Dear Raghunathan,

things are rather complicated and to suggest a quick solution is difficult. It's not only the connection of your cable shield what counts, but also the grounding technique provided at each individual modul. So, alone with improper connection of shield of sensor cable signal integrity can be eroded, even without having anything else connected to your signal conditioner. A careful analysis is needed to find the optimum solution. Here, what I would recommend you:

First, about pressure sensors and signal conditioners:
In order to avoid hum loops, many signal conditioners do use safety class II power supply, means a connection between safety earth ('Power Earth' in your schematic) and signal ground ('Sig Zero' in your schematic) is avoided. Now, all seems to be fine, a real floating signal ground is expected. But unfortunately, there is always this damned interwinding capacitance of several 100pF between primary winding and secondary winding of mains transformer present, which can make trouble, big trouble! If you, for instance, measure the potential between 'Sig Zero' and 'Power Earth' by the help of high ohmic digital voltage meter (DVM), you can measure a rather high AC voltage of 50Hz (or 60Hz, depending where you live). Dozens of volt can be present at 'Sig Zero'! Of course, any stray capacitance or ohmic impedance between 'Sig Zero' and 'Power Earth' will create a voltage divider in combination with interwinding capacitance, which results in a decrease of AC voltage between 'Sig Zero' and 'Power Earth'. When connecting 'Sig Zero' directly to 'Power Earth', this AC voltage will totally vanish. But then there's again this danger of ground loops, of course.
In any case, there's always this interwinding capacitance present, which makes high frequency interference running on mains voltage appearing directly at 'Sig Zero', means, for very narrow voltage spikes travelling on mains voltage the interwinding capacitance looks like a short circuit between mains voltage and 'Sig Zero'!!! This is very very often overlooked and is the cause of many problems, problems which might not be allowed to occur, because we expect a real isolated and floating supply voltage...

Pressure sensors come in two flavors: With active signal conditioner, and without. The parts with additional electronics provide a signal voltage of 0...10V, or 0...5V or they deliver a signal current of 4...20mA. The parts without additional electronics do only contain the naked DMS bridge. The latter sensor type is difficult to use in a noisy environment. Extreme care must be taken to achieve proper shielding and noise filtering. I hope you do not use them...
The active parts are much easier to use, because signal is heavily amplified before leaving the sensor. Shielding and noise filtering is much easier, because the relative noise contribution is much lower with increased signal voltage. But nevertheless, in very noisy environment the use of reliable shielding and grounding technique is also essential.
In any case, the sensor electronics is nearly always isolated from sensor case. No direct connection, no resistance and no capacitance. Only unavoidable stray capacitance, of course. The cable has a shield, which is connected to sensor case. If the sensor is CE approved, customer is advised not to disconnect cable shield from sensor case.

If the sensor is now connected to 'Signal Conditioner' situation becomes interesting: Where to connect the cable shield of sensor cable?
At sensor side case of pressure sensor is screwed into measuring position, which is very often a machine, or something else, made of metal and, surprise, having a direct connection to 'Power Earth' for safety purposes.
As signal ground of sensor is directly connected to 'Sig Zero', of course, leaving the cable shield of sensor cable at 'Signal Conditioner' side unconnected to 'Sig Zero' would have the unwanted consequence, that the above discussed AC voltage would now drop between sensor electronics and sensor case, and this directly in the sensor! Why? Because then, only the voltage divider formed by interwinding capacitance and stray capacitance (the sum of cable capacitance and stray capacitance between sensor electronics and sensor case) would be able to decrease this AC voltage.
Such a high AC voltage between sensor electronics and sensor case directly in the sensor is highly disadvantageous, of course. Keep in mind, that intrinsic sensor signal is much much smaller than this AC voltage, what would result in a tremendeously high noise coupling to sensor signal. If signal voltage in the millivolt range has to be amplified very high, surrounding case must work as a shield, but not as an antenna, means the sensor case must be at same potential as signal ground of sensor electronics. And this can only be accomplished by connecting the cable shield of sensor cable at 'Signal Conditioner' side to 'Sig Zero'. But this means, that now there exists a direct connection between 'Sig Zero' and 'Power Earth', at least if the machine where the pressure sensor is mounted at is connected to 'Power Earth', for safety purposes!!

Beside this above discussed grounding and shielding scheme, also some others are used, which use rather big capacitors instead of direct connections, in order to prevent ground loops. But these extravagant 'solutions' might even be more difficult to understand and to get them work...

