Chapter 13. Simulate DSN Range and Doppler Data

In this tutorial, we will use GMAT to generate simulated DSN range and Doppler measurement data for a sample spacecraft in orbit about the Sun. The spacecraft in this tutorial is in an Earth “drift away” type orbit about 1 AU away from the Sun and almost 300 million km away from the Earth.

The basic steps of this tutorial are:

Note that this tutorial, unlike most of the mission design tutorials, will be entirely script based. This is because most of the resources and commands related to navigation are not implemented in the GUI and are only available via the script interface.

As you go through the tutorial below, it is recommended that you paste the script segments into GMAT as you go along. After each paste into GMAT, you should perform a syntax check by hitting the Save, Sync button (). To avoid syntax errors, where needed, don’t forget to add the following command to the last line of the script segment you are checking.

BeginMissionSequence

We note that in addition to the material presented here, you should also look at the individual Help resources for all the objects and commands we create and use here. For example, Spacecraft, Transponder, Transmitter, GroundStation, ErrorModel, TrackingFileSet, RunSimulator, etc all have their own Help pages.

For this tutorial, you’ll need GMAT open, with a new empty script open. To create a new script, click New Script, ()

%  Create the Sun-centered J2000 frame.
Create CoordinateSystem SunMJ2000Eq;
SunMJ2000Eq.Origin = Sun;
SunMJ2000Eq.Axes   = MJ2000Eq;  %Earth mean equator axes

Create Spacecraft Sat;
Sat.DateFormat       = UTCGregorian;
Sat.CoordinateSystem = SunMJ2000Eq;
Sat.DisplayStateType = Cartesian;
Sat.Epoch            = 19 Aug 2015 00:00:00.000;
Sat.X                = -126544968
Sat.Y                =  61978514
Sat.Z                =  24133221
Sat.VX               = -13.789
Sat.VY               = -24.673
Sat.VZ               = -10.662

Sat.Id               = 11111;

Create Antenna HGA;

Create Transponder SatTransponder;
SatTransponder.PrimaryAntenna      = HGA;
SatTransponder.HardwareDelay       = 1e-06; %seconds
SatTransponder.TurnAroundRatio     = '880/749';

Sat.AddHardware                    = {SatTransponder, HGA};

Now we will create and configure a TrackingFileSet resource. This resource defines the type of data to be simulated, the ground stations that will be used, and the file name of the output GMD file which will contain the simulated data. In addition, the TrackingFileSet resource will define needed simulation parameters for the various data types.

Create TrackingFileSet DSNsimData;
DSNsimData.AddTrackingConfig        = {{CAN, Sat, CAN}, 'DSN_SeqRange'};   
DSNsimData.AddTrackingConfig        = {{CAN, Sat, CAN}, 'DSN_TCP'};                 
DSNsimData.FileName                 = ...
                     {'Sat_dsn_range_and_doppler_measurements.gmd'};

DSNsimData.UseLightTi               = true;
DSNsimData.UseRelativityCorrection  = true;
DSNsimData.UseETminusTAI            = true;

DSNsimData.SimDopplerCountInterval  = 10.0;
DSNsimData.SimRangeModuloConstant   = 3.3554432e+07;

The script lines above are broken into three sections. In the first section, the resource name, DSNsimData, is declared, the data types are defined, and the output file name is specified. AddTrackingConfig is the field that is used to define the data types. The first AddTrackingConfig line tells GMAT to simulate DSN range two way measurements for the CAN to Sat to CAN measurement strand. The second AddTrackingConfig line tells GMAT to simulate DSN Doppler two way measurements for the CAN to Sat to CAN measurement strand.

The second section above sets some simulation parameters that apply to both the range and Doppler measurements. We set UseLightTime to True in order to generate realistic measurements where GMAT takes into account the finite speed of light. The last two parameters in this section, UseRelativityCorrection and UseETminusTAI, are set to True so that general relativistic corrections, as described in Moyer [2000], are applied to the light time equations.

