Using GEKKO for Moving Horizon Estimation online 3

This is the following question after Using GEKKO for Moving Horizon Estimation online 2.

My code:

from gekko import GEKKO
import numpy as np
import matplotlib.pyplot as plt
import matplotlib; matplotlib.use('TkAgg')

class Observer():

    def __init__(self, window_size, r_init, alpha_init):
        self.m = GEKKO(remote=False)
        self.dt = 0.05
        self.m.time = [i*self.dt for i in range(window_size)]
        #Parameters
        self.m.u = self.m.MV()
        #Variables
        self.m.r = self.m.CV(lb=0.01) # value=r_init) #ub=20 can be over 20
        self.m.alpha = self.m.CV() # value=alpha_init) #ub lb for angle?
        #Equations
        self.m.Equation(self.m.r.dt() == -self.m.cos(self.m.alpha))
        self.m.Equation(self.m.alpha.dt() == self.m.sin(self.m.alpha)/self.m.r - self.m.u)  # differential equation
        #Options
        # self.m.options.MV_STEP_HOR = 2
        self.m.options.IMODE = 5   # dynamic estimation
        self.m.options.EV_TYPE = 1 #Default 1: absolute error form 2: squared error form
        self.m.options.DIAGLEVEL = 0 #diagnostic level
        self.m.options.NODES = 3 #nodes   # collocation nodes default:2
        self.m.options.SOLVER = 2 #solver_num

        # STATUS = 0, optimizer doesn't adjust value
        # STATUS = 1, optimizer can adjust
        self.m.u.STATUS = 0
        self.m.r.STATUS = 1
        self.m.alpha.STATUS = 1
        # FSTATUS = 0, no measurement
        # FSTATUS = 1, measurement used to update model
        self.m.u.FSTATUS = 1 #default
        self.m.r.FSTATUS = 1
        self.m.alpha.FSTATUS = 1

        self.m.r.MEAS_GAP = 2
        self.m.alpha.MEAS_GAP = 1

        self.m.r.TR_INIT = 1
        self.m.alpha.TR_INIT = 1

        self.count = 0

    def MHE(self, observed_state, u_data):
        self.count =+ 1
        self.m.u.MEAS = u_data
        self.m.r.MEAS = observed_state[0]
        self.m.alpha.MEAS = observed_state[1]
        self.m.solve(disp=True)
        return self.m.r.MODEL, self.m.alpha.MODEL

if __name__=="__main__":
    FILE_PATH00 = '/home/shane16/Project/model_guard/uav_paper/adversarial/SA_PPO/src/DATA/4end_estimation_results_r.csv'
    FILE_PATH01 = '/home/shane16/Project/model_guard/uav_paper/adversarial/SA_PPO/src/DATA/4end_estimation_results_alpha.csv'
    FILE_PATH02 = '/home/shane16/Project/model_guard/uav_paper/adversarial/SA_PPO/src/DATA/4end_action_buffer_eps0.0_sig0.0.csv'
    cycles = 250
    
    x = np.arange(cycles) # 1...300
    matrix00 = np.loadtxt(FILE_PATH00, delimiter=',')
    matrix01 = np.loadtxt(FILE_PATH01, delimiter=',')
    matrix02 = np.loadtxt(FILE_PATH02, delimiter=',')

    vanilla_action_sigma_0 = matrix02

    vanilla_estimation_matrix_r = np.zeros(cycles)
    vanilla_estimation_matrix_alpha = np.zeros(cycles)

    # sigma = 0.0
    # vanilla model true/observed states
    r_vanilla_sigma_0_true = matrix00[0, 3:] # from step 1
    r_vanilla_sigma_0_observed = matrix00[1, 3:] # from step1
    alpha_vanilla_sigma_0_true = matrix01[0, 3:]
    alpha_vanilla_sigma_0_observed = matrix01[1, 3:]

    # initialize estimator
    sigma = 0.0 #1.0
    solver_num = 2
    nodes = 5
    # for window_size in [5, 10, 20, 30, 40, 50]:
    window_size = 8
    observer = Observer(window_size, r_vanilla_sigma_0_observed[0], alpha_vanilla_sigma_0_observed[0])
    for i in range(cycles):
        if i % 100 == 0:
            print('cylcle: {}'.format(i))
        vanilla_observed_states = np.hstack((r_vanilla_sigma_0_observed[i], alpha_vanilla_sigma_0_observed[i])) # from current observed state
        r_hat, alpha_hat = observer.MHE(vanilla_observed_states, vanilla_action_sigma_0[i]) # and current action -> estimate current state
        vanilla_estimation_matrix_r[i] = r_hat
        vanilla_estimation_matrix_alpha[i] = alpha_hat

