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GOODWILL - Narrative (Details) - USD ($)
3 Months Ended 6 Months Ended 12 Months Ended
Jun. 29, 2019
Apr. 02, 2021
Jan. 01, 2021
Jul. 03, 2020
Jan. 03, 2020
Dec. 28, 2018
Dec. 31, 2021
Jan. 01, 2021
Jan. 03, 2020
Jun. 28, 2019
Apr. 03, 2020
Finite-Lived Intangible Assets [Line Items]                      
Goodwill impairment $ 0           $ 62,000,000 $ 480,000,000      
Non-cash impairment charges for long-lived assets         $ 46,000,000 $ 0 207,000,000 767,000,000 $ 46,000,000 $ 0  
Impairment of marketable software         $ 46,000,000   $ 244,000,000 767,000,000   $ 0  
Commercial Aviation Solutions                      
Finite-Lived Intangible Assets [Line Items]                      
Impairment of intangible assets     $ 113,000,000                
Impairment charge for property, plant and equipment               257,000,000      
Commercial Aviation Solutions | COVID                      
Finite-Lived Intangible Assets [Line Items]                      
Goodwill impairment     111,000,000         461,000,000      
Goodwill impairment loss attributable to noncontrolling interests               34,000,000      
Non-cash impairment charges for long-lived assets     257,000,000                
Impairment charge for property, plant and equipment     103,000,000                
Impairment charge for ROU asset     31,000,000                
Impairment of marketable software     $ 10,000,000                
CPS business | Disposal Group, Held-for-sale, Not Discontinued Operations                      
Finite-Lived Intangible Assets [Line Items]                      
Goodwill impairment   $ 62,000,000                  
CPS business | Aviation Systems | Disposal Group, Held-for-sale, Not Discontinued Operations                      
Finite-Lived Intangible Assets [Line Items]                      
Goodwill impairment   62,000,000                  
Goodwill assigned to disposal group   $ 174,000,000                  
Applied Kilovolts and Analytical Instrumentation Business | Space & Airborne Systems | Disposal Group, Held-for-sale, Not Discontinued Operations                      
Finite-Lived Intangible Assets [Line Items]                      
Goodwill impairment               $ 5,000,000      
Goodwill assigned to disposal group                     $ 6,000,000
VSE disposal group | Disposal Group, Held-for-sale, Not Discontinued Operations                      
Finite-Lived Intangible Assets [Line Items]                      
Goodwill impairment       $ 14,000,000              
VSE disposal group | Aviation Systems | Disposal Group, Held-for-sale, Not Discontinued Operations                      
Finite-Lived Intangible Assets [Line Items]                      
Goodwill assigned to disposal group       $ 14,000,000