The third section above sets simulation parameters that apply to a specific measurement type. SimDopplerCountInterval applies only to Doppler measurements and SimRangeModuloConstant applies only to range measurements. We note that the “Sim” in the field names is used to indicate that these fields only are applicable when GMAT is in simulation mode (i.e., when using the RunSimulator command) data and not when GMAT is in estimation mode (i.e., when using the RunEstimator command). SimDopplerCountInterval, the Doppler Count Interval, is set to 10 seconds and SimRangeModuloConstant, the maximum possible range value, is set to 33554432. See the RunSimulator Help and Appendix A – Determination of Measurement Noise Values for a description of how these parameters are used to calculate the measurement values.

We now create and configure the force model and propagator that will be used for the simulation. For this deep space drift away orbit, we naturally choose the Sun as our central body. Since we are far away from all the planets, we use point mass gravity models and we include the effects of the Sun, Earth, Moon, and most of the other planets. In addition, we model Solar Radiation Pressure (SRP) affects and we include the affect of general relativity on the dynamics. The script segment accomplishing this is shown below.

Create ForceModel Fm;
Create Propagator Prop;
Fm.CentralBody            = Sun;
Fm.PointMasses            = {Sun, Earth, Luna, Mars, Saturn, ...
                             Uranus, Mercury, Venus, Jupiter};
Fm.SRP                    = On;
Fm.RelativisticCorrection = On;
Fm.ErrorControl           = None;
Prop.FM                   = Fm;
Prop.MinStep              = 0;

As shown below, we create and configure the Simulator object used to define our simulation.

Create Simulator Sim;
Sim.AddData             = {DSNsimData};
Sim.EpochFormat         = UTCGregorian;
Sim.InitialEpoch        = '19 Aug 2015 00:00:00.000';
Sim.FinalEpoch          = '19 Aug 2015 00:12:00.000';
Sim.MeasurementTimeStep = 600;
Sim.Propagator          = Prop;
Sim.AddNoise            = Off;

In the first script line above, we create a Simulator object, Sim. The next field set is AddData which is used to specify which TrackingFileSet should be used. Recall that the TrackingFileSet specifies the type of data to be simulated and the file name specifying where to store the data. The TrackingFileSet, DSNsimData, that we created in the Define the types of measurements to be simulated section, specified that we wanted to simulate two way DSN range and Doppler data that involved the CAN GroundStation.

The next three script lines, which set the EpochFormat, InitialEpoch, and FinalEpoch fields, specify the time period of the simulation. Here, we choose a short 12 minute duration.

The next script line sets the MeasurementTimeStep field which specifies the requested time between measurements. We choose a value of 10 minutes. This means that our data file will contain a maximum of two range measurements and two Doppler measurements.

The next script line sets the Propagator field which specifies which Propagator object should be used. We set this field to the Prop Propagator object which we created in the Create and configure Force model and propagator section.

Finally, in the last line of the script segment, we set the AddNoise field which specifies whether or not we want to add noise to our simulated measurements. The noise that can be added is defined by the ErrorModel objects that we created in the Create and configure the Ground Station and related parameters section. As discussed in the Create and configure the Ground Station and related parameters section and Appendix A – Determination of Measurement Noise Values, the noise added to the range measurements would be Gaussian with a one sigma value of 10.63 Range Units and the noise added to the Doppler measurements would be Gaussian with a one sigma value of 0.0282 Hz. For this simulation, we choose not to add noise.

The script segment used to run the mission is shown below.

BeginMissionSequence
 
RunSimulator Sim

The first script line, BeginMissionSequence, is a required command which indicates that the “Command” section of the GMAT script has begun. The second line of the script issues the RunSimulator command with the Sim Simulator resource, defined in the Create and configure Simulator object section, as an argument. This tells GMAT to perform the simulation specified by the Sim resource.

We have now completed all of our script segments. See the file, Simulate DSN Range and Doppler Data.script, for a listing of the entire script. We are now ready to run the script. Hit the Save,Sync,Run button, (). Because we are only simulating a small amount of data, the script should finish execution in about one second.

Let’s take a look at the output created. The file created, Sat_dsn_range_and_doppler_measurements.gmd, was specified in the TrackingFileSet resource, DSNsimData, that we created in the Define the types of measurements to be simulated section. The default directory, if none is specified, is the GMAT ‘output’ directory. Let’s analyze the contents of this “GMAT Measurement Data” or GMD file as shown below.