    #plot vanilla
    plt.figure()
    plt.subplot(3,1,1)
    plt.title('Vanilla model_sig{}'.format(sigma))
    plt.plot(x, vanilla_action_sigma_0[:cycles],'b:',label='action (w)')
    plt.legend()
    plt.subplot(3,1,2)
    plt.ylabel('r')
    plt.plot(x, r_vanilla_sigma_0_true[:cycles], 'k-', label='true_r')
    plt.plot(x, r_vanilla_sigma_0_observed[:cycles], 'gx', label='observed_r')
    plt.plot(x, vanilla_estimation_matrix_r, 'r--', label='time window: 10')
    # plt.legend()
    plt.subplot(3,1,3)
    plt.xlabel('time steps')
    plt.ylabel('alpha')
    plt.plot(x, alpha_vanilla_sigma_0_true[:cycles], 'k-', label='true_alpha')
    plt.plot(x, alpha_vanilla_sigma_0_observed[:cycles], 'gx', label='observed_alpha')
    plt.plot(x, vanilla_estimation_matrix_alpha, 'r--', label='time window: {}'.format(window_size))
    plt.legend()
    plt.savefig('plot/revision/4estimated_STATES_vanilla_sig{}_window{}_cycles{}_solver{}_nodes{}.png'.format(sigma, window_size,cycles, solver_num, nodes))
    plt.show()

I have studied and did set the problem as the example https://apmonitor.com/do/index.php/Main/EstimatorTypes.

But when I set window_size in my code over 10, the solution is not found: (result of terminal when options.SOLVER = 0)

apm 165.132.48.158_gk_model0 <br><pre>
----------------------------------------------------------------  APMonitor, Version 1.0.1  APMonitor Optimization Suite 
----------------------------------------------------------------
     --------- APM Model Size ------------  Each time step contains    Objects      :            0    Constants    :            0    Variables    :            3    Intermediates:            0    Connections  :            0    Equations    :            2    Residuals    :            2    Warning: CV(           1 ) on at cycle  1 with no MVs on  Warning: CV(           2 ) on at cycle            1 with no MVs on  Number of state variables:            261  Number of total equations: -          261  Number of slack variables: -          0  ---------------------------------------  Degrees of freedom       : 0    ----------------------------------------------  Dynamic Estimation with APOPT Solver 
----------------------------------------------    Iter    Objective  Convergence
    0  5.30547E+02  1.04898E+01
    1  3.70823E+02  3.25000E-01
    2  3.70724E+02  7.49963E-02
    3  3.70689E+02  3.74995E-01
    4  3.70716E+02  1.00000E-01
    5  3.70717E+02  2.00000E-01
    6  2.33359E+03  1.73260E-01
    7  2.56047E+04  1.00000E-01
    8  2.56261E+04  1.18140E-01
    9  1.52748E+21  1.39682E+00    Iter    Objective  Convergence    10  1.08739E+30  1.39682E+00    11  1.06063E+30  1.39682E+00    12 
1.03450E+30  1.39682E+00    13  2.40101E+32  1.39682E+00    14  2.34191E+32  1.39682E+00    15  2.28418E+32  1.39682E+00    16  1.68770E+32  1.39682E+00    17  1.64616E+32  1.39682E+00    18  1.60560E+32  1.39682E+00    19  1.72636E+32  1.39682E+00    Iter    Objective  Convergence    20  1.68387E+32  1.39682E+00    21 
1.64239E+32  1.39682E+00    22  1.72644E+32  1.39682E+00    23  1.68395E+32  1.39682E+00    24  1.64243E+32  1.39682E+00    25  1.72645E+32  1.39682E+00    26  1.68395E+32  1.39682E+00    27  1.64243E+32  1.39682E+00    28  1.72645E+32  1.39682E+00    29  1.68395E+32  1.39682E+00    Iter    Objective  Convergence    30  1.64243E+32  1.39682E+00    31  1.72645E+32  1.39682E+00    32  1.68395E+32  1.39682E+00    33  1.64244E+32  1.39682E+00    34  1.72645E+32  1.39682E+00    35  1.68395E+32  1.39682E+00    36  1.64244E+32  1.39682E+00    37  1.72645E+32  1.39682E+00    38  1.68395E+32  1.39682E+00    39  1.64244E+32  1.39682E+00    Iter    Objective  Convergence    40  1.72645E+32  1.39682E+00    41 
1.68395E+32  1.39682E+00    42  1.64244E+32  1.39682E+00    43  1.72645E+32  1.39682E+00    44  1.68395E+32  1.39682E+00    45  1.64245E+32  1.39682E+00    46  1.72645E+32  1.39682E+00    47  1.68395E+32  1.39682E+00    48  1.64243E+32  1.39682E+00    49  1.72645E+32  1.39682E+00    Iter    Objective  Convergence    50  1.68395E+32  1.39682E+00    51  1.64243E+32  1.39682E+00    52  1.72645E+32  1.39682E+00    53  1.68395E+32  1.39682E+00    54  1.64244E+32  1.39682E+00    55  1.72645E+32  1.39682E+00    56  1.68395E+32  1.39682E+00    57  1.64244E+32  1.39682E+00    58  1.72645E+32  1.39682E+00    59  1.68395E+32  1.39682E+00    Iter    Objective  Convergence    60  1.64244E+32  1.39682E+00    61 
1.72645E+32  1.39682E+00    62  1.68395E+32  1.39682E+00    63  1.64243E+32  1.39682E+00    64  1.72645E+32  1.39682E+00    65  1.68395E+32  1.39682E+00    66  1.64243E+32  1.39682E+00    67  1.72645E+32  1.39682E+00    68  1.68395E+32  1.39682E+00    69  1.64244E+32  1.39682E+00    Iter    Objective  Convergence    70  1.72645E+32  1.39682E+00    71  1.68395E+32  1.39682E+00    