So, very probably, your 'Sig Zero' is connected to 'Power Earth'!


Now, about 'Adc+Mcu':
This modul does also contain such a 'floating' power supply. So, 'Adc Com' is allowed to be directly connected to 'Sig Zero'. No ground loop will result. But: Due to interwinding capacitance of this second mains transformer, high frequency noise can run from mains via ground connection between 'Adc Com' and 'Sig Zero' to 'Signal Conditioner' and finally to sensor case. So, this ground connection should not possess too high impedance, otherwise voltage drop across this ground impedance will directly be added to signal voltage, which appears to be superimposed to it! This is the reason, why signal transmission between two such analog signal modules should always be provided by a true differential signal. Then, most of this voltage drop will vanish.
But as you do use unsymmetrical signal routing only a significant reduce of ground impedance between 'Adc Com' and 'Sig Zero' can help to maintain signal integritiy. This is best achieved by using a shielded cable for the connection between 'ADC+MCU' and 'Signal conditioner', with the shield connected to signal ground at both ends, means to 'Sig Zero' at 'Signal Conditioner' and to 'Adc Com' at 'Adc+Mcu'.

Care must be taken, that common mode noise comming from 'Adc+Mcu' board will not cause radiation of this cable. Also, high frequency interference travelling along this cable to 'Signal Conditioner' and finally to pressure sensor could degrade signal integrity by demudulating effects at slow analog stages. Because of that, some common mode filtering should be provided. Although a well designed common mode filter inside 'Adc+Mcu' would do the job much better, common mode filtering can also be accomplished by mounting a ferrite choke at both ends of cable, you know the type that can be bend arround cables.
Of course, also the sensor cable benefits of such ferrite chokes, mounted at both ends, but as the 'Adc+Mcu' is the origin of common mode noise, the ferrites at the cable to 'Adc+Mcu' are more important.

If unsymmetrical signal routing is used, it can help, to feed the primary winding of both transformers by the same mains voltage. So, do not plug the both mains cables into different mains plugs, but connect them by an additional cable, which carries the mains current of only these two modules.

Now, about 'Pc'.
Connecting the above discussed modules additionally to the 'Pc' will present problems, because then a ground loop is formed. Also, signal cable would carry even more common mode noise, I guess. Keep in mind, that the 'Pc' is powered by a SMPS, which is known to produce common mode noise. So, even the 'Power Earth' cable can be very noisy. This means, that signal ground of 'Pc' is not a good place for a common ground star point. It's not quiet enough. So, I would recommend the use of an opto isolated digital signal routing between 'Adc+Mcu' and 'Pc'. Take care, that 'Pc' is always connected to 'Power Earth'. Only by this, potential difference between 'Gnd' of 'Adc+Mcu' and signal ground of 'PC' can be limited to a sane value. Nevertheless, provide the opto isolator with enough headroom, regarding to isolation voltage! Connect a high voltage bidirectional transzorb of low capacitance or an equivalent varistor between both grounds, so that short overvoltage spikes, for instance generated by lightnings, will not damage the barrier.

And don't forget the ferrite chokes at both ends of the according connection cable.
The mains cable of 'Pc' should be connected to mains next to the both other modules. By this the common mode voltage between these involved modules can be kept at minimum.


Options:
Sometimes, more than only one pressure sensor is connected to 'Signal Conditioner'. Will this make trouble? Are then new ground loops formed?
As each cable has its shield connected to 'Sig Zero' at 'Signal Conditioner' side and to individual sensor case at sensor side, additional ground loops are formed, if these individual sensor cases are mounted at machines, which have their metal body connected to 'Power Earth' for safety purposes. But: Because internal sensor electronics does not have any connection to sensor case, these ground loops do not affect the signal ground return connections. Means, the loop current is only flowing in the cable shields.
There's one reason, why nevertheless these new ground loops should be avoided or at least kept at minimum: If the cable shields are not properly connected to 'Sig Zero' at 'Signal Conditioner', means if the technique of star point grounding was neglected, then ground loop currents can flow across 'Sig Zero' connections internally of 'Signal Conditioner' and produce voltage drops, which appear to be superimposed to sensor signal.

What doing if this grounding of cable shields at 'Signal Conditioner' was provided improperly?
Then, keep the loop area of these ground loops minimal, by keeping the cables as short as possible, by bending the cables together and by routing them next to the machines' metal body. Of course, not in next proximity to heavy noise generators like motors, transformers etc. There can always be found an optimum routing scheme, where the noise is minimal.

Good luck,
Kai