Doppler shift between a moving ship on the ocean and a satellite in LEO

[nicolewreyford]

Summary:: I would like to calculate the Doppler shift for a signal sent by a moving ship to a moving satellite.

I want to calculate the frequency observed by an LEO satellite when a signal is transmitted from a moving ship. The LEO satellite has a velocity of 7120m/s and orbits at a height of 1500km. The ship can have a velocity anywhere between 0 and 30m/s. The ship will be located in the near vicinity below the satellite, but will not necessarily be directly below the satellite. I am only considering movement in the four cardinal directions, N, W, S, E. For the scenario I can let the satellite be moving west and the ship in any of the four directions. I would then need to calculate the relative velocity between the satellite and ship, in order to obtain the Doppler shift. Since this is for an S-AIS system, the frequency at which the signal will be transmitted is 162MHz.

 

[berkeman]

Welcome to PF.

What would be the maximum Doppler shift if the satellite were moving directly away from the ship (just to put an upper bound on it, even though geometrically it will not happen). How does that compare to the 25kHz BW of each channel?

https://en.wikipedia.org/wiki/Automatic_identification_system

 

[Baluncore]

Welcome to PF.

Differential velocity max = 7120 m/s + 30 m/s = 7150 m/s
162 MHz; λ = 1.85 metres.
Maximum doppler shift will be 7150 / 1.85 = 3865. cycles per second.
That is small compared with the data rate = 9600 bit/sec, over 25 kHz channels, so it should not be a problem fitting in the IF of the receiver.

You will need to predict the position and velocity of the satellite in Earth relative coordinates from the ephemeris, which is available code. You will need to know the GPS lat, long, course and velocity for the ship, then convert that to Earth centred WGS84 coordinates. You can then work out the differential velocity and from that the doppler shift.

Why are you concerned about the satellite receiver?

 

[nicolewreyford]

Welcome to PF.

What would be the maximum Doppler shift if the satellite were moving directly away from the ship (just to put an upper bound on it, even though geometrically it will not happen). How does that compare to the 25kHz BW of each channel?

https://en.wikipedia.org/wiki/Automatic_identification_system

I am looking at a satellite AIS system and I need to see what the effect of the Doppler shift is on the transmission.

 

[nicolewreyford]

Welcome to PF.

Differential velocity max = 7120 m/s + 30 m/s = 7150 m/s
162 MHz; λ = 1.85 metres.
Maximum doppler shift will be 7150 / 1.85 = 3865. cycles per second.
That is small compared with the data rate = 9600 bit/sec, over 25 kHz channels, so it should not be a problem fitting in the IF of the receiver.

You will need to predict the position and velocity of the satellite in Earth relative coordinates from the ephemeris, which is available code. You will need to know the GPS lat, long, course and velocity for the ship, then convert that to Earth centred WGS84 coordinates. You can then work out the differential velocity and from that the doppler shift.

Why are you concerned about the satellite receiver?

Thank you, do you have a link to this code? I would like to show the mathematics behind the code as well. I am concerned with this as I am setting up a mock satellite AIS system and want to see the effect of the Doppler shift on the transmission. I know what the maximum Doppler shift is but need to be able to calculate the Doppler shift for ships with different velocities and positions.

 

[berkeman]

I am looking at a satellite AIS system and I need to see what the effect of the Doppler shift is on the transmission.

BTW, is this question for schoolwork? I can move the thread to the schoolwork forums if so.

 

[nicolewreyford]

BTW, is this question for schoolwork? I can move the thread to the schoolwork forums if so.

No, it is for a university project, it is not the main topic of the project and just something i am struggling to get my head around.

 

[berkeman]

it is for a university project

That makes it schoolwork under the PF rules. I'll go ahead and move the thread now. You will get good help in either location, as long as you show good effort.

Are you familiar yet with the coordinate systems mentioned by @Baluncore ?

 

[nicolewreyford]

That makes it schoolwork under the PF rules. I'll go ahead and move the thread now. You will get good help in either location, as long as you show good effort.

Are you familiar yet with the coordinate systems mentioned by @Baluncore ?

Okay, thank you. No, i am not familiar with that.

 

[Baluncore]

This is the sort of computation you will be faced with calculating Earth Relative Earth Fixed position and velocity of a satellite from the available ephemeris data.
https://ascelibrary.org/doi/pdf/10.1061/9780784411506.ap03
Google to find other explanations that you can understand, or ask very specific questions.

I am concerned with this as I am setting up a mock satellite AIS system and want to see the effect of the Doppler shift on the transmission.

Is it a computer simulation ?