% GMAT Internal Measurement Data File
27253.500405092593 DSN_SeqRange 9004 22222 11111 26016945.24902344 2 7.2e+009 3.3554432e+007
27253.500405092593 DSN_TCP  9006 22222 11111 2 10 -8459336323.89349840 
27253.507349537038 DSN_SeqRange 9004 22222 11111 21728172.10375977 2 7.2e+009 3.3554432e+007 
27253.507349537038 DSN_TCP  9006 22222 11111 2 10 -8459335611.28409770

The first line of the file is a comment line indicating that this is a file containing measurement data stored in GMAT’s internal format. There are 4 lines of data representing range data at two successive times and Doppler data at two successive times. As we expected, we have no more than 4 total measurements. Refer to the TrackingFileSet Help for a description of the range and Doppler GMD file format.

We now analyze the first line of data which represents a DSN two way range measurement at the start of the simulation at '19 Aug 2015 00:00:00.000 UTCG’ which corresponds to the output TAI modified Julian Day of 27253.500405092593 TAIMJD.

The second and third fields, DSN_SeqRange and 9004, are just internal GMAT codes indicating the use of DSN range (Trk 2-34 type 7) data.

The 4th field, 22222, is the Downlink station ID. This is the ID we gave the CAN GroundStation object that we created in the Create and configure the Ground Station and related parameters section. The 5th field, 11111, is the spacecraft ID. This is the ID we gave the Sat Spacecraft object that we created in the Create and configure the spacecraft, spacecraft transponder, and related parameters section.

The 6th field, 26016945.24902344, is the actual DSN range observation value in RU.

The 7th field, 2, is an integer which represents the Uplink Band of the uplink GroundStation, CAN. The designation, 2, represents X-band. See the RunSimulator Help for a detailed discussion of how GMAT determines what value should be written here. As described in the Help, since we are not using a ramp table, GMAT determines the Uplink Band by looking at the transmit frequency of the Transmitter object attached to the CAN ground station. GMAT knows that the 7200 MHz value that we assigned to CAN’s Transmitter resource, DSNTransmitter, corresponds to an X-band frequency.

The 8th field, 7.2e+009, is the transmit frequency of CAN at the time of the measurement. Since we are not using a ramp table, this value will be constant for all measurements and it is given by the value of the frequency of the Transmitter object, DSNTransmitter, that we attached to the CAN ground station. Recall the following script segment, DSNTransmitter.Frequency = 7200; %MHz, from the Create and configure the Ground Station and related parameters section.

The 9th field, 3.3554432e+007, represents the integer range modulo number that helps define the DSN range measurement. This is the value that we set when we created and configured the TrackingFileSet DSNsimData object in the Define the types of measurements to be simulated section. Recall the following script command,

This range modulo number is discussed in Appendix A – Determination of Measurement Noise Values and is defined as M, the length of the ranging code in RU.

We now analyze the second line of data which represents a DSN two way Doppler measurement at the start of the simulation at '19 Aug 2015 00:00:00.000 UTCG’ which corresponds to the output TAI modified Julian Day of 27253.500405092593 TAIMJD.

The second and third fields, Doppler and 9006, are just internal GMAT codes indicating the use of DSN Doppler (derived from two successive Trk 2-34 type 17 Total Count Phase measurements) data.

The 4th field, 22222, is the Downlink station ID. This is the ID we gave the CAN GroundStation object that we created in the Create and configure the Ground Station and related parameters section. The 5th field, 11111, is the spacecraft ID. This is the ID we gave the Sat Spacecraft object that we created in the Create and configure the spacecraft, spacecraft transponder, and related parameters section.

The 6th field, 2, is an integer which represents the Uplink Band of the uplink GroundStation, CAN. As we mentioned when discussing the range measurement, the designation, 2, represents X-band.

The 7th field, 10, is the Doppler Count Interval (DCI) used to help define the Doppler measurement. This is the value that we set when we created and configured the TrackingFileSet DSNsimData object in the Define the types of measurements to be simulated section. Recall the following script command,

The DCI is also discussed in Appendix A – Determination of Measurement Noise Values.

The 8th field, -7819057474.22393610, is the actual DSN Doppler observation value in Hz.

The third line of data represents the second DSN two way range measurement at '19 Aug 2015 00:10:00.000 UTCG’ which corresponds to the output TAI modified Julian Day time of 27253.507349537038 TAIMJD. The fourth line of data represents the second DSN two way Doppler measurement at '19 Aug 2015 00:10:00.000 UTCG.’

