In Episode IV, Vader senses Obi-Wan's presence on the Death Star. In a conversation with Governor Tarkin, he states that, "Escape is not his plan. I must face him alone".
How does he know what Obi-Wan's plans are? What does he believe them to be?
Any Jedi of significant power has the ability to hide their use of the Force from another Jedi. While Vergere was by far the best at this - she described the process as "making myself small" - it is a skill that is shown, in the Star Wars Expanded Universe, to have been reasonably prevalent among the Jedi.
In Destiny's Way Vergere, a Sith apprentice and former Jedi Knight, describes the process and successfully eludes Luke Skywalker's ability to detect her through the Force despite sitting several metres in front of him in plain sight. In Before the Storm Luke Skywalker states that Obi-Wan Kenobi and Yoda must have been "at least as powerful" as the Emperor in order to remain hidden from him. Skywalker also needed to actively probe potential Jedi's minds to confirm to himself that they were really Jedi in The Jedi Academy Trilogy. Simply being in the same room as them or nearby was not enough for him to sense their presence. Vader also failed to recognise Princess Leia as possessing Jedi capabilities, even while he was torturing her, when such latent abilities are reasonably likely to have manifested.
It seems apparent, from these hints, that Kenobi could have kept his presence on the Death Star hidden from Vader had he wished. It is likely, then, that Kenobi deliberately allowed Vader to sense his presence. You will also note that Vader does not simply storm the ship to face Kenobi then and there. It is possible, then, that Obi-Wan allowed Vader to sense his presence but deliberately misled Vader as to his location and/ or intentions. What Vader actually believe Kenobi's intentions to be is never stated, but there are several possibilities, of which destroying the Death Star and/ or killing Vader could have occurred to Vader.
As for facing Kenobi alone; the last time Vader saw Kenobi, the latter defeated him in battle, cut him in half and left him for dead. It's quite conceivable that Vader wanted to gain revenge on Kenobi as well as prove - to Kenobi, Palpatine, and himself - that he was the better warrior of the two.
Obi Wan and Anakin Skywalker served together as Jedi for many years. During that time the two of them grew to know each other in the force and be able to read each others intentions. This is demonstrated though out the Clone Wars books and Television series.
So while the years would have dulled that sense it is quite reasonable that Vader would have been able to sense his basic intent. The desire to engage is quite different from the desire to escape. The ripples in the forces would have felt more on the hunt rather than must escape.
Vader leaped to the conclusion that he was hunting Vader, rather than trying to find and deactivate the tractor beam power source. Especially when he found out the Jedi came alone in a craft that would require more than just himself to escape the Death star. This was the type of mission that Vader had gone on many times with Obi Wan(see the TV Series). A suicide mission into a heavily fortified enemy space station was just another day in the order. This leads to a reasonable conclusion that Vader is the Jedi's target. Had Vader considered that he might lose then the Dark Lord might have set in place some defenses to prevent the escape post battle.