... 81 1.64244E+32 1.39682E+00 82 1.72645E+32 1.39682E+00 83 1.68395E+32 1.39682E+00 84 1.64243E+32 1.39682E+00 85 1.72645E+32 1.39682E+00 86 1.68395E+32 1.39682E+00 87 1.64243E+32 1.39682E+00 88 1.72645E+32 1.39682E+00 89 1.68395E+32 1.39682E+00 Iter Objective Convergence 90 1.64243E+32 1.39682E+00 91 1.72645E+32 1.39682E+00 92 1.68395E+32 1.39682E+00 93 1.64243E+32 1.39682E+00 94 1.72645E+32 1.39682E+00 95 1.68395E+32 1.39682E+00 96 1.64243E+32 1.39682E+00 97 1.72645E+32 1.39682E+00 98 1.68395E+32 1.39682E+00 99 1.64243E+32 1.39682E+00 Iter Objective Convergence 100 1.72645E+32 1.39682E+00 101 1.68395E+32 1.39682E+00 102 1.64244E+32 1.39682E+00 103 1.72645E+32 1.39682E+00 104 1.68395E+32 1.39682E+00 105 1.64244E+32 1.39682E+00 106 1.72645E+32 1.39682E+00 107 1.68395E+32 1.39682E+00 108 1.64244E+32 1.39682E+00 109 1.72645E+32 1.39682E+00 Iter Objective Convergence 110 1.68395E+32 1.39682E+00 111 1.64243E+32 1.39682E+00 112 1.72645E+32 1.39682E+00 113 1.68395E+32 1.39682E+00 114 1.64243E+32 1.39682E+00 115 1.72645E+32 1.39682E+00 116 1.68395E+32 1.39682E+00 117 1.64244E+32 1.39682E+00 118 1.72645E+32 1.39682E+00 119 1.68395E+32 1.39682E+00 Iter Objective Convergence 120 1.64244E+32 1.39682E+00 121 1.72645E+32 1.39682E+00 122 1.68395E+32 1.39682E+00 123 1.64243E+32 1.39682E+00 124 1.72645E+32 1.39682E+00 125 1.68395E+32 1.39682E+00 126 1.64244E+32 1.39682E+00 127 1.72645E+32 1.39682E+00 128 1.68395E+32 1.39682E+00 129 1.64243E+32 1.39682E+00 Iter Objective Convergence 130 1.72645E+32 1.39682E+00 131 1.68395E+32 1.39682E+00 132 1.64244E+32 1.39682E+00 133 1.72645E+32 1.39682E+00 134 1.68395E+32 1.39682E+00 135 1.64243E+32 1.39682E+00 136 1.72645E+32 1.39682E+00 137 1.68395E+32 1.39682E+00 138 1.64243E+32 1.39682E+00 139 1.72645E+32 1.39682E+00 Iter Objective Convergence 140 1.68395E+32 1.39682E+00 141 1.64243E+32 1.39682E+00 142 1.72645E+32 1.39682E+00 143 1.68395E+32 1.39682E+00 144 1.64243E+32 1.39682E+00 145 1.72645E+32 1.39682E+00 146 1.68395E+32 1.39682E+00 147 1.64244E+32 1.39682E+00 148 1.72645E+32 1.39682E+00 149 1.68395E+32 1.39682E+00 Iter Objective Convergence 150 1.64243E+32 1.39682E+00 151 1.72645E+32 1.39682E+00 152 1.68395E+32 1.39682E+00 153 1.64244E+32 1.39682E+00 154 1.72645E+32 1.39682E+00 155 1.68395E+32 1.39682E+00 156 1.64244E+32 1.39682E+00 157 1.72645E+32 1.39682E+00 158 1.68395E+32 1.39682E+00 159 1.64243E+32 1.39682E+00 Iter Objective Convergence 160 1.72645E+32 1.39682E+00 161 1.68395E+32 1.39682E+00 162 1.64243E+32 1.39682E+00 163 1.72645E+32 1.39682E+00 164 1.68395E+32 1.39682E+00 165 1.64244E+32 1.39682E+00 166 1.72645E+32 1.39682E+00 167 1.68395E+32 1.39682E+00 168 1.64244E+32 1.39682E+00 169 1.72645E+32 1.39682E+00 Iter Objective Convergence 170 1.68395E+32 1.39682E+00 171 1.64243E+32 1.39682E+00 172 1.72645E+32 