Date: 201503
Local time of day: 1801-2400
Location: ZZZ.ARTCC, US
Flight conditions: Mixed
Light: Night
Aircraft: B737-700
Operator: Air Carrier
Operating under: Part 121
Flight plan: IFR
Mission: Passenger
Flight phase: Climb
Airspace: Class A ZZZ
ATC / advisory: Center ZZZ
Reporter organization: Air Carrier
Reporter function: Captain; Pilot Flying
Reporter qualification: Flight Crew Air Transport Pilot (ATP)
Human factors: Workload; Troubleshooting; Distraction; Human-Machine Interface; Situational Awareness
Second reporter function: Pilot Not Flying; First Officer
Anomaly: Aircraft Equipment Problem Critical
Detector: Automation Aircraft Other Automation; Person Flight Crew
When detected: In-flight
Result: Aircraft Automation Overrode Flight Crew; Flight Crew FLC complied w / Automation / Advisory; Flight Crew Landed in Emergency Condition; Flight Crew FLC Overrode Automation; Flight Crew Returned To Departure Airport; Flight Crew Took Evasive Action; General Maintenance Action
Contributing factors: Aircraft
Primary problem: Aircraft

Narrative: Passing through 37;500 for a cruise at flight level 380 the autopilot went into control wheel steering pitch mode. It appeared that the autopilot was not going to level off at the assigned altitude. Both the First Officer (FO) and myself reached for the controls and disconnected both the autopilot and autothrottles.At about the same time the Captain's primary flight display (PFD) started showing mulitple erratic indications on both airspeed and altimeter. These were accompanied by multiple aural alerts. I switched the flying duties to the FO's side while getting out the QRH. Nothing could be found; at first; in the QRH that matched our situation. I went to the airspeed unreliable checklist first but other items were failing so we weren't sure if that was the correct check list to follow.We notified ATC that we had some navigational problems and inquired about our course.  They said our altitude was erratic and showing quick changes from 38;000 feet. We switched to our number 2 transponder to see if that would solve the problem. Center then showed us level at 38;000 feet. Then I got a unable required Nav Perf-RNP. Both the RNP and ANP were amber. I went to the POS page 2 and saw that our IRS were drifting apart. Left side showed 13 miles while the right side showed 5 miles and drifting even more apart. We inquired about our track and was told it appeared we were drifting off course. We requested a vector to a nearby vortac. This was given and told to proceed when able.About that time I got an IRS fault and again checking the POS page 2 saw that I had lost the left IRS. Followed the QRH I switched the IRS to both on the right side. Nothing happened to my PFD and the FO's PFD started to drift off making his side worse. I switched the IRS back to the normal position and for a short time that fixed the FO's instruments.I called both Dispatch and Maintenance Control advising them of the situation. By this time we had been hand flying and the navigational instruments were in question. I informed both that we were going to return to the departure airport. Dispatch re-dispatched us for our return via ACARS. We advised ATC of our intentions and were given a heading back. We noticed that our standby heading indicator was showing us on a 120 heading while we were still flying a 300 heading. It also had a flag showing it was inop.As soon as the FO started his turn we received two uncommanded rudder inputs causing a sharp roll to the left. The captains instruments were showing both pitch and bank angle in excess and was getting both aural alerts to each. Then my PFD went blank since I still had the overhead switch in the normal position on the IRS.After the uncommanded rudder input I advised ATC that we were no longer RVSM qualified. We requested a lower altitude and was assigned flight level 280. As we started the descent we realized that 28;000 would put in IMC. Not wanting to go IMC with our faulty navigational instruments I requested to stop at 34;000 to stay VMC and that was approved.We checked weather at several different locations but none had the weather we felt comfortable flying in considering our current problems. We flew back to our departure airport via radar vectors and using our whiskey compass. Weather at our departure airport was VMC and we knew a visual approach could be made easily. Both the FO and myself took turns doing the flying. We elected not to trim or change the configuration of the aircraft since we weren't sure exactly what was wrong with the jet and what caused the rudder input to roll the plane. We talked about our approach and how we would configure the plane for landing.Since we had uncommanded input to the rudder we elected not to arm the speed brake for fear of early deployment. Flaps would be at 15 for a higher approach speed in case of a hard rudder throw. The ground prox flap inhibit switch was turned off used the single engine check list since that covered our abnormal landing configuration. Autobrakes 3 were selected but they had failed too. Autobrakes were turned off and normal braking was to be used.While descending through 12;000 feet on our approach we experienced a third and more violent roll to the left; again caused by a uncommanded rudder input. At this point I instructed the FO to turn off the yaw damper. While on approach we still were receiving many false warnings concerning airspeed and windshear. The Captain's barber pole and yellow stall indicator were touching during the approach. After touch down the Captain's stick shaker went off throughout the roll out. After clearing the runway we taxied to the gate. The taxi in was uneventful.All decisions made were based on the interest of safety. At no time did we deviate from any altitude; clearance; or FARs.

Callback: The reporter stated that the Captain's PFD was ultimately blank. The only heading source available was the wet compass which the crew was not certain they could trust. After the flight; passengers and flight attendants reported several significant rudder 'kicks'; several more than the crew experienced. Maintenance reported an IRS transfer switch anomaly was apparently the cause. That component was replaced and the aircraft returned to service.

Second narrative: [Report narrative contained no additional information].


Synopsis: A B737-700 autopilot transitioned to Control Wheel Steering uncommanded; followed by the loss of both IRS; erratic airspeed; altimeter; pitch and bank indications as well as intermittent uncommanded rudder inputs. The flight returned to the departure airport where Maintenance suspected an IRS Transfer Switch Fault.