Table 1: Mathematical models of incomplete information.

Types Mathematical models

Missing measurements 𝑥 𝑘 + 1 = 𝑓 ( 𝑥 𝑘 ) + 𝐸 1 𝑣 𝑘 + 𝑔 ( 𝑥 𝑘 ) 𝑤 𝑘 , 𝑦 𝑘 = 𝛾 𝑘 ( 𝑥 𝑘 ) + 𝐸 2 𝑣 𝑘 , where 𝛾 𝑘 is a stochastic variable taking value on 1 or 0.

Randomly varying sensor delays 𝑥 𝑘 + 1 = 𝑓 ( 𝑥 𝑘 ) + 𝐸 1 𝑣 𝑘 + 𝑔 ( 𝑥 𝑘 ) 𝑤 𝑘 , 𝑦 𝑘 = 𝛾 𝑘 ( 𝑥 𝑘 ) + ( 1 𝛾 𝑘 ) ( 𝑥 𝑘 1 ) + 𝐸 2 𝑣 𝑘 , where 𝛾 𝑘 is a stochastic variable taking value on 1 or 0.

Signal quantization 𝑥 𝑘 + 1 = 𝑓 ( 𝑥 𝑘 ) + 𝐸 1 𝑣 𝑘 + 𝑔 ( 𝑥 𝑘 ) 𝑤 𝑘 , 𝑦 𝑘 = 𝑞 ( ( 𝑥 𝑘 ) ) + 𝐸 2 𝑣 𝑘 , where 𝑞 ( ) is a quantization function.

Sensor saturations 𝑥 𝑘 + 1 = 𝑓 ( 𝑥 𝑘 ) + 𝐸 1 𝑣 𝑘 + 𝑔 ( 𝑥 𝑘 ) 𝑤 𝑘 , 𝑦 𝑘 = S a t ( ( 𝑥 𝑘 ) ) + 𝐸 2 𝑣 𝑘 , where S a t ( ) is a saturation function.

Signal sampling ̇ 𝑥 𝑡 = 𝑓 ( 𝑥 𝑡 ) + 𝐸 1 𝑣 𝑡 + 𝑔 ( 𝑥 𝑡 ) 𝑤 𝑡 , 𝑦 𝑡 = ( 𝑥 𝑡 𝑘 ) + 𝐸 2 𝑣 𝑡 𝑘 , 𝑡 𝑘 𝑡 < 𝑡 𝑘 + 1 .