1.39682E+00 173 1.68395E+32 1.39682E+00 174 1.64244E+32 1.39682E+00 175 1.72645E+32 1.39682E+00 176 1.68395E+32 1.39682E+00 177 1.64243E+32 1.39682E+00 178 1.72645E+32 1.39682E+00 179 1.68395E+32 1.39682E+00 Iter Objective Convergence 180 1.64244E+32 1.39682E+00 181 1.72645E+32 1.39682E+00 182 1.68395E+32 1.39682E+00 183 1.64243E+32 1.39682E+00 184 1.72645E+32 1.39682E+00 185 1.68395E+32 1.39682E+00 186 1.64243E+32 1.39682E+00 187 1.72645E+32 1.39682E+00 188 1.68395E+32 1.39682E+00 189 1.64243E+32 1.39682E+00 Iter Objective Convergence 190 1.72645E+32 1.39682E+00 191 1.68395E+32 1.39682E+00 192 1.64243E+32 1.39682E+00 193 1.72645E+32 1.39682E+00 194 1.68395E+32 1.39682E+00 195 1.64244E+32 1.39682E+00 196 1.72645E+32 1.39682E+00 197 1.68395E+32 1.39682E+00 198 1.64243E+32 1.39682E+00 199 1.72645E+32 1.39682E+00 Iter Objective Convergence 200 1.68395E+32 1.39682E+00 201 1.64244E+32 1.39682E+00 202 1.72645E+32 1.39682E+00 203 1.68395E+32 1.39682E+00 204 1.64244E+32 1.39682E+00 205 1.72645E+32 1.39682E+00 206 1.68395E+32 1.39682E+00 207 1.64243E+32 1.39682E+00 208 1.72645E+32 1.39682E+00 209 1.68395E+32 1.39682E+00 Iter Objective Convergence 210 1.64243E+32 1.39682E+00 211 1.72645E+32 1.39682E+00 212 1.68395E+32 1.39682E+00 213 1.64244E+32 1.39682E+00 214 1.72645E+32 1.39682E+00 215 1.68395E+32 1.39682E+00 216 1.64244E+32 1.39682E+00 217 1.72645E+32 1.39682E+00 218 1.68395E+32 1.39682E+00 219 1.64243E+32 1.39682E+00 Iter Objective Convergence 220 1.72645E+32 1.39682E+00 221 1.68395E+32 1.39682E+00 222 1.64244E+32 1.39682E+00 223 1.72645E+32 1.39682E+00 224 1.68395E+32 1.39682E+00 225 1.64243E+32 1.39682E+00 226 1.72645E+32 1.39682E+00 227 1.68395E+32 1.39682E+00 228 1.64244E+32 1.39682E+00 229 1.72645E+32 1.39682E+00 Iter Objective Convergence 230 1.68395E+32 1.39682E+00 231 1.64243E+32 1.39682E+00 232 1.72645E+32 1.39682E+00 233 1.68395E+32 1.39682E+00 234 1.64243E+32 1.39682E+00 235 1.72645E+32 1.39682E+00 236 1.68395E+32 1.39682E+00 237 1.64243E+32 1.39682E+00 238 1.72645E+32 1.39682E+00 239 1.68395E+32 1.39682E+00 Iter Objective Convergence 240 1.64243E+32 1.39682E+00 241 1.72645E+32 1.39682E+00 242 1.68395E+32 1.39682E+00 243 1.64244E+32 1.39682E+00 244 1.72645E+32 1.39682E+00 245 1.68395E+32 1.39682E+00 246 1.64243E+32 1.39682E+00 247 1.72645E+32 1.39682E+00 248 1.68395E+32 1.39682E+00 249 1.64244E+32 1.39682E+00 Iter Objective Convergence 250 1.72645E+32 1.39682E+00 Maximum iterations --------------------------------------------------- Solver : APOPT (v1.0) Solution time : 5.02409999999873 sec Objective : 217.772371342953 Unsuccessful with error code 0 --------------------------------------------------- ---------------------------------------------- Dynamic Estimation with BPOPT Solver ----------------------------------------------

