A method of controlling polishing includes polishing a substrate, monitoring the substrate during polishing with an in-situ monitoring system, filtering a signal from the monitoring system to generate a filtered signal, and determining at least one of a polishing endpoint or an adjustment for a polishing rate from the filtered signal. The filtering includes modelling a plurality of periodic disturbances at a plurality of different frequencies using a plurality of disturbance states, modelling an underlying signal using a plant state, and applying a linear prediction filter to the plant state and the plurality of disturbance states to generate a filtered signal representing the underlying signal.

A method of controlling polishing includes storing a base spectrum, the base spectrum being a spectrum of light reflected from a substrate after deposition of a deposited dielectric layers overlying a metallic layer or semiconductor wafer and before deposition of a non-metallic layer over the plurality of deposited dielectric layer. After deposition of the non-metallic layer and during polishing of the non-metallic layer on the substrate, measurements of a sequence of raw spectra of light reflected the substrate during polishing are received from an in-situ optical monitoring system. Each raw spectrum is normalized to generate a sequence of normalized spectra using the raw spectrum and the base spectrum. At least one of a polishing endpoint or an adjustment for a polishing rate is determined based on at least one normalized predetermined spectrum from the sequence of normalized spectra.

A method of controlling polishing includes polishing a substrate, monitoring the substrate during polishing with an in-situ monitoring system, filtering a signal from the monitoring system to generate a filtered signal, and determining at least one of a polishing endpoint or an adjustment for a polishing rate from the filtered signal. The filtering includes modelling a plurality of periodic disturbances at a plurality of different frequencies using a plurality of disturbance states, modelling an underlying signal using a plant state, and applying a linear prediction filter to the plant state and the plurality of disturbance states to generate a filtered signal representing the underlying signal.

A method of controlling polishing includes polishing a substrate, monitoring the substrate during polishing with an in-situ monitoring system, filtering a signal from the monitoring system to generate a filtered signal, and determining at least one of a polishing endpoint or an adjustment for a polishing rate from the filtered signal. The filtering includes modelling a plurality of periodic disturbances at a plurality of different frequencies using a plurality of disturbance states, modelling an underlying signal using a plant state, and applying a linear prediction filter to the plant state and the plurality of disturbance states to generate a filtered signal representing the underlying signal.

A method of controlling polishing includes polishing a substrate, monitoring the substrate during polishing with an in-situ monitoring system, filtering a signal from the monitoring system to generate a filtered signal, and determining at least one of a polishing endpoint or an adjustment for a polishing rate from the filtered signal. The filtering includes modelling a plurality of periodic disturbances at a plurality of different frequencies using a plurality of disturbance states, modelling an underlying signal using a plant state, and applying a linear prediction filter to the plant state and the plurality of disturbance states to generate a filtered signal representing the underlying signal.

A method of controlling polishing includes polishing a substrate, monitoring the substrate during polishing with an in-situ monitoring system, filtering a signal from the monitoring system to generate a filtered signal, and determining at least one of a polishing endpoint or an adjustment for a polishing rate from the filtered signal. The filtering includes modelling a plurality of periodic disturbances at a plurality of different frequencies using a plurality of disturbance states, modelling an underlying signal using a plant state, and applying a linear prediction filter to the plant state and the plurality of disturbance states to generate a filtered signal representing the underlying signal.

A method of controlling polishing includes polishing a substrate, monitoring the substrate during polishing with an in-situ monitoring system, filtering a signal from the monitoring system to generate a filtered signal, and determining at least one of a polishing endpoint or an adjustment for a polishing rate from the filtered signal. The filtering includes modelling a plurality of periodic disturbances at a plurality of different frequencies using a plurality of disturbance states, modelling an underlying signal using a plant state, and applying a linear prediction filter to the plant state and the plurality of disturbance states to generate a filtered signal representing the underlying signal.