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GOODWILL AND OTHER INTANGIBLE ASSETS - Goodwill (Details) - USD ($)
$ in Millions
3 Months Ended 9 Months Ended
Oct. 02, 2021
Oct. 02, 2021
Dec. 31, 2020
Changes in the carrying amount of goodwill      
Gross goodwill, beginning of the period   $ 843.7  
Accumulated impairment, balance at the beginning of the period   (475.1)  
Goodwill, balance at the beginning of the period   368.6  
Goodwill Resulting from Business Combinations   64.2  
Impairments   0.0  
Accumulated impairment   (23.3)  
Goodwill, impairment, net of accumulation   (23.3)  
Gross goodwill related to foreign currency translation   (10.1)  
Accumulated impairments related to foreign currency translation   4.6  
Goodwill related to foreign currency translation   (5.5)  
Gross goodwill, end of the period $ 897.8 897.8  
Accumulated impairment, balance at the end of the period (493.8) (493.8)  
Goodwill, balance at the end of the period 404.0 404.0  
Sealite Acquisition      
Changes in the carrying amount of goodwill      
Goodwill Resulting from Business Combinations   38.5  
Enterprise Control Systems Ltd      
Changes in the carrying amount of goodwill      
Goodwill Resulting from Business Combinations   20.6  
Contingent consideration liability 8.2 8.2  
ULC Robotics      
Changes in the carrying amount of goodwill      
Goodwill Resulting from Business Combinations   3.1  
Contingent consideration liability     $ 24.3
ULC Robotics | Goodwill      
Changes in the carrying amount of goodwill      
Impairments (23.3)    
ULC Robotics | Other Operating Income (Expense)      
Changes in the carrying amount of goodwill      
Impairments (24.3)    
Sensors & Software      
Changes in the carrying amount of goodwill      
Goodwill Resulting from Business Combinations   2.0  
HVAC reportable segment      
Changes in the carrying amount of goodwill      
Gross goodwill, beginning of the period   492.2  
Accumulated impairment, balance at the beginning of the period   (340.6)  
Goodwill, balance at the beginning of the period   151.6  
Goodwill Resulting from Business Combinations   0.0  
Impairments   0.0  
Goodwill, impairment, net of accumulation   0.0  
Gross goodwill related to foreign currency translation   (6.5)  
Accumulated impairments related to foreign currency translation   4.5  
Goodwill related to foreign currency translation   (2.0)  
Gross goodwill, end of the period 485.7 485.7  
Accumulated impairment, balance at the end of the period (336.1) (336.1)  
Goodwill, balance at the end of the period 149.6 149.6  
Detection and Measurement reportable segment      
Changes in the carrying amount of goodwill      
Gross goodwill, beginning of the period   351.5  
Accumulated impairment, balance at the beginning of the period   (134.5)  
Goodwill, balance at the beginning of the period   217.0  
Goodwill Resulting from Business Combinations   64.2  
Impairments   0.0  
Accumulated impairment   (23.3)  
Goodwill, impairment, net of accumulation   (23.3)  
Gross goodwill related to foreign currency translation   (3.6)  
Accumulated impairments related to foreign currency translation   0.1  
Goodwill related to foreign currency translation   (3.5)  
Gross goodwill, end of the period 412.1 412.1  
Accumulated impairment, balance at the end of the period (157.7) (157.7)  
Goodwill, balance at the end of the period 254.4 254.4  
Other      
Changes in the carrying amount of goodwill      
Gross goodwill, beginning of the period   0.0  
Accumulated impairment, balance at the beginning of the period   0.0  
Goodwill, balance at the beginning of the period   0.0  
Goodwill Resulting from Business Combinations   0.0  
Impairments   0.0  
Goodwill, impairment, net of accumulation   0.0  
Gross goodwill related to foreign currency translation   0.0  
Accumulated impairments related to foreign currency translation   0.0  
Goodwill related to foreign currency translation   0.0  
Gross goodwill, end of the period 0.0 0.0  
Accumulated impairment, balance at the end of the period 0.0 0.0  
Goodwill, balance at the end of the period $ 0.0 $ 0.0