has one non-optional keyword BDA_TIME_AXIS_VERSION. The new subtable specifies regularity only for the time axis, since for the frequency axis metadata can be specified in the SPECTRAL_WINDOW subtable.

A measurement set selection might also be on FEED1, FEED2, SCAN_ID or PROCESSOR_ID. Because this is very rare, we don’t want to burden all software with supporting such a selection, and therefore we explicitly decided not to include these.

Name	Format	Units	Comments
Columns
Keywords
BDA_TIME_AXIS_VERSION	String		Version tag
Key
FIELD_ID	Int		Field id
BDA_FREQ_AXIS_ID	Int		Spectral window id.
(BDA_TIME_AXIS_ID)	Int		Row id, Only in MSv3
Data
IS_BDA_APPLIED	Bool		BDA applied
(SINGLE_FACTOR_PER_BASELINE)	Bool		Single factor used
(MAX_TIME_INTERVAL)	Double	s	Maximum time interval
(MIN_TIME_INTERVAL)	Double	s	Minimum time interval
(UNIT_TIME_INTERVAL)	Double	s	Time interval
(INTEGER_INTERVAL_FACTORS)	Bool		Interval factors
(HAS_BDA_ORDERING)	Bool		Ordered

FIELD_ID

Field identiﬁer (≥ 0).

BDA_FREQ_AXIS_ID

Spectral window identifier (≥ 0). Together with the field identifier, this key uniquely identifies a row. The BDA_SET_ID values in the SPECTRAL_WINDOW table refer to this key.

BDA_TIME_AXIS_ID

Unique id.

IS_BDA_APPLIED

BDA has been applied to the time axis.

SINGLE_FACTOR_PER_BASELINE

For every baseline, the averaging factor is constant in time. If a specific baseline is averaged to 10 seconds for one timestep, it will be averaged to 10 seconds for every timestep over the selected data range. We expect this property to be true in the normal BDA cases.

MAX_TIME_INTERVAL

Maximum TIME_INTERVAL over this subset. With BDA applied, this normally is the time interval of the smallest baselines. This value, together with ordering properties (discussed below), helps a software tool by telling it how long a baseline might have a contribution to an interval.

MIN_TIME_INTERVAL

Minimum TIME_INTERVAL over this subset.

UNIT_TIME_INTERVAL

This is basically the original TIME_INTERVAL. If BDA is applied and the shortest baseline has not been averaged down, this value will be equal to MIN_TIME_INTERVAL. If a high-time resolution measurement set is averaged down immediately with BDA, it might be that the shortest baseline is averaged and the longest baseline is not an integer factor of the shortest baseline averaging factor (and thus MIN_TIME_INTERVAL), whereas all baselines are still a multiple of some underlying time interval.

INTEGER_INTERVAL_FACTORS

The TIME_INTERVAL – and therefore also the distance (difference between two TIMEs) between two consecutive timesteps – is an integer multiple of the UNIT_TIME_INTERVAL value. This implies that for all baselines, the first intervals starts at the same time, i.e. there is no offset.

HAS_BDA_ORDERING

If a row starts at T_0 (where T_0 = TIME - 0.5 * TIME_INTERVAL) then all visibilities that end before T_0 are before this row. In other words, only overlapping intervals are allowed to not obey time ordering: non-overlapping intervals are strictly ordered.

BDA_FACTORS¶

This optional table describes fixed BDA time averaging factors for a baseline. When this table is present, some values in the BDA_TIME_AXIS table are redundant and can be derived from this table.


Name	Format	Units	Measure	Comments
Columns
Key
BDA_TIME_AXIS_ID	Int			Reference to BDA_TIME_AXIS
SPECTRAL_WINDOW_ID	Int			Reference to SPECTRAL_WINDOW
ANTENNA1	Int			Antenna 1
ANTENNA2	Int			Antenna 2
(ANTENNA3)	Int			Antenna 3
Data
TIME_FACTOR	Int			Time averaging factor

BDA_TIME_AXIS_ID

Refers to a row in the BDA_TIME_AXIS table, since a single baseline may have different fields. The BDA_TIME_AXIS row contains the FIELD_ID and common values for multiple baselines regarding time averaging.