 

[nicolewreyford]

This is the sort of computation you will be faced with calculating Earth Relative Earth Fixed position and velocity of a satellite from the available ephemeris data.
https://ascelibrary.org/doi/pdf/10.1061/9780784411506.ap03
Google to find other explanations that you can understand, or ask very specific questions.Is it a computer simulation ?

I will have a look at the coordinates, I am however only looking at a small area. I don't need to use the real coordinates to calculate teh shift. I would just like to understand how it can be calculated in a real world scenario.

 

[anorlunda]

I don't think the doppler effect figures in at all with AIS. The position and speed info are generated on the ship and sent as a digital message. The satellite just relays the message.

the ship can use any method, including GPS, to estimate position, course, and speed.

 

[Baluncore]

I don't think the doppler effect figures in at all with AIS.

Correct. Doppler is irrelevant to the navigation, but the satellite receivers must be able to handle the frequency shift of signals from ships in different directions relative to the satellite's path.

If a synthetic aperture antenna is used on the satellite, then due to satellite velocity each patch on the Earth's surface would feed a channel with a direction dependent doppler frequency shift. Many patches may be receiving AIS messages on the same channel, at the same time, from different vessels.

For the scenario I can let the satellite be moving west and the ship in any of the four directions.

That feels a bit backwards. Most satellites are launched towards the East because of the launch fuel saving. They then enter an orbit that will approach a ship from the western quadrant between SW and NW of the ship, and then depart into the Eastern quadrant between NE and SE.

Which satellite will be simulated? There are many to choose from.
Take a look at satellite tracking on the “Heavens-Above” website. Setup your location then pick a satellite. The ISS is a good visible example.
https://www.heavens-above.com/main.aspx

 

[Steve4Physics]

Not sure if this thread has fizzled out, but I think there is a fairly accurate (and simple) approach if we make some reasonable assumptions/approximations.

A few points first...

1. The Doppler shift (DS) depends on the relative velocity’s component along the line of sight (ship to satellite).

For example if the satellite’s velocity is perpendicular to the line of sight (e.g. satellite directly above ship) then the DS is zero at that moment.

The DS changes as the satellite passes oer - the DS is not a simple, single value.

2. We must not forget that the satellite’s orbital speed (7120m/s) is presumably relative to a ‘fixed’ frame of reference – i.e. one not rotating with the earth. We will require the satellite’s speed relative to the sea below it. Therefore the local (latitude dependent) speed of the sea due to the Earth's rotation needs to be accounted.

3. For LEO satellites, the speed of the satellite relative to the sea below it is large compared to the speed of a ship relative to the sea. Consequently the ship’s velocity (speed and direction) has only a small affect on the DS. We can treat the ship as stationary without introducing significant errors.

For example, the DS with the ship moving at (say) 5m/s north will be virtually the same as for the ship moving at (say) 30m/s west (that would be very fast ship by the way!).

4. We are interested in the DS with the ship “located in the near vicinity below the satellite”. This allows us to ignore the curvature of the earth.

For convenience, define θ as the angle between the ship’s vertical and the line of sight to the satellite.
_____________________

Here's an example calculation.

Speed of satellite relative to the sea = 7000 m/s (calculated somehow in accordance with point 2 above).

Take max. angle between the ship’s vertical and line of sight to satellite, as satellite passes over, as, say, |θ| = 1º.

(Note, if the satellite passes directly over the ship, this 1º angle corresponds to a circular region of sea around the ship, of radius 1500km tan(1º) = 26km; the satellite passes over this region.)

Max. velocity component along line of sight = 7000m/s sin(1º) = 122m/s

Max. frequency shift = (v/c)f₀ = (122/3E8)*162E6 ≈ 70Hz

So (to a reasonable approximation),the frequency-change will vary from -70Hz to +70Hz (or +70Hz to -70Hz) as the satellite passes over the ship from θ = -1º to θ = +1º.

Maybe |θ| = 1º is too small, but I hope you can understand the approach.

 

[anorlunda]

I may have misread your question. In my mind, AIS stands for Automatic Identification System. That is in place worldwide to report the position, course and speed of vessels at sea.

You may have meant AIS to mean Air Interface Specification as below from the Iridium Technical Manual. The quoted text talks about the doppler effect. That is maybe what you asked about.

https://www.icao.int/safety/acp/Ina...-Draft Iridium AMS(R)S Tech Manual 092005.pdf

2.2 Frequency Accuracy
The information provided in this subsection is for reference only. The Iridium manufactured and certified ISU will meet the frequency and timing accuracy requirements specified in the Iridium Air Interface Specification.

The [AIS] requires that once signal acquisition has been accomplished, the satellite and AES adjust their transmitted signal to account for Doppler and Doppler rate such that the received signal maintains an accuracy of 600 Hz or better relative to the designated radio frequency (RF) channel.