Captain reported a runway and taxiway incursion at BUR due to inadequate markings. ATC provided further taxi instructions to the runway.

Reporter 1

Aircraft was located on the ramp at BUR for an night departure. SIC called for taxi clearance after crew completed the After Start checklist. ATC cleared us to taxi to runway 33 for departure via D8 - D - B - hold short of runway 26. Crew briefed the taxi route, noted no hotspots along the cleared route and departed the ramp. The taxi checklist was completed while on D and shortly after ATC cleared us across runway 26. The crew did not see the turn onto B as the markings were very poor or non-existent (I don't recall seeing any lighted signs and there was no center line taxi lighting on D or B) and continued to taxi on D. There were no other aircraft on the ground control frequency. Upon reaching the intersection of runway 33 (which neither crew member realized was the wrong runway to be crossing) the SIC turned on all strobes and landing lights per SOP. The PIC checked the runway to the left for traffic on the runway and final and the SIC checked the runway and final to the right. Both stated verbally that the runway was clear as per SOP. Shortly after crossing the runway ATC called to say we were not cleared to cross the runway. The PIC stopped the aircraft east of runway 33 on taxiway D to sort out the situation. After some discussions with ATC the PIC asked for progressive taxi instructions to the approach end of runway 33. ATC instructed us to taxi southbound on taxiway A, westbound on runway 26 and turn left onto runway 33. We were subsequently told to turn right onto taxiway C, and after doing that ATC instructed us to turn left onto taxiway G and continue to the approach end of runway 33. We departed without further incident. This report has been reviewed by the SIC and he reports that, while he had Ownship position enabled for his iPad it was behaving erratically and not reliable. Tower controller said there was no loss of separation between our aircraft and any landing/departing/ taxiing aircraft.

Reporter 2

Initially I instructed the pilot to Taxi to RWY 33 via D hold short of RWY 26 at B. Once the aircraft was on Taxiway D, I've coordinated with LC (Local Control) and got the RWY 26 crossing at B. I instructed Aircraft X to Cross RWY 26 at B and taxi via Charlie, Golf. The pilot read back correctly. However, the pilot never made the right turn to cross RWY 26, and it looked like he was going Straight ahead. I saw that there was no traffic to RWY 33, so I called LC to cross RWY 33 at D. However, by the time I could give the pilot the RWY 33 crossing he was already on RWY 33. So, once he crossed the RWY 33 with no harm, I told him to hold short. It was a pilot deviation that occurred so I do not think there could have been any recommendation to prevent.

Reporter 3

[Report narrative contained no additional information.]