Code for Optimal State Estimation:

• Verifications/Duplication of Figures or Results from the Text
  • direct_propagation_of_state_uncertainty.nb (some matrix multiplications)
    
  • sect_2_dup_example_4_2_2.m (evaluate the system dependent process noise)
    
  • sect_2_dup_example_4_2_3.m (evaluate the system dependent process noise)
    
  • sect_3_dup_example_4_3_1.m (the Kalman filter for the weathervane example)
    
  • example_4_2_2_compute_qkm1.m (computes the process noise covariance)
    
  • sect_7_dup_example_4_7_1.m (estimates a constant using an extended Kalman filter)
    
  • example_4_7_1_extended_kf.m (performs the extended Kalman filtering)
    
  • example_4_7_1_extended_kf_fn.m (function for use with ode45)
    
  • sect_7_dup_example_4_7_2.m (estimates a constant parameter using multiple models)
    
  • weathervane_system.m (computes Q and Phi for the weathervane model)
    
• Problem Solutions Section 1
  • sect_1_1.m (least squares estimates to fit polynomial models)
    
  • sect_1_2.m (polynomial models with different variances)
    
  • sect_1_3.m (fitting polynomial models with one more data point)
    
  • sect_1_5.m (least square mapping of an input/output relationship)
    
  • sect_1_6.m (fitting a nonlinear input/output relationship)
    
• Problem Solutions Section 2
  • sect_2_prob_2.m (simulating a discrete-time system)
    
  • sect_2_prob_3.m (a sampled-data disturbance covariance matrix)
    
• Problem Solutions Section 3
  • sect_3_prob_3_N_4.m (simulating a continuous-time system)
    
  • sect_3_prob_7.m (sequential processing to compute P(+))
    
  • sect_3_prob_8.m (Joseph form to compute P(+))
    
• Problem Solutions Section 4
  • sect_4_2.m (driver for this problem)
    
  • sect_4_2_gen_xz.m (generates needed cross-correlated data)
    
  • sect_4_2_kfilter_z.m (implements the Kalman filter)
    
  • sect_4_3.m (driver for this problem)
    
  • sect_4_3_gen_xz.m (generates needed time-correlated measurement data)
    
  • sect_4_3_kfilter_z.m (implements the Kalman filter)
    
  • sect_4_4.m (driver for this problem)
    
  • sect_4_4_gen_xz.m (generates two-dimensional time-correlated measurement data)
    
  • sect_4_4_kfilter_z.m (implements the Kalman filter)
    
  • sect_4_5.m (driver for this problem)
    
  • sect_4_5_gen_xz.m (generates noise for our augmented system)
    
  • sect_4_5_kfilter_z.m (implements the Kalman filter)
    
• Problem Solutions Section 5
  • sect_5_1.m (driver for this problem)
    
  • sect_5_1_ode_fn.m (the common integration terms)
    
  • sect_5_1_ode_fn_part_a.m (integration function needed for ode45 Part~a)
    
  • sect_5_1_ode_fn_part_b.m (integration function needed for ode45 Part~b)
    
  • sect_5_1_ode_fn_part_c.m (integration function needed for ode45 Part~c)
    
  • sect_5_2.m (driver for this problem)
    
  • sect_5_3.m (driver for using the Chandrasekhar filter)
    
  • sect_5_3_ode_fn_part_a.m (integration function needed for ode45 Part~a)
    
  • sect_5_3_ode_fn_part_b.m (integration function needed for ode45 Part~b)
    
  • sect_5_3_ode_fn_part_c.m (integration function needed for ode45 Part~c)
    
  • evaluate_MUT.nb (evaluates some algebra needed for square root filtering)
    
  • sect_5_4.m (driver for using the square root filter)
    
  • sect_5_4_ode_fn.m (the common integration terms)
    
  • sect_5_4_ode_fn_part_a.m (integration function needed for ode45 Part~a)
    
  • sect_5_4_ode_fn_part_b.m (integration function needed for ode45 Part~b)
    
  • sect_5_4_ode_fn_part_c.m (integration function needed for ode45 Part~c)
    
• Problem Solutions Section 6
  • sect_6_1.m (driver for performing nonlinear filtering)
    
  • sect_6_1_gen_xz.m (generates the true state and measurements)
    
  • sect_6_1_linear_kf.m (drop the x^4 term and estimate with the standard Kalman filter)
    
  • sect_6_1_extended_kf.m (keep the x^4 term and use the extended Kalman filter)
    
  • sect_6_1_extended_kf_fn.m (function needed for ode45 for integration)
    
  • sect_6_1_roots.R (some root calculations)
    
  • sect_6_2.m (driver for performing extended Kalman filtering)
    
  • sect_6_2_gen_xz.m (generates the true state and measurements)
    
  • sect_6_2_extended_kf.m (does the extended Kalman filtering)
    
  • sect_6_2_h_fn.m (function needed to evaluate nonlinear and linear measurement)
    
• Problem Solutions Section 7
  • sect_7_prob_1.m (a parameter adaptive filter)
    
  • sect_7_prob_1_extended_kf.m (extended Kalman filtering for the parameter adaptive filter)
    
  • sect_7_prob_2.R (whiteness of various sequences)
    
  • sect_7_prob_3.m (estimating noise and measurement covariances)
    
  • sect_7_prob_3_noise_adaptive_filtering.m (noise adaptive filtering)
    
  • sect_7_prob_4.m (multiple-model estimation of the (2,1) element)