We have run a short simple simulation and generated a sample GMD file. Our next goal is to generate a realistic GMD file that a different script can read in and generate an orbit determination solution. To add more realism, we will do the following:

In order to generate measurement data from additional ground stations, we must first create and configure additional GroundStation objects. Below, we create and configure two new ground stations, GDS and MAD.

Create GroundStation GDS;  
GDS.CentralBody           = Earth;
GDS.StateType             = Cartesian;
GDS.HorizonReference      = Ellipsoid;
GDS.Location1             = -2353.621251;
GDS.Location2             = -4641.341542;
GDS.Location3             = 3677.052370;
GDS.Id                    = '33333';
GDS.AddHardware           = {DSNTransmitter, DSNAntenna, DSNReceiver};
GDS.MinimumElevationAngle = 7.0;
GDS.IonosphereModel       = 'IRI2007';
GDS.TroposphereModel      = 'HopfieldSaastamoinen';

Create GroundStation MAD;  
MAD.CentralBody           = Earth;
MAD.StateType             = Cartesian;
MAD.HorizonReference      = Ellipsoid;
MAD.Location1             = 4849.519988;
MAD.Location2             = -0360.641653;
MAD.Location3             = 4114.504590;
MAD.Id                    = '44444';
MAD.AddHardware           = {DSNTransmitter, DSNAntenna, DSNReceiver};
MAD.MinimumElevationAngle = 7.0;
MAD.IonosphereModel       = 'IRI2007';
MAD.TroposphereModel      = 'HopfieldSaastamoinen';

Now that we have defined two additional ground stations, we must specify the measurement noise associated with these new ground stations. This can be done using the previously created ErrorModel resources as shown below.

GDS.ErrorModels           = {DSNrange, DSNdoppler};
MAD.ErrorModels           = {DSNrange, DSNdoppler};

Next, we must add the corresponding two way range and Doppler measurements associated with our new ground stations to our TrackingFileSet object, DSNsimData, as shown below.

DSNsimData.AddTrackingConfig = {{GDS, Sat, GDS}, 'DSN_SeqRange'};   
DSNsimData.AddTrackingConfig = {{GDS, Sat, GDS}, 'DSN_TCP'};

DSNsimData.AddTrackingConfig = {{MAD, Sat, MAD}, 'DSN_SeqRange'};   
DSNsimData.AddTrackingConfig = {{MAD, Sat, MAD}, 'DSN_TCP'};

We now create our ramp table that many but not all missions use. A ramp table is a table that allows GMAT to calculate the transmit frequency of all the ground stations involved in our simulation. Recall that GMAT needs to know the transmit frequency, as a function of time, in order to calculate the value of the observations. The term “ramp” is used because the transmit frequency increases linearly with time and a graph of transmit frequency vs. time would typically show a ramp. A mission that does not use a ramp table simply uses a constant transmit frequency for a given ground station.

To modify our script to accommodate the use of a ramp table, we modify our TrackingFileSet object, DSNsimData, as shown below.

DSNsimData.RampTable = ...
{'../output/Simulate DSN Range and Doppler Data 3 weeks.rmp'};

We must now create a file with the name shown above in the GMAT ‘output’ directory. Refer to the TrackingFileSet Help for a description of the ramp table file format. In order for GMAT to determine the transmit frequencies of all the ground stations, the ramp table must have at least one row of data for every ground station providing measurement data. The contents of our ramp table is shown below.

Each row of data above is called a ramp record. Let’s analyze the first ramp record. The first field, 27252, is the TAIMJD date of the ramp record.

The second field, 22222, is the ground station ID of the GroundStation object whose frequency is being specified. We note that the ID 22222 corresponds to the CAN ground station. The third field, 11111, is the ID of the spacecraft that the CAN ground station is transmitting to. We recognize 11111 as the ID of the Sat spacecraft.

The 4th field, 2, is an integer representing the uplink band of the transmission. The integer 2 represents X-band. The 5th field, 1, is an integer describing the ramp type. The integer 1 represents the start of a new ramp.

The 6th field, 7.2e9, is the transmission frequency in Hz, from CAN to Sat at the time given by the first field. The 7th input is the ramp rate in Hz/s.