-----------------------------------------------------  BPOPT Solver v1.0.6
-----------------------------------------------------  Adjusting variables to interior region of bounds  Iter    Objective  Convergence
    0 -1.85748E+02  3.38018E+01
    1 -1.05777E+02  2.71532E+01
    2  1.26905E+02  2.76867E+02
    3  4.04640E+03  7.58592E+02
    4  1.22410E+08  1.22407E+04
    5  1.88476E+03  1.95147E+04
      -1.77050E+00  4.25888E+02
       9.23784E+02  9.96666E+03
       1.38670E+03  1.47370E+04
       1.61835E+03  1.71234E+04
       1.74542E+03  1.83168E+04
    6  1.81543E+03  1.89153E+04
       2.56695E+02  1.43715E+03
       1.01483E+03  1.00785E+04
       1.40039E+03  1.44630E+04
       1.59401E+03  1.66629E+04
       1.69819E+03  1.77867E+04
    7  1.75705E+03  1.83500E+04
    8  6.72094E+08  6.72094E+04
       5.65658E+02  6.07154E+03
       3.69827E+03  3.62246E+04
       5.28094E+03  5.14597E+04
       6.09958E+03  5.93489E+04
       6.50835E+03  6.32875E+04
    9  6.71243E+03  6.52535E+04    10  3.42908E+02  3.74813E+03    11  8.25957E+03  3.79110E+03    12  4.75089E+07  4.75089E+03    13  1.75564E+04  1.44171E+04
       7.14522E+07  7.14522E+03
       9.29139E+07  9.29140E+03
       1.14506E+08  1.14506E+04
       1.26204E+08  1.26204E+04
       1.32081E+08  1.32081E+04    14  1.37395E+08  1.37395E+04  Iter    Objective  Convergence    15  9.73361E+07  9.73356E+03    16 
5.10815E+08  5.10812E+04
       3.34519E+03  1.54614E+04
       5.68490E+03  3.27431E+04
       6.90872E+03  4.19233E+04
       7.53574E+03  4.66639E+04
       7.82826E+03  4.88168E+04    17  7.97497E+03  4.98979E+04    18  1.02392E+09  1.02392E+05    19  7.77468E+09  7.77468E+05    20  9.02530E+09  1.30137E+06    21  8.22402E+12  8.22402E+08
       8.27849E+07  7.85323E+08
       6.67868E+07  6.46502E+08
       6.68851E+07  6.58066E+08
       7.40486E+07  7.34991E+08
       7.80379E+07  7.77529E+08    22  8.00766E+07  7.99239E+08    23  8.85462E+12  8.85424E+08
       3.10775E+08  2.89271E+08
       3.88079E+08  5.70603E+08
       4.28405E+08  7.28006E+08
       4.48567E+08  8.06703E+08
       4.58649E+08  8.46059E+08    24  4.63690E+08  8.65737E+08    25  1.86029E+07  1.48320E+08
       1.17713E+10  1.17712E+06
       7.44218E+11  7.44216E+07
       1.11371E+12  1.11370E+08
       1.29845E+12  1.29844E+08
       1.39082E+12  1.39082E+08    26  1.43700E+12  1.43700E+08
       9.97937E+09  9.97933E+05
       7.20196E+11  7.20194E+07
       1.07860E+12  1.07860E+08
       1.25780E+12  1.25780E+08
       1.34740E+12  1.34740E+08    27  1.39221E+12  1.39220E+08
       4.87457E+09  4.87453E+05
       6.97347E+11  6.97346E+07
       1.04477E+12  1.04477E+08
       1.21849E+12  1.21848E+08
       1.30535E+12  1.30534E+08    28  1.34878E+12  1.34877E+08
       7.02507E+04  6.33467E+05
       8.46417E+06  6.74433E+07
       1.26923E+07  1.01160E+08
       1.48064E+07  1.18019E+08
       1.58634E+07  1.26448E+08    29  1.63920E+07  1.30662E+08  Iter    Objective  Convergence    30  6.88703E+05  1.60107E+06
       1.15163E+08  8.31826E+05
       1.68185E+08  1.21658E+06
       1.94691E+08  1.40891E+06
       2.07914E+08  1.50487E+06
       2.14555E+08  1.55306E+06    31  2.17836E+08  1.57686E+06  *** WARNING MESSAGE FROM SUBROUTINE MA27BD  *** INFO(1) = 3
     MATRIX IS SINGULAR. RANK=  683  Problem with linear solver, INFO:            3    ---------------------------------------------------  Solver       :  BPOPT (v1.0)  Solution time  :   4.249999999956344E-002 sec  Objective      :    528860.935305211       Unsuccessful with error code            0  ---------------------------------------------------
**********************************************  Dynamic Estimation with Interior Point Solver 
**********************************************
     Info: Exact Hessian

