Navigation Apparatus and Method in Which Measurement Quantization Errors are Modeled as States

A navigation apparatus determines an estimated position of an object. Navigation information that includes a sequence of quantized measurements is received. Each quantized measurement has a corresponding quantization error that is negatively correlated with the quantization error of a prior quantized measurement. The apparatus iteratively performs a navigation update operation that includes determining a state and a covariance matrix of the object for a current iteration based on a state and covariance matrix in a prior iteration. The state includes an end quantization error and a start quantization error. The covariance matrix includes end and start covariance values corresponding to the end and start quantization errors, respectively. Determining the state and the covariance matrix for the current iteration includes replacing the start quantization error with the end quantization error determined in a prior iteration, and updating the state and the covariance matrix via a Kalman filter update operation.