We now describe how GMAT uses the ramp record to determine the transmit frequency of CAN to Sat at a given time. We let TAIMJD be the time associated with the ramp record. Then GMAT will calculate the value of the transmit frequency at t = 27252.5 TAIMJD as shown below.

where

Note that, in the typical case where there are numerous ramp records, it is assumed that t o < t is chosen as close to time t as possible. For our case above, the transmit frequency from CAN to Sat at time t is

The second and third rows of the ramp table allow GMAT to calculate the transmit frequency from GDS to Sat and MAD to Sat, respectively. We now create a file, Simulate DSN Range and Doppler Data Realistic GMD.rmp, with the contents shown above and place it in GMAT’s ‘output’ folder.

We make one final comment about the use of a ramp table. We note that when a ramp table is used, GMAT uses the various script inputs (e.g., SatTransponder.TurnAroundRatio and DSNTransmitter.Frequency) differently. See the RunSimulator Help for details.

We only have two steps remaining in order to create a script that generates more realistic measurement data. The first step is to increase the simulation time from 10 minutes to the more realistic 3 weeks worth of data that is typically needed to generate an orbit determination solution for a spacecraft in this type of deep space orbit. The second step is to turn on the measurement noise. These two steps are accomplished by making the following changes to our TrackingFileSet object, DSNsimData.

Sim.FinalEpoch          = '09 Sep 2015 00:00:00.000';
Sim.AddNoise            = On;
Sim.MeasurementTimeStep = 3600;

Note that above, in addition to implementing the two needed steps, we also changed the measurement time step from 600 seconds to 3600 seconds. This is not a realistic time step as many missions would use a time step that might even be less than 600 seconds. We used this larger time step for tutorial purposes only so that the script would not take too long to run.

A complete script, containing all the changes we have made in the Create a more realistic GMAT Measurement Data (GMD) section, is contained in the file, Tut_Simulate_DSN_Range_and_Doppler_Data_3_weeks.script. Note that in this file, in addition to the changes above, we have also changed the GMD output file name to Simulate DSN Range and Doppler Data 3 weeks.gmd.

Now run the script which should take approximately 1-2 minutes since we are generating much more data than previously. We will use the GMD file we have created here as input to an estimation script we will build in the next tutorial, Orbit Estimation using DSN Range and Doppler Data.

We now say a few words on how we determined the values for NoiseSigma for the two ErrorModel resources we created. The computed value of the DSN range measurement is given by (Moyer [2000]):

where

We note that M as defined above is equal to SimRangeModuloConstant which was discussed in the Define the types of measurements to be simulated section.

By manipulation of the equation above, we can find a relationship between RU and meters, as shown below.

where

If we assume the round trip distance is 1 meter, we have

Recall that in the Create and configure the Ground Station and related parameters section, we set DSNTransmitter.Frequency = 7200; This corresponds to an X-band frequency (so, C=221/1498) of 7200e6 Hz. For the case where a ramp table is not used, we have a constant frequency, f ¯ T = f T , and thus

For this example, for DSN range measurements, we want to use a 1 sigma noise bias of 3 meters (Schanzle [1995]). From the calculations above, we determine that this corresponds to 3*3.543172 ≈ 10.63 RU.

We now turn our attention to the DSN Doppler measurement. The DSN Doppler measurement that GMAT uses is actually a derived observation, O, calculated using two successive Total Count Phase, ϕ , (type 17 Trk 2-34 record) measurements as shown below.

where

In the absence of measurement noise, one can show (Moyer [2000]), that the Observed value (O) above equals the Computed (C) value below.

where

Neglecting ionospheric media corrections, further calculation (Mesarch [2007]) shows that the values of O and C can be related to an average range rate value, ρ ˙ ¯ , as shown below.

where

Thus, we determine that

The quantity, ( O − C ) , above represents the measurement noise and thus the equation gives us a way to convert measurement noise in Hz to measurement noise in mm/s. To convert from mm/s to Hz, simply multiply by M 2 f ¯ T c = M 2 f ¯ T 299792458000 . In our case, where we use a constant X-band frequency of 7.2e9, the conversion factor is given by 880 749 7.2 e 9 299792458000 ≈ 0 .0282 . For this tutorial, we use a 1 sigma noise value of 1 mm/s (Schanzle [1995]) which corresponds to this value of 0.0282 Hz.