Depth Issues

The INS calculates the depth solution by fusing data from the pressure sensor with the inertial data for the Z world axis. It calculates depth of seawater as a function of pressure and latitude using the UNESCO 1983 formula and assumes a salinity of 35ppt and temperature of 0deg Celcius.

Illustration 1: Pressure to depth conversion with inertial compensation.

Illustration 2: Pressure to depth conversion formula.

Real time compensation of the salinity and temperature is also possible in some INS units where these values are available from sensors. Alternatively, most navigation systems calculating depth will provide means to manually set the temperature and salinity based on the local operating area.

Several issues are common with the final depth calculation.

• Depth is drifting but the sensor is not moving in the water column. Typical INS configurations tune the state estimate algorithm to heavily weight the pressure-based Z calculation so drift due to inertial drift is rare. The transducer may drift as a function of temperature, though. Short-scale drift or, more commonly, oscillations about a value, may be due to inertial drift. This may also be seen if the depth solution overshoots the settling point when moving in one direction and very slowly approaches the settling point in the other direction. Inertial drift may be due to a faulty sensor or a poor spin up period. Rebooting the INS and allowing it to spin up in a stable environment or allowing the INS to perform a ZVC may fix this.

• Depth is "wrong". The pressure sensor, through the conversion formula, aids the inertial system for the final Z estimate. If the depth is "wrong" but not moving (drifting) the issue is with the pressure transducer. Often the pressure sensor senses absolute pressure and requires a calibration at sea level to compensate for atmospheric pressure at the sea surface. If this is not done, either automatically within the INS or manually, the depth will be off by approximately 10m. During spin up, most INS units with integrated pressure sensors will calculate the pressure bias and compensate the depth calculation with this pressure bias. Other common sources of a "wrong" depth are improper positional transforms for the depth sensor or an improper mounting of the pressure sensor resulting in a constant pressure on the transducer element.

• Calculated depth is slightly different between instruments. Greensea's INS estimates depth by fusing the pressure-based depth calculation with the inertial state. This typically results in a smoothing of the depth estimate compared to the pressure-based depth calculation. This may cause the real time depth estimate to be different from that of other sensors. There are also many variables used in most depth calculations, such as temperature and depth, that are either estimated or updated in real time. If these are different between two sensors, the final depth calculation will be slightly different.

• Depth is "slow". The depth solution coming out of the INS may not correlate exactly to the perceived vertical motion. This may be a function of several things. Many digital pressure sensors perform internal filtering to smooth the transducer noise, which results in a measurement lag and slower update rates. Another common factor affecting the "speed" of the depth estimate is the tuning of the state estimation filter. The IMU will typically have very fast update rates (>50Hz) but the filter is usually tuned to heavily weight the transducer measurement. If the filter is very tight to the measurement source, the state estimate will more closely match the update rate of the measurement and be less dynamic, but if the filter is tuned less tightly to the measurement source, the state estimate will reflect the state estimate based on the inertial contribution and likely be more lively. A proper filter tuning will provide the fastest update rate possible with the available sensor set.

• Depth is "noisy". Noise sources in the depth channel are often the measurement transducer itself, the inertial sensor, or wave action. Pressure transducers are noisy instruments but are usually filtered by the electronics in the pressure sensor unit. If the state estimate filter is set up to weight the inertial contribution significantly and the inertial component is noisy, this noise will show up in the depth channel. Because the inertial sensor has a much higher update rate than most pressure sensors, it should be obvious which sensor is contributing the noise. Greensea provides a software prefilter on most transducer-based measurements. The parameters for this filter are usually available in a configuration file. Prefilters can introduce a lag in the measurement though and should be used very carefully. Tuning the state estimate filter to weight the inertial contribution less may reduce any inertial-based noise in the depth channel, but may also reduce the dynamics of the final depth solution. Finally, for high-accuracy pressure sensors, seeing wave action from the surface in the final depth solution is not uncommon. This will typically be associated with rather long period noise though and should be easily discriminated from either transducer noise or inertial noise.