****************************************************************************** This program contains Ipopt, a library for large-scale nonlinear optimization.  Ipopt is released as open source code under the Eclipse Public License (EPL).
         For more information visit http://projects.coin-or.org/Ipopt
******************************************************************************

This is Ipopt version 3.12.10, running with linear solver ma57.

Number of nonzeros in equality constraint Jacobian...:      257 Number of nonzeros in inequality constraint Jacobian.:      324 Number of nonzeros in Lagrangian Hessian.............:       54

Total number of variables............................:      261
                     variables with only lower bounds:      180
                variables with lower and upper bounds:        0
                     variables with only upper bounds:        0 Total number of equality constraints.................:       99 Total number of inequality constraints...............:      162
        inequality constraints with only lower bounds:      162    inequality constraints with lower and upper bounds:        0
        inequality constraints with only upper bounds:        0

iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls    0  8.8000164e-01 1.05e+01 9.00e+00   0.0 0.00e+00    -
0.00e+00 0.00e+00   0    1  1.0609900e+00 1.05e+01 9.02e+00  -6.7 3.88e+01    -  1.84e-03 1.78e-03h  1    2  9.3143493e+00 1.02e+01 2.21e+01   0.4 3.87e+01    -  1.79e-02 1.98e-02f  1    3  9.3142593e+00 1.02e+01 1.15e+04  -0.3 3.79e+01    -  2.86e-01 2.02e-04h  1    4r 9.3142593e+00 1.02e+01 1.00e+03   1.0 0.00e+00    -  0.00e+00 2.53e-07R  4    5r 5.3654124e+01 8.37e+00 1.16e+03   1.6 2.57e+02    -  2.05e-03 7.22e-03f  1    6  5.3675353e+01 8.36e+00 2.99e+02  -6.2 4.01e+01    -  2.12e-01 7.00e-04h  1    7r 5.3675353e+01 8.36e+00 9.99e+02   0.9 0.00e+00    -  0.00e+00 4.38e-07R  5    8r 1.6618000e+02 2.86e+00 9.90e+02   1.0 6.80e+02    -  2.20e-02 8.16e-03f  1    9  1.6613771e+02 2.86e+00 7.01e+02  -6.2 3.78e+01    -  4.05e-01 5.72e-04h  1 iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls   10r 1.6613771e+02
2.86e+00 9.99e+02   0.5 0.00e+00    -  0.00e+00 3.58e-07R  5   11r 2.2518286e+02 1.89e+00 9.97e+02   1.8 1.58e+03    -  5.31e-03 1.80e-03f  1   12  2.2512388e+02 1.89e+00 1.12e+03  -6.1 3.77e+01    -  4.42e-01 3.90e-04f  1   13r 2.2512388e+02 1.89e+00 1.00e+03   0.3 0.00e+00    -  0.00e+00 4.87e-07R  4   14r 2.2721384e+02 1.87e+00 9.91e+02  -5.9 6.07e+01    -  3.73e-03 7.55e-03f  1   15r 2.2764670e+02 6.34e-01 9.89e+02   1.5 2.10e+04    -  3.96e-03 1.18e-03f  1   16  2.2763736e+02 6.34e-01 5.40e+03  -6.1 1.48e+02    -  4.36e-01 7.99e-05h  1   17r 2.2763736e+02 6.34e-01 1.00e+03  -0.0 0.00e+00    -  0.00e+00 4.00e-07R  2   18r 2.3088007e+02 5.58e-01 9.95e+02   1.9 9.63e+02    -  7.10e-03 2.87e-03f  1   19  2.3089464e+02 5.58e-01 5.63e+04   0.1 1.19e+02    -  4.79e-01 4.76e-04h  1 iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls   20r 2.3089464e+02 5.58e-01 1.00e+03 
-0.3 0.00e+00    -  0.00e+00 2.98e-07R  5   21r 2.3319530e+02 5.24e-01 1.31e+03   1.7 1.33e+03    -  1.50e-02 3.54e-03f  1   22r 2.5899287e+02 3.78e-01 1.77e+03   1.9 1.04e+02    -  5.59e-02 4.32e-02f  1   23  2.5842489e+02 3.78e-01 6.85e+02   0.2 6.86e+01    -  8.90e-01 1.48e-03f  3   24  2.5843511e+02 3.82e-01 3.36e+04   0.2 6.84e+01    -  2.20e-01 4.46e-03f  1   25  2.5843515e+02 3.82e-01 1.36e+08   0.2 6.48e+01    -  1.80e-01 4.47e-05h  1   26r 2.5843515e+02 3.82e-01 1.00e+03   0.2 0.00e+00    -  0.00e+00 2.24e-07R  2   27r 2.6284498e+02 2.08e-01 1.34e+03   1.9 1.55e+02    -  7.63e-02 5.34e-03f  1   28  2.6244784e+02 2.08e-01 4.34e+03   0.2 4.59e+01    -  9.14e-01 9.61e-04h  1   29r 2.6244784e+02 2.08e-01 1.00e+03   0.2 0.00e+00    -  0.00e+00 3.01e-07R  6 iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls   30r
