The "standard" RC protocol is to transmit bursts of AM pulses[1], the relative positions of which are translated by the receiver into variable-width control pulses that get sent to the servos. It should be fairly straightforward for the smartphone app to send pulses out the headphone jack, which are then used to key a simple RF transmitter on a standard RC control frequency. Then, in the car, you'd use an off-the-shelf RC receiver and servos to control the car.
A standard RC servo requires a control pulse that has a variable width of 1-2 ms (sometimes this is extended to 0.5-2.5 ms) and repeats at a 20-50 Hz rate. A basic RC car might have as few as two servos, while a complex plane might have six or more, each of which needs its independently-controlled pulse.
Rather than sending variable-width pulses over the air, which would be subject to noise and distortion of various types, the transmitter instead sends a series of fixed-width pulses (on the order of 0.5 ms or so), and it's the spacing among these RF pulses that becomes the width of the servo control pulse at the output of the receiver.
For example, a six-channel transmitter will send 7 pulses at a time. The time between the rising edge of the first pulse and the rising edge of the second pulse is turned by the receiver into the control pulse for servo #1. Similarly, the time from the second RF pulse to the third RF pulse becomes the control pulse for servo #2, and so on. After the seventh RF pulse, there's a relatively long gap (10 ms or more), which signals the receiver to reset its decoder back to servo #1.
[1]: I might be wrong about the modulation. Certainly, the earliest systems used AM, but indications are that modern systems are FM.
This is a harder problem than I think you realize. The basic Loc8tor system works primarily by virtue of a directional antenna in the receiver, and it doesn't really give you the position of the tag directly, it just indicates what direction it is from the location of the receiver, along with a very rough estimate of how far away it might be.
If you want to create a mesh of automatic receivers, each of these receivers will need to do direction finding, either mechanically by physically spinning its antenna in a circle, or by using multiple antennas and electrically "spinning" the reception pattern. Neither method is going to be simple to implement or particularly low-power.
It is only by combining direction information from two or more receivers (plus knowing exactly where these receivers themselves are located) will you be able to derive an absolute position for the tag.
Best Answer
I used to sell modules that look like they came from the same reference design, and found they were normally good for about 100 meters but out of thousands sold here are the most common problems with range:
The SparkFun pages say lists them as being a 5V module but the datasheet says the operating voltage is up to 12V, you should definitely use that.
Those simple ASK transmitter / receiver pairs need to have a balanced signal to work well like Manchester or NRZ encoding, but the VirtualWire library you've mentioned in a comment should take care of that.
The bitrates they mention are probably somewhat optimistic, try lowering it so something like 1200bps and experiment with going even lower.
They also need a preamble for the receiver to lock on, but once again the VirtualWire library should take care of that.
Also take a took at sending the data multiple times and additional error detection - that may help if the packets are mostly received but you get the odd inteference from being on an ISM frequency.
On the receiver side you can also look at using a larger antenna that won't have any regulatory implications. As Olin mentioned a proper ground plane for the antenna is worth looking at if practical.