Side view chess

Variant with incomplete information. Idea of it was born during thinking about 1D variants, however it is regular 2D (though the board from player's point of view looks as 1D).

Rules

Game is played as if players would watch at the board not from above, but from the east (if white pieces are considered being at the south, and black ones - at the north, i. e. queen side).
Of course, players are always aware of positions of their own pieces. But information about opponent's pieces is restricted because of watching from side.
There are 3 variants of physics of this game. One must be chosen before playing.

1) Player can't see the file piece located on, only the rank. Moreover, player can see only the most east piece of the rank - all other pieces of this rank are covered by it.
This one is the most 1D-like (though still not 1D, strictly speaking, of course).

2) As in variant above, but here it is considered that pieces covers other pieces only partially. All pieces are always visible, but their files are still unknown, only their order. For example, if rook is on c4, and knight is on d4, opponent may think that rook is a4, and knight is somewhere from b4 to h4, or rook is on b4 and kinght is from c4 to h4 (but not on a4), etc, there are total 28 possible assumptions. If rank is completely filled with pieces, their positions are  monosemantic.

3) Two variants above are quite abstract. This one is the closest to real life (if pieces are shaped as, e. g., identical cubes with piece symbols drawn on them). As in first variant, the most east piece covers all other pieces on it's rank. But, unlike both previous variants, exact positions of visible pieces are always known (it's closer to real life because position can easily be figured out by means of perspective).

Common rules regarding incomplete information. These are only my proposals, players may choose to play with rules of other variants with incomplete information.
If there are doubts about move, player want to made, referee must state whether this move is legal or not (taking into account protecting king from check and castling limitations), but the reason of move's illegality must not be said. Once legal move is chosen, player can't refuse of it.

Notes

It seems fun to combine this variant with any other, that have setup phase (well, just like many other variants with incomplete information).
Even more ticklish twist is to combine it with variant with random setup or with seting up opponent's pieces. In it, player is not completely aware even about positions of his own pieces. If first or third type of physics is chosen, in the beggining player can move only visible pieces, but once invisible one became uncovered, it will be able to move even while being hidden again. To move, player must chose direction and number of steps, and referee should confirm it's legality (see above).