2.7090035e+02 2.28e-01 9.50e+02   1.6 7.37e+01    -  2.96e-01 1.63e-02f  1   31r 2.7157286e+02 2.27e-01 9.22e+02   0.4 2.45e+00    -  4.94e-01 3.05e-02f  1   32r 2.7252200e+02 2.29e-01 5.15e+02  -1.1 1.18e+00    -  8.32e-01 4.55e-01f  1   33r 2.8772420e+02 2.25e-01 9.40e+01  -0.7 2.22e+00    -  9.83e-01 9.15e-01f  1   34r 2.8769913e+02 1.95e+00 1.26e+02  -6.6 1.40e+03    -  1.66e-04 1.08e-03f  1   35r 2.9223102e+02 1.54e+00 1.29e+03  -1.2 1.05e+00   0.0 3.03e-01 8.71e-01f  1   36r 2.9225465e+02 1.07e+00 9.01e+02  -0.9 5.35e-01   2.2 4.81e-01 6.15e-01f  1   37r 2.9231013e+02 5.11e-01 1.06e+03  -0.4 2.19e-01   2.7 1.36e-01 1.00e+00f  1   38r 2.9231181e+02 4.23e-01 9.15e+02  -0.6 1.86e-01   3.1 9.06e-02 1.77e-01f  1   39r 2.9231198e+02 4.04e-01 1.12e+03  -0.6 2.11e-01   3.5 2.88e-01 4.46e-02f  1 iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls   40r 2.9231360e+02 3.01e-01
9.53e+02  -0.6 2.60e-01   3.0 6.51e-02 1.35e-01f  1   41r 2.9231693e+02 2.72e-01 1.66e+03  -0.6 2.67e-01   2.6 1.00e+00 9.33e-02f  1   42r 2.9232719e+02 1.98e-01 2.41e+02  -0.6 1.29e-01   3.0 2.20e-01 7.65e-01h  1   43r 2.9243143e+02 2.09e-01 5.65e+02   0.3 2.98e-01   2.5 1.00e+00 2.52e-01f  1   44r 2.9246350e+02 2.10e-01 8.61e+02  -0.4 2.92e-01   2.0 9.92e-01 2.01e-01f  1   45r 2.9245480e+02 2.09e-01 1.93e+02  -1.4 1.20e-01   2.5 1.00e+00 7.37e-01f  1   46r 2.9259452e+02 2.03e-01 1.27e+03   0.2 1.80e+00   2.0 7.20e-01 1.20e-01f  1   47r 2.9277900e+02 2.04e-01 7.72e+02  -0.3 1.25e+00   1.5 3.93e-01 2.34e-01f  1   48r 2.9280994e+02 2.04e-01 5.33e+02  -0.3 1.78e+00   1.0 3.76e-01 1.16e-02h  1   49r 2.9962583e+02 2.28e-01 3.45e+02  -0.3 7.89e-01   0.5 7.13e-01 1.00e+00f  1 iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls   50r 3.2677031e+02 4.59e-01 7.44e+01 
-0.3 6.06e-01    -  1.00e+00 7.82e-01f  1   51r 4.2678794e+02 4.44e-01 1.12e+01  -0.3 4.39e+00    -  1.00e+00 1.00e+00f  1   52r 3.4495773e+02 1.99e-01 1.01e+01  -1.0 2.60e+00    -  8.72e-01 1.00e+00f  1   53r 3.4520580e+02 2.23e-01 3.63e+02  -1.0 4.22e-01   0.1 1.00e+00 3.00e-01f  2   54r 3.2340242e+02 2.25e-01 2.00e+00  -1.1 1.11e+00    -  1.00e+00 1.00e+00f  1   55r 2.9817629e+02 2.31e-01 6.43e+01  -2.2 7.79e-01    -  9.99e-01 7.57e-01f  1   56r 2.8673872e+02 2.25e-01 4.58e-01  -2.7 2.41e-01    -  1.00e+00 1.00e+00f  1   57r 2.7428826e+02 2.23e-01 8.35e-02  -3.9 3.26e-01    -  1.00e+00 1.00e+00f  1   58r 2.7154701e+02 2.21e-01 1.36e+00  -4.8 2.86e+00    -  9.99e-01 6.82e-01f  1   59r 2.7155377e+02 2.21e-01 5.33e-03  -4.2 2.28e-02  -0.4 1.00e+00 1.00e+00h  1 iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls   60r
2.7041602e+02 2.21e-01 8.88e+00  -4.9 4.62e+00    -  9.97e-01 1.64e-01h  1   61r 2.7039401e+02 2.21e-01 1.33e-02  -6.0 7.91e-02  -0.9 1.00e+00 9.97e-01h  1   62r 2.7037446e+02 2.21e-01 1.52e-02  -7.6 3.26e-01  -1.4 1.00e+00 1.00e+00f  1   63r 2.7036542e+02 2.21e-01 1.24e-01  -8.6 1.25e+00  -1.8 1.00e+00 1.00e+00f  1   64r 2.7035672e+02 2.21e-01 3.74e+00  -9.0 7.13e+00  -2.3 1.00e+00 1.00e+00f  1   65r 2.7035462e+02 2.21e-01 7.83e-01  -8.7 3.27e+00  -1.9 1.00e+00 1.00e+00h  1   66r 2.7034622e+02 5.19e-01 3.07e+01  -8.5 2.10e+01  -2.4 1.00e+00 1.00e+00f  1   67r 2.7034197e+02 2.66e-01 7.12e+00  -8.8 1.02e+01  -1.9 1.00e+00 1.00e+00f  1   68r 2.7033259e+02 3.97e+01 2.03e+02  -8.9 9.24e+01  -2.4 1.00e+00 1.00e+00f  1   69r 2.6360194e+02 1.39e+01 5.98e+02  -7.3 4.14e+01    -  1.00e+00 1.00e+00h  1 iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls   70r 2.6287479e+02 1.17e+01
4.25e+02  -7.1 1.33e+01    -  1.00e+00 1.00e+00h  1   71r 2.6399459e+02 4.20e+00 3.71e+02  -6.2 1.24e+01    -  1.00e+00 6.63e-01h  1   72r 2.6277485e+02 2.15e-01 1.34e+00  -6.7 5.00e+00    -  1.00e+00 1.00e+00h  1   73r 2.6249804e+02 2.14e-01 8.71e-02  -8.0 2.35e-01    -  1.00e+00 1.00e+00h  1   74r 2.6246138e+02 2.14e-01 1.06e-01  -9.0 1.43e-01    -  1.00e+00 1.00e+00h  1   75r 2.6248456e+02 2.15e-01 3.45e-03  -9.0 2.17e-02    -  1.00e+00 1.00e+00h  1   76r 2.6248458e+02 2.15e-01 3.74e-03  -9.0 2.15e-03    -  1.00e+00 1.00e+00h  1   77r 2.6248458e+02 2.15e-01 1.26e-04  -9.0 4.26e-04    -  1.00e+00 1.00e+00h  1

Number of Iterations....: 77

                                   (scaled)                 (unscaled) Objective...............:   2.6248457642008947e+02   
2.6248457642008947e+02 Dual infeasibility......:   1.9999999998163066e+01    1.9999999998163066e+01 Constraint violation....:   2.1450238157252022e-01    2.1450238157252022e-01 Complementarity.........:   1.0000004294468675e-09   
1.0000004294468675e-09 Overall NLP error.......:   1.9999999998163066e+01    1.9999999998163066e+01


Number of objective function evaluations             = 118 Number of objective gradient evaluations             = 29 Number of equality constraint evaluations            = 118 Number of inequality constraint evaluations          = 118 Number of equality constraint Jacobian evaluations   = 87 Number of inequality constraint Jacobian evaluations = 87 Number of Lagrangian Hessian evaluations            
= 78 Total CPU secs in IPOPT (w/o function evaluations)   =      0.131 Total CPU secs in NLP function evaluations           =      0.053

EXIT: Converged to a point of local infeasibility. Problem may be infeasible.    An error occured.  The error code is            2

and if I set window_size = 5, the estimation result does not follow true states:

What am I doing wrong? How should I fix this?

Sorry if I'm asking something that is easily known through studying example, but I still don't get the solution. Thank you for your kind instruction.

Sincerely, Shane K.

The objective function value from the solver iterations gives a clue that one of the variables is getting very large. It could be related to the divide-by-zero issue that is in the response to Using GEKKO for Moving Horizon Estimation online 2.

One of the equations may be the source of the problem:

self.m.alpha.dt() == self.m.sin(self.m.alpha)/self.m.r - self.m.u

The initial value of r is zero (default) because no initial value is provided when it is declared as self.m.r = self.m.CV(lb=0). A comment suggests that it was formerly initialized with value r_init. The zero value creates a divide-by-zero for that equation. Try rearranging the equation into an equivalent form that avoids the potential for divide-by-zero either with the initial guess or when the solver is iterating.

self.m.r*self.m.alpha.dt() == self.m.sin(self.m.alpha) - self.m.r*self.m.u

The initialization strategies article also gives suggestions on methods to obtain a successful solution:

Safdarnejad, S.M., Hedengren, J.D., Lewis, N.R., Haseltine, E., Initialization Strategies for Optimization of Dynamic Systems, Computers and Chemical Engineering, 2015, Vol. 78, pp. 39-50, DOI: 10.1016/j.compchemeng.2015.04.016.