This at least sounds interesting in theory, especially for open-water use where predictions aren’t dependent on surrounding structures. Would you be able to explain a bit more about what you mean by tidal currents, and how you envisage that prediction playing a meaningful role in motion estimation?
For an underwater vehicle, there are two inertial frames of reference; the moving body of water, and the fixed underwater terrain. Propulsion is in relation to the water frame of reference. Navigation is usually in relation to the underwater terrain.
You can estimate motion by knowing what the local water body speed and direction is at any time and your measurement of motion in relation to the water body.
Tidal currents are the cyclic flow of water under the influence of gravitational fields from the sun and moon and significant harmonics of the basic solar and lunar frequencies.
Tidal currents are significant in shallow water and not so significant in deep water.
Knowing the tidal data parameters at a location enables you to predict decades in advance (or retrograde) what the tidal component of a current will be. These will be a vector of water speed and direction. This vector varies over distance and underwater terrain, but can be estimated by interpolation, and can be established precisely by measurement at fixed points for a period of time.
Tidal currents and tide height are related in that the tide height is a function of the accumulated ebb and flow of water via a tidal current.
In addition to the tidal current component, there is usually ‘noise’ caused by wind and air pressure generated currents. Over a long period, these have a fixed value, often zero amplitude.
For mission planning, you can predict the tidal current at a location over time and then plan the propulsion of the vehicle in relation to the water so that you can then navigate in relation to the fixed terrain.
For navigation, you can generate the tidal component of the water current in real-time and use that as an input to your navigation filter (often a Kalman filter). This can be subtracted from the actual water current to feed only the error values to the filter – that is non-tidal components of the current. You are effectively giving the filter the water inertial frame data values and letting it work on the differences between that frame and what is actually measured.
To some extent, this is similar to using a GPS fixed location receiver as a reference to the values measured by a mobile GPS receiver.
The prediction is done using as few as 4 components and time. Each component is phase and amplitude in the X and Y axes. So 16 pre-computed floating-point numbers and a timestamp. You can use more components for better accuracy with an insignificant increase in computation time – which is measured in microseconds per cycle.