SPECTRAL_WINDOW_ID

Refers to a row in the SPECTRAL_WINDOW table, since a single baseline may have multiple spectral windows.

ANTENNAn

Antenna identiﬁer, as indexed from ANTENNAn*\ in MAIN. Together, the antenna identifiers determine the baseline.

TIME_FACTOR

Time averaging factor for the given baseline, field (via the BDA_TIME_AXIS_ID table) and spectral window. The effective time interval for the baseline is this TIME_FACTOR times the UNIT_TIME_INTERVAL value in the BDA_TIME_AXIS table.

SPECTRAL_WINDOW: continued (Metadata for frequency)¶

All other requirements (such as specified for the time metadata) can be deduced from the metadata already in the SPECTRAL_WINDOW table. Spectral BDA has been applied when: i) the BDA_SET_ID column exists; and ii) multiple SPWs (rows in the table) have the same value in the BDA_SET_ID column.


Name	Format	Units	Measure	Comments
Data
(BDA_SET_ID)	Int

BDA_SET_ID

An id that links a set of spectral windows that cover the same (true/original) spectral window. It is the equal for all spectral windows where the only difference is the amount of frequency averaging. This id refers to the BDA_FREQ_AXIS_ID in the BDA_TIME_AXIS table, which contains information regarding the time averaging for the spectral window.

Ordering¶

For BDA data, the keyword SORT_COLUMNS in the main table does not suffice to determine the ordering (in time) of the rows. In the case of BDA with non-strictly ordered overlapping intervals the SORT_COLUMNS should be “None” and more detail should be specified in the column HAS_BDA_ORDERING in the table BDA_TIME_AXIS. In case the data is still also strictly ordered in TIME, this can of course still be registered in the SORT_COLUMNS keyword.

Use cases¶

Cut a BDA set half in time. If the set is cut half in time through a time averaged interval, the set becomes non-regular, and the integer factors do not make sense anymore. If the set is cut at a point where all intervals end, it can remain regular.
Cut a BDA set half in frequency. A frequency bin can be cut in half, then the spectral window mapping table needs updating. It may make more sense to cut at a point where all frequency bins have a matching end point.
Expand a BDA set back to what it was in a sensible way. If the table BDA_FACTOR is filled, this can be done. If INTEGER_INTERVAL_FACTORS is False, going back to original time resolution will probably not be possible. Frequency averaging has integer factors always, so expanding back to the original channels should always be possible.
Determine the maximum number of samples in a given interval. This can be done if INTEGER_INTERVAL_FACTORS is True, using MAX_TIME_INTERVAL and MIN_TIME_INTERVAL, and the metadata computed from the SPECTRAL_WINDOW table for each of the BDA_SET_IDs. If the BDA_FACTOR table is filled, the max and min factor in that table can be used.
Use different time averaging for different parts of the observation. E.g. if a specific part of the observation requires higher time accuracy (e.g. due to ionospheric behavior). For this, in the current design, a new FIELD_ID needs to be made for the different time windows. Each of the different FIELDs can then have regular BDA averaging. It may make sense to add back SCAN_ID to the selection criteria.

Example¶

Original MS, before applying BDA:¶

SPECTRAL_WINDOW table:

SPECTRAL_WINDOW_ID	CHAN_FREQ (MHz)	CHAN_WIDTH (MHz)
0	[100,110,120,130]	[10,10,10,10]
1	[1000,1100,1200,1300,1400,1500]	[100,100,100,100,100,100]

Main table:

TIME	SPECTRAL_WINDOW_ID	ANT1	ANT2	shape(DATA)[0]
0:00.0	0	0	1	6	(short baseline)
0:00.0	0	0	2	6	(long baseline)
0:00.0	1	0	1	6	(short baseline)
0:00.0	1	0	2	6	(long baseline)
0:01.0, 0:02.0, …	Four rows, similar the four rows above, for each time step.

After applying BDA to the original MS:¶

In this example, the time averaging factor and the frequency averaging factor are equal. In reality, they may differ.

BDA_FACTORS table:

BDA_TIME_AXIS_ID	BDA_FREQ_AXIS_ID	ANTENNA2	TIME_FACTOR
0	0	1	4	(short baseline)
0	1	2	3	(long baseline)
1	2	1	3	(short baseline)
1	3	2	